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http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #ATS | ATS | (*------------------------------------------------------------------*)
#define ATS_DYNLOADFLAG 0
#include "share/atspre_staload.hats"
(*------------------------------------------------------------------*)
(*
Persistent AVL trees.
References:
* Niklaus Wirth, 1976. Algorithms + Data Structures =
Programs. Prentice-Hall, Englewood Cliffs, New Jersey.
* Niklaus Wirth, 2004. Algorithms and Data Structures. Updated
by Fyodor Tkachov, 2014.
(Note: Wirth’s implementations, which are in Pascal and Oberon, are
for non-persistent trees.)
*)
(*------------------------------------------------------------------*)
(*
For now, a very simple interface, without much provided in the way
of proofs.
You could put all this interface stuff into a .sats file. (You would
have to remove the word ‘extern’ from the definitions.)
You might also make avl_t abstract, and put these details in the
.dats file; you would use ‘assume’ to identify the abstract type
with an implemented type. That approach would require some name
changes, and also would make pattern matching on the trees
impossible outside their implementation. Having users do pattern
matching on the AVL trees probably is a terrible idea, anyway.
*)
datatype bal_t =
| bal_minus1
| bal_zero
| bal_plus1
datatype avl_t (key_t : t@ype+,
data_t : t@ype+,
size : int) =
| avl_t_nil (key_t, data_t, 0)
| {size_L, size_R : nat}
avl_t_cons (key_t, data_t, size_L + size_R + 1) of
(key_t, data_t, bal_t,
avl_t (key_t, data_t, size_L),
avl_t (key_t, data_t, size_R))
typedef avl_t (key_t : t@ype+,
data_t : t@ype+) =
[size : int] avl_t (key_t, data_t, size)
extern prfun
lemma_avl_t_param :
{key_t, data_t : t@ype}
{size : int}
avl_t (key_t, data_t, size) -<prf> [0 <= size] void
(* Implement this template, for whichever type of key you are
using. It should return a negative number if u < v, zero if
u = v, or a positive number if u > v. *)
extern fun {key_t : t@ype}
avl_t$compare (u : key_t, v : key_t) :<> int
(* Is the AVL tree empty? *)
extern fun
avl_t_is_empty
{key_t : t@ype}
{data_t : t@ype}
{size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[b : bool | b == (size == 0)]
bool b
(* Does the AVL tree contain at least one association? *)
extern fun
avl_t_isnot_empty
{key_t : t@ype}
{data_t : t@ype}
{size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[b : bool | b == (size <> 0)]
bool b
(* How many associations are stored in the AVL tree? (Currently we
have no way to do an avl_t_size that preserves the ‘size’ static
value. This is the best we can do.) *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_size {size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[sz : int | (size == 0 && sz == 0) || (0 < size && 0 < sz)]
size_t sz
(* Does the AVL tree contain the given key? *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_has_key
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t) :<>
bool
(* Search for a key. If the key is found, return the data value
associated with it. Otherwise return the value of ‘dflt’. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_search_dflt
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t,
dflt : data_t) :<>
data_t
(* Search for a key. If the key is found, return
‘Some(data)’. Otherwise return ‘None()’. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_search_opt
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t) :<>
Option (data_t)
(* Search for a key. If the key is found, set ‘found’ to true, and set
‘data’. Otherwise set ‘found’ to false. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_search_ref
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t,
data : &data_t? >> opt (data_t, found),
found : &bool? >> bool found) :<!wrt>
#[found : bool]
void
(* Overload avl_t_search; these functions are easy for the compiler to
distinguish. *)
overload avl_t_search with avl_t_search_dflt
overload avl_t_search with avl_t_search_opt
overload avl_t_search with avl_t_search_ref
(* If a key is not present in the AVL tree, insert the key-data
association; return the new AVL tree. If the key *is* present in
the AVL tree, then *replace* the key-data association; return the
new AVL tree. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_insert
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t,
data : data_t) :<>
[sz : pos]
avl_t (key_t, data_t, sz)
(* If a key is not present in the AVL tree, insert the key-data
association; return the new AVL tree and ‘true’. If the key *is*
present in the AVL tree, then *replace* the key-data association;
return the new AVL tree and ‘false’. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_insert_or_replace
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t,
data : data_t) :<>
[sz : pos]
(avl_t (key_t, data_t, sz), bool)
(* If a key is present in the AVL tree, delete the key-data
association; otherwise return the tree as it came. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_delete
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t) :<>
[sz : nat]
avl_t (key_t, data_t, sz)
(* If a key is present in the AVL tree, delete the key-data
association; otherwise return the tree as it came. Also, return a
bool to indicate whether or not the key was found; ‘true’ if found,
‘false’ if not. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_delete_if_found
{size : int}
(avl : avl_t (key_t, data_t, size),
key : key_t) :<>
[sz : nat]
(avl_t (key_t, data_t, sz), bool)
(* Return a sorted list of the association pairs in an AVL
tree. (Currently we have no way to do an avl_t_pairs that preserves
the ‘size’ static value. This is the best we can do.) *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_pairs {size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[sz : int | (size == 0 && sz == 0) || (0 < size && 0 < sz)]
list ((key_t, data_t), sz)
(* Return a sorted list of the keys in an AVL tree. (Currently we have
no way to do an avl_t_keys that preserves the ‘size’ static
value. This is the best we can do.) *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_keys {size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[sz : int | (size == 0 && sz == 0) || (0 < size && 0 < sz)]
list (key_t, sz)
(* Return a list of the data values in an AVL tree, sorted in the
order of their keys. (Currently we have no way to do an avl_t_data
that preserves the ‘size’ static value. This is the best we can
do.) *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_data {size : int}
(avl : avl_t (key_t, data_t, size)) :<>
[sz : int | (size == 0 && sz == 0) || (0 < size && 0 < sz)]
list (data_t, sz)
(* list2avl_t does the reverse of what avl_t_pairs does (although
they are not inverses of each other).
Currently we have no way to do a list2avl_t that preserves the
‘size’ static value. This is the best we can do. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
list2avl_t {size : int}
(lst : list ((key_t, data_t), size)) :<>
[sz : int | (size == 0 && sz == 0) || (0 < size && 0 < sz)]
avl_t (key_t, data_t, sz)
(* Make a closure that returns association pairs in either forwards or
reverse order. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_make_pairs_generator
{size : int}
(avl : avl_t (key_t, data_t, size),
direction : int) :
() -<cloref1> Option @(key_t, data_t)
(* Make a closure that returns keys in either forwards or reverse
order. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_make_keys_generator
{size : int}
(avl : avl_t (key_t, data_t, size),
direction : int) :
() -<cloref1> Option key_t
(* Make a closure that returns data values in forwards or reverse
order of their keys. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_make_data_generator
{size : int}
(avl : avl_t (key_t, data_t, size),
direction : int) :
() -<cloref1> Option data_t
(* Raise an assertion if the AVL condition is not met. This template
is for testing the code. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_check_avl_condition
{size : int}
(avl : avl_t (key_t, data_t, size)) :
void
(* Print an AVL tree to standard output, in some useful and perhaps
even pretty format. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_pretty_print
{size : int}
(avl : avl_t (key_t, data_t, size)) :
void
(* Implement this template for whichever types of keys and data you
wish to pretty print. *)
extern fun {key_t : t@ype}
{data_t : t@ype}
avl_t_pretty_print$key_and_data
(key : key_t,
data : data_t) :
void
(*------------------------------------------------------------------*)
(*
What follows is the implementation. It would go into a .dats
file. Note, however, that the .dats file would have to be staloaded!
(Preferably anonymously.) This is because the implementation
contains template functions.
Notice there are several assertions with ‘$effmask_ntm’ (as opposed
to proofs) that the routines are terminating. One hopes to remedy
that problem (with proofs).
Also there are some ‘$effmask_wrt’, but these effect masks are safe,
because the writing is to our own stack variables.
*)
#define NIL avl_t_nil ()
#define CONS avl_t_cons
#define LNIL list_nil ()
#define :: list_cons
#define F false
#define T true
typedef fixbal_t = bool
primplement
lemma_avl_t_param avl =
case+ avl of
| NIL => ()
| CONS _ => ()
fn {}
minus_neg_bal (bal : bal_t) :<> bal_t =
case+ bal of
| bal_minus1 () => bal_plus1
| _ => bal_zero ()
fn {}
minus_pos_bal (bal : bal_t) :<> bal_t =
case+ bal of
| bal_plus1 () => bal_minus1
| _ => bal_zero ()
fn {}
bal2int (bal : bal_t) :<> int =
case+ bal of
| bal_minus1 () => ~1
| bal_zero () => 0
| bal_plus1 () => 1
implement
avl_t_is_empty avl =
case+ avl of
| NIL => T
| CONS _ => F
implement
avl_t_isnot_empty avl =
~avl_t_is_empty avl
implement {key_t} {data_t}
avl_t_size {siz} avl =
let
fun
traverse {size : int}
(p : avl_t (key_t, data_t, size)) :<!ntm>
[sz : int | (size == 0 && sz == 0) ||
(0 < size && 0 < sz)]
size_t sz =
case+ p of
| NIL => i2sz 0
| CONS (_, _, _, left, right) =>
let
val [sz_L : int] sz_L = traverse left
val [sz_R : int] sz_R = traverse right
prval _ = prop_verify {0 <= sz_L} ()
prval _ = prop_verify {0 <= sz_R} ()
in
succ (sz_L + sz_R)
end
val [sz : int] sz = $effmask_ntm (traverse {siz} avl)
prval _ = prop_verify {(siz == 0 && sz == 0) ||
(0 < siz && 0 < sz)} ()
in
sz
end
implement {key_t} {data_t}
avl_t_has_key (avl, key) =
let
fun
search {size : int}
(p : avl_t (key_t, data_t, size)) :<!ntm>
bool =
case+ p of
| NIL => F
| CONS (k, _, _, left, right) =>
begin
case+ avl_t$compare<key_t> (key, k) of
| cmp when cmp < 0 => search left
| cmp when cmp > 0 => search right
| _ => T
end
in
$effmask_ntm search avl
end
implement {key_t} {data_t}
avl_t_search_dflt (avl, key, dflt) =
let
var data : data_t?
var found : bool?
val _ = $effmask_wrt avl_t_search_ref (avl, key, data, found)
in
if found then
let
prval _ = opt_unsome data
in
data
end
else
let
prval _ = opt_unnone data
in
dflt
end
end
implement {key_t} {data_t}
avl_t_search_opt (avl, key) =
let
var data : data_t?
var found : bool?
val _ = $effmask_wrt avl_t_search_ref (avl, key, data, found)
in
if found then
let
prval _ = opt_unsome data
in
Some {data_t} data
end
else
let
prval _ = opt_unnone data
in
None {data_t} ()
end
end
implement {key_t} {data_t}
avl_t_search_ref (avl, key, data, found) =
let
fun
search (p : avl_t (key_t, data_t),
data : &data_t? >> opt (data_t, found),
found : &bool? >> bool found) :<!wrt,!ntm>
#[found : bool] void =
case+ p of
| NIL =>
{
prval _ = opt_none {data_t} data
val _ = found := F
}
| CONS (k, d, _, left, right) =>
begin
case+ avl_t$compare<key_t> (key, k) of
| cmp when cmp < 0 => search (left, data, found)
| cmp when cmp > 0 => search (right, data, found)
| _ =>
{
val _ = data := d
prval _ = opt_some {data_t} data
val _ = found := T
}
end
in
$effmask_ntm search (avl, data, found)
end
implement {key_t} {data_t}
avl_t_insert (avl, key, data) =
let
val (avl, _) =
avl_t_insert_or_replace<key_t><data_t> (avl, key, data)
in
avl
end
implement {key_t} {data_t}
avl_t_insert_or_replace (avl, key, data) =
let
fun
search {size : nat}
(p : avl_t (key_t, data_t, size),
fixbal : fixbal_t,
found : bool) :<!ntm>
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t, bool) =
case+ p of
| NIL =>
(* The key was not found. Insert a new node. The tree will
need rebalancing. *)
(CONS (key, data, bal_zero, NIL, NIL), T, F)
| CONS (k, d, bal, left, right) =>
case+ avl_t$compare<key_t> (key, k) of
| cmp when cmp < 0 =>
let
val (p1, fixbal, found) = search (left, fixbal, found)
in
(* If fixbal is T, then a node has been inserted
on the left, and rebalancing may be necessary. *)
case+ (fixbal, bal) of
| (F, _) =>
(* No rebalancing is necessary. *)
(CONS (k, d, bal, p1, right), F, found)
| (T, bal_plus1 ()) =>
(* No rebalancing is necessary. *)
(CONS (k, d, bal_zero (), p1, right), F, found)
| (T, bal_zero ()) =>
(* Rebalancing might still be necessary. *)
(CONS (k, d, bal_minus1 (), p1, right), fixbal, found)
| (T, bal_minus1 ()) =>
(* Rebalancing is necessary. *)
let
val+ CONS (k1, d1, bal1, left1, right1) = p1
in
case+ bal1 of
| bal_minus1 () =>
(* A single LL rotation. *)
let
val q = CONS (k, d, bal_zero (), right1, right)
val q1 = CONS (k1, d1, bal_zero (), left1, q)
in
(q1, F, found)
end
| _ =>
(* A double LR rotation. *)
let
val p2 = right1
val- CONS (k2, d2, bal2, left2, right2) = p2
val q = CONS (k, d, minus_neg_bal bal2,
right2, right)
val q1 = CONS (k1, d1, minus_pos_bal bal2,
left1, left2)
val q2 = CONS (k2, d2, bal_zero (), q1, q)
in
(q2, F, found)
end
end
end
| cmp when cmp > 0 =>
let
val (p1, fixbal, found) = search (right, fixbal, found)
in
(* If fixbal is T, then a node has been inserted
on the right, and rebalancing may be necessary. *)
case+ (fixbal, bal) of
| (F, _) =>
(* No rebalancing is necessary. *)
(CONS (k, d, bal, left, p1), F, found)
| (T, bal_minus1 ()) =>
(* No rebalancing is necessary. *)
(CONS (k, d, bal_zero (), left, p1), F, found)
| (T, bal_zero ()) =>
(* Rebalancing might still be necessary. *)
(CONS (k, d, bal_plus1 (), left, p1), fixbal, found)
| (T, bal_plus1 ()) =>
(* Rebalancing is necessary. *)
let
val+ CONS (k1, d1, bal1, left1, right1) = p1
in
case+ bal1 of
| bal_plus1 () =>
(* A single RR rotation. *)
let
val q = CONS (k, d, bal_zero (), left, left1)
val q1 = CONS (k1, d1, bal_zero (), q, right1)
in
(q1, F, found)
end
| _ =>
(* A double RL rotation. *)
let
val p2 = left1
val- CONS (k2, d2, bal2, left2, right2) = p2
val q = CONS (k, d, minus_pos_bal bal2,
left, left2)
val q1 = CONS (k1, d1, minus_neg_bal bal2,
right2, right1)
val q2 = CONS (k2, d2, bal_zero (), q, q1)
in
(q2, F, found)
end
end
end
| _ =>
(* The key was found; p is an existing node. Replace
it. The tree needs no rebalancing. *)
(CONS (key, data, bal, left, right), F, T)
in
if avl_t_is_empty avl then
(* Start a new tree. *)
(CONS (key, data, bal_zero, NIL, NIL), F)
else
let
prval _ = lemma_avl_t_param avl
val (avl, _, found) = $effmask_ntm search (avl, F, F)
in
(avl, found)
end
end
fn {key_t : t@ype}
{data_t : t@ype}
balance_for_shrunken_left
{size : pos}
(p : avl_t (key_t, data_t, size)) :<>
(* Returns a new avl_t, and a ‘fixbal’ flag. *)
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
let
val+ CONS (k, d, bal, left, right) = p
in
case+ bal of
| bal_minus1 () => (CONS (k, d, bal_zero, left, right), T)
| bal_zero () => (CONS (k, d, bal_plus1, left, right), F)
| bal_plus1 () =>
(* Rebalance. *)
let
val p1 = right
val- CONS (k1, d1, bal1, left1, right1) = p1
in
case+ bal1 of
| bal_zero () =>
(* A single RR rotation. *)
let
val q = CONS (k, d, bal_plus1, left, left1)
val q1 = CONS (k1, d1, bal_minus1, q, right1)
in
(q1, F)
end
| bal_plus1 () =>
(* A single RR rotation. *)
let
val q = CONS (k, d, bal_zero, left, left1)
val q1 = CONS (k1, d1, bal_zero, q, right1)
in
(q1, T)
end
| bal_minus1 () =>
(* A double RL rotation. *)
let
val p2 = left1
val- CONS (k2, d2, bal2, left2, right2) = p2
val q = CONS (k, d, minus_pos_bal bal2, left, left2)
val q1 = CONS (k1, d1, minus_neg_bal bal2, right2, right1)
val q2 = CONS (k2, d2, bal_zero, q, q1)
in
(q2, T)
end
end
end
fn {key_t : t@ype}
{data_t : t@ype}
balance_for_shrunken_right
{size : pos}
(p : avl_t (key_t, data_t, size)) :<>
(* Returns a new avl_t, and a ‘fixbal’ flag. *)
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
let
val+ CONS (k, d, bal, left, right) = p
in
case+ bal of
| bal_plus1 () => (CONS (k, d, bal_zero, left, right), T)
| bal_zero () => (CONS (k, d, bal_minus1, left, right), F)
| bal_minus1 () =>
(* Rebalance. *)
let
val p1 = left
val- CONS (k1, d1, bal1, left1, right1) = p1
in
case+ bal1 of
| bal_zero () =>
(* A single LL rotation. *)
let
val q = CONS (k, d, bal_minus1, right1, right)
val q1 = CONS (k1, d1, bal_plus1, left1, q)
in
(q1, F)
end
| bal_minus1 () =>
(* A single LL rotation. *)
let
val q = CONS (k, d, bal_zero, right1, right)
val q1 = CONS (k1, d1, bal_zero, left1, q)
in
(q1, T)
end
| bal_plus1 () =>
(* A double LR rotation. *)
let
val p2 = right1
val- CONS (k2, d2, bal2, left2, right2) = p2
val q = CONS (k, d, minus_neg_bal bal2, right2, right)
val q1 = CONS (k1, d1, minus_pos_bal bal2, left1, left2)
val q2 = CONS (k2, d2, bal_zero, q1, q)
in
(q2, T)
end
end
end
implement {key_t} {data_t}
avl_t_delete (avl, key) =
(avl_t_delete_if_found (avl, key)).0
implement {key_t} {data_t}
avl_t_delete_if_found (avl, key) =
let
fn
balance_L__ {size : pos}
(p : avl_t (key_t, data_t, size)) :<>
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
balance_for_shrunken_left<key_t><data_t> p
fn
balance_R__ {size : pos}
(p : avl_t (key_t, data_t, size)) :<>
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
balance_for_shrunken_right<key_t><data_t> p
fn {}
balance_L {size : pos}
(p : avl_t (key_t, data_t, size),
fixbal : fixbal_t) :<>
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
if fixbal then
balance_L__ p
else
(p, F)
fn {}
balance_R {size : pos}
(p : avl_t (key_t, data_t, size),
fixbal : fixbal_t) :<>
[sz : pos]
(avl_t (key_t, data_t, sz), fixbal_t) =
if fixbal then
balance_R__ p
else
(p, F)
fun
del {size : pos}
(r : avl_t (key_t, data_t, size),
fixbal : fixbal_t) :<!ntm>
(* Returns a new avl_t, a new fixbal, and key and data to be
‘moved up the tree’. *)
[sz : nat]
(avl_t (key_t, data_t, sz), fixbal_t, key_t, data_t) =
case+ r of
| CONS (k, d, bal, left, right) =>
begin
case+ right of
| CONS _ =>
let
val (q, fixbalq, kq, dq) = del (right, fixbal)
val q1 = CONS (k, d, bal, left, q)
val (q1bal, fixbal) = balance_R (q1, fixbalq)
in
(q1bal, fixbal, kq, dq)
end
| NIL => (left, T, k, d)
end
fun
search {size : nat}
(p : avl_t (key_t, data_t, size),
fixbal : fixbal_t) :<!ntm>
(* Return three values: a new avl_t, a new fixbal, and
whether the key was found. *)
[sz : nat]
(avl_t (key_t, data_t, sz), fixbal_t, bool) =
case+ p of
| NIL => (p, F, F)
| CONS (k, d, bal, left, right) =>
case+ avl_t$compare<key_t> (key, k) of
| cmp when cmp < 0 =>
(* Recursive search down the left branch. *)
let
val (q, fixbal, found) = search (left, fixbal)
val (q1, fixbal) =
balance_L (CONS (k, d, bal, q, right), fixbal)
in
(q1, fixbal, found)
end
| cmp when cmp > 0 =>
(* Recursive search down the right branch. *)
let
val (q, fixbal, found) = search (right, fixbal)
val (q1, fixbal) =
balance_R (CONS (k, d, bal, left, q), fixbal)
in
(q1, fixbal, found)
end
| _ =>
if avl_t_is_empty right then
(* Delete p, replace it with its left branch, then
rebalance. *)
(left, T, T)
else if avl_t_is_empty left then
(* Delete p, replace it with its right branch, then
rebalance. *)
(right, T, T)
else
(* Delete p, but it has both left and right branches, and
therefore may have complicated branch structure. *)
let
val (q, fixbal, k1, d1) = del (left, fixbal)
val (q1, fixbal) =
balance_L (CONS (k1, d1, bal, q, right), fixbal)
in
(q1, fixbal, T)
end
in
if avl_t_is_empty avl then
(avl, F)
else
let
prval _ = lemma_avl_t_param avl
val (avl1, _, found) = $effmask_ntm search (avl, F)
in
(avl1, found)
end
end
implement {key_t} {data_t}
avl_t_pairs (avl) =
let
fun
traverse {size : pos}
{n : nat}
(p : avl_t (key_t, data_t, size),
lst : list ((key_t, data_t), n)) :<!ntm>
[sz : pos] list ((key_t, data_t), sz) =
(* Reverse in-order traversal, to make an in-order list by
consing. *)
case+ p of
| CONS (k, d, _, left, right) =>
if avl_t_is_empty left then
begin
if avl_t_is_empty right then
(k, d) :: lst
else
(k, d) :: traverse (right, lst)
end
else
begin
if avl_t_is_empty right then
traverse (left, (k, d) :: lst)
else
traverse (left, (k, d) :: traverse (right, lst))
end
in
case+ avl of
| NIL => LNIL
| CONS _ => $effmask_ntm traverse (avl, LNIL)
end
implement {key_t} {data_t}
avl_t_keys (avl) =
let
fun
traverse {size : pos}
{n : nat}
(p : avl_t (key_t, data_t, size),
lst : list (key_t, n)) :<!ntm>
[sz : pos] list (key_t, sz) =
(* Reverse in-order traversal, to make an in-order list by
consing. *)
case+ p of
| CONS (k, _, _, left, right) =>
if avl_t_is_empty left then
begin
if avl_t_is_empty right then
k :: lst
else
k :: traverse (right, lst)
end
else
begin
if avl_t_is_empty right then
traverse (left, k :: lst)
else
traverse (left, k :: traverse (right, lst))
end
in
case+ avl of
| NIL => LNIL
| CONS _ => $effmask_ntm traverse (avl, LNIL)
end
implement {key_t} {data_t}
avl_t_data (avl) =
let
fun
traverse {size : pos}
{n : nat}
(p : avl_t (key_t, data_t, size),
lst : list (data_t, n)) :<!ntm>
[sz : pos] list (data_t, sz) =
(* Reverse in-order traversal, to make an in-order list by
consing. *)
case+ p of
| CONS (_, d, _, left, right) =>
if avl_t_is_empty left then
begin
if avl_t_is_empty right then
d :: lst
else
d :: traverse (right, lst)
end
else
begin
if avl_t_is_empty right then
traverse (left, d :: lst)
else
traverse (left, d :: traverse (right, lst))
end
in
case+ avl of
| NIL => LNIL
| CONS _ => $effmask_ntm traverse (avl, LNIL)
end
implement {key_t} {data_t}
list2avl_t lst =
let
fun
traverse {n : pos}
{size : nat} .<n>.
(lst : list ((key_t, data_t), n),
p : avl_t (key_t, data_t, size)) :<>
[sz : pos] avl_t (key_t, data_t, sz) =
case+ lst of
| (k, d) :: LNIL => avl_t_insert<key_t><data_t> (p, k, d)
| (k, d) :: (_ :: _) =>
let
val+ _ :: tail = lst
in
traverse (tail, avl_t_insert<key_t><data_t> (p, k, d))
end
in
case+ lst of
| LNIL => NIL
| (_ :: _) => traverse (lst, NIL)
end
fun {key_t : t@ype}
{data_t : t@ype}
push_all_the_way_left (stack : List (avl_t (key_t, data_t)),
p : avl_t (key_t, data_t)) :
List0 (avl_t (key_t, data_t)) =
let
prval _ = lemma_list_param stack
in
case+ p of
| NIL => stack
| CONS (_, _, _, left, _) =>
push_all_the_way_left (p :: stack, left)
end
fun {key_t : t@ype}
{data_t : t@ype}
push_all_the_way_right (stack : List (avl_t (key_t, data_t)),
p : avl_t (key_t, data_t)) :
List0 (avl_t (key_t, data_t)) =
let
prval _ = lemma_list_param stack
in
case+ p of
| NIL => stack
| CONS (_, _, _, _, right) =>
push_all_the_way_right (p :: stack, right)
end
fun {key_t : t@ype}
{data_t : t@ype}
push_all_the_way (stack : List (avl_t (key_t, data_t)),
p : avl_t (key_t, data_t),
direction : int) :
List0 (avl_t (key_t, data_t)) =
if direction < 0 then
push_all_the_way_right<key_t><data_t> (stack, p)
else
push_all_the_way_left<key_t><data_t> (stack, p)
fun {key_t : t@ype}
{data_t : t@ype}
update_generator_stack (stack : List (avl_t (key_t, data_t)),
left : avl_t (key_t, data_t),
right : avl_t (key_t, data_t),
direction : int) :
List0 (avl_t (key_t, data_t)) =
let
prval _ = lemma_list_param stack
in
if direction < 0 then
begin
if avl_t_is_empty left then
stack
else
push_all_the_way_right<key_t><data_t> (stack, left)
end
else
begin
if avl_t_is_empty right then
stack
else
push_all_the_way_left<key_t><data_t> (stack, right)
end
end
implement {key_t} {data_t}
avl_t_make_pairs_generator (avl, direction) =
let
typedef avl_t = avl_t (key_t, data_t)
val stack = push_all_the_way (LNIL, avl, direction)
val stack_ref = ref stack
(* Cast stack_ref to its (otherwise untyped) pointer, so it can be
enclosed within ‘generate’. *)
val p_stack_ref = $UNSAFE.castvwtp0{ptr} stack_ref
fun
generate () :<cloref1> Option @(key_t, data_t) =
let
(* Restore the type information for stack_ref. *)
val stack_ref =
$UNSAFE.castvwtp0{ref (List avl_t)} p_stack_ref
var stack : List0 avl_t = !stack_ref
var retval : Option @(key_t, data_t)
in
begin
case+ stack of
| LNIL => retval := None ()
| p :: tail =>
let
val- CONS (k, d, _, left, right) = p
in
retval := Some @(k, d);
stack :=
update_generator_stack<key_t><data_t>
(tail, left, right, direction)
end
end;
!stack_ref := stack;
retval
end
in
generate
end
implement {key_t} {data_t}
avl_t_make_keys_generator (avl, direction) =
let
typedef avl_t = avl_t (key_t, data_t)
val stack = push_all_the_way (LNIL, avl, direction)
val stack_ref = ref stack
(* Cast stack_ref to its (otherwise untyped) pointer, so it can be
enclosed within ‘generate’. *)
val p_stack_ref = $UNSAFE.castvwtp0{ptr} stack_ref
fun
generate () :<cloref1> Option key_t =
let
(* Restore the type information for stack_ref. *)
val stack_ref =
$UNSAFE.castvwtp0{ref (List avl_t)} p_stack_ref
var stack : List0 avl_t = !stack_ref
var retval : Option key_t
in
begin
case+ stack of
| LNIL => retval := None ()
| p :: tail =>
let
val- CONS (k, _, _, left, right) = p
in
retval := Some k;
stack :=
update_generator_stack<key_t><data_t>
(tail, left, right, direction)
end
end;
!stack_ref := stack;
retval
end
in
generate
end
implement {key_t} {data_t}
avl_t_make_data_generator (avl, direction) =
let
typedef avl_t = avl_t (key_t, data_t)
val stack = push_all_the_way (LNIL, avl, direction)
val stack_ref = ref stack
(* Cast stack_ref to its (otherwise untyped) pointer, so it can be
enclosed within ‘generate’. *)
val p_stack_ref = $UNSAFE.castvwtp0{ptr} stack_ref
fun
generate () :<cloref1> Option data_t =
let
(* Restore the type information for stack_ref. *)
val stack_ref =
$UNSAFE.castvwtp0{ref (List avl_t)} p_stack_ref
var stack : List0 avl_t = !stack_ref
var retval : Option data_t
in
begin
case+ stack of
| LNIL => retval := None ()
| p :: tail =>
let
val- CONS (_, d, _, left, right) = p
in
retval := Some d;
stack :=
update_generator_stack<key_t><data_t>
(tail, left, right, direction)
end
end;
!stack_ref := stack;
retval
end
in
generate
end
implement {key_t} {data_t}
avl_t_check_avl_condition (avl) =
(* If any of the assertions here is triggered, there is a bug. *)
let
fun
get_heights (p : avl_t (key_t, data_t)) : (int, int) =
case+ p of
| NIL => (0, 0)
| CONS (k, d, bal, left, right) =>
let
val (height_LL, height_LR) = get_heights left
val (height_RL, height_RR) = get_heights right
in
assertloc (abs (height_LL - height_LR) <= 1);
assertloc (abs (height_RL - height_RR) <= 1);
(height_LL + height_LR, height_RL + height_RR)
end
in
if avl_t_isnot_empty avl then
let
val (height_L, height_R) = get_heights avl
in
assertloc (abs (height_L - height_R) <= 1)
end
end
implement {key_t} {data_t}
avl_t_pretty_print (avl) =
let
fun
pad {depth : nat} .<depth>.
(depth : int depth) : void =
if depth <> 0 then
begin
print! (" ");
pad (pred depth)
end
fun
traverse {size : nat}
{depth : nat}
(p : avl_t (key_t, data_t, size),
depth : int depth) : void =
if avl_t_isnot_empty p then
let
val+ CONS (k, d, bal, left, right) = p
in
traverse (left, succ depth);
pad depth;
avl_t_pretty_print$key_and_data<key_t><data_t> (k, d);
println! ("\t\tdepth = ", depth, " bal = ", bal2int bal);
traverse (right, succ depth)
end
in
if avl_t_isnot_empty avl then
let
val+ CONS (k, d, bal, left, right) = avl
in
traverse (left, 1);
avl_t_pretty_print$key_and_data<key_t><data_t> (k, d);
println! ("\t\tdepth = 0 bal = ", bal2int bal);
traverse (right, 1)
end
end
(*------------------------------------------------------------------*)
(*
Here is a little demonstration program.
Assuming you are using Boehm GC, compile this source file with
patscc -O2 -DATS_MEMALLOC_GCBDW avl_trees-postiats.dats -lgc
and run it with
./a.out
*)
%{^
#include <time.h>
ATSinline() atstype_uint64
get_the_time (void)
{
return (atstype_uint64) time (NULL);
}
%}
(* An implementation of avl_t$compare for keys of type ‘int’. *)
implement
avl_t$compare<int> (u, v) =
if u < v then
~1
else if u > v then
1
else
0
(* An implementation of avl_t_pretty_print$key_and_data for keys of
type ‘int’ and values of type ‘double’. *)
implement
avl_t_pretty_print$key_and_data<int><double> (key, data) =
print! ("(", key, ", ", data, ")")
implement
main0 () =
let
(* A linear congruential random number generator attributed
to Donald Knuth. *)
fn
next_random (seed : &uint64) : uint64 =
let
val a : uint64 = $UNSAFE.cast 6364136223846793005ULL
val c : uint64 = $UNSAFE.cast 1442695040888963407ULL
val retval = seed
in
seed := (a * seed) + c;
retval
end
fn {t : t@ype}
fisher_yates_shuffle
{n : nat}
(a : &(@[t][n]),
n : size_t n,
seed : &uint64) : void =
let
var i : [i : nat | i <= n] size_t i
in
for (i := i2sz 0; i < n; i := succ i)
let
val randnum = $UNSAFE.cast{Size_t} (next_random seed)
val j = randnum mod n (* This is good enough for us. *)
val xi = a[i]
val xj = a[j]
in
a[i] := xj;
a[j] := xi
end
end
var seed : uint64 = $extfcall (uint64, "get_the_time")
#define N 20
var keys : @[int][N] = @[int][N] (0)
var a : avl_t (int, double)
var a_saved : avl_t (int, double)
var a1 : (avl_t (int, double), bool)
var i : [i : nat] int i
val dflt = ~99999999.0
val not_dflt = 123456789.0
in
println! ("----------------------------------------------------");
print! ("\n");
(* Initialize a shuffled array of keys. *)
for (i := 0; i < N; i := succ i)
keys[i] := succ i;
fisher_yates_shuffle<int> {N} (keys, i2sz N, seed);
print! ("The keys\n ");
for (i := 0; i < N; i := succ i)
print! (" ", keys[i]);
print! ("\n");
print! ("\nRunning some tests... ");
(* Insert key-data pairs in the shuffled order, checking aspects
of the implementation while doing so. *)
a := avl_t_nil ();
for (i := 0; i < N; i := succ i)
let
var j : [j : nat] int j
in
a := avl_t_insert<int> (a, keys[i], g0i2f keys[i]);
avl_t_check_avl_condition (a);
assertloc (avl_t_size a = succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
a := avl_t_insert<int> (a, keys[i], not_dflt);
avl_t_check_avl_condition (a);
assertloc (avl_t_search<int><double> (a, keys[i], dflt)
= not_dflt);
assertloc (avl_t_size a = succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
a := avl_t_insert<int> (a, keys[i], g0i2f keys[i]);
avl_t_check_avl_condition (a);
assertloc (avl_t_size a = succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
for (j := 0; j < N; j := succ j)
let
val k = keys[j]
val has_key = avl_t_has_key<int> (a, k)
val data_opt = avl_t_search<int><double> (a, k)
val data_dflt = avl_t_search<int><double> (a, k, dflt)
in
assertloc (has_key = (j <= i));
assertloc (option_is_some data_opt = (j <= i));
if (j <= i) then
let
val- Some data = data_opt
in
assertloc (data = g0i2f k);
assertloc (data_dflt = g0i2f k);
end
else
let
val- None () = data_opt
in
assertloc (data_dflt = dflt);
end
end
end;
(* Do it again, but using avl_t_insert_or_replace and checking its
second return value. *)
a1 := (avl_t_nil (), false);
for (i := 0; i < N; i := succ i)
let
var j : [j : nat] int j
in
a1 :=
avl_t_insert_or_replace<int> (a1.0, keys[i], g0i2f keys[i]);
avl_t_check_avl_condition (a1.0);
assertloc (~(a1.1));
assertloc (avl_t_size (a1.0) = succ i);
assertloc (avl_t_is_empty a1.0 = iseqz (avl_t_size a1.0));
assertloc (avl_t_isnot_empty a1.0 = isneqz (avl_t_size a1.0));
a1 := avl_t_insert_or_replace<int> (a1.0, keys[i], not_dflt);
avl_t_check_avl_condition (a1.0);
assertloc (avl_t_search<int><double> (a1.0, keys[i], dflt)
= not_dflt);
assertloc (avl_t_size (a1.0) = succ i);
assertloc (avl_t_is_empty a1.0 = iseqz (avl_t_size a1.0));
assertloc (avl_t_isnot_empty a1.0 = isneqz (avl_t_size a1.0));
a1 :=
avl_t_insert_or_replace<int> (a1.0, keys[i], g0i2f keys[i]);
avl_t_check_avl_condition (a1.0);
assertloc (a1.1);
assertloc (avl_t_size (a1.0) = succ i);
assertloc (avl_t_is_empty a1.0 = iseqz (avl_t_size a1.0));
assertloc (avl_t_isnot_empty a1.0 = isneqz (avl_t_size a1.0));
for (j := 0; j < N; j := succ j)
let
val k = keys[j]
val has_key = avl_t_has_key<int> (a1.0, k)
val data_opt = avl_t_search<int><double> (a1.0, k)
val data_dflt = avl_t_search<int><double> (a1.0, k, dflt)
in
assertloc (has_key = (j <= i));
assertloc (option_is_some data_opt = (j <= i));
if (j <= i) then
let
val- Some data = data_opt
in
assertloc (data = g0i2f k);
assertloc (data_dflt = g0i2f k);
end
else
let
val- None () = data_opt
in
assertloc (data_dflt = dflt);
end
end
end;
a := a1.0;
(* The trees are PERSISTENT, so SAVE THE CURRENT VALUE! *)
a_saved := a;
(* Reshuffle the keys, and test deletion, using the reshuffled
keys. *)
fisher_yates_shuffle<int> {N} (keys, i2sz N, seed);
for (i := 0; i < N; i := succ i)
let
val ix = keys[i]
var j : [j : nat] int j
in
a := avl_t_delete<int> (a, ix);
avl_t_check_avl_condition (a);
assertloc (avl_t_size a = N - succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
a := avl_t_delete<int> (a, ix);
avl_t_check_avl_condition (a);
assertloc (avl_t_size a = N - succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
for (j := 0; j < N; j := succ j)
let
val k = keys[j]
val has_key = avl_t_has_key<int> (a, k)
val data_opt = avl_t_search<int><double> (a, k)
val data_dflt = avl_t_search<int><double> (a, k, dflt)
in
assertloc (has_key = (i < j));
assertloc (option_is_some data_opt = (i < j));
if (i < j) then
let
val- Some data = data_opt
in
assertloc (data = g0i2f k);
assertloc (data_dflt = g0i2f k);
end
else
let
val- None () = data_opt
in
assertloc (data_dflt = dflt);
end
end
end;
(* Get back the PERSISTENT VALUE from before the deletions. *)
a := a_saved;
(* Reshuffle the keys, and test deletion again, this time using
avl_t_delete_if_found. *)
fisher_yates_shuffle<int> {N} (keys, i2sz N, seed);
for (i := 0; i < N; i := succ i)
let
val ix = keys[i]
var j : [j : nat] int j
in
a1 := avl_t_delete_if_found<int> (a, ix);
a := a1.0;
avl_t_check_avl_condition (a);
assertloc (a1.1);
assertloc (avl_t_size a = N - succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
a1 := avl_t_delete_if_found<int> (a, ix);
a := a1.0;
avl_t_check_avl_condition (a);
assertloc (~(a1.1));
assertloc (avl_t_size a = N - succ i);
assertloc (avl_t_is_empty a = iseqz (avl_t_size a));
assertloc (avl_t_isnot_empty a = isneqz (avl_t_size a));
for (j := 0; j < N; j := succ j)
let
val k = keys[j]
val has_key = avl_t_has_key<int> (a, k)
val data_opt = avl_t_search<int><double> (a, k)
val data_dflt = avl_t_search<int><double> (a, k, dflt)
in
assertloc (has_key = (i < j));
assertloc (option_is_some data_opt = (i < j));
if (i < j) then
let
val- Some data = data_opt
in
assertloc (data = g0i2f k);
assertloc (data_dflt = g0i2f k);
end
else
let
val- None () = data_opt
in
assertloc (data_dflt = dflt);
end
end
end;
print! ("passed\n");
(* Get back the PERSISTENT VALUE from before the deletions. *)
a := a_saved;
print! ("\n");
println! ("----------------------------------------------------");
print! ("\n");
print! ("*** PRETTY-PRINTING OF THE TREE ***\n\n");
avl_t_pretty_print<int><double> a;
print! ("\n");
println! ("----------------------------------------------------");
print! ("\n");
print! ("*** GENERATORS ***\n\n");
let
val gen = avl_t_make_pairs_generator (a, 1)
var x : Option @(int, double)
in
print! ("Association pairs in order\n ");
for (x := gen (); option_is_some (x); x := gen ())
let
val @(k, d) = option_unsome x
in
print! (" (", k : int, ", ", d : double, ")")
end
end;
print! ("\n\n");
let
val gen = avl_t_make_pairs_generator (a, ~1)
var x : Option @(int, double)
in
print! ("Association pairs in reverse order\n ");
for (x := gen (); option_is_some (x); x := gen ())
let
val @(k, d) = option_unsome x
in
print! (" (", k : int, ", ", d : double, ")")
end
end;
print! ("\n\n");
let
val gen = avl_t_make_keys_generator (a, 1)
var x : Option int
in
print! ("Keys in order\n ");
for (x := gen (); option_is_some (x); x := gen ())
print! (" ", (option_unsome x) : int)
end;
print! ("\n\n");
let
val gen = avl_t_make_keys_generator (a, ~1)
var x : Option int
in
print! ("Keys in reverse order\n ");
for (x := gen (); option_is_some (x); x := gen ())
print! (" ", (option_unsome x) : int)
end;
print! ("\n\n");
let
val gen = avl_t_make_data_generator (a, 1)
var x : Option double
in
print! ("Data values in order of their keys\n ");
for (x := gen (); option_is_some (x); x := gen ())
print! (" ", (option_unsome x) : double)
end;
print! ("\n\n");
let
val gen = avl_t_make_data_generator (a, ~1)
var x : Option double
in
print! ("Data values in reverse order of their keys\n ");
for (x := gen (); option_is_some (x); x := gen ())
print! (" ", (option_unsome x) : double)
end;
print! ("\n");
print! ("\n");
println! ("----------------------------------------------------");
print! ("\n");
print! ("*** AVL TREES TO LISTS ***\n\n");
print! ("Association pairs in order\n ");
print! (avl_t_pairs<int><double> a);
print! ("\n\n");
print! ("Keys in order\n ");
print! (avl_t_keys<int> a);
print! ("\n\n");
print! ("Data values in order of their keys\n ");
print! (avl_t_data<int><double> a);
print! ("\n");
print! ("\n");
println! ("----------------------------------------------------");
print! ("\n");
print! ("*** LISTS TO AVL TREES ***\n\n");
let
val lst = (3, 3.0) :: (1, 1.0) :: (4, 4.0) :: (2, 2.0) :: LNIL
val avl = list2avl_t<int><double> lst
in
print! (lst : List @(int, double));
print! ("\n\n =>\n\n");
avl_t_pretty_print<int><double> avl
end;
print! ("\n");
println! ("----------------------------------------------------")
end
(*------------------------------------------------------------------*) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AWK | AWK | #!/usr/bin/awk -f
{
PI = atan2(0,-1);
x=0.0; y=0.0;
for (i=1; i<=NF; i++) {
p = $i*PI/180.0;
x += sin(p);
y += cos(p);
}
p = atan2(x,y)*180.0/PI;
if (p<0) p += 360;
print p;
} |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BBC_BASIC | BBC BASIC | *FLOAT 64
DIM angles(3)
angles() = 350,10
PRINT FNmeanangle(angles(), 2)
angles() = 90,180,270,360
PRINT FNmeanangle(angles(), 4)
angles() = 10,20,30
PRINT FNmeanangle(angles(), 3)
END
DEF FNmeanangle(angles(), N%)
LOCAL I%, sumsin, sumcos
FOR I% = 0 TO N%-1
sumsin += SINRADangles(I%)
sumcos += COSRADangles(I%)
NEXT
= DEGFNatan2(sumsin, sumcos)
DEF FNatan2(y,x) : ON ERROR LOCAL = SGN(y)*PI/2
IF x>0 THEN = ATN(y/x) ELSE IF y>0 THEN = ATN(y/x)+PI ELSE = ATN(y/x)-PI |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AntLang | AntLang | median[list] |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #APL | APL | median←{v←⍵[⍋⍵]⋄.5×v[⌈¯1+.5×⍴v]+v[⌊.5×⍴v]} ⍝ Assumes ⎕IO←0 |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Erlang | Erlang | %% Author: Abhay Jain <[email protected]>
-module(mean_calculator).
-export([find_mean/0]).
find_mean() ->
%% This is function calling. First argument is the the beginning number
%% and second argument is the initial value of sum for AM & HM and initial value of product for GM.
arithmetic_mean(1, 0),
geometric_mean(1, 1),
harmonic_mean(1, 0).
%% Function to calculate Arithmetic Mean
arithmetic_mean(Number, Sum) when Number > 10 ->
AM = Sum / 10,
io:format("Arithmetic Mean ~p~n", [AM]);
arithmetic_mean(Number, Sum) ->
NewSum = Sum + Number,
arithmetic_mean(Number+1, NewSum).
%% Function to calculate Geometric Mean
geometric_mean(Number, Product) when Number > 10 ->
GM = math:pow(Product, 0.1),
io:format("Geometric Mean ~p~n", [GM]);
geometric_mean(Number, Product) ->
NewProd = Product * Number,
geometric_mean(Number+1, NewProd).
%% Function to calculate Harmonic Mean
harmonic_mean(Number, Sum) when Number > 10 ->
HM = 10 / Sum,
io:format("Harmonic Mean ~p~n", [HM]);
harmonic_mean(Number, Sum) ->
NewSum = Sum + (1/Number),
harmonic_mean(Number+1, NewSum). |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Elixir | Elixir | defmodule Ternary do
def to_string(t), do: ( for x <- t, do: to_char(x) ) |> List.to_string
def from_string(s), do: ( for x <- to_char_list(s), do: from_char(x) )
defp to_char(-1), do: ?-
defp to_char(0), do: ?0
defp to_char(1), do: ?+
defp from_char(?-), do: -1
defp from_char(?0), do: 0
defp from_char(?+), do: 1
def to_ternary(n) when n > 0, do: to_ternary(n,[])
def to_ternary(n), do: neg(to_ternary(-n))
defp to_ternary(0,acc), do: acc
defp to_ternary(n,acc) when rem(n, 3) == 0, do: to_ternary(div(n, 3), [0|acc])
defp to_ternary(n,acc) when rem(n, 3) == 1, do: to_ternary(div(n, 3), [1|acc])
defp to_ternary(n,acc), do: to_ternary(div((n+1), 3), [-1|acc])
def from_ternary(t), do: from_ternary(t,0)
defp from_ternary([],acc), do: acc
defp from_ternary([h|t],acc), do: from_ternary(t, acc*3 + h)
def mul(a,b), do: mul(b,a,[])
defp mul(_,[],acc), do: acc
defp mul(b,[a|as],acc) do
bp = case a do
-1 -> neg(b)
0 -> [0]
1 -> b
end
a = add(bp, acc ++ [0])
mul(b,as,a)
end
defp neg(t), do: ( for h <- t, do: -h )
def sub(a,b), do: add(a,neg(b))
def add(a,b) when length(a) < length(b),
do: add(List.duplicate(0, length(b)-length(a)) ++ a, b)
def add(a,b) when length(a) > length(b), do: add(b,a)
def add(a,b), do: add(Enum.reverse(a), Enum.reverse(b), 0, [])
defp add([],[],0,acc), do: acc
defp add([],[],c,acc), do: [c|acc]
defp add([a|as],[b|bs],c,acc) do
[c1,d] = add_util(a+b+c)
add(as,bs,c1,[d|acc])
end
defp add_util(-3), do: [-1,0]
defp add_util(-2), do: [-1,1]
defp add_util(-1), do: [0,-1]
defp add_util(3), do: [1,0]
defp add_util(2), do: [1,-1]
defp add_util(1), do: [0,1]
defp add_util(0), do: [0,0]
end
as = "+-0++0+"; at = Ternary.from_string(as); a = Ternary.from_ternary(at)
b = -436; bt = Ternary.to_ternary(b); bs = Ternary.to_string(bt)
cs = "+-++-"; ct = Ternary.from_string(cs); c = Ternary.from_ternary(ct)
rt = Ternary.mul(at,Ternary.sub(bt,ct))
r = Ternary.from_ternary(rt)
rs = Ternary.to_string(rt)
IO.puts "a = #{as} -> #{a}"
IO.puts "b = #{bs} -> #{b}"
IO.puts "c = #{cs} -> #{c}"
IO.puts "a x (b - c) = #{rs} -> #{r}" |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #MAXScript | MAXScript | -- MAXScript : Babbage problem : N.H.
posInt = 1
while posInt < 1000000 do
(
if (matchPattern((posInt * posInt) as string) pattern: "*269696") then exit
posInt += 1
)
Print "The smallest number whose square ends in 269696 is " + ((posInt) as string)
Print "Its square is " + (((pow posInt 2) as integer) as string)
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #AutoHotkey | AutoHotkey | ; Generate 10 strings with equal left and right brackets
Loop, 5
{
B = %A_Index%
loop 2
{
String =
Loop % B
String .= "[`n"
Loop % B
String .= "]`n"
Sort, String, Random
StringReplace, String, String,`n,,All
Example .= String " - " IsBalanced(String) "`n"
}
}
MsgBox % Example
return
IsBalanced(Str)
{
Loop, PARSE, Str
{
If A_LoopField = [
i++
Else if A_LoopField = ]
i--
If i < 0
return "NOT OK"
}
Return "OK"
} |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Elena | Elena | import system'routines;
import system'collections;
import extensions;
extension op
{
get Mode()
{
var countMap := Dictionary.new(0);
self.forEach:(item)
{
countMap[item] := countMap[item] + 1
};
countMap := countMap.Values.sort:(p,n => p > n);
var max := countMap.FirstMember;
^ countMap
.filterBy:(kv => max.equal(kv.Value))
.selectBy:(kv => kv.Key)
.toArray()
}
}
public program()
{
var array1 := new int[]{1, 1, 2, 4, 4};
var array2 := new int[]{1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17};
var array3 := new object[]{1, "blue", 2, 7.5r, 5, "green", "red", 5, 2, "blue", "white"};
console
.printLine("mode of (",array1.asEnumerable(),") is (",array1.Mode,")")
.printLine("mode of (",array2.asEnumerable(),") is (",array2.Mode,")")
.printLine("mode of (",array3.asEnumerable(),") is (",array3.Mode,")")
.readChar()
} |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Elixir | Elixir | defmodule Average do
def mode(list) do
gb = Enum.group_by(list, &(&1))
max = Enum.map(gb, fn {_,val} -> length(val) end) |> Enum.max
for {key,val} <- gb, length(val)==max, do: key
end
end
lists = [[3,1,4,1,5,9,2,6,5,3,5,8,9],
[1, 2, "qwe", "asd", 1, 2, "qwe", "asd", 2, "qwe"]]
Enum.each(lists, fn list ->
IO.puts "mode: #{inspect list}"
IO.puts " => #{inspect Average.mode(list)}"
end) |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #OxygenBasic | OxygenBasic | def max 1000
Class MovingAverage
'==================
indexbase 1
double average,invperiod,mdata[max]
sys index,period
method Setup(double a,p)
sys i
Period=p
invPeriod=1/p
index=0
average=a
for i=1 to period
mdata[i]=a
next
end method
method Data(double v) as double
sys i
index++
if index>period then index=1 'recycle
i=index+1 'for oldest data
if i>period then i=1 'recycle
mdata[index]=v
average=average+invperiod*(v-mdata[i])
end method
end class
'TEST
'====
MovingAverage A
A.Setup 100,10 'initial value and period
A.data 50
'...
print A.average 'reult 95
|
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #11l | 11l | F is_prime(n)
I n < 2
R 0B
L(i) 2 .. Int(sqrt(n))
I n % i == 0
R 0B
R 1B
F get_pfct(=n)
V i = 2
[Int] factors
L i * i <= n
I n % i
i++
E
n I/= i
factors.append(i)
I n > 1
factors.append(n)
R factors.len
[Int] pool
L(each) 0..120
pool.append(get_pfct(each))
[Int] r
L(each) pool
I is_prime(each)
r.append(L.index)
print(r.map(String).join(‘,’)) |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #D | D | import std.stdio, std.range, std.algorithm, std.complex, std.math,
std.format, std.conv;
double radians(in double d) pure nothrow @safe @nogc {
return d * PI / 180;
}
double degrees(in double r) pure nothrow @safe @nogc {
return r * 180 / PI;
}
double meanAngle(in double[] deg) pure nothrow @safe @nogc {
return (deg.map!(d => fromPolar(1, d.radians)).sum / deg.length).arg.degrees;
}
string meanTime(in string[] times) pure @safe {
auto t = times.map!(times => times.split(':').to!(int[3]));
assert(t.all!(hms => 24.iota.canFind(hms[0]) &&
60.iota.canFind(hms[1]) &&
60.iota.canFind(hms[2])),
"Invalid time");
auto seconds = t.map!(hms => hms[2] + hms[1] * 60 + hms[0] * 3600);
enum day = 24 * 60 * 60;
const to_angles = seconds.map!(s => s * 360.0 / day).array;
immutable mean_as_angle = to_angles.meanAngle;
auto mean_seconds_fp = mean_as_angle * day / 360.0;
if (mean_seconds_fp < 0)
mean_seconds_fp += day;
immutable mean_seconds = mean_seconds_fp.to!uint;
immutable h = mean_seconds / 3600;
immutable m = mean_seconds % 3600;
return "%02d:%02d:%02d".format(h, m / 60, m % 60);
}
void main() @safe {
["23:00:17", "23:40:20", "00:12:45", "00:17:19"].meanTime.writeln;
} |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #C | C |
#include <algorithm>
#include <iostream>
/* AVL node */
template <class T>
class AVLnode {
public:
T key;
int balance;
AVLnode *left, *right, *parent;
AVLnode(T k, AVLnode *p) : key(k), balance(0), parent(p),
left(NULL), right(NULL) {}
~AVLnode() {
delete left;
delete right;
}
};
/* AVL tree */
template <class T>
class AVLtree {
public:
AVLtree(void);
~AVLtree(void);
bool insert(T key);
void deleteKey(const T key);
void printBalance();
private:
AVLnode<T> *root;
AVLnode<T>* rotateLeft ( AVLnode<T> *a );
AVLnode<T>* rotateRight ( AVLnode<T> *a );
AVLnode<T>* rotateLeftThenRight ( AVLnode<T> *n );
AVLnode<T>* rotateRightThenLeft ( AVLnode<T> *n );
void rebalance ( AVLnode<T> *n );
int height ( AVLnode<T> *n );
void setBalance ( AVLnode<T> *n );
void printBalance ( AVLnode<T> *n );
};
/* AVL class definition */
template <class T>
void AVLtree<T>::rebalance(AVLnode<T> *n) {
setBalance(n);
if (n->balance == -2) {
if (height(n->left->left) >= height(n->left->right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
}
else if (n->balance == 2) {
if (height(n->right->right) >= height(n->right->left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n->parent != NULL) {
rebalance(n->parent);
}
else {
root = n;
}
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeft(AVLnode<T> *a) {
AVLnode<T> *b = a->right;
b->parent = a->parent;
a->right = b->left;
if (a->right != NULL)
a->right->parent = a;
b->left = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRight(AVLnode<T> *a) {
AVLnode<T> *b = a->left;
b->parent = a->parent;
a->left = b->right;
if (a->left != NULL)
a->left->parent = a;
b->right = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeftThenRight(AVLnode<T> *n) {
n->left = rotateLeft(n->left);
return rotateRight(n);
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRightThenLeft(AVLnode<T> *n) {
n->right = rotateRight(n->right);
return rotateLeft(n);
}
template <class T>
int AVLtree<T>::height(AVLnode<T> *n) {
if (n == NULL)
return -1;
return 1 + std::max(height(n->left), height(n->right));
}
template <class T>
void AVLtree<T>::setBalance(AVLnode<T> *n) {
n->balance = height(n->right) - height(n->left);
}
template <class T>
void AVLtree<T>::printBalance(AVLnode<T> *n) {
if (n != NULL) {
printBalance(n->left);
std::cout << n->balance << " ";
printBalance(n->right);
}
}
template <class T>
AVLtree<T>::AVLtree(void) : root(NULL) {}
template <class T>
AVLtree<T>::~AVLtree(void) {
delete root;
}
template <class T>
bool AVLtree<T>::insert(T key) {
if (root == NULL) {
root = new AVLnode<T>(key, NULL);
}
else {
AVLnode<T>
*n = root,
*parent;
while (true) {
if (n->key == key)
return false;
parent = n;
bool goLeft = n->key > key;
n = goLeft ? n->left : n->right;
if (n == NULL) {
if (goLeft) {
parent->left = new AVLnode<T>(key, parent);
}
else {
parent->right = new AVLnode<T>(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
template <class T>
void AVLtree<T>::deleteKey(const T delKey) {
if (root == NULL)
return;
AVLnode<T>
*n = root,
*parent = root,
*delNode = NULL,
*child = root;
while (child != NULL) {
parent = n;
n = child;
child = delKey >= n->key ? n->right : n->left;
if (delKey == n->key)
delNode = n;
}
if (delNode != NULL) {
delNode->key = n->key;
child = n->left != NULL ? n->left : n->right;
if (root->key == delKey) {
root = child;
}
else {
if (parent->left == n) {
parent->left = child;
}
else {
parent->right = child;
}
rebalance(parent);
}
}
}
template <class T>
void AVLtree<T>::printBalance() {
printBalance(root);
std::cout << std::endl;
}
int main(void)
{
AVLtree<int> t;
std::cout << "Inserting integer values 1 to 10" << std::endl;
for (int i = 1; i <= 10; ++i)
t.insert(i);
std::cout << "Printing balance: ";
t.printBalance();
}
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C | C | #include<math.h>
#include<stdio.h>
double
meanAngle (double *angles, int size)
{
double y_part = 0, x_part = 0;
int i;
for (i = 0; i < size; i++)
{
x_part += cos (angles[i] * M_PI / 180);
y_part += sin (angles[i] * M_PI / 180);
}
return atan2 (y_part / size, x_part / size) * 180 / M_PI;
}
int
main ()
{
double angleSet1[] = { 350, 10 };
double angleSet2[] = { 90, 180, 270, 360};
double angleSet3[] = { 10, 20, 30};
printf ("\nMean Angle for 1st set : %lf degrees", meanAngle (angleSet1, 2));
printf ("\nMean Angle for 2nd set : %lf degrees", meanAngle (angleSet2, 4));
printf ("\nMean Angle for 3rd set : %lf degrees\n", meanAngle (angleSet3, 3));
return 0;
} |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AppleScript | AppleScript | set alist to {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0}
set med to medi(alist)
on medi(alist)
set temp to {}
set lcount to count alist
if lcount is equal to 2 then
return ((item 1 of alist) + (item 2 of alist)) / 2
else if lcount is less than 2 then
return item 1 of alist
else --if lcount is greater than 2
set min to findmin(alist)
set max to findmax(alist)
repeat with x from 1 to lcount
if x is not equal to min and x is not equal to max then set end of temp to item x of alist
end repeat
set med to medi(temp)
end if
return med
end medi
on findmin(alist)
set min to 1
set alength to count every item of alist
repeat with x from 1 to alength
if item x of alist is less than item min of alist then set min to x
end repeat
return min
end findmin
on findmax(alist)
set max to 1
set alength to count every item of alist
repeat with x from 1 to alength
if item x of alist is greater than item max of alist then set max to x
end repeat
return max
end findmax |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ERRE | ERRE |
PROGRAM MEANS
DIM A[9]
PROCEDURE ARITHMETIC_MEAN(A[]->M)
LOCAL S,I%
NEL%=UBOUND(A,1)
S=0
FOR I%=0 TO NEL% DO
S+=A[I%]
END FOR
M=S/(NEL%+1)
END PROCEDURE
PROCEDURE GEOMETRIC_MEAN(A[]->M)
LOCAL S,I%
NEL%=UBOUND(A,1)
S=1
FOR I%=0 TO NEL% DO
S*=A[I%]
END FOR
M=S^(1/(NEL%+1))
END PROCEDURE
PROCEDURE HARMONIC_MEAN(A[]->M)
LOCAL S,I%
NEL%=UBOUND(A,1)
S=0
FOR I%=0 TO NEL% DO
S+=1/A[I%]
END FOR
M=(NEL%+1)/S
END PROCEDURE
BEGIN
A[]=(1,2,3,4,5,6,7,8,9,10)
ARITHMETIC_MEAN(A[]->M)
PRINT("Arithmetic mean = ";M)
GEOMETRIC_MEAN(A[]->M)
PRINT("Geometric mean = ";M)
HARMONIC_MEAN(A[]->M)
PRINT("Harmonic mean = ";M)
END PROGRAM
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Erlang | Erlang |
-module(ternary).
-compile(export_all).
test() ->
AS = "+-0++0+", AT = from_string(AS), A = from_ternary(AT),
B = -436, BT = to_ternary(B), BS = to_string(BT),
CS = "+-++-", CT = from_string(CS), C = from_ternary(CT),
RT = mul(AT,sub(BT,CT)),
R = from_ternary(RT),
RS = to_string(RT),
io:fwrite("A = ~s -> ~b~n",[AS, A]),
io:fwrite("B = ~s -> ~b~n",[BS, B]),
io:fwrite("C = ~s -> ~b~n",[CS, C]),
io:fwrite("A x (B - C) = ~s -> ~b~n", [RS, R]).
to_string(T) -> [to_char(X) || X <- T].
from_string(S) -> [from_char(X) || X <- S].
to_char(-1) -> $-;
to_char(0) -> $0;
to_char(1) -> $+.
from_char($-) -> -1;
from_char($0) -> 0;
from_char($+) -> 1.
to_ternary(N) when N > 0 ->
to_ternary(N,[]);
to_ternary(N) ->
neg(to_ternary(-N)).
to_ternary(0,Acc) ->
Acc;
to_ternary(N,Acc) when N rem 3 == 0 ->
to_ternary(N div 3, [0|Acc]);
to_ternary(N,Acc) when N rem 3 == 1 ->
to_ternary(N div 3, [1|Acc]);
to_ternary(N,Acc) ->
to_ternary((N+1) div 3, [-1|Acc]).
from_ternary(T) -> from_ternary(T,0).
from_ternary([],Acc) ->
Acc;
from_ternary([H|T],Acc) ->
from_ternary(T,Acc*3 + H).
mul(A,B) -> mul(B,A,[]).
mul(_,[],Acc) ->
Acc;
mul(B,[A|As],Acc) ->
BP = case A of
-1 -> neg(B);
0 -> [0];
1 -> B
end,
A1 = Acc++[0],
A2=add(BP,A1),
mul(B,As,A2).
neg(T) -> [ -H || H <- T].
sub(A,B) -> add(A,neg(B)).
add(A,B) when length(A) < length(B) ->
add(lists:duplicate(length(B)-length(A),0)++A,B);
add(A,B) when length(A) > length(B) ->
add(B,A);
add(A,B) ->
add(lists:reverse(A),lists:reverse(B),0,[]).
add([],[],0,Acc) ->
Acc;
add([],[],C,Acc) ->
[C|Acc];
add([A|As],[B|Bs],C,Acc) ->
[C1,D] = add_util(A+B+C),
add(As,Bs,C1,[D|Acc]).
add_util(-3) -> [-1,0];
add_util(-2) -> [-1,1];
add_util(-1) -> [0,-1];
add_util(3) -> [1,0];
add_util(2) -> [1,-1];
add_util(1) -> [0,1];
add_util(0) -> [0,0].
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Microsoft_Small_Basic | Microsoft Small Basic | ' Babbage problem
' The quote (') means a comment
' The equals sign (=) means assign
n = 500
' 500 is stored in variable n*n
' 500 because 500*500=250000 less than 269696
' The nitty-gritty is in the 3 lines between "While" and "EndWhile".
' So, we start with 500, n is being incremented by 1 at each round
' while its square (n*n) (* means multiplication) does not have
' a remainder (function Math.Remainder) of 269696 when divided by one million.
' This means that the loop will stop when the smallest positive integer
' whose square ends in 269696
' is found and stored in n.
' (<>) means "not equal to"
While Math.Remainder( n*n , 1000000 ) <> 269696
n = n + 1
EndWhile
' (TextWindow.WriteLine) displays the string to the monitor
' (+) concatenates strings or variables to be displayed
TextWindow.WriteLine("The smallest positive integer whose square ends in 269696 is " + (n) + ".")
TextWindow.WriteLine("Its square is " + (n*n) + ".")
' End of Program. |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #AutoIt | AutoIt |
#include <Array.au3>
Local $Array[1]
_ArrayAdd($Array, "[]")
_ArrayAdd($Array, "[][]")
_ArrayAdd($Array, "[[][]]")
_ArrayAdd($Array, "][")
_ArrayAdd($Array, "][][")
_ArrayAdd($Array, "[]][[]")
For $i = 0 To UBound($Array) -1
Balanced_Brackets($Array[$i])
If @error Then
ConsoleWrite($Array[$i] &" = NOT OK"&@CRLF)
Else
ConsoleWrite($Array[$i] &" = OK"&@CRLF)
EndIf
Next
Func Balanced_Brackets($String)
Local $cnt = 0
$Split = Stringsplit($String, "")
For $i = 1 To $Split[0]
If $split[$i] = "[" Then $cnt += 1
If $split[$i] = "]" Then $cnt -= 1
If $cnt < 0 Then Return SetError(1,0,0)
Next
Return 1
EndFunc
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Erlang | Erlang |
-module( mode ).
-export( [example/0, values/1] ).
example() ->
Set = [1, 2, "qwe", "asd", 1, 2, "qwe", "asd", 2, "qwe"],
io:fwrite( "In ~p the mode(s) is(are): ~p~n", [Set, values(Set)] ).
values( Set ) ->
Dict = lists:foldl( fun values_count/2, dict:new(), Set ),
[X || {X, _Y} <- dict:fold( fun keep_maxs/3, [{0, 0}], Dict )].
keep_maxs( Key, Value, [{_Max_key, Max_value} | _] ) when Value > Max_value ->
[{Key, Value}];
keep_maxs( Key, Value, [{_Max_key, Max_value} | _]=Maxs ) when Value =:= Max_value ->
[{Key, Value} | Maxs];
keep_maxs( _Key, _Value, Maxs ) ->
Maxs.
values_count( Value, Dict ) -> dict:update_counter( Value, 1, Dict ).
|
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #0815 | 0815 |
{x{+=<:2:x/%<:d:~$<:01:~><:02:~><:03:~><:04:~><:05:~><:06:~><:07:~><:08:
~><:09:~><:0a:~><:0b:~><:0c:~><:0d:~><:0e:~><:0f:~><:10:~><:11:~><:12:~>
<:13:~><:14:~><:15:~><:16:~><:17:~><:18:~><:19:~><:ffffffffffffffff:~>{x
{+>}:8f:{&={+>{~>&=x<:ffffffffffffffff:/#:8f:{{=<:19:x/%
|
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #11l | 11l | F ffactorial(n)
V result = 1.0
L(i) 2..n
result *= i
R result
V MAX_N = 20
V TIMES = 1000000
F analytical(n)
R sum((1..n).map(i -> ffactorial(@n) / pow(Float(@n), Float(i)) / ffactorial(@n - i)))
F test(n, times)
V count = 0
L(i) 0 .< times
V (x, bits) = (1, 0)
L (bits [&] x) == 0
count++
bits [|]= x
x = 1 << random:(n)
R Float(count) / times
print(" n avg exp. diff\n-------------------------------")
L(n) 1 .. MAX_N
V avg = test(n, TIMES)
V theory = analytical(n)
V diff = (avg / theory - 1) * 100
print(‘#2 #3.4 #3.4 #2.3%’.format(n, avg, theory, diff)) |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Oz | Oz | declare
fun {CreateSMA Period}
Xs = {NewCell nil}
in
fun {$ X}
Xs := {List.take X|@Xs Period}
{FoldL @Xs Number.'+' 0.0}
/
{Int.toFloat {Min Period {Length @Xs}}}
end
end
in
for Period in [3 5] do
SMA = {CreateSMA Period}
in
{System.showInfo "\nSTART PERIOD "#Period}
for I in 1..5 do
{System.showInfo " Number = "#I#" , SMA = "#{SMA {Int.toFloat I}}}
end
for I in 5..1;~1 do
{System.showInfo " Number = "#I#" , SMA = "#{SMA {Int.toFloat I}}}
end
end |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #8080_Assembly | 8080 Assembly | ;;; Show attractive numbers up to 120
MAX: equ 120 ; can be up to 255 (8 bit math is used)
;;; CP/M calls
puts: equ 9
bdos: equ 5
org 100h
;;; -- Zero memory ------------------------------------------------
lxi b,fctrs ; page 2
mvi e,2 ; zero out two pages
xra a
mov d,a
zloop: stax b
inx b
dcr d
jnz zloop
dcr e
jnz zloop
;;; -- Generate primes --------------------------------------------
lxi h,plist ; pointer to beginning of primes list
mvi e,2 ; first prime is 2
pstore: mov m,e ; begin prime list
pcand: inr e ; next candidate
jz factor ; if 0, we've rolled over, so we're done
mov l,d ; beginning of primes list (D=0 here)
mov c,m ; C = prime to test against
ptest: mov a,e
ploop: sub c ; test by repeated subtraction
jc notdiv ; if carry, not divisible
jz pcand ; if zero, next candidate
jmp ploop
notdiv: inx h ; get next prime
mov c,m
mov a,c ; is it zero?
ora a
jnz ptest ; if not, test against next prime
jmp pstore ; otherwise, add E to the list of primes
;;; -- Count factors ----------------------------------------------
factor: mvi c,2 ; start with two
fnum: mvi a,MAX ; is candidate beyond maximum?
cmp c
jc output ; then stop
mvi d,0 ; D = number of factors of C
mov l,d ; L = first prime
mov e,c ; E = number we're factorizing
fprim: mvi h,ppage ; H = current prime
mov h,m
ftest: mvi b,0
mov a,e
cpi 1 ; If one, we've counted all the factors
jz nxtfac
fdiv: sub h
jz divi
jc ndivi
inr b
jmp fdiv
divi: inr d ; we found a factor
inr b
mov e,b ; we've removed it, try again
jmp ftest
ndivi: inr l ; not divisible, try next prime
jmp fprim
nxtfac: mov a,d ; store amount of factors
mvi b,fcpage
stax b
inr c ; do next number
jmp fnum
;;; -- Check which numbers are attractive and print them ----------
output: lxi b,fctrs+2 ; start with two
mvi h,ppage ; H = page of primes
onum: mvi a,MAX ; is candidate beyond maximum?
cmp c
rc ; then stop
ldax b ; get amount of factors
mvi l,0 ; start at beginning of prime list
chprm: cmp m ; check against current prime
jz print ; if it's prime, then print the number
inr l ; otherwise, check next prime
jp chprm
next: inr c ; check next number
jmp onum
print: push b ; keep registers
push h
mov a,c ; print number
call printa
pop h ; restore registers
pop b
jmp next
;;; Subroutine: print the number in A
printa: lxi d,num ; DE = string
mvi b,10 ; divisor
digit: mvi c,-1 ; C = quotient
divlp: inr c
sub b
jnc divlp
adi '0'+10 ; make digit
dcx d ; store digit
stax d
mov a,c ; again with new quotient
ora a ; is it zero?
jnz digit ; if not, do next digit
mvi c,puts ; CP/M print string (in DE)
jmp bdos
db '000' ; placeholder for number
num: db ' $'
fcpage: equ 2 ; factors in page 2
ppage: equ 3 ; primes in page 3
fctrs: equ 256*fcpage
plist: equ 256*ppage |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Action.21 | Action! | INCLUDE "H6:SIEVE.ACT"
BYTE FUNC IsAttractive(BYTE n BYTE ARRAY primes)
BYTE count,f
IF n<=1 THEN
RETURN (0)
ELSEIF primes(n) THEN
RETURN (0)
FI
count=0 f=2
DO
IF n MOD f=0 THEN
count==+1
n==/f
IF n=1 THEN
EXIT
ELSEIF primes(n) THEN
f=n
FI
ELSEIF f>=3 THEN
f==+2
ELSE
f=3
FI
OD
IF primes(count) THEN
RETURN (1)
FI
RETURN (0)
PROC Main()
DEFINE MAX="120"
BYTE ARRAY primes(MAX+1)
BYTE i
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
PrintF("Attractive numbers in range 1..%B:%E",MAX)
FOR i=1 TO MAX
DO
IF IsAttractive(i,primes) THEN
PrintF("%B ",i)
FI
OD
RETURN |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Delphi | Delphi |
program Averages_Mean_time_of_day;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
System.Math;
const
Inputs: TArray<string> = ['23:00:17', '23:40:20', '00:12:45', '00:17:19'];
function ToTimes(ts: TArray<string>): TArray<TTime>;
begin
SetLength(result, length(ts));
for var i := 0 to High(ts) do
Result[i] := StrToTime(ts[i]);
end;
function MeanTime(times: TArray<TTime>): TTime;
var
ssum, csum: TTime;
h, m, s, ms: word;
dayFrac, fsec, ssin, ccos: double;
begin
if Length(times) = 0 then
exit(0);
ssum := 0;
csum := 0;
for var t in times do
begin
DecodeTime(t, h, m, s, ms);
fsec := (h * 60 + m) * 60 + s + ms / 1000;
ssin := sin(fsec * Pi / (12 * 60 * 60));
ccos := cos(fsec * Pi / (12 * 60 * 60));
ssum := ssum + ssin;
csum := csum + ccos;
end;
if (ssum = 0) and (csum = 0) then
raise Exception.Create('Error MeanTime: Mean undefined');
dayFrac := frac(1 + ArcTan2(ssum, csum) / (2 * Pi));
fsec := dayFrac * 24 * 3600;
ms := Trunc(frac(fsec) * 1000);
s := trunc(fsec) mod 60;
m := trunc(fsec) div 60 mod 60;
h := trunc(fsec) div 3600;
Result := EncodeTime(h, m, s, ms);
end;
begin
writeln(TimeToStr(MeanTime(ToTimes(Inputs))));
readln;
end. |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #C.23 | C# |
#include <algorithm>
#include <iostream>
/* AVL node */
template <class T>
class AVLnode {
public:
T key;
int balance;
AVLnode *left, *right, *parent;
AVLnode(T k, AVLnode *p) : key(k), balance(0), parent(p),
left(NULL), right(NULL) {}
~AVLnode() {
delete left;
delete right;
}
};
/* AVL tree */
template <class T>
class AVLtree {
public:
AVLtree(void);
~AVLtree(void);
bool insert(T key);
void deleteKey(const T key);
void printBalance();
private:
AVLnode<T> *root;
AVLnode<T>* rotateLeft ( AVLnode<T> *a );
AVLnode<T>* rotateRight ( AVLnode<T> *a );
AVLnode<T>* rotateLeftThenRight ( AVLnode<T> *n );
AVLnode<T>* rotateRightThenLeft ( AVLnode<T> *n );
void rebalance ( AVLnode<T> *n );
int height ( AVLnode<T> *n );
void setBalance ( AVLnode<T> *n );
void printBalance ( AVLnode<T> *n );
};
/* AVL class definition */
template <class T>
void AVLtree<T>::rebalance(AVLnode<T> *n) {
setBalance(n);
if (n->balance == -2) {
if (height(n->left->left) >= height(n->left->right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
}
else if (n->balance == 2) {
if (height(n->right->right) >= height(n->right->left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n->parent != NULL) {
rebalance(n->parent);
}
else {
root = n;
}
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeft(AVLnode<T> *a) {
AVLnode<T> *b = a->right;
b->parent = a->parent;
a->right = b->left;
if (a->right != NULL)
a->right->parent = a;
b->left = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRight(AVLnode<T> *a) {
AVLnode<T> *b = a->left;
b->parent = a->parent;
a->left = b->right;
if (a->left != NULL)
a->left->parent = a;
b->right = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeftThenRight(AVLnode<T> *n) {
n->left = rotateLeft(n->left);
return rotateRight(n);
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRightThenLeft(AVLnode<T> *n) {
n->right = rotateRight(n->right);
return rotateLeft(n);
}
template <class T>
int AVLtree<T>::height(AVLnode<T> *n) {
if (n == NULL)
return -1;
return 1 + std::max(height(n->left), height(n->right));
}
template <class T>
void AVLtree<T>::setBalance(AVLnode<T> *n) {
n->balance = height(n->right) - height(n->left);
}
template <class T>
void AVLtree<T>::printBalance(AVLnode<T> *n) {
if (n != NULL) {
printBalance(n->left);
std::cout << n->balance << " ";
printBalance(n->right);
}
}
template <class T>
AVLtree<T>::AVLtree(void) : root(NULL) {}
template <class T>
AVLtree<T>::~AVLtree(void) {
delete root;
}
template <class T>
bool AVLtree<T>::insert(T key) {
if (root == NULL) {
root = new AVLnode<T>(key, NULL);
}
else {
AVLnode<T>
*n = root,
*parent;
while (true) {
if (n->key == key)
return false;
parent = n;
bool goLeft = n->key > key;
n = goLeft ? n->left : n->right;
if (n == NULL) {
if (goLeft) {
parent->left = new AVLnode<T>(key, parent);
}
else {
parent->right = new AVLnode<T>(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
template <class T>
void AVLtree<T>::deleteKey(const T delKey) {
if (root == NULL)
return;
AVLnode<T>
*n = root,
*parent = root,
*delNode = NULL,
*child = root;
while (child != NULL) {
parent = n;
n = child;
child = delKey >= n->key ? n->right : n->left;
if (delKey == n->key)
delNode = n;
}
if (delNode != NULL) {
delNode->key = n->key;
child = n->left != NULL ? n->left : n->right;
if (root->key == delKey) {
root = child;
}
else {
if (parent->left == n) {
parent->left = child;
}
else {
parent->right = child;
}
rebalance(parent);
}
}
}
template <class T>
void AVLtree<T>::printBalance() {
printBalance(root);
std::cout << std::endl;
}
int main(void)
{
AVLtree<int> t;
std::cout << "Inserting integer values 1 to 10" << std::endl;
for (int i = 1; i <= 10; ++i)
t.insert(i);
std::cout << "Printing balance: ";
t.printBalance();
}
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.23 | C# | using System;
using System.Linq;
using static System.Math;
class Program
{
static double MeanAngle(double[] angles)
{
var x = angles.Sum(a => Cos(a * PI / 180)) / angles.Length;
var y = angles.Sum(a => Sin(a * PI / 180)) / angles.Length;
return Atan2(y, x) * 180 / PI;
}
static void Main()
{
Action<double[]> printMean = x => Console.WriteLine("{0:0.###}", MeanAngle(x));
printMean(new double[] { 350, 10 });
printMean(new double[] { 90, 180, 270, 360 });
printMean(new double[] { 10, 20, 30 });
}
} |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Applesoft_BASIC | Applesoft BASIC | 100 REMMEDIAN
110 K = INT(L/2) : GOSUB 150
120 R = X(K)
130 IF L - 2 * INT (L / 2) THEN R = (R + X(K + 1)) / 2
140 RETURN
150 REMQUICK SELECT
160 LT = 0:RT = L - 1
170 FOR J = LT TO RT STEP 0
180 PT = X(K)
190 P1 = K:P2 = RT: GOSUB 300
200 P = LT
210 FOR I = P TO RT - 1
220 IF X(I) < PT THEN P1 = I:P2 = P: GOSUB 300:P = P + 1
230 NEXT I
240 P1 = RT:P2 = P: GOSUB 300
250 IF P = K THEN RETURN
260 IF P < K THEN LT = P + 1
270 IF P > = K THEN RT = P - 1
280 NEXT J
290 RETURN
300 REMSWAP
310 H = X(P1):X(P1) = X(P2)
320 X(P2) = H: RETURN |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Arturo | Arturo | arr: [1 2 3 4 5 6 7]
arr2: [1 2 3 4 5 6]
print median arr
print median arr2 |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Euler_Math_Toolbox | Euler Math Toolbox |
>function A(x) := mean(x)
>function G(x) := exp(mean(log(x)))
>function H(x) := 1/mean(1/x)
>x=1:10; A(x), G(x), H(x)
5.5
4.52872868812
3.41417152147
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Factor | Factor | USING: kernel combinators locals formatting lint literals
sequences assocs strings arrays
math math.functions math.order ;
IN: rosetta-code.bt
CONSTANT: addlookup {
{ 0 CHAR: 0 }
{ 1 CHAR: + }
{ -1 CHAR: - }
}
<PRIVATE
: bt-add-digits ( a b c -- d e )
+ + 3 +
{ { 0 -1 } { 1 -1 } { -1 0 } { 0 0 } { 1 0 } { -1 1 } { 0 1 } }
nth first2
;
PRIVATE>
! Conversion
: bt>integer ( seq -- x ) 0 [ swap 3 * + ] reduce ;
: integer>bt ( x -- x ) [ dup zero? not ] [
dup 3 rem {
{ 0 [ 3 / 0 ] }
{ 1 [ 3 / round 1 ] }
{ 2 [ 1 + 3 / round -1 ] }
} case
] produce nip reverse
;
: bt>string ( seq -- str ) [ addlookup at ] map >string ;
: string>bt ( str -- seq ) [ addlookup value-at ] { } map-as ;
! Arithmetic
: bt-neg ( a -- -a ) [ neg ] map ;
:: bt-add ( u v -- w )
u v max-length :> maxl
u v [ maxl 0 pad-head reverse ] bi@ :> ( u v )
0 :> carry!
u v { } [ carry bt-add-digits carry! prefix ] 2reduce
carry prefix [ zero? ] trim-head
;
: bt-sub ( u v -- w ) bt-neg bt-add ;
:: bt-mul ( u v -- w ) u { } [
{
{ -1 [ v bt-neg ] }
{ 0 [ { } ] }
{ 1 [ v ] }
} case bt-add 0 suffix
] reduce
1 head*
;
[let
"+-0++0+" string>bt :> a
-436 integer>bt :> b
"+-++-" string>bt :> c
b c bt-sub a bt-mul :> d
"a" a bt>integer a bt>string "%s: %d, %s\n" printf
"b" b bt>integer b bt>string "%s: %d, %s\n" printf
"c" c bt>integer c bt>string "%s: %d, %s\n" printf
"a*(b-c)" d bt>integer d bt>string "%s: %d, %s\n" printf
] |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #MiniScript | MiniScript | // Lines that start with "//" are "comments" that are ignored
// by the computer. We use them to explain the code.
// Start by finding the smallest number that could possibly
// square to 269696. sqrt() returns the square root of a
// number, and floor() truncates any fractional part.
k = floor(sqrt(269696))
// Since 269696 is even, we are only going to consider even
// roots. We use the % (modulo) operator, which returns the
// remainder after division, to tell if k is odd; if so, we
// add 1 to make it even.
if k % 2 == 1 then k = k + 1
// Now we count up by 2 from k, until we find a number that,
// when squared, ends in 269696 (using % again).
while k^2 % 1000000 != 269696
k = k + 2
end while
// The first such number we find is our answer.
print k + "^2 = " + k^2 |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Modula-2 | Modula-2 | MODULE BabbageProblem;
FROM FormatString IMPORT FormatString;
FROM RealMath IMPORT sqrt;
FROM Terminal IMPORT WriteString,ReadChar;
VAR
buf : ARRAY[0..63] OF CHAR;
k : INTEGER;
BEGIN
(* Find the greatest integer less than the square root *)
k := TRUNC(sqrt(269696.0));
(* Odd numbers cannot be solutions, so decrement *)
IF k MOD 2 = 1 THEN
DEC(k);
END;
(* Find a number that meets the criteria *)
WHILE (k*k) MOD 1000000 # 269696 DO
INC(k,2)
END;
FormatString("%i * %i = %i", buf, k, k, k*k);
WriteString(buf);
ReadChar
END BabbageProblem. |
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #AWK | AWK | #!/usr/bin/awk -f
BEGIN {
print isbb("[]")
print isbb("][")
print isbb("][][")
print isbb("[][]")
print isbb("[][][]")
print isbb("[]][[]")
}
function isbb(x) {
s = 0
for (k=1; k<=length(x); k++) {
c = substr(x,k,1)
if (c=="[") {s++}
else { if (c=="]") s-- }
if (s<0) {return 0}
}
return (s==0)
}
|
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ERRE | ERRE | PROGRAM MODE_AVG
!$INTEGER
DIM A[10],B[10],Z[10]
PROCEDURE SORT(Z[],P->Z[])
LOCAL N,FLIPS
FLIPS=TRUE
WHILE FLIPS DO
FLIPS=FALSE
FOR N=0 TO P-1 DO
IF Z[N]>Z[N+1] THEN SWAP(Z[N],Z[N+1]) FLIPS=TRUE
END FOR
END WHILE
END PROCEDURE
PROCEDURE CALC_MODE(Z[],P->MODES$)
LOCAL I,OCCURRENCE,MAXOCCURRENCE,OLDVAL
SORT(Z[],P->Z[])
OCCURENCE=1
MAXOCCURENCE=0
OLDVAL=Z[0]
MODES$=""
FOR I=1 TO P DO
IF Z[I]=OLDVAL THEN
OCCURENCE=OCCURENCE+1
ELSE
IF OCCURENCE>MAXOCCURENCE THEN
MAXOCCURENCE=OCCURENCE
MODES$=STR$(OLDVAL)
ELSIF OCCURENCE=MAXOCCURENCE THEN
MODES$=MODES$+STR$(OLDVAL)
ELSE
!$NULL
END IF
OCCURENCE=1
END IF
OLDVAL=Z[I]
END FOR
!check after loop
IF OCCURENCE>MAXOCCURENCE THEN
MAXOCCURENCE=OCCURENCE
MODES$=STR$(OLDVAL)
ELSIF OCCURENCE=MAXOCCURENCE THEN
MODES$=MODES$+STR$(OLDVAL)
ELSE
!$NULL
END IF
END PROCEDURE
BEGIN
A[]=(1,3,6,6,6,6,7,7,12,12,17)
B[]=(1,2,4,4,1)
PRINT("Modes for array A (1,3,6,6,6,6,7,7,12,12,17)";)
CALC_MODE(A[],10->MODES$)
PRINT(MODES$)
PRINT("Modes for array B (1,2,4,4,1)";)
CALC_MODE(B[],4->MODES$)
PRINT(MODES$)
END PROGRAM |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Euphoria | Euphoria | include misc.e
function mode(sequence s)
sequence uniques, counts, modes
integer j,max
uniques = {}
counts = {}
for i = 1 to length(s) do
j = find(s[i], uniques)
if j then
counts[j] += 1
else
uniques = append(uniques, s[i])
counts = append(counts, 1)
end if
end for
max = counts[1]
for i = 2 to length(counts) do
if counts[i] > max then
max = counts[i]
end if
end for
j = 1
modes = {}
while j <= length(s) do
j = find_from(max, counts, j)
if j = 0 then
exit
end if
modes = append(modes, uniques[j])
j += 1
end while
return modes
end function
constant s = { 1, "blue", 2, 7.5, 5, "green", "red", 5, 2, "blue", "white" }
pretty_print(1,mode(s),{3}) |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #11l | 11l | F average(x)
R sum(x) / Float(x.len)
print(average([0, 0, 3, 1, 4, 1, 5, 9, 0, 0])) |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #Ada | Ada | with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Numerics.Discrete_Random;
procedure Avglen is
package IIO is new Ada.Text_IO.Integer_IO (Positive); use IIO;
package LFIO is new Ada.Text_IO.Float_IO (Long_Float); use LFIO;
subtype FactN is Natural range 0..20;
TESTS : constant Natural := 1_000_000;
function Factorial (N : FactN) return Long_Float is
Result : Long_Float := 1.0;
begin
for I in 2..N loop Result := Result * Long_Float(I); end loop;
return Result;
end Factorial;
function Analytical (N : FactN) return Long_Float is
Sum : Long_Float := 0.0;
begin
for I in 1..N loop
Sum := Sum + Factorial(N) / Factorial(N - I) / Long_Float(N)**I;
end loop;
return Sum;
end Analytical;
function Experimental (N : FactN) return Long_Float is
subtype RandInt is Natural range 1..N;
package Random is new Ada.Numerics.Discrete_Random(RandInt);
seed : Random.Generator;
Num : RandInt;
count : Natural := 0;
bits : array(RandInt'Range) of Boolean;
begin
Random.Reset(seed);
for run in 1..TESTS loop
bits := (others => false);
for I in RandInt'Range loop
Num := Random.Random(seed); exit when bits(Num);
bits(Num) := True; count := count + 1;
end loop;
end loop;
return Long_Float(count)/Long_Float(TESTS);
end Experimental;
A, E, err : Long_Float;
begin
Put_Line(" N avg calc %diff");
for I in 1..20 loop
A := Analytical(I); E := Experimental(I); err := abs(E-A)/A*100.0;
Put(I, Width=>2); Put(E ,Aft=>4, exp=>0); Put(A, Aft=>4, exp=>0);
Put(err, Fore=>3, Aft=>3, exp=>0); New_line;
end loop;
end Avglen; |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #PARI.2FGP | PARI/GP | sma_per(n)={
sma_v=vector(n);
sma_i = 0;
n->if(sma_i++>#sma_v,sma_v[sma_i=1]=n;0,sma_v[sma_i]=n;0)+sum(i=1,#sma_v,sma_v[i])/#sma_v
}; |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Ada | Ada | with Ada.Text_IO;
procedure Attractive_Numbers is
function Is_Prime (N : in Natural) return Boolean is
D : Natural := 5;
begin
if N < 2 then return False; end if;
if N mod 2 = 0 then return N = 2; end if;
if N mod 3 = 0 then return N = 3; end if;
while D * D <= N loop
if N mod D = 0 then return False; end if;
D := D + 2;
if N mod D = 0 then return False; end if;
D := D + 4;
end loop;
return True;
end Is_Prime;
function Count_Prime_Factors (N : in Natural) return Natural is
NC : Natural := N;
Count : Natural := 0;
F : Natural := 2;
begin
if NC = 1 then return 0; end if;
if Is_Prime (NC) then return 1; end if;
loop
if NC mod F = 0 then
Count := Count + 1;
NC := NC / F;
if NC = 1 then
return Count;
end if;
if Is_Prime (NC) then F := NC; end if;
elsif F >= 3 then
F := F + 2;
else
F := 3;
end if;
end loop;
end Count_Prime_Factors;
procedure Show_Attractive (Max : in Natural)
is
use Ada.Text_IO;
package Integer_IO is
new Ada.Text_IO.Integer_IO (Integer);
N : Natural;
Count : Natural := 0;
begin
Put_Line ("The attractive numbers up to and including " & Max'Image & " are:");
for I in 1 .. Max loop
N := Count_Prime_Factors (I);
if Is_Prime (N) then
Integer_IO.Put (I, Width => 5);
Count := Count + 1;
if Count mod 20 = 0 then New_Line; end if;
end if;
end loop;
end Show_Attractive;
begin
Show_Attractive (Max => 120);
end Attractive_Numbers; |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EchoLisp | EchoLisp |
;; string hh:mm:ss to radians
(define (time->radian time)
(define-values (h m s) (map string->number (string-split time ":")))
(+ (* h (/ PI 12)) (* m (/ PI 12 60)) (* s (/ PI 12 3600))))
;; radians to string hh:mm;ss
(define (radian->time rad)
(when (< rad 0) (+= rad (* 2 PI)))
(define t (round (/ (* 12 3600 rad) PI)))
(define h (quotient t 3600))
(define m (quotient (- t (* h 3600)) 60))
(define s (- t (* 3600 h) (* 60 m)))
(string-join (map number->string (list h m s)) ":"))
(define (mean-time times)
(radian->time
(angle
(for/sum ((t times)) (make-polar 1 (time->radian t))))))
(mean-time '{"23:00:17" "23:40:20" "00:12:45" "00:17:19"})
→ "23:47:43"
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #C.2B.2B | C++ |
#include <algorithm>
#include <iostream>
/* AVL node */
template <class T>
class AVLnode {
public:
T key;
int balance;
AVLnode *left, *right, *parent;
AVLnode(T k, AVLnode *p) : key(k), balance(0), parent(p),
left(NULL), right(NULL) {}
~AVLnode() {
delete left;
delete right;
}
};
/* AVL tree */
template <class T>
class AVLtree {
public:
AVLtree(void);
~AVLtree(void);
bool insert(T key);
void deleteKey(const T key);
void printBalance();
private:
AVLnode<T> *root;
AVLnode<T>* rotateLeft ( AVLnode<T> *a );
AVLnode<T>* rotateRight ( AVLnode<T> *a );
AVLnode<T>* rotateLeftThenRight ( AVLnode<T> *n );
AVLnode<T>* rotateRightThenLeft ( AVLnode<T> *n );
void rebalance ( AVLnode<T> *n );
int height ( AVLnode<T> *n );
void setBalance ( AVLnode<T> *n );
void printBalance ( AVLnode<T> *n );
};
/* AVL class definition */
template <class T>
void AVLtree<T>::rebalance(AVLnode<T> *n) {
setBalance(n);
if (n->balance == -2) {
if (height(n->left->left) >= height(n->left->right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
}
else if (n->balance == 2) {
if (height(n->right->right) >= height(n->right->left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n->parent != NULL) {
rebalance(n->parent);
}
else {
root = n;
}
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeft(AVLnode<T> *a) {
AVLnode<T> *b = a->right;
b->parent = a->parent;
a->right = b->left;
if (a->right != NULL)
a->right->parent = a;
b->left = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRight(AVLnode<T> *a) {
AVLnode<T> *b = a->left;
b->parent = a->parent;
a->left = b->right;
if (a->left != NULL)
a->left->parent = a;
b->right = a;
a->parent = b;
if (b->parent != NULL) {
if (b->parent->right == a) {
b->parent->right = b;
}
else {
b->parent->left = b;
}
}
setBalance(a);
setBalance(b);
return b;
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateLeftThenRight(AVLnode<T> *n) {
n->left = rotateLeft(n->left);
return rotateRight(n);
}
template <class T>
AVLnode<T>* AVLtree<T>::rotateRightThenLeft(AVLnode<T> *n) {
n->right = rotateRight(n->right);
return rotateLeft(n);
}
template <class T>
int AVLtree<T>::height(AVLnode<T> *n) {
if (n == NULL)
return -1;
return 1 + std::max(height(n->left), height(n->right));
}
template <class T>
void AVLtree<T>::setBalance(AVLnode<T> *n) {
n->balance = height(n->right) - height(n->left);
}
template <class T>
void AVLtree<T>::printBalance(AVLnode<T> *n) {
if (n != NULL) {
printBalance(n->left);
std::cout << n->balance << " ";
printBalance(n->right);
}
}
template <class T>
AVLtree<T>::AVLtree(void) : root(NULL) {}
template <class T>
AVLtree<T>::~AVLtree(void) {
delete root;
}
template <class T>
bool AVLtree<T>::insert(T key) {
if (root == NULL) {
root = new AVLnode<T>(key, NULL);
}
else {
AVLnode<T>
*n = root,
*parent;
while (true) {
if (n->key == key)
return false;
parent = n;
bool goLeft = n->key > key;
n = goLeft ? n->left : n->right;
if (n == NULL) {
if (goLeft) {
parent->left = new AVLnode<T>(key, parent);
}
else {
parent->right = new AVLnode<T>(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
template <class T>
void AVLtree<T>::deleteKey(const T delKey) {
if (root == NULL)
return;
AVLnode<T>
*n = root,
*parent = root,
*delNode = NULL,
*child = root;
while (child != NULL) {
parent = n;
n = child;
child = delKey >= n->key ? n->right : n->left;
if (delKey == n->key)
delNode = n;
}
if (delNode != NULL) {
delNode->key = n->key;
child = n->left != NULL ? n->left : n->right;
if (root->key == delKey) {
root = child;
}
else {
if (parent->left == n) {
parent->left = child;
}
else {
parent->right = child;
}
rebalance(parent);
}
}
}
template <class T>
void AVLtree<T>::printBalance() {
printBalance(root);
std::cout << std::endl;
}
int main(void)
{
AVLtree<int> t;
std::cout << "Inserting integer values 1 to 10" << std::endl;
for (int i = 1; i <= 10; ++i)
t.insert(i);
std::cout << "Printing balance: ";
t.printBalance();
}
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #C.2B.2B | C++ | #include <iomanip>
#include <iostream>
#include <vector>
#define _USE_MATH_DEFINES
#include <math.h>
template<typename C>
double meanAngle(const C& c) {
auto it = std::cbegin(c);
auto end = std::cend(c);
double x = 0.0;
double y = 0.0;
double len = 0.0;
while (it != end) {
x += cos(*it * M_PI / 180);
y += sin(*it * M_PI / 180);
len++;
it = std::next(it);
}
return atan2(y, x) * 180 / M_PI;
}
void printMean(std::initializer_list<double> init) {
std::cout << std::fixed << std::setprecision(3) << meanAngle(init) << '\n';
}
int main() {
printMean({ 350, 10 });
printMean({ 90, 180, 270, 360 });
printMean({ 10, 20, 30 });
return 0;
} |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AutoHotkey | AutoHotkey | seq = 4.1, 7.2, 1.7, 9.3, 4.4, 3.2, 5
MsgBox % median(seq, "`,") ; 4.1
median(seq, delimiter)
{
Sort, seq, ND%delimiter%
StringSplit, seq, seq, % delimiter
median := Floor(seq0 / 2)
Return seq%median%
} |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Euphoria | Euphoria | function arithmetic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += s[i]
end for
return sum/length(s)
end if
end function
function geometric_mean(sequence s)
atom p
p = 1
for i = 1 to length(s) do
p *= s[i]
end for
return power(p,1/length(s))
end function
function harmonic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += 1/s[i]
end for
return length(s) / sum
end if
end function
function true_or_false(atom x)
if x then
return "true"
else
return "false"
end if
end function
constant s = {1,2,3,4,5,6,7,8,9,10}
constant arithmetic = arithmetic_mean(s),
geometric = geometric_mean(s),
harmonic = harmonic_mean(s)
printf(1,"Arithmetic: %g\n", arithmetic)
printf(1,"Geometric: %g\n", geometric)
printf(1,"Harmonic: %g\n", harmonic)
printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n",
{true_or_false(arithmetic>=geometric and geometric>=harmonic)}) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #FreeBASIC | FreeBASIC |
#define MAX(a, b) iif((a) > (b), (a), (b))
Dim Shared As Integer pow, signo
Dim Shared As String t
t = "-0+"
Function deci(cadena As String) As Integer
Dim As Integer i, deci1
Dim As String c1S
pow = 1
For i = Len(cadena) To 1 Step -1
c1S = Mid(cadena,i,1)
signo = Instr(t, c1S)-2
deci1 = deci1 + pow * signo
pow *= 3
Next i
Return deci1
End Function
Function ternary(n As Integer) As String
Dim As String ternario
Dim As Integer i, k
While Abs(n) > 3^k/2
k += 1
Wend
k -= 1
pow = 3^k
For i = k To 0 Step -1
signo = (n>0) - (n<0)
signo *= (Abs(n) > pow/2)
ternario += Mid(t,signo+2,1)
n -= signo*pow
pow /= 3
Next
If ternario = "" Then ternario = "0"
Return ternario
End Function
Function negate(cadena As String) As String
Dim As String negar = ""
For i As Integer = 1 To Len(cadena)
negar += Mid(t, 4-Instr(t, Mid(cadena,i,1)), 1)
Next i
Return negar
End Function
Function pad(cadenaA As String, n As Integer) As String
Dim As String relleno = cadenaA
While Len(relleno) < n
relleno = "0" + relleno
Wend
Return relleno
End Function
Function addTernary(cadenaA As String, cadenaB As String) As String
Dim As Integer l = max(Len(cadenaA), Len(cadenaB))
Dim As Integer i, x, y, z
cadenaA = pad(cadenaA, l)
cadenaB = pad(cadenaB, l)
Dim As String resultado = ""
Dim As Byte llevar = 0
For i = l To 1 Step -1
x = Instr(t, Mid(cadenaA,i,1))-2
y = Instr(t, Mid(cadenaB,i,1))-2
z = x + y + llevar
If Abs(z) < 2 Then
llevar = 0
Elseif z > 0 Then
llevar = 1: z -= 3
Elseif z < 0 Then
llevar = -1: z += 3
End If
resultado = Mid(t,z+2,1) + resultado
Next i
If llevar <> 0 Then resultado = Mid(t,llevar+2,1) + resultado
i = 0
While Mid(resultado,i+1,1) = "0"
i += 1
Wend
resultado = Mid(resultado,i+1)
If resultado = "" Then resultado = "0"
Return resultado
End Function
Function subTernary(cadenaA As String, cadenaB As String) As String
Return addTernary(cadenaA, negate(cadenaB))
End Function
Function multTernary(cadenaA As String, cadenaB As String) As String
Dim As String resultado = ""
Dim As String tS = "", cambio = ""
For i As Integer = Len(cadenaA) To 1 Step -1
Select Case Mid(cadenaA,i,1)
Case "+": tS = cadenaB
Case "0": tS = "0"
Case "-": tS = negate(cadenaB)
End Select
resultado = addTernary(resultado, tS + cambio)
cambio += "0"
Next i
Return resultado
End Function
Dim As String cadenaA = "+-0++0+"
Dim As Integer a = deci(cadenaA)
Print " a:", a, cadenaA
Dim As Integer b = -436
Dim As String cadenaB = ternary(b)
Print " b:", b, cadenaB
Dim As String cadenaC = "+-++-"
Dim As Integer c = deci(cadenaC)
Print " c:", c, cadenaC
'calcular en ternario
Dim As String resS = multTernary(cadenaA, subTernary(cadenaB, cadenaC))
Print "a*(b-c):", deci(resS), resS
Print !"\nComprobamos:"
Print "a*(b-c): ", a * (b - c)
Sleep
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Nanoquery | Nanoquery | n = 0
while not (n ^ 2 % 1000000) = 269696
n += 1
end
println n |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #NetRexx | NetRexx | /* NetRexx */
options replace format comments java crossref symbols nobinary utf8
numeric digits 5000 -- set up numeric precision
babbageNr = babbage() -- call a function to perform the analysis and capture the result
babbageSq = babbageNr ** 2 -- calculate the square of the result
-- display results using a library function
System.out.printf("%,10d\u00b2 == %,12d%n", [Integer(babbageNr), Integer(babbageSq)])
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- A function method to answer Babbage's question:
-- "What is the smallest positive integer whose square ends in the digits 269,696?"
-- — Babbage, letter to Lord Bowden, 1837;
-- see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
-- (He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.)
method babbage() public static binary
n = int 104 -- (integer arithmatic)
-- begin a processing loop to determine the value
-- starting point: 104
loop while ((n * n) // 1000000) \= 269696
-- loop continues while the remainder of n squared divided by 1,000,000 is not equal to 269,696
if n // 10 == 4 then do
-- increment n by 2 if the remainder of n divided by 10 equals 4
n = n + 2
end
if n // 10 == 6 then do
-- increment n by 8 if the remainder of n divided by 10 equals 6
n = n + 8
end
end
return n -- end the function and return the result
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #BaCon | BaCon | FOR len = 0 TO 18 STEP 2
str$ = ""
DOTIMES len
str$ = str$ & CHR$(IIF(RANDOM(2) = 0, 91, 93))
DONE
status = 0
FOR x = 1 TO LEN(str$)
IF MID$(str$, x, 1) = "[" THEN
INCR status
ELSE
DECR status
FI
IF status < 0 THEN BREAK
NEXT
IF status = 0 THEN
PRINT "OK: ", str$
ELSE
PRINT "BAD: ", str$
ENDIF
NEXT |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #F.23 | F# | let mode (l:'a seq) =
l
|> Seq.countBy (fun item -> item) // Count individual items
|> Seq.fold // Find max counts
(fun (cp, lst) (item, c) -> // State is (count, list of items with that count)
if c > cp then (c, [item]) // New max - keep count and a list of the single item
elif c = cp then (c, item :: lst) // New element with max count - prepend it to the list
else (cp,lst)) // else just keep old count/list
(0, [Unchecked.defaultof<'a>]) // Start with a count of 0 and a dummy item
|> snd // From (count, list) we just want the second item (the list) |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Factor | Factor | { 11 9 4 9 4 9 } mode ! 9 |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #360_Assembly | 360 Assembly | AVGP CSECT
USING AVGP,12
LR 12,15
SR 3,3 i=0
SR 6,6 sum=0
LOOP CH 3,=AL2(NN-T-1) for i=1 to nn
BH ENDLOOP
L 2,T(3) t(i)
MH 2,=H'100' scaling factor=2
AR 6,2 sum=sum+t(i)
LA 3,4(3) next i
B LOOP
ENDLOOP LR 5,6 sum
LA 4,0
D 4,NN sum/nn
XDECO 5,Z edit binary
MVC U,Z+10 descale
MVI Z+10,C'.'
MVC Z+11(2),U
XPRNT Z,80 output
XR 15,15
BR 14
T DC F'10',F'9',F'8',F'7',F'6',F'5',F'4',F'3',F'2',F'1'
NN DC A((NN-T)/4)
Z DC CL80' '
U DS CL2
END AVGP |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #6502_Assembly | 6502 Assembly | ArithmeticMean: PHA
TYA
PHA ;push accumulator and Y register onto stack
LDA #0
STA Temp
STA Temp+1 ;temporary 16-bit storage for total
LDY NumberInts
BEQ Done ;if NumberInts = 0 then return an average of zero
DEY ;start with NumberInts-1
AddLoop: LDA (ArrayPtr),Y
CLC
ADC Temp
STA Temp
LDA Temp+1
ADC #0
STA Temp+1
DEY
CPY #255
BNE AddLoop
LDY #-1
DivideLoop: LDA Temp
SEC
SBC NumberInts
STA Temp
LDA Temp+1
SBC #0
STA Temp+1
INY
BCS DivideLoop
Done: STY ArithMean ;store result here
PLA ;restore accumulator and Y register from stack
TAY
PLA
RTS ;return from routine |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #BBC_BASIC | BBC BASIC | @% = &2040A
MAX_N = 20
TIMES = 1000000
FOR n = 1 TO MAX_N
avg = FNtest(n, TIMES)
theory = FNanalytical(n)
diff = (avg / theory - 1) * 100
PRINT STR$(n), avg, theory, diff "%"
NEXT
END
DEF FNanalytical(n)
LOCAL i, s
FOR i = 1 TO n
s += FNfactorial(n) / n^i / FNfactorial(n-i)
NEXT
= s
DEF FNtest(n, times)
LOCAL i, b, c, x
FOR i = 1 TO times
x = 1 : b = 0
WHILE (b AND x) = 0
c += 1
b OR= x
x = 1 << (RND(n) - 1)
ENDWHILE
NEXT
= c / times
DEF FNfactorial(n)
IF n=1 OR n=0 THEN =1 ELSE = n * FNfactorial(n-1) |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #C | C | #include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define MAX_N 20
#define TIMES 1000000
double factorial(int n) {
double f = 1;
int i;
for (i = 1; i <= n; i++) f *= i;
return f;
}
double expected(int n) {
double sum = 0;
int i;
for (i = 1; i <= n; i++)
sum += factorial(n) / pow(n, i) / factorial(n - i);
return sum;
}
int randint(int n) {
int r, rmax = RAND_MAX / n * n;
while ((r = rand()) >= rmax);
return r / (RAND_MAX / n);
}
int test(int n, int times) {
int i, count = 0;
for (i = 0; i < times; i++) {
int x = 1, bits = 0;
while (!(bits & x)) {
count++;
bits |= x;
x = 1 << randint(n);
}
}
return count;
}
int main(void) {
srand(time(0));
puts(" n\tavg\texp.\tdiff\n-------------------------------");
int n;
for (n = 1; n <= MAX_N; n++) {
int cnt = test(n, TIMES);
double avg = (double)cnt / TIMES;
double theory = expected(n);
double diff = (avg / theory - 1) * 100;
printf("%2d %8.4f %8.4f %6.3f%%\n", n, avg, theory, diff);
}
return 0;
} |
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Pascal | Pascal | program sma;
type
tsma = record
smaValue : array of double;
smaAverage,
smaSumOld,
smaSumNew,
smaRezActLength : double;
smaActLength,
smaLength,
smaPos :NativeInt;
smaIsntFull: boolean;
end;
procedure smaInit(var sma:tsma;p: NativeUint);
Begin
with sma do
Begin
setlength(smaValue,0);
setlength(smaValue,p);
smaLength:= p;
smaActLength := 0;
smaAverage:= 0.0;
smaSumOld := 0.0;
smaSumNew := 0.0;
smaPos := p-1;
smaIsntFull := true
end;
end;
function smaAddValue(var sma:tsma;v: double):double;
Begin
with sma do
Begin
IF smaIsntFull then
Begin
inc(smaActLength);
smaRezActLength := 1/smaActLength;
smaIsntFull := smaActLength < smaLength ;
end;
smaSumOld := smaSumOld+v-smaValue[smaPos];
smaValue[smaPos] := v;
smaSumNew := smaSumNew+v;
smaPos := smaPos-1;
if smaPos < 0 then
begin
smaSumOld:= smaSumNew;
smaSumNew:= 0.0;
smaPos := smaLength-1;
end;
smaAverage := smaSumOld *smaRezActLength;
smaAddValue:= smaAverage;
end;
end;
var
sma3,sma5:tsma;
i : LongInt;
begin
smaInit(sma3,3);
smaInit(sma5,5);
For i := 1 to 5 do
Begin
write('Inserting ',i,' into sma3 ',smaAddValue(sma3,i):0:4);
writeln(' Inserting ',i,' into sma5 ',smaAddValue(sma5,i):0:4);
end;
For i := 5 downto 1 do
Begin
write('Inserting ',i,' into sma3 ',smaAddValue(sma3,i):0:4);
writeln(' Inserting ',i,' into sma5 ',smaAddValue(sma5,i):0:4);
end;
//speed test
smaInit(sma3,3);
For i := 1 to 100000000 do
smaAddValue(sma3,i);
writeln('100''000''000 insertions ',sma3.smaAverage:0:4);
end. |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #ALGOL_68 | ALGOL 68 | BEGIN # find some attractive numbers - numbers whose prime factor counts are #
# prime, n must be > 1 #
PR read "primes.incl.a68" PR
# find the attractive numbers #
INT max number = 120;
[]BOOL sieve = PRIMESIEVE ENTIER sqrt( max number );
print( ( "The attractve numbers up to ", whole( max number, 0 ), newline ) );
INT a count := 0;
FOR i FROM 2 TO max number DO
IF INT v := i;
INT f count := 0;
WHILE NOT ODD v DO
f count +:= 1;
v OVERAB 2
OD;
FOR j FROM 3 BY 2 TO max number WHILE v > 1 DO
WHILE v > 1 AND v MOD j = 0 DO
f count +:= 1;
v OVERAB j
OD
OD;
f count > 0
THEN
IF sieve[ f count ] THEN
print( ( " ", whole( i, -3 ) ) );
IF ( a count +:= 1 ) MOD 20 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline, "Found ", whole( a count, 0 ), " attractive numbers", newline ) )
END |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Erlang | Erlang |
-module( mean_time_of_day ).
-export( [from_times/1, task/0] ).
from_times( Times ) ->
Seconds = [seconds_from_time(X) || X <- Times],
Degrees = [degrees_from_seconds(X) || X <- Seconds],
Average = mean_angle:from_degrees( Degrees ),
time_from_seconds( seconds_from_degrees(Average) ).
task() ->
Times = ["23:00:17", "23:40:20", "00:12:45", "00:17:19"],
io:fwrite( "The mean time of ~p is: ~p~n", [Times, from_times(Times)] ).
degrees_from_seconds( Seconds ) when Seconds < (24 * 3600) -> (Seconds * 360) / (24 * 3600).
seconds_from_degrees( Degrees ) when Degrees < 0 -> seconds_from_degrees( Degrees + 360 );
seconds_from_degrees( Degrees ) when Degrees < 360 -> (Degrees * 24 * 3600) / 360.
seconds_from_time( Time ) ->
{ok, [Hours, Minutes, Seconds], _Rest} = io_lib:fread( "~d:~d:~d", Time ),
Hours * 3600 + Minutes * 60 + Seconds.
time_from_seconds( Seconds_float ) ->
Seconds = erlang:round( Seconds_float ),
Hours = Seconds div 3600,
Minutes = (Seconds - (Hours * 3600)) div 60,
Secs = Seconds - (Hours * 3600) - (Minutes * 60),
lists:flatten( io_lib:format("~2.10.0B:~2.10.0B:~2.10.0B", [Hours, Minutes, Secs]) ).
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #C.2B.2B.2FCLI | C++/CLI | (defpackage :avl-tree
(:use :cl)
(:export
:avl-tree
:make-avl-tree
:avl-tree-count
:avl-tree-p
:avl-tree-key<=
:gettree
:remtree
:clrtree
:dfs-maptree
:bfs-maptree))
(in-package :avl-tree)
(defstruct %tree
key
value
(height 0 :type fixnum)
left
right)
(defstruct (avl-tree (:constructor %make-avl-tree))
key<=
tree
(count 0 :type fixnum))
(defun make-avl-tree (key<=)
"Create a new AVL tree using the given comparison function KEY<=
for emplacing keys into the tree."
(%make-avl-tree :key<= key<=))
(declaim (inline
recalc-height
height balance
swap-kv
right-right-rotate
right-left-rotate
left-right-rotate
left-left-rotate
rotate))
(defun recalc-height (tree)
"Calculate the new height of the tree from the heights of the children."
(when tree
(setf (%tree-height tree)
(1+ (the fixnum (max (height (%tree-right tree))
(height (%tree-left tree))))))))
(declaim (ftype (function (t) fixnum) height balance))
(defun height (tree)
(if tree (%tree-height tree) 0))
(defun balance (tree)
(if tree
(- (height (%tree-right tree))
(height (%tree-left tree)))
0))
(defmacro swap (place-a place-b)
"Swap the values of two places."
(let ((tmp (gensym)))
`(let ((,tmp ,place-a))
(setf ,place-a ,place-b)
(setf ,place-b ,tmp))))
(defun swap-kv (tree-a tree-b)
"Swap the keys and values of two trees."
(swap (%tree-value tree-a) (%tree-value tree-b))
(swap (%tree-key tree-a) (%tree-key tree-b)))
;; We should really use gensyms for the variables in here.
(defmacro slash-rotate (tree right left)
"Rotate nodes in a slash `/` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,right b))
(a-left (,left a))
(b-left (,left b)))
(setf (,right a) c)
(setf (,left a) b)
(setf (,left b) a-left)
(setf (,right b) b-left)
(swap-kv a b)
(recalc-height b)
(recalc-height a)))
(defmacro angle-rotate (tree right left)
"Rotate nodes in an angle bracket `<` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,left b))
(a-left (,left a))
(c-left (,left c))
(c-right (,right c)))
(setf (,left a) c)
(setf (,left c) a-left)
(setf (,right c) c-left)
(setf (,left b) c-right)
(swap-kv a c)
(recalc-height c)
(recalc-height b)
(recalc-height a)))
(defun right-right-rotate (tree)
(slash-rotate tree %tree-right %tree-left))
(defun left-left-rotate (tree)
(slash-rotate tree %tree-left %tree-right))
(defun right-left-rotate (tree)
(angle-rotate tree %tree-right %tree-left))
(defun left-right-rotate (tree)
(angle-rotate tree %tree-left %tree-right))
(defun rotate (tree)
(declare (type %tree tree))
"Perform a rotation on the given TREE if it is imbalanced."
(recalc-height tree)
(with-slots (left right) tree
(let ((balance (balance tree)))
(cond ((< 1 balance) ;; Right imbalanced tree
(if (<= 0 (balance right))
(right-right-rotate tree)
(right-left-rotate tree)))
((> -1 balance) ;; Left imbalanced tree
(if (<= 0 (balance left))
(left-right-rotate tree)
(left-left-rotate tree)))))))
(defun gettree (key avl-tree &optional default)
"Finds an entry in AVL-TREE whos key is KEY and returns the
associated value and T as multiple values, or returns DEFAULT and NIL
if there was no such entry. Entries can be added using SETF."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(if tree
(with-slots ((t-key key) left right value) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(values value t)
(rec right))
(rec left)))
(values default nil))))
(rec tree))))
(defun puttree (value key avl-tree)
;;(declare (optimize speed))
(declare (type avl-tree avl-tree))
"Emplace the the VALUE with the given KEY into the AVL-TREE, or
overwrite the value if the given key already exists."
(let ((node (make-%tree :key key :value value)))
(with-slots (key<= tree count) avl-tree
(cond (tree
(labels
((rec (tree)
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(setf (%tree-value tree) value)
(cond (right (rec right))
(t (setf right node)
(incf count))))
(cond (left (rec left))
(t (setf left node)
(incf count))))
(rotate tree))))
(rec tree)))
(t (setf tree node)
(incf count))))
value))
(defun (setf gettree) (value key avl-tree &optional default)
(declare (ignore default))
(puttree value key avl-tree))
(defun remtree (key avl-tree)
(declare (type avl-tree avl-tree))
"Remove the entry in AVL-TREE associated with KEY. Return T if
there was such an entry, or NIL if not."
(with-slots (key<= tree count) avl-tree
(labels
((find-left (tree)
(with-slots ((t-key key) left right) tree
(if left
(find-left left)
tree)))
(rec (tree &optional parent type)
(when tree
(prog1
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(cond
((funcall key<= key t-key)
(cond
((and left right)
(let ((sub-left (find-left right)))
(swap-kv sub-left tree)
(rec right tree :right)))
(t
(let ((sub (or left right)))
(case type
(:right (setf (%tree-right parent) sub))
(:left (setf (%tree-left parent) sub))
(nil (setf (avl-tree-tree avl-tree) sub))))
(decf count)))
t)
(t (rec right tree :right)))
(rec left tree :left)))
(when parent (rotate parent))))))
(rec tree))))
(defun clrtree (avl-tree)
"This removes all the entries from AVL-TREE and returns the tree itself."
(setf (avl-tree-tree avl-tree) nil)
(setf (avl-tree-count avl-tree) 0)
avl-tree)
(defun dfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in depth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(when tree
(with-slots ((t-key key) left right key value) tree
(rec left)
(funcall function key value)
(rec right)))))
(rec tree))))
(defun bfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in breadth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(let* ((queue (cons nil nil))
(end queue))
(labels ((pushend (value)
(when value
(setf (cdr end) (cons value nil))
(setf end (cdr end))))
(empty-p () (eq nil (cdr queue)))
(popfront ()
(prog1 (pop (cdr queue))
(when (empty-p) (setf end queue)))))
(when tree
(pushend tree)
(loop until (empty-p)
do (let ((current (popfront)))
(with-slots (key value left right) current
(funcall function key value)
(pushend left)
(pushend right)))))))))
(defun test ()
(let ((tree (make-avl-tree #'<=))
(printer (lambda (k v) (print (list k v)))))
(loop for key in '(0 8 6 4 2 3 7 9 1 5 5)
for value in '(a b c d e f g h i j k)
do (setf (gettree key tree) value))
(loop for key in '(0 1 2 3 4 10)
do (print (multiple-value-list (gettree key tree))))
(terpri)
(print tree)
(terpri)
(dfs-maptree printer tree)
(terpri)
(bfs-maptree printer tree)
(terpri)
(loop for key in '(0 1 2 3 10 7)
do (print (remtree key tree)))
(terpri)
(print tree)
(terpri)
(clrtree tree)
(print tree))
(values))
(defun profile-test ()
(let ((tree (make-avl-tree #'<=))
(randoms (loop repeat 1000000 collect (random 100.0))))
(loop for key in randoms do (setf (gettree key tree) key)))) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Clojure | Clojure | (defn mean-fn
[k coll]
(let [n (count coll)
trig (get {:sin #(Math/sin %) :cos #(Math/cos %)} k)]
(* (/ 1 n) (reduce + (map trig coll)))))
(defn mean-angle
[degrees]
(let [radians (map #(Math/toRadians %) degrees)
a (mean-fn :sin radians)
b (mean-fn :cos radians)]
(Math/toDegrees (Math/atan2 a b)))) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Common_Lisp | Common Lisp | (defun average (list)
(/ (reduce #'+ list) (length list)))
(defun radians (angle)
(* pi 1/180 angle))
(defun degrees (angle)
(* (/ 180 pi) angle))
(defun mean-angle (angles)
(let* ((angles (map 'list #'radians angles))
(cosines (map 'list #'cos angles))
(sines (map 'list #'sin angles)))
(degrees (atan (average sines) (average cosines)))))
(loop for angles in '((350 10) (90 180 270 360) (10 20 30))
do (format t "~&The mean angle of ~a is ~$°." angles (mean-angle angles)))
;; or using complex numbers (cis and phase)
(defun mean-angle-2 (angles)
(degrees (phase (reduce #'+ angles :key (lambda (deg) (cis (radians deg)))))))
|
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #AWK | AWK | #!/usr/bin/awk -f
BEGIN {
d[1] = 3.0
d[2] = 4.0
d[3] = 1.0
d[4] = -8.4
d[5] = 7.2
d[6] = 4.0
d[7] = 1.0
d[8] = 1.2
showD("Before: ")
gnomeSortD()
showD("Sorted: ")
printf "Median: %f\n", medianD()
exit
}
function medianD( len, mid) {
len = length(d)
mid = int(len/2) + 1
if (len % 2) return d[mid]
else return (d[mid] + d[mid-1]) / 2.0
}
function gnomeSortD( i) {
for (i = 2; i <= length(d); i++) {
if (d[i] < d[i-1]) gnomeSortBackD(i)
}
}
function gnomeSortBackD(i, t) {
for (; i > 1 && d[i] < d[i-1]; i--) {
t = d[i]
d[i] = d[i-1]
d[i-1] = t
}
}
function showD(p, i) {
printf p
for (i = 1; i <= length(d); i++) {
printf d[i] " "
}
print ""
}
|
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Excel | Excel |
=AVERAGE(1;2;3;4;5;6;7;8;9;10)
=GEOMEAN(1;2;3;4;5;6;7;8;9;10)
=HARMEAN(1;2;3;4;5;6;7;8;9;10)
|
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Glagol | Glagol | ОТДЕЛ Сетунь+;
ИСПОЛЬЗУЕТ
Параметр ИЗ "...\Отделы\Обмен\",
Текст ИЗ "...\Отделы\Числа\",
Вывод ИЗ "...\Отделы\Обмен\";
ПЕР
зч: РЯД 10 ИЗ ЗНАК;
счпоз: ЦЕЛ;
число: ЦЕЛ;
память: ДОСТУП К НАБОР
ячейки: РЯД 20 ИЗ ЦЕЛ;
размер: УЗКЦЕЛ;
отрицательное: КЛЮЧ
КОН;
ЗАДАЧА СоздатьПамять;
УКАЗ
СОЗДАТЬ(память);
память.размер := 0;
память.отрицательное := ОТКЛ
КОН СоздатьПамять;
ЗАДАЧА ДобавитьВПамять(что: ЦЕЛ);
УКАЗ
память.ячейки[память.размер] := что;
УВЕЛИЧИТЬ(память.размер)
КОН ДобавитьВПамять;
ЗАДАЧА ОбратитьПамять;
ПЕР
зчсл: ЦЕЛ;
сч: ЦЕЛ;
УКАЗ
ОТ сч := 0 ДО память.размер ДЕЛИТЬ 2 - 1 ВЫП
зчсл := память.ячейки[сч];
память.ячейки[сч] := память.ячейки[память.размер-сч-1];
память.ячейки[память.размер-сч-1] := зчсл
КОН
КОН ОбратитьПамять;
ЗАДАЧА ВывестиПамять;
ПЕР
сч: ЦЕЛ;
УКАЗ
ОТ сч := 0 ДО память.размер-1 ВЫП
ЕСЛИ память.ячейки[сч] < 0 ТО
Вывод.Цепь("-")
АЕСЛИ память.ячейки[сч] > 0 ТО
Вывод.Цепь("+")
ИНАЧЕ Вывод.Цепь("0") КОН
КОН
КОН ВывестиПамять;
ЗАДАЧА УдалитьПамять;
УКАЗ
память := ПУСТО
КОН УдалитьПамять;
ЗАДАЧА Перевести(число: ЦЕЛ);
ПЕР
о: ЦЕЛ;
з: КЛЮЧ;
ЗАДАЧА ВПамять(что: ЦЕЛ);
УКАЗ
ЕСЛИ память.отрицательное ТО
ЕСЛИ что < 0 ТО ДобавитьВПамять(1)
АЕСЛИ что > 0 ТО ДобавитьВПамять(-1)
ИНАЧЕ ДобавитьВПамять(0) КОН
ИНАЧЕ
ДобавитьВПамять(что)
КОН
КОН ВПамять;
УКАЗ
ЕСЛИ число < 0 ТО память.отрицательное := ВКЛ КОН;
число := МОДУЛЬ(число);
з := ОТКЛ;
ПОКА число > 0 ВЫП
о := число ОСТАТОК 3;
число := число ДЕЛИТЬ 3;
ЕСЛИ з ТО
ЕСЛИ о = 2 ТО ВПамять(0) АЕСЛИ о = 1 ТО ВПамять(-1) ИНАЧЕ ВПамять(1); з := ОТКЛ КОН
ИНАЧЕ
ЕСЛИ о = 2 ТО ВПамять(-1); з := ВКЛ ИНАЧЕ ВПамять(о) КОН
КОН
КОН;
ЕСЛИ з ТО ВПамять(1) КОН;
ОбратитьПамять;
ВывестиПамять(ВКЛ);
КОН Перевести;
ЗАДАЧА ВЧисло(): ЦЕЛ;
ПЕР
сч, мн: ЦЕЛ;
результат: ЦЕЛ;
УКАЗ
результат := 0;
мн := 1;
ОТ сч := 0 ДО память.размер-1 ВЫП
УВЕЛИЧИТЬ(результат, память.ячейки[память.размер-сч-1]*мн);
мн := мн * 3
КОН;
ВОЗВРАТ результат
КОН ВЧисло;
УКАЗ
Параметр.Текст(1, зч); счпоз := 0;
число := Текст.ВЦел(зч, счпоз);
СоздатьПамять;
Перевести(число);
Вывод.ЧЦел(" = %d.", ВЧисло(), 0, 0, 0);
УдалитьПамять
КОН Сетунь.
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #NewLisp | NewLisp |
;;; Start by assigning n the integer square root of 269696
;;; minus 1 to be even
(setq n 518)
;;; Increment n by 2 till the last 6 digits of its square are 269696
(while (!= (% (* n n) 1000000) 269696)
(++ n 2))
;;; Show the result and its square
(println n "^2 = " (* n n))
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #BASIC | BASIC | DECLARE FUNCTION checkBrackets% (brackets AS STRING)
DECLARE FUNCTION generator$ (length AS INTEGER)
RANDOMIZE TIMER
DO
x$ = generator$ (10)
PRINT x$,
IF checkBrackets(x$) THEN
PRINT "OK"
ELSE
PRINT "NOT OK"
END IF
LOOP WHILE LEN(x$)
FUNCTION checkBrackets% (brackets AS STRING)
'returns -1 (TRUE) if everything's ok, 0 (FALSE) if not
DIM L0 AS INTEGER, sum AS INTEGER
FOR L0 = 1 TO LEN(brackets)
SELECT CASE MID$(brackets, L0, 1)
CASE "["
sum = sum + 1
CASE "]"
sum = sum - 1
END SELECT
IF sum < 0 THEN
checkBrackets% = 0
EXIT FUNCTION
END IF
NEXT
IF 0 = sum THEN
checkBrackets% = -1
ELSE
checkBrackets% = 0
END IF
END FUNCTION
FUNCTION generator$ (length AS INTEGER)
z = INT(RND * length)
IF z < 1 THEN generator$ = "": EXIT FUNCTION
REDIM x(z * 2) AS STRING
FOR i = 0 TO z STEP 2
x(i) = "["
x(i + 1) = "]"
NEXT
FOR i = 1 TO UBOUND(x)
z = INT(RND * 2)
IF z THEN SWAP x(i), x(i - 1)
NEXT
xx$ = ""
FOR i = 0 TO UBOUND(x)
xx$ = xx$ + x(i)
NEXT
generator$ = xx$
END FUNCTION |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Fortran | Fortran | program mode_test
use Qsort_Module only Qsort => sort
implicit none
integer, parameter :: S = 10
integer, dimension(S) :: a1 = (/ -1, 7, 7, 2, 2, 2, -1, 7, -3, -3 /)
integer, dimension(S) :: a2 = (/ 1, 1, 1, 1, 1, 0, 2, 2, 2, 2 /)
integer, dimension(S) :: a3 = (/ 0, 0, -1, -1, 9, 9, 3, 3, 7, 7 /)
integer, dimension(S) :: o
integer :: l, trash
print *, stat_mode(a1)
trash = stat_mode(a1, o, l)
print *, o(1:l)
trash = stat_mode(a2, o, l)
print *, o(1:l)
trash = stat_mode(a3, o, l)
print *, o(1:l)
contains
! stat_mode returns the lowest (if not unique) mode
! others can hold other modes, if the mode is not unique
! if others is provided, otherslen should be provided too, and
! it says how many other modes are there.
! ok can be used to know if the return value has a meaning
! or the mode can't be found (void arrays)
integer function stat_mode(a, others, otherslen, ok)
integer, dimension(:), intent(in) :: a
logical, optional, intent(out) :: ok
integer, dimension(size(a,1)), optional, intent(out) :: others
integer, optional, intent(out) :: otherslen
! ta is a copy of a, we sort ta modifying it, freq
! holds the frequencies and idx the index (for ta) so that
! the value appearing freq(i)-time is ta(idx(i))
integer, dimension(size(a, 1)) :: ta, freq, idx
integer :: rs, i, tm, ml, tf
if ( present(ok) ) ok = .false.
select case ( size(a, 1) )
case (0) ! no mode... ok is false
return
case (1)
if ( present(ok) ) ok = .true.
stat_mode = a(1)
return
case default
if ( present(ok) ) ok = .true.
ta = a ! copy the array
call sort(ta) ! sort it in place (cfr. sort algos on RC)
freq = 1
idx = 0
rs = 1 ! rs will be the number of different values
do i = 2, size(ta, 1)
if ( ta(i-1) == ta(i) ) then
freq(rs) = freq(rs) + 1
else
idx(rs) = i-1
rs = rs + 1
end if
end do
idx(rs) = i-1
ml = maxloc(freq(1:rs), 1) ! index of the max value of freq
tf = freq(ml) ! the max frequency
tm = ta(idx(ml)) ! the value with that freq
! if we want all the possible modes, we provide others
if ( present(others) ) then
i = 1
others(1) = tm
do
freq(ml) = 0
ml = maxloc(freq(1:rs), 1)
if ( tf == freq(ml) ) then ! the same freq
i = i + 1 ! as the max one
others(i) = ta(idx(ml))
else
exit
end if
end do
if ( present(otherslen) ) then
otherslen = i
end if
end if
stat_mode = tm
end select
end function stat_mode
end program mode_test |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #8th | 8th |
: avg \ a -- avg(a)
dup ' n:+ 0 a:reduce
swap a:len nip n:/ ;
\ test:
[ 1.0, 2.3, 1.1, 5.0, 3, 2.8, 2.01, 3.14159 ] avg . cr
[ ] avg . cr
[ 10 ] avg . cr
bye
|
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ACL2 | ACL2 | (defun mean-r (xs)
(if (endp xs)
(mv 0 0)
(mv-let (m j)
(mean-r (rest xs))
(mv (+ (first xs) m) (+ j 1)))))
(defun mean (xs)
(if (endp xs)
0
(mv-let (n d)
(mean-r xs)
(/ n d)))) |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #11l | 11l | V base = [‘name’ = ‘Rocket Skates’, ‘price’ = ‘12.75’, ‘color’ = ‘yellow’]
V update = [‘price’ = ‘15.25’, ‘color’ = ‘red’, ‘year’ = ‘1974’]
V result = copy(base)
result.update(update)
print(result) |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #C.23 | C# | public class AverageLoopLength {
private static int N = 100000;
private static double analytical(int n) {
double[] factorial = new double[n + 1];
double[] powers = new double[n + 1];
powers[0] = 1.0;
factorial[0] = 1.0;
for (int i = 1; i <= n; i++) {
factorial[i] = factorial[i - 1] * i;
powers[i] = powers[i - 1] * n;
}
double sum = 0;
for (int i = 1; i <= n; i++) {
sum += factorial[n] / factorial[n - i] / powers[i];
}
return sum;
}
private static double average(int n) {
Random rnd = new Random();
double sum = 0.0;
for (int a = 0; a < N; a++) {
int[] random = new int[n];
for (int i = 0; i < n; i++) {
random[i] = rnd.Next(n);
}
var seen = new HashSet<double>(n);
int current = 0;
int length = 0;
while (seen.Add(current)) {
length++;
current = random[current];
}
sum += length;
}
return sum / N;
}
public static void Main(string[] args) {
Console.WriteLine(" N average analytical (error)");
Console.WriteLine("=== ========= ============ =========");
for (int i = 1; i <= 20; i++) {
var average = AverageLoopLength.average(i);
var analytical = AverageLoopLength.analytical(i);
Console.WriteLine("{0,3} {1,10:N4} {2,13:N4} {3,8:N2}%", i, average, analytical, (analytical - average) / analytical * 100);
}
}
}
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Perl | Perl | sub sma_generator {
my $period = shift;
my (@list, $sum);
return sub {
my $number = shift;
push @list, $number;
$sum += $number;
$sum -= shift @list if @list > $period;
return $sum / @list;
}
}
# Usage:
my $sma = sma_generator(3);
for (1, 2, 3, 2, 7) {
printf "append $_ --> sma = %.2f (with period 3)\n", $sma->($_);
} |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #ALGOL_W | ALGOL W | % find some attractive numbers - numbers whose prime factor count is prime %
begin
% implements the sieve of Eratosthenes %
% s(i) is set to true if i is prime, false otherwise %
% algol W doesn't have a upb operator, so we pass the size of the %
% array in n %
procedure sieve( logical array s ( * ); integer value n ) ;
begin
% start with everything flagged as prime %
for i := 1 until n do s( i ) := true;
% sieve out the non-primes %
s( 1 ) := false;
for i := 2 until truncate( sqrt( n ) ) do begin
if s( i ) then for p := i * i step i until n do s( p ) := false
end for_i ;
end sieve ;
% returns the count of prime factors of n, using the sieve of primes s %
% n must be greater than 0 %
integer procedure countPrimeFactors ( integer value n; logical array s ( * ) ) ;
if s( n ) then 1
else begin
integer count, rest;
rest := n;
count := 0;
while rest rem 2 = 0 do begin
count := count + 1;
rest := rest div 2
end while_divisible_by_2 ;
for factor := 3 step 2 until n - 1 do begin
if s( factor ) then begin
while rest > 1 and rest rem factor = 0 do begin
count := count + 1;
rest := rest div factor
end while_divisible_by_factor
end if_prime_factor
end for_factor ;
count
end countPrimeFactors ;
% maximum number for the task %
integer maxNumber;
maxNumber := 120;
% show the attractive numbers %
begin
logical array s ( 1 :: maxNumber );
sieve( s, maxNumber );
i_w := 2; % set output field width %
s_w := 1; % and output separator width %
% find and display the attractive numbers %
for i := 2 until maxNumber do if s( countPrimeFactors( i, s ) ) then writeon( i )
end
end. |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #AppleScript | AppleScript | on isPrime(n)
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
repeat with i from 5 to (n ^ 0.5) div 1 by 6
if ((n mod i is 0) or (n mod (i + 2) is 0)) then return false
end repeat
return true
end isPrime
on primeFactorCount(n)
set x to n
set counter to 0
if (n > 1) then
repeat while (n mod 2 = 0)
set counter to counter + 1
set n to n div 2
end repeat
repeat while (n mod 3 = 0)
set counter to counter + 1
set n to n div 3
end repeat
set i to 5
set limit to (n ^ 0.5) div 1
repeat until (i > limit)
repeat while (n mod i = 0)
set counter to counter + 1
set n to n div i
end repeat
tell (i + 2) to repeat while (n mod it = 0)
set counter to counter + 1
set n to n div it
end repeat
set i to i + 6
set limit to (n ^ 0.5) div 1
end repeat
if (n > 1) then set counter to counter + 1
end if
return counter
end primeFactorCount
-- Task code:
local output, n
set output to {}
repeat with n from 1 to 120
if (isPrime(primeFactorCount(n))) then set end of output to n
end repeat
return output |
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Euphoria | Euphoria |
include std/console.e
include std/math.e
include std/mathcons.e
include std/sequence.e
include std/get.e
function T2D(sequence TimeSeq)
return (360 * TimeSeq[1] / 24 + 360 * TimeSeq[2] / (24 * 60) +
360 * TimeSeq[3] / (24 * 3600))
end function
function D2T(atom angle)
sequence TimeSeq = {0,0,0}
atom seconds = 24 * 60 * 60 * angle / 360
TimeSeq[3] = mod(seconds,60)
TimeSeq[2] = (mod(seconds,3600) - TimeSeq[3]) / 60
TimeSeq[1] = seconds / 3600
return TimeSeq
end function
function MeanAngle(sequence angles)
atom x = 0, y = 0
integer l = length(angles)
for i = 1 to length(angles) do
x += cos(angles[i] * PI / 180)
y += sin(angles[i] * PI / 180)
end for
return atan2(y / l, x / l) * 180 / PI
end function
sequence TimeEntry, TimeList = {}, TimeSeq
puts(1,"Enter times. Enter with no input to end\n")
while 1 do
TimeEntry = prompt_string("")
if equal(TimeEntry,"") then -- no more entries
for i = 1 to length(TimeList) do
TimeList[i] = split(TimeList[i],":") -- split the times into sequences
for j = 1 to 3 do
TimeList[i][j] = defaulted_value(TimeList[i][j],0) -- convert to numerical values
end for
end for
exit
end if
TimeList = append(TimeList,TimeEntry)
end while
sequence AngleList = repeat({},length(TimeList))
for i = 1 to length(AngleList) do
AngleList[i] = T2D(TimeList[i])
end for
sequence MeanTime = D2T(360+MeanAngle(AngleList))
printf(1,"\nMean Time: %d:%d:%d\n",MeanTime)
if getc(0) then end if
|
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #Common_Lisp | Common Lisp | (defpackage :avl-tree
(:use :cl)
(:export
:avl-tree
:make-avl-tree
:avl-tree-count
:avl-tree-p
:avl-tree-key<=
:gettree
:remtree
:clrtree
:dfs-maptree
:bfs-maptree))
(in-package :avl-tree)
(defstruct %tree
key
value
(height 0 :type fixnum)
left
right)
(defstruct (avl-tree (:constructor %make-avl-tree))
key<=
tree
(count 0 :type fixnum))
(defun make-avl-tree (key<=)
"Create a new AVL tree using the given comparison function KEY<=
for emplacing keys into the tree."
(%make-avl-tree :key<= key<=))
(declaim (inline
recalc-height
height balance
swap-kv
right-right-rotate
right-left-rotate
left-right-rotate
left-left-rotate
rotate))
(defun recalc-height (tree)
"Calculate the new height of the tree from the heights of the children."
(when tree
(setf (%tree-height tree)
(1+ (the fixnum (max (height (%tree-right tree))
(height (%tree-left tree))))))))
(declaim (ftype (function (t) fixnum) height balance))
(defun height (tree)
(if tree (%tree-height tree) 0))
(defun balance (tree)
(if tree
(- (height (%tree-right tree))
(height (%tree-left tree)))
0))
(defmacro swap (place-a place-b)
"Swap the values of two places."
(let ((tmp (gensym)))
`(let ((,tmp ,place-a))
(setf ,place-a ,place-b)
(setf ,place-b ,tmp))))
(defun swap-kv (tree-a tree-b)
"Swap the keys and values of two trees."
(swap (%tree-value tree-a) (%tree-value tree-b))
(swap (%tree-key tree-a) (%tree-key tree-b)))
;; We should really use gensyms for the variables in here.
(defmacro slash-rotate (tree right left)
"Rotate nodes in a slash `/` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,right b))
(a-left (,left a))
(b-left (,left b)))
(setf (,right a) c)
(setf (,left a) b)
(setf (,left b) a-left)
(setf (,right b) b-left)
(swap-kv a b)
(recalc-height b)
(recalc-height a)))
(defmacro angle-rotate (tree right left)
"Rotate nodes in an angle bracket `<` imbalance."
`(let* ((a ,tree)
(b (,right a))
(c (,left b))
(a-left (,left a))
(c-left (,left c))
(c-right (,right c)))
(setf (,left a) c)
(setf (,left c) a-left)
(setf (,right c) c-left)
(setf (,left b) c-right)
(swap-kv a c)
(recalc-height c)
(recalc-height b)
(recalc-height a)))
(defun right-right-rotate (tree)
(slash-rotate tree %tree-right %tree-left))
(defun left-left-rotate (tree)
(slash-rotate tree %tree-left %tree-right))
(defun right-left-rotate (tree)
(angle-rotate tree %tree-right %tree-left))
(defun left-right-rotate (tree)
(angle-rotate tree %tree-left %tree-right))
(defun rotate (tree)
(declare (type %tree tree))
"Perform a rotation on the given TREE if it is imbalanced."
(recalc-height tree)
(with-slots (left right) tree
(let ((balance (balance tree)))
(cond ((< 1 balance) ;; Right imbalanced tree
(if (<= 0 (balance right))
(right-right-rotate tree)
(right-left-rotate tree)))
((> -1 balance) ;; Left imbalanced tree
(if (<= 0 (balance left))
(left-right-rotate tree)
(left-left-rotate tree)))))))
(defun gettree (key avl-tree &optional default)
"Finds an entry in AVL-TREE whos key is KEY and returns the
associated value and T as multiple values, or returns DEFAULT and NIL
if there was no such entry. Entries can be added using SETF."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(if tree
(with-slots ((t-key key) left right value) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(values value t)
(rec right))
(rec left)))
(values default nil))))
(rec tree))))
(defun puttree (value key avl-tree)
;;(declare (optimize speed))
(declare (type avl-tree avl-tree))
"Emplace the the VALUE with the given KEY into the AVL-TREE, or
overwrite the value if the given key already exists."
(let ((node (make-%tree :key key :value value)))
(with-slots (key<= tree count) avl-tree
(cond (tree
(labels
((rec (tree)
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(if (funcall key<= key t-key)
(setf (%tree-value tree) value)
(cond (right (rec right))
(t (setf right node)
(incf count))))
(cond (left (rec left))
(t (setf left node)
(incf count))))
(rotate tree))))
(rec tree)))
(t (setf tree node)
(incf count))))
value))
(defun (setf gettree) (value key avl-tree &optional default)
(declare (ignore default))
(puttree value key avl-tree))
(defun remtree (key avl-tree)
(declare (type avl-tree avl-tree))
"Remove the entry in AVL-TREE associated with KEY. Return T if
there was such an entry, or NIL if not."
(with-slots (key<= tree count) avl-tree
(labels
((find-left (tree)
(with-slots ((t-key key) left right) tree
(if left
(find-left left)
tree)))
(rec (tree &optional parent type)
(when tree
(prog1
(with-slots ((t-key key) left right) tree
(if (funcall key<= t-key key)
(cond
((funcall key<= key t-key)
(cond
((and left right)
(let ((sub-left (find-left right)))
(swap-kv sub-left tree)
(rec right tree :right)))
(t
(let ((sub (or left right)))
(case type
(:right (setf (%tree-right parent) sub))
(:left (setf (%tree-left parent) sub))
(nil (setf (avl-tree-tree avl-tree) sub))))
(decf count)))
t)
(t (rec right tree :right)))
(rec left tree :left)))
(when parent (rotate parent))))))
(rec tree))))
(defun clrtree (avl-tree)
"This removes all the entries from AVL-TREE and returns the tree itself."
(setf (avl-tree-tree avl-tree) nil)
(setf (avl-tree-count avl-tree) 0)
avl-tree)
(defun dfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in depth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(labels
((rec (tree)
(when tree
(with-slots ((t-key key) left right key value) tree
(rec left)
(funcall function key value)
(rec right)))))
(rec tree))))
(defun bfs-maptree (function avl-tree)
"For each entry in AVL-TREE call the two-argument FUNCTION on
the key and value of each entry in breadth-first order from left to right.
Consequences are undefined if AVL-TREE is modified during this call."
(with-slots (key<= tree) avl-tree
(let* ((queue (cons nil nil))
(end queue))
(labels ((pushend (value)
(when value
(setf (cdr end) (cons value nil))
(setf end (cdr end))))
(empty-p () (eq nil (cdr queue)))
(popfront ()
(prog1 (pop (cdr queue))
(when (empty-p) (setf end queue)))))
(when tree
(pushend tree)
(loop until (empty-p)
do (let ((current (popfront)))
(with-slots (key value left right) current
(funcall function key value)
(pushend left)
(pushend right)))))))))
(defun test ()
(let ((tree (make-avl-tree #'<=))
(printer (lambda (k v) (print (list k v)))))
(loop for key in '(0 8 6 4 2 3 7 9 1 5 5)
for value in '(a b c d e f g h i j k)
do (setf (gettree key tree) value))
(loop for key in '(0 1 2 3 4 10)
do (print (multiple-value-list (gettree key tree))))
(terpri)
(print tree)
(terpri)
(dfs-maptree printer tree)
(terpri)
(bfs-maptree printer tree)
(terpri)
(loop for key in '(0 1 2 3 10 7)
do (print (remtree key tree)))
(terpri)
(print tree)
(terpri)
(clrtree tree)
(print tree))
(values))
(defun profile-test ()
(let ((tree (make-avl-tree #'<=))
(randoms (loop repeat 1000000 collect (random 100.0))))
(loop for key in randoms do (setf (gettree key tree) key)))) |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #D | D | import std.stdio, std.algorithm, std.complex;
import std.math: PI;
auto radians(T)(in T d) pure nothrow @nogc { return d * PI / 180; }
auto degrees(T)(in T r) pure nothrow @nogc { return r * 180 / PI; }
real meanAngle(T)(in T[] D) pure nothrow @nogc {
immutable t = reduce!((a, d) => a + d.radians.expi)(0.complex, D);
return (t / D.length).arg.degrees;
}
void main() {
foreach (angles; [[350, 10], [90, 180, 270, 360], [10, 20, 30]])
writefln("The mean angle of %s is: %.2f degrees",
angles, angles.meanAngle);
} |
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BaCon | BaCon | DECLARE a[] = { 4.1, 5.6, 7.2, 1.7, 9.3, 4.4, 3.2 } TYPE FLOATING
DECLARE b[] = { 4.1, 7.2, 1.7, 9.3, 4.4, 3.2 } TYPE FLOATING
DEF FN Dim(x) = SIZEOF(x) / SIZEOF(double)
DEF FN Median(x) = IIF(ODD(Dim(x)), x[(Dim(x)-1)/2], (x[Dim(x)/2-1]+x[Dim(x)/2])/2 )
SORT a
PRINT "Median of a: ", Median(a)
SORT b
PRINT "Median of b: ", Median(b) |
http://rosettacode.org/wiki/Averages/Pythagorean_means | Averages/Pythagorean means | Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).
Show that
A
(
x
1
,
…
,
x
n
)
≥
G
(
x
1
,
…
,
x
n
)
≥
H
(
x
1
,
…
,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
A
(
x
1
,
…
,
x
n
)
=
x
1
+
⋯
+
x
n
n
{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}
The geometric mean is the
n
{\displaystyle n}
th root of the product of the list:
G
(
x
1
,
…
,
x
n
)
=
x
1
⋯
x
n
n
{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}
The harmonic mean is
n
{\displaystyle n}
divided by the sum of the reciprocal of each item in the list:
H
(
x
1
,
…
,
x
n
)
=
n
1
x
1
+
⋯
+
1
x
n
{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #F.23 | F# | let P = [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 9.0; 10.0]
let arithmeticMean (x : float list) =
x |> List.sum
|> (fun acc -> acc / float (List.length(x)))
let geometricMean (x: float list) =
x |> List.reduce (*)
|> (fun acc -> Math.Pow(acc, 1.0 / (float (List.length(x)))))
let harmonicMean (x: float list) =
x |> List.map (fun a -> 1.0 / a)
|> List.sum
|> (fun acc -> float (List.length(x)) / acc)
printfn "Arithmetic Mean: %A" (arithmeticMean P)
printfn "Geometric Mean: %A" (geometricMean P)
printfn "Harmonic Mean: %A" (harmonicMean P) |
http://rosettacode.org/wiki/Balanced_ternary | Balanced ternary | Balanced ternary is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
Examples
Decimal 11 = 32 + 31 − 30, thus it can be written as "++−"
Decimal 6 = 32 − 31 + 0 × 30, thus it can be written as "+−0"
Task
Implement balanced ternary representation of integers with the following:
Support arbitrarily large integers, both positive and negative;
Provide ways to convert to and from text strings, using digits '+', '-' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type is balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do not convert to native integers first.
Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
Test case With balanced ternaries a from string "+-0++0+", b from native integer -436, c "+-++-":
write out a, b and c in decimal notation;
calculate a × (b − c), write out the result in both ternary and decimal notations.
Note: The pages generalised floating point addition and generalised floating point multiplication have code implementing arbitrary precision floating point balanced ternary.
| #Go | Go | package main
import (
"fmt"
"strings"
)
// R1: representation is a slice of int8 digits of -1, 0, or 1.
// digit at index 0 is least significant. zero value of type is
// representation of the number 0.
type bt []int8
// R2: string conversion:
// btString is a constructor. valid input is a string of any length
// consisting of only '+', '-', and '0' characters.
// leading zeros are allowed but are trimmed and not represented.
// false return means input was invalid.
func btString(s string) (*bt, bool) {
s = strings.TrimLeft(s, "0")
b := make(bt, len(s))
for i, last := 0, len(s)-1; i < len(s); i++ {
switch s[i] {
case '-':
b[last-i] = -1
case '0':
b[last-i] = 0
case '+':
b[last-i] = 1
default:
return nil, false
}
}
return &b, true
}
// String method converts the other direction, returning a string of
// '+', '-', and '0' characters representing the number.
func (b bt) String() string {
if len(b) == 0 {
return "0"
}
last := len(b) - 1
r := make([]byte, len(b))
for i, d := range b {
r[last-i] = "-0+"[d+1]
}
return string(r)
}
// R3: integer conversion
// int chosen as "native integer"
// btInt is a constructor like btString.
func btInt(i int) *bt {
if i == 0 {
return new(bt)
}
var b bt
var btDigit func(int)
btDigit = func(digit int) {
m := int8(i % 3)
i /= 3
switch m {
case 2:
m = -1
i++
case -2:
m = 1
i--
}
if i == 0 {
b = make(bt, digit+1)
} else {
btDigit(digit + 1)
}
b[digit] = m
}
btDigit(0)
return &b
}
// Int method converts the other way, returning the value as an int type.
// !ok means overflow occurred during conversion, not necessarily that the
// value is not representable as an int. (Of course there are other ways
// of doing it but this was chosen as "reasonable.")
func (b bt) Int() (r int, ok bool) {
pt := 1
for _, d := range b {
dp := int(d) * pt
neg := r < 0
r += dp
if neg {
if r > dp {
return 0, false
}
} else {
if r < dp {
return 0, false
}
}
pt *= 3
}
return r, true
}
// R4: negation, addition, and multiplication
func (z *bt) Neg(b *bt) *bt {
if z != b {
if cap(*z) < len(*b) {
*z = make(bt, len(*b))
} else {
*z = (*z)[:len(*b)]
}
}
for i, d := range *b {
(*z)[i] = -d
}
return z
}
func (z *bt) Add(a, b *bt) *bt {
if len(*a) < len(*b) {
a, b = b, a
}
r := *z
r = r[:cap(r)]
var carry int8
for i, da := range *a {
if i == len(r) {
n := make(bt, len(*a)+4)
copy(n, r)
r = n
}
sum := da + carry
if i < len(*b) {
sum += (*b)[i]
}
carry = sum / 3
sum %= 3
switch {
case sum > 1:
sum -= 3
carry++
case sum < -1:
sum += 3
carry--
}
r[i] = sum
}
last := len(*a)
if carry != 0 {
if len(r) == last {
n := make(bt, last+4)
copy(n, r)
r = n
}
r[last] = carry
*z = r[:last+1]
return z
}
for {
if last == 0 {
*z = nil
break
}
last--
if r[last] != 0 {
*z = r[:last+1]
break
}
}
return z
}
func (z *bt) Mul(a, b *bt) *bt {
if len(*a) < len(*b) {
a, b = b, a
}
var na bt
for _, d := range *b {
if d == -1 {
na.Neg(a)
break
}
}
r := make(bt, len(*a)+len(*b))
for i := len(*b) - 1; i >= 0; i-- {
switch (*b)[i] {
case 1:
p := r[i:]
p.Add(&p, a)
case -1:
p := r[i:]
p.Add(&p, &na)
}
}
i := len(r)
for i > 0 && r[i-1] == 0 {
i--
}
*z = r[:i]
return z
}
func main() {
a, _ := btString("+-0++0+")
b := btInt(-436)
c, _ := btString("+-++-")
show("a:", a)
show("b:", b)
show("c:", c)
show("a(b-c):", a.Mul(a, b.Add(b, c.Neg(c))))
}
func show(label string, b *bt) {
fmt.Printf("%7s %12v ", label, b)
if i, ok := b.Int(); ok {
fmt.Printf("%7d\n", i)
} else {
fmt.Println("int overflow")
}
} |
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Nim | Nim |
var n : int = 0
while n*n mod 1_000_000 != 269_696:
inc(n)
echo n
|
http://rosettacode.org/wiki/Babbage_problem | Babbage problem |
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.
For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].
Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.
| #Objeck | Objeck | class Babbage {
function : Main(args : String[]) ~ Nil {
cur := 0;
do {
cur++;
}
while(cur * cur % 1000000 <> 269696);
cur_sqr := cur * cur;
"The square of {$cur} is {$cur_sqr}!"->PrintLine();
}
}
|
http://rosettacode.org/wiki/Balanced_brackets | Balanced brackets | Task:
Generate a string with N opening brackets [ and with N closing brackets ], in some arbitrary order.
Determine whether the generated string is balanced; that is, whether it consists entirely of pairs of opening/closing brackets (in that order), none of which mis-nest.
Examples
(empty) OK
[] OK
[][] OK
[[][]] OK
][ NOT OK
][][ NOT OK
[]][[] NOT OK
| #BASIC256 | BASIC256 | s$ = "[[]][]"
print s$; " = ";
if not check_brackets(s$) then print "not ";
print "ok"
end
function check_brackets(s$)
level = 0
for i = 1 to length(s$)
c$ = mid(s$, i, 1)
begin case
case c$ = "["
level = level + 1
case c$ = "]"
level = level - 1
if level < 0 then exit for
end case
next i
return level = 0
end function |
http://rosettacode.org/wiki/Averages/Mode | Averages/Mode | Task[edit]
Write a program to find the mode value of a collection.
The case where the collection is empty may be ignored. Care must be taken to handle the case where the mode is non-unique.
If it is not appropriate or possible to support a general collection, use a vector (array), if possible. If it is not appropriate or possible to support an unspecified value type, use integers.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #FreeBASIC | FreeBASIC | ' FB 1.05.0 Win64
Sub quicksort(a() As Integer, first As Integer, last As Integer)
Dim As Integer length = last - first + 1
If length < 2 Then Return
Dim pivot As Integer = a(first + length\ 2)
Dim lft As Integer = first
Dim rgt As Integer = last
While lft <= rgt
While a(lft) < pivot
lft +=1
Wend
While a(rgt) > pivot
rgt -= 1
Wend
If lft <= rgt Then
Swap a(lft), a(rgt)
lft += 1
rgt -= 1
End If
Wend
quicksort(a(), first, rgt)
quicksort(a(), lft, last)
End Sub
' The modal value(s) is/are stored in 'm'.
' The function returns the modal count.
Function mode(a() As Integer, m() As Integer, sorted As Boolean = false) As Integer
Dim lb As Integer = LBound(a)
Dim ub As Integer = UBound(a)
If ub = -1 Then Return 0 '' empty array
If Not sorted Then quicksort(a(), lb, ub)
Dim cValue As Integer = a(lb)
Dim cCount As Integer = 1
Dim cMax As Integer = 0
'' We iterate to the end of the array plus 1 to ensure the
'' final value is dealt with properly
For i As Integer = lb + 1 To ub + 1
If i <= ub AndAlso a(i) = cValue Then
cCount += 1
Else
If cCount > cMax Then
Erase m
Redim m(1 To 1)
m(1) = cValue
cMax = cCount
ElseIf cCount = cMax Then
Redim Preserve m(1 To UBound(m) + 1)
m(UBound(m)) = cValue
End If
If i = ub + 1 Then Exit For
cValue = a(i)
cCount = 1
End If
Next
Return cMax
End Function
Dim a(1 To 14) As Integer = {1, 2, 3, 1, 2, 4, 2, 5, 2, 3, 3, 1, 3, 6}
Dim m() As Integer '' to store the mode(s)
Dim mCount As Integer = mode(a(), m())
Print "The following are the modes which occur"; mCount; " times : "
For i As Integer = LBound(m) To UBound(m) : Print m(i); " "; : Next
Print
Print "Press any key to quit"
Sleep |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Action.21 | Action! | INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
PROC Mean(INT ARRAY a INT count REAL POINTER result)
INT i
REAL x,sum,tmp
IntToReal(0,sum)
FOR i=0 TO count-1
DO
IntToReal(a(i),x)
RealAdd(sum,x,tmp)
RealAssign(tmp,sum)
OD
IntToReal(count,tmp)
RealDiv(sum,tmp,result)
RETURN
PROC Test(INT ARRAY a INT count)
INT i
REAL result
Mean(a,count,result)
Print("mean(")
FOR i=0 TO count-1
DO
PrintI(a(i))
IF i<count-1 THEN
Put(',)
FI
OD
Print(")=")
PrintRE(result)
RETURN
PROC Main()
INT ARRAY a1=[1 2 3 4 5 6]
INT ARRAY a2=[1 10 100 1000 10000]
INT ARRAY a3=[9]
Put(125) PutE() ;clear screen
Test(a1,6)
Test(a2,5)
Test(a3,1)
Test(a3,0)
RETURN |
http://rosettacode.org/wiki/Averages/Arithmetic_mean | Averages/Arithmetic mean | Task[edit]
Write a program to find the mean (arithmetic average) of a numeric vector.
In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #ActionScript | ActionScript | function mean(vector:Vector.<Number>):Number
{
var sum:Number = 0;
for(var i:uint = 0; i < vector.length; i++)
sum += vector[i];
return vector.length == 0 ? 0 : sum / vector.length;
} |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #Ada | Ada | with Ada.Text_Io;
with Ada.Containers.Indefinite_Ordered_Maps;
procedure Merge_Maps is
use Ada.Text_Io;
type Key_Type is new String;
type Value_Type is new String;
package Maps is
new Ada.Containers.Indefinite_Ordered_Maps (Key_Type => Key_Type,
Element_Type => Value_Type);
use Maps;
function Merge (Original : Map; Update : Map) return Map is
Result : Map := Original;
Cur : Cursor := Update.First;
begin
while Has_Element (Cur) loop
if Original.Contains (Key (Cur)) then
Result.Replace_Element (Result.Find (Key (Cur)),
Element (Cur));
else
Result.Insert (Key (Cur), Element (Cur));
end if;
Next (Cur);
end loop;
return Result;
end Merge;
procedure Put_Map (M : Map) is
Cur : Cursor := M.First;
begin
while Has_Element (Cur) loop
Put (String (Key (Cur)));
Set_Col (12);
Put (String (Element (Cur)));
New_Line;
Next (Cur);
end loop;
end Put_Map;
Original : Map;
Update : Map;
Result : Map;
begin
Original.Insert ("name", "Rocket Skates");
Original.Insert ("price", "12.75");
Original.Insert ("color", "yellow");
Update.Insert ("price", "15.25");
Update.Insert ("color", "red");
Update.Insert ("year", "1974");
Result := Merge (Original, Update);
Put_Line ("Original:");
Put_Map (Original);
New_Line;
Put_Line ("Update:");
Put_Map (Update);
New_Line;
Put_Line ("Result of merge:");
Put_Map (Result);
New_Line;
end Merge_Maps; |
http://rosettacode.org/wiki/Associative_array/Merging | Associative array/Merging | Task
Define two associative arrays, where one represents the following "base" data:
Key
Value
"name"
"Rocket Skates"
"price"
12.75
"color"
"yellow"
And the other represents "update" data:
Key
Value
"price"
15.25
"color"
"red"
"year"
1974
Merge these into a new associative array that contains every key found in either of the source ones. Each key should map to the value in the second (update) table if that exists, or else to the value in the first (base) table. If possible, do this in a way that does not mutate the original two associative arrays. Obviously this should be done in a way that would work for any data, not just the specific data given here, but in this example the result should be:
Key
Value
"name"
"Rocket Skates"
"price"
15.25
"color"
"red"
"year"
1974
| #ALGOL_68 | ALGOL 68 | # associative array merging #
# the modes allowed as associative array element values - change to suit #
MODE AAVALUE = UNION( STRING, INT, REAL );
# the modes allowed as associative array element keys - change to suit #
MODE AAKEY = STRING;
# initial value for an array element #
AAVALUE init element value = "";
# include the associative array code #
PR read "aArrayBase.a68" PR
# adds or replaces all elements from b into a #
PRIO UPDATE = 9;
OP UPDATE = ( REF AARRAY a, REF AARRAY b )REF AARRAY:
BEGIN
REF AAELEMENT e := FIRST b;
WHILE e ISNT nil element DO
a // key OF e := value OF e;
e := NEXT b
OD;
a
END # UPDATE # ;
# construct the associative arrays for the task #
REF AARRAY a := INIT LOC AARRAY;
REF AARRAY b := INIT LOC AARRAY;
a // "name" := "Rocket Skates";
a // "price" := 12.75;
a // "color" := "yellow";
b // "price" := 15.25;
b // "color" := "red";
b // "year" := 1974;
# merge the arrays #
REF AARRAY c := INIT LOC AARRAY;
c UPDATE a UPDATE b;
# show the merged array #
REF AAELEMENT e := FIRST c;
WHILE e ISNT nil element DO
print( ( key OF e
, ": "
, CASE value OF e
IN (STRING s): s
, (INT i): whole( i, 0 )
, (REAL r): fixed( r, -12, 2 )
OUT "????"
ESAC
, newline
)
);
e := NEXT c
OD |
http://rosettacode.org/wiki/Average_loop_length | Average loop length | Let f be a uniformly-randomly chosen mapping from the numbers 1..N to the numbers 1..N (note: not necessarily a permutation of 1..N; the mapping could produce a number in more than one way or not at all). At some point, the sequence 1, f(1), f(f(1))... will contain a repetition, a number that occurring for the second time in the sequence.
Task
Write a program or a script that estimates, for each N, the average length until the first such repetition.
Also calculate this expected length using an analytical formula, and optionally compare the simulated result with the theoretical one.
This problem comes from the end of Donald Knuth's Christmas tree lecture 2011.
Example of expected output:
N average analytical (error)
=== ========= ============ =========
1 1.0000 1.0000 ( 0.00%)
2 1.4992 1.5000 ( 0.05%)
3 1.8784 1.8889 ( 0.56%)
4 2.2316 2.2188 ( 0.58%)
5 2.4982 2.5104 ( 0.49%)
6 2.7897 2.7747 ( 0.54%)
7 3.0153 3.0181 ( 0.09%)
8 3.2429 3.2450 ( 0.07%)
9 3.4536 3.4583 ( 0.14%)
10 3.6649 3.6602 ( 0.13%)
11 3.8091 3.8524 ( 1.12%)
12 3.9986 4.0361 ( 0.93%)
13 4.2074 4.2123 ( 0.12%)
14 4.3711 4.3820 ( 0.25%)
15 4.5275 4.5458 ( 0.40%)
16 4.6755 4.7043 ( 0.61%)
17 4.8877 4.8579 ( 0.61%)
18 4.9951 5.0071 ( 0.24%)
19 5.1312 5.1522 ( 0.41%)
20 5.2699 5.2936 ( 0.45%)
| #C.2B.2B | C++ | #include <random>
#include <vector>
#include <iostream>
#define MAX_N 20
#define TIMES 1000000
/**
* Used to generate a uniform random distribution
*/
static std::random_device rd; //Will be used to obtain a seed for the random number engine
static std::mt19937 gen(rd()); //Standard mersenne_twister_engine seeded with rd()
static std::uniform_int_distribution<> dis;
int randint(int n) {
int r, rmax = RAND_MAX / n * n;
dis=std::uniform_int_distribution(0,rmax) ;
r = dis(gen);
return r / (RAND_MAX / n);
}
unsigned long factorial(size_t n) {
//Factorial using dynamic programming to memoize the values.
static std::vector<unsigned long>factorials{1,1,2};
for (;factorials.size() <= n;)
factorials.push_back(factorials.back()*factorials.size());
return factorials[n];
}
long double expected(size_t n) {
long double sum = 0;
for (size_t i = 1; i <= n; i++)
sum += factorial(n) / pow(n, i) / factorial(n - i);
return sum;
}
int test(int n, int times) {
int i, count = 0;
for (i = 0; i < times; i++) {
unsigned int x = 1, bits = 0;
while (!(bits & x)) {
count++;
bits |= x;
x = static_cast<unsigned int>(1 << randint(n));
}
}
return count;
}
int main() {
puts(" n\tavg\texp.\tdiff\n-------------------------------");
int n;
for (n = 1; n <= MAX_N; n++) {
int cnt = test(n, TIMES);
long double avg = (double)cnt / TIMES;
long double theory = expected(static_cast<size_t>(n));
long double diff = (avg / theory - 1) * 100;
printf("%2d %8.4f %8.4f %6.3f%%\n", n, static_cast<double>(avg), static_cast<double>(theory), static_cast<double>(diff));
}
return 0;
}
|
http://rosettacode.org/wiki/Averages/Simple_moving_average | Averages/Simple moving average | Computing the simple moving average of a series of numbers.
Task[edit]
Create a stateful function/class/instance that takes a period and returns a routine that takes a number as argument and returns a simple moving average of its arguments so far.
Description
A simple moving average is a method for computing an average of a stream of numbers by only averaging the last P numbers from the stream, where P is known as the period.
It can be implemented by calling an initialing routine with P as its argument, I(P), which should then return a routine that when called with individual, successive members of a stream of numbers, computes the mean of (up to), the last P of them, lets call this SMA().
The word stateful in the task description refers to the need for SMA() to remember certain information between calls to it:
The period, P
An ordered container of at least the last P numbers from each of its individual calls.
Stateful also means that successive calls to I(), the initializer, should return separate routines that do not share saved state so they could be used on two independent streams of data.
Pseudo-code for an implementation of SMA is:
function SMA(number: N):
stateful integer: P
stateful list: stream
number: average
stream.append_last(N)
if stream.length() > P:
# Only average the last P elements of the stream
stream.delete_first()
if stream.length() == 0:
average = 0
else:
average = sum( stream.values() ) / stream.length()
return average
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Phix | Phix | with javascript_semantics
sequence sma = {} -- ((period,history,circnxt)) (private to sma.e)
integer sma_free = 0
global function new_sma(integer period)
integer res
if sma_free then
res = sma_free
sma_free = sma[sma_free]
sma[res] = {period,{},0}
else
sma = append(sma,{period,{},0})
res = length(sma)
end if
return res
end function
global procedure add_sma(integer sidx, atom val)
integer period, circnxt
sequence history
{period,history,circnxt} = sma[sidx]
sma[sidx][2] = 0 -- (kill refcount)
if length(history)<period then
history = append(history,val)
else
circnxt += 1
if circnxt>period then
circnxt = 1
end if
sma[sidx][3] = circnxt
history[circnxt] = val
end if
sma[sidx][2] = history
end procedure
global function get_sma_average(integer sidx)
sequence history = sma[sidx][2]
integer l = length(history)
if l=0 then return 0 end if
return sum(history)/l
end function
global function moving_average(integer sidx, atom val)
add_sma(sidx,val)
return get_sma_average(sidx)
end function
global procedure free_sma(integer sidx)
sma[sidx] = sma_free
sma_free = sidx
end procedure
|
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #Arturo | Arturo | attractive?: function [x] -> prime? size factors.prime x
print select 1..120 => attractive? |
http://rosettacode.org/wiki/Attractive_numbers | Attractive numbers | A number is an attractive number if the number of its prime factors (whether distinct or not) is also prime.
Example
The number 20, whose prime decomposition is 2 × 2 × 5, is an attractive number because the number of its prime factors (3) is also prime.
Task
Show sequence items up to 120.
Reference
The OEIS entry: A063989: Numbers with a prime number of prime divisors.
| #AWK | AWK |
# syntax: GAWK -f ATTRACTIVE_NUMBERS.AWK
# converted from C
BEGIN {
limit = 120
printf("attractive numbers from 1-%d:\n",limit)
for (i=1; i<=limit; i++) {
n = count_prime_factors(i)
if (is_prime(n)) {
printf("%d ",i)
}
}
printf("\n")
exit(0)
}
function count_prime_factors(n, count,f) {
f = 2
if (n == 1) { return(0) }
if (is_prime(n)) { return(1) }
while (1) {
if (!(n % f)) {
count++
n /= f
if (n == 1) { return(count) }
if (is_prime(n)) { f = n }
}
else if (f >= 3) { f += 2 }
else { f = 3 }
}
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
|
http://rosettacode.org/wiki/Averages/Mean_time_of_day | Averages/Mean time of day | Task[edit]
A particular activity of bats occurs at these times of the day:
23:00:17, 23:40:20, 00:12:45, 00:17:19
Using the idea that there are twenty-four hours in a day,
which is analogous to there being 360 degrees in a circle,
map times of day to and from angles;
and using the ideas of Averages/Mean angle
compute and show the average time of the nocturnal activity
to an accuracy of one second of time.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #F.23 | F# | open System
open System.Numerics
let deg2rad d = d * Math.PI / 180.
let rad2deg r = r * 180. / Math.PI
let makeComplex = fun r -> Complex.FromPolarCoordinates(1., r)
// 1 msec = 10000 ticks
let time2deg = TimeSpan.Parse >> (fun ts -> ts.Ticks) >> (float) >> (*) (10e-9/24.)
let deg2time = (*) (24. * 10e7) >> (int64) >> TimeSpan
[<EntryPoint>]
let main argv =
let msg = "Average time for [" + (String.Join("; ",argv)) + "] is"
argv
|> Seq.map (time2deg >> deg2rad >> makeComplex)
|> Seq.fold (fun x y -> Complex.Add(x,y)) Complex.Zero
|> fun c -> c.Phase |> rad2deg
|> fun d -> if d < 0. then d + 360. else d
|> deg2time |> fun t -> t.ToString(@"hh\:mm\:ss")
|> printfn "%s: %s" msg
0 |
http://rosettacode.org/wiki/AVL_tree | AVL tree |
This page uses content from Wikipedia. The original article was at AVL tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; at no time do they differ by more than one because rebalancing is done ensure this is the case. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. Note the tree of nodes comprise a set, so duplicate node keys are not allowed.
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n) time for the basic operations. Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup-intensive applications. Similar to red-black trees, AVL trees are height-balanced, but in general not weight-balanced nor μ-balanced; that is, sibling nodes can have hugely differing numbers of descendants.
Task
Implement an AVL tree in the language of choice, and provide at least basic operations.
| #D | D | import std.stdio, std.algorithm;
class AVLtree {
private Node* root;
private static struct Node {
private int key, balance;
private Node* left, right, parent;
this(in int k, Node* p) pure nothrow @safe @nogc {
key = k;
parent = p;
}
}
public bool insert(in int key) pure nothrow @safe {
if (root is null)
root = new Node(key, null);
else {
Node* n = root;
Node* parent;
while (true) {
if (n.key == key)
return false;
parent = n;
bool goLeft = n.key > key;
n = goLeft ? n.left : n.right;
if (n is null) {
if (goLeft) {
parent.left = new Node(key, parent);
} else {
parent.right = new Node(key, parent);
}
rebalance(parent);
break;
}
}
}
return true;
}
public void deleteKey(in int delKey) pure nothrow @safe @nogc {
if (root is null)
return;
Node* n = root;
Node* parent = root;
Node* delNode = null;
Node* child = root;
while (child !is null) {
parent = n;
n = child;
child = delKey >= n.key ? n.right : n.left;
if (delKey == n.key)
delNode = n;
}
if (delNode !is null) {
delNode.key = n.key;
child = n.left !is null ? n.left : n.right;
if (root.key == delKey) {
root = child;
} else {
if (parent.left is n) {
parent.left = child;
} else {
parent.right = child;
}
rebalance(parent);
}
}
}
private void rebalance(Node* n) pure nothrow @safe @nogc {
setBalance(n);
if (n.balance == -2) {
if (height(n.left.left) >= height(n.left.right))
n = rotateRight(n);
else
n = rotateLeftThenRight(n);
} else if (n.balance == 2) {
if (height(n.right.right) >= height(n.right.left))
n = rotateLeft(n);
else
n = rotateRightThenLeft(n);
}
if (n.parent !is null) {
rebalance(n.parent);
} else {
root = n;
}
}
private Node* rotateLeft(Node* a) pure nothrow @safe @nogc {
Node* b = a.right;
b.parent = a.parent;
a.right = b.left;
if (a.right !is null)
a.right.parent = a;
b.left = a;
a.parent = b;
if (b.parent !is null) {
if (b.parent.right is a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node* rotateRight(Node* a) pure nothrow @safe @nogc {
Node* b = a.left;
b.parent = a.parent;
a.left = b.right;
if (a.left !is null)
a.left.parent = a;
b.right = a;
a.parent = b;
if (b.parent !is null) {
if (b.parent.right is a) {
b.parent.right = b;
} else {
b.parent.left = b;
}
}
setBalance(a, b);
return b;
}
private Node* rotateLeftThenRight(Node* n) pure nothrow @safe @nogc {
n.left = rotateLeft(n.left);
return rotateRight(n);
}
private Node* rotateRightThenLeft(Node* n) pure nothrow @safe @nogc {
n.right = rotateRight(n.right);
return rotateLeft(n);
}
private int height(in Node* n) const pure nothrow @safe @nogc {
if (n is null)
return -1;
return 1 + max(height(n.left), height(n.right));
}
private void setBalance(Node*[] nodes...) pure nothrow @safe @nogc {
foreach (n; nodes)
n.balance = height(n.right) - height(n.left);
}
public void printBalance() const @safe {
printBalance(root);
}
private void printBalance(in Node* n) const @safe {
if (n !is null) {
printBalance(n.left);
write(n.balance, ' ');
printBalance(n.right);
}
}
}
void main() @safe {
auto tree = new AVLtree();
writeln("Inserting values 1 to 10");
foreach (immutable i; 1 .. 11)
tree.insert(i);
write("Printing balance: ");
tree.printBalance;
} |
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #Delphi | Delphi |
(define-syntax-rule (deg->radian deg) (* deg 1/180 PI))
(define-syntax-rule (radian->deg rad) (* 180 (/ PI) rad))
(define (mean-angles angles)
(radian->deg
(angle
(for/sum ((a angles)) (make-polar 1 (deg->radian a))))))
(mean-angles '( 350 10))
→ -0
(mean-angles '[90 180 270 360])
→ -90
(mean-angles '[10 20 30])
→ 20
|
http://rosettacode.org/wiki/Averages/Mean_angle | Averages/Mean angle | When calculating the average or mean of an angle one has to take into account how angles wrap around so that any angle in degrees plus any integer multiple of 360 degrees is a measure of the same angle.
If one wanted an average direction of the wind over two readings where the first reading was of 350 degrees and the second was of 10 degrees then the average of the numbers is 180 degrees, whereas if you can note that 350 degrees is equivalent to -10 degrees and so you have two readings at 10 degrees either side of zero degrees leading to a more fitting mean angle of zero degrees.
To calculate the mean angle of several angles:
Assume all angles are on the unit circle and convert them to complex numbers expressed in real and imaginary form.
Compute the mean of the complex numbers.
Convert the complex mean to polar coordinates whereupon the phase of the complex mean is the required angular mean.
(Note that, since the mean is the sum divided by the number of numbers, and division by a positive real number does not affect the angle, you can also simply compute the sum for step 2.)
You can alternatively use this formula:
Given the angles
α
1
,
…
,
α
n
{\displaystyle \alpha _{1},\dots ,\alpha _{n}}
the mean is computed by
α
¯
=
atan2
(
1
n
⋅
∑
j
=
1
n
sin
α
j
,
1
n
⋅
∑
j
=
1
n
cos
α
j
)
{\displaystyle {\bar {\alpha }}=\operatorname {atan2} \left({\frac {1}{n}}\cdot \sum _{j=1}^{n}\sin \alpha _{j},{\frac {1}{n}}\cdot \sum _{j=1}^{n}\cos \alpha _{j}\right)}
Task[edit]
write a function/method/subroutine/... that given a list of angles in degrees returns their mean angle.
(You should use a built-in function if you have one that does this for degrees or radians).
Use the function to compute the means of these lists of angles (in degrees):
[350, 10]
[90, 180, 270, 360]
[10, 20, 30]
Show your output here.
See also
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #EchoLisp | EchoLisp |
(define-syntax-rule (deg->radian deg) (* deg 1/180 PI))
(define-syntax-rule (radian->deg rad) (* 180 (/ PI) rad))
(define (mean-angles angles)
(radian->deg
(angle
(for/sum ((a angles)) (make-polar 1 (deg->radian a))))))
(mean-angles '( 350 10))
→ -0
(mean-angles '[90 180 270 360])
→ -90
(mean-angles '[10 20 30])
→ 20
|
http://rosettacode.org/wiki/Averages/Median | Averages/Median | Task[edit]
Write a program to find the median value of a vector of floating-point numbers.
The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements. In that case, return the average of the two middle values.
There are several approaches to this. One is to sort the elements, and then pick the element(s) in the middle.
Sorting would take at least O(n logn). Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s). This would also take O(n logn). The best solution is to use the selection algorithm to find the median in O(n) time.
See also
Quickselect_algorithm
Tasks for calculating statistical measures
in one go
moving (sliding window)
moving (cumulative)
Mean
Arithmetic
Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means
Averages/Simple moving average
Geometric
Averages/Pythagorean means
Harmonic
Averages/Pythagorean means
Quadratic
Averages/Root mean square
Circular
Averages/Mean angle
Averages/Mean time of day
Median
Averages/Median
Mode
Averages/Mode
Standard deviation
Statistics/Basic
Cumulative standard deviation
| #BASIC | BASIC | DECLARE FUNCTION median! (vector() AS SINGLE)
DIM vec1(10) AS SINGLE, vec2(11) AS SINGLE, n AS INTEGER
RANDOMIZE TIMER
FOR n = 0 TO 10
vec1(n) = RND * 100
vec2(n) = RND * 100
NEXT
vec2(11) = RND * 100
PRINT median(vec1())
PRINT median(vec2())
FUNCTION median! (vector() AS SINGLE)
DIM lb AS INTEGER, ub AS INTEGER, L0 AS INTEGER
lb = LBOUND(vector)
ub = UBOUND(vector)
REDIM v(lb TO ub) AS SINGLE
FOR L0 = lb TO ub
v(L0) = vector(L0)
NEXT
quicksort v(), lb, ub
IF ((ub - lb + 1) MOD 2) THEN
median = v((ub + lb) / 2)
ELSE
median = (v(INT((ub + lb) / 2)) + v(INT((ub + lb) / 2) + 1)) / 2
END IF
END FUNCTION |
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