task_url
stringlengths 30
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14.4k
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|---|---|---|---|---|---|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#Kotlin
|
Kotlin
|
// version 1.0.6
import java.security.MessageDigest
fun main(args: Array<String>) {
val text = "Rosetta code"
val bytes = text.toByteArray()
val md = MessageDigest.getInstance("SHA-256")
val digest = md.digest(bytes)
for (byte in digest) print("%02x".format(byte))
println()
}
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Go
|
Go
|
package main
import "fmt"
func countDivisors(n int) int {
count := 0
for i := 1; i*i <= n; i++ {
if n%i == 0 {
if i == n/i {
count++
} else {
count += 2
}
}
}
return count
}
func main() {
const max = 15
fmt.Println("The first", max, "terms of the sequence are:")
for i, next := 1, 1; next <= max; i++ {
if next == countDivisors(i) {
fmt.Printf("%d ", i)
next++
}
}
fmt.Println()
}
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#Lua
|
Lua
|
#!/usr/bin/lua
local sha1 = require "sha1"
for i, str in ipairs{"Rosetta code", "Rosetta Code"} do
print(string.format("SHA-1(%q) = %s", str, sha1(str)))
end
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#PicoLisp
|
PicoLisp
|
(de dice5 ()
(rand 1 5) )
(de dice7 ()
(use R
(until (> 21 (setq R (+ (* 5 (dice5)) (dice5) -6))))
(inc (% R 7)) ) )
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#PureBasic
|
PureBasic
|
Procedure dice5()
ProcedureReturn Random(4) + 1
EndProcedure
Procedure dice7()
Protected x
x = dice5() * 5 + dice5() - 6
If x > 20
ProcedureReturn dice7()
EndIf
ProcedureReturn x % 7 + 1
EndProcedure
|
http://rosettacode.org/wiki/Sexy_primes
|
Sexy primes
|
This page uses content from Wikipedia. The original article was at Sexy_prime. 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 mathematics, sexy primes are prime numbers that differ from each other by six.
For example, the numbers 5 and 11 are both sexy primes, because 11 minus 6 is 5.
The term "sexy prime" is a pun stemming from the Latin word for six: sex.
Sexy prime pairs: Sexy prime pairs are groups of two primes that differ by 6. e.g. (5 11), (7 13), (11 17)
See sequences: OEIS:A023201 and OEIS:A046117
Sexy prime triplets: Sexy prime triplets are groups of three primes where each differs from the next by 6. e.g. (5 11 17), (7 13 19), (17 23 29)
See sequences: OEIS:A046118, OEIS:A046119 and OEIS:A046120
Sexy prime quadruplets: Sexy prime quadruplets are groups of four primes where each differs from the next by 6. e.g. (5 11 17 23), (11 17 23 29)
See sequences: OEIS:A023271, OEIS:A046122, OEIS:A046123 and OEIS:A046124
Sexy prime quintuplets: Sexy prime quintuplets are groups of five primes with a common difference of 6. One of the terms must be divisible by 5, because 5 and 6 are relatively prime. Thus, the only possible sexy prime quintuplet is (5 11 17 23 29)
Task
For each of pairs, triplets, quadruplets and quintuplets, Find and display the count of each group type of sexy primes less than one million thirty-five (1,000,035).
Display at most the last 5, less than one million thirty-five, of each sexy prime group type.
Find and display the count of the unsexy primes less than one million thirty-five.
Find and display the last 10 unsexy primes less than one million thirty-five.
Note that 1000033 SHOULD NOT be counted in the pair count. It is sexy, but not in a pair within the limit. However, it also SHOULD NOT be listed in the unsexy primes since it is sexy.
|
#XPL0
|
XPL0
|
func IsPrime(N); \Return 'true' if N is prime
int N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];
int CU, C2, C3, C4, C5, N, I;
int Unsexy(10), Pairs(5), Trips(5), Quads(5), Quins(5);
[CU:= 0; C2:= 0; C3:= 0; C4:= 0; C5:= 0;
for N:= 1000035 downto 2 do
[if IsPrime(N) then
[if IsPrime(N-6) then
[if C2 < 5 then Pairs(C2):= N;
C2:= C2+1;
if IsPrime(N-12) then
[if C3 < 5 then Trips(C3):= N;
C3:= C3+1;
if IsPrime(N-18) then
[if C4 < 5 then Quads(C4):= N;
C4:= C4+1;
if IsPrime(N-24) then
[if C5 < 5 then Quins(C5):= N;
C5:= C5+1;
];
];
];
]
else if not IsPrime(N+6) then
[if CU < 10 then Unsexy(CU):= N;
CU:= CU+1;
];
];
];
IntOut(0, C2); Text(0, " pairs ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Pairs(I)-6); Text(0, ", ");
IntOut(0, Pairs(I)); Text(0, "]^m^j");
];
IntOut(0, C3); Text(0, " triplets ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Trips(I)-12); Text(0, ", ");
IntOut(0, Trips(I)-6); Text(0, ", ");
IntOut(0, Trips(I)); Text(0, "]^m^j");
];
IntOut(0, C4); Text(0, " quadruplets ending with:^m^j");
for I:= 4 downto 0 do
[Text(0, " [");
IntOut(0, Quads(I)-18); Text(0, ", ");
IntOut(0, Quads(I)-12); Text(0, ", ");
IntOut(0, Quads(I)-6); Text(0, ", ");
IntOut(0, Quads(I)); Text(0, "]^m^j");
];
IntOut(0, C5); Text(0, " quintuplet(s) ending with:^m^j");
I:= if C5 > 5 then 5 else C5;
for I:= I-1 downto 0 do
[Text(0, " [");
IntOut(0, Quins(I)-24); Text(0, ", ");
IntOut(0, Quins(I)-18); Text(0, ", ");
IntOut(0, Quins(I)-12); Text(0, ", ");
IntOut(0, Quins(I)-6); Text(0, ", ");
IntOut(0, Quins(I)); Text(0, "]^m^j");
];
IntOut(0, CU); Text(0, " unsexy primes ending with:^m^j");
for I:= 9 downto 0 do
[IntOut(0, Unsexy(I)); if I then Text(0, ", ")];
CrLf(0);
]
|
http://rosettacode.org/wiki/Sexy_primes
|
Sexy primes
|
This page uses content from Wikipedia. The original article was at Sexy_prime. 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 mathematics, sexy primes are prime numbers that differ from each other by six.
For example, the numbers 5 and 11 are both sexy primes, because 11 minus 6 is 5.
The term "sexy prime" is a pun stemming from the Latin word for six: sex.
Sexy prime pairs: Sexy prime pairs are groups of two primes that differ by 6. e.g. (5 11), (7 13), (11 17)
See sequences: OEIS:A023201 and OEIS:A046117
Sexy prime triplets: Sexy prime triplets are groups of three primes where each differs from the next by 6. e.g. (5 11 17), (7 13 19), (17 23 29)
See sequences: OEIS:A046118, OEIS:A046119 and OEIS:A046120
Sexy prime quadruplets: Sexy prime quadruplets are groups of four primes where each differs from the next by 6. e.g. (5 11 17 23), (11 17 23 29)
See sequences: OEIS:A023271, OEIS:A046122, OEIS:A046123 and OEIS:A046124
Sexy prime quintuplets: Sexy prime quintuplets are groups of five primes with a common difference of 6. One of the terms must be divisible by 5, because 5 and 6 are relatively prime. Thus, the only possible sexy prime quintuplet is (5 11 17 23 29)
Task
For each of pairs, triplets, quadruplets and quintuplets, Find and display the count of each group type of sexy primes less than one million thirty-five (1,000,035).
Display at most the last 5, less than one million thirty-five, of each sexy prime group type.
Find and display the count of the unsexy primes less than one million thirty-five.
Find and display the last 10 unsexy primes less than one million thirty-five.
Note that 1000033 SHOULD NOT be counted in the pair count. It is sexy, but not in a pair within the limit. However, it also SHOULD NOT be listed in the unsexy primes since it is sexy.
|
#zkl
|
zkl
|
var [const] BI=Import("zklBigNum"); // libGMP
const N=1_000_035, M=N+24; // M allows prime group to span N, eg N=100, (97,103)
const OVR=6; // 6 if prime group can NOT span N, else 0
ps,p := Data(M+50).fill(0), BI(1); // slop at the end (for reverse wrap around)
while(p.nextPrime()<=M){ ps[p]=1 } // bitmap of primes
ns:=(N-OVR).filter('wrap(n){ 2==(ps[n] + ps[n+6]) }); # know 2 isn't, check anyway
msg(N,"sexy prime pairs",ns,5,1);
ns:=[3..N-(6+OVR),2].filter('wrap(n){ 3==(ps[n] + ps[n+6] + ps[n+12]) }); # can't be even
msg(N,"sexy triplet primes",ns,5,2);
ns:=[3..N-(12+OVR),2].filter('wrap(n){ 4==(ps[n] + ps[n+6] + ps[n+12] + ps[n+18]) }); # no evens
msg(N,"sexy quadruplet primes",ns,5,3);
ns:=[3..N-(18+OVR),2].filter('wrap(n){ 5==(ps[n] + ps[n+6] + ps[n+12] + ps[n+18] + ps[n+24]) });
msg(N,"sexy quintuplet primes",ns,1,4);
ns:=(N-OVR).filter('wrap(n){ ps[n] and 0==(ps[n-6] + ps[n+6]) }); // include 2
msg(N,"unsexy primes",ns,10,0);
fcn msg(N,s,ps,n,g){
n=n.min(ps.len()); // if the number of primes is less than n
gs:=ps[-n,*].apply('wrap(n){ [0..g*6,6].apply('+(n)) })
.pump(String,T("concat", ","),"(%s) ".fmt);
println("Number of %s less than %,d is %,d".fmt(s,N,ps.len()));
println("The last %d %s:\n %s\n".fmt(n, (n>1 and "are" or "is"), gs));
}
|
http://rosettacode.org/wiki/Show_ASCII_table
|
Show ASCII table
|
Task
Show the ASCII character set from values 32 to 127 (decimal) in a table format.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
|
#Groovy
|
Groovy
|
class ShowAsciiTable {
static void main(String[] args) {
for (int i = 32; i <= 127; i++) {
if (i == 32 || i == 127) {
String s = i == 32 ? "Spc" : "Del"
printf("%3d: %s ", i, s)
} else {
printf("%3d: %c ", i, i)
}
if ((i - 1) % 6 == 0) {
println()
}
}
}
}
|
http://rosettacode.org/wiki/Sierpinski_triangle
|
Sierpinski triangle
|
Task
Produce an ASCII representation of a Sierpinski triangle of order N.
Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Related tasks
Sierpinski triangle/Graphical for graphics images of this pattern.
Sierpinski carpet
|
#PHP
|
PHP
|
<?php
function sierpinskiTriangle($order) {
$char = '#';
$n = 1 << $order;
$line = array();
for ($i = 0 ; $i <= 2 * $n ; $i++) {
$line[$i] = ' ';
}
$line[$n] = $char;
for ($i = 0 ; $i < $n ; $i++) {
echo implode('', $line), PHP_EOL;
$u = $char;
for ($j = $n - $i ; $j < $n + $i + 1 ; $j++) {
$t = ($line[$j - 1] == $line[$j + 1] ? ' ' : $char);
$line[$j - 1] = $u;
$u = $t;
}
$line[$n + $i] = $t;
$line[$n + $i + 1] = $char;
}
}
sierpinskiTriangle(4);
|
http://rosettacode.org/wiki/Sierpinski_carpet
|
Sierpinski carpet
|
Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
Related task
Sierpinski triangle
|
#Kotlin
|
Kotlin
|
// version 1.1.2
fun inCarpet(x: Int, y: Int): Boolean {
var xx = x
var yy = y
while (xx != 0 && yy != 0) {
if (xx % 3 == 1 && yy % 3 == 1) return false
xx /= 3
yy /= 3
}
return true
}
fun carpet(n: Int) {
val power = Math.pow(3.0, n.toDouble()).toInt()
for(i in 0 until power) {
for(j in 0 until power) print(if (inCarpet(i, j)) "*" else " ")
println()
}
}
fun main(args: Array<String>) = carpet(3)
|
http://rosettacode.org/wiki/Short-circuit_evaluation
|
Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
|
#Nim
|
Nim
|
proc a(x): bool =
echo "a called"
result = x
proc b(x): bool =
echo "b called"
result = x
let x = a(false) and b(true) # echoes "a called"
let y = a(true) or b(true) # echoes "a called"
|
http://rosettacode.org/wiki/Short-circuit_evaluation
|
Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
|
#Objeck
|
Objeck
|
class ShortCircuit {
function : a(a : Bool) ~ Bool {
"a"->PrintLine();
return a;
}
function : b(b : Bool) ~ Bool {
"b"->PrintLine();
return b;
}
function : Main(args : String[]) ~ Nil {
result := a(false) & b(false);
"F and F = {$result}"->PrintLine();
result := a(false) | b(false);
"F or F = {$result}"->PrintLine();
result := a(false) & b(true);
"F and T = {$result}"->PrintLine();
result := a(false) | b(true);
"F or T = {$result}"->PrintLine();
result := a(true) & b(false);
"T and F = {$result}"->PrintLine();
result := a(true) | b(false);
"T or F = {$result}"->PrintLine();
result := a(true) & b(true);
"T and T = {$result}"->PrintLine();
result := a(true) | b(true);
"T or T = {$result}"->PrintLine();
}
}
|
http://rosettacode.org/wiki/Set_puzzle
|
Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#Ruby
|
Ruby
|
COLORS = %i(red green purple) #use [:red, :green, :purple] in Ruby < 2.0
SYMBOLS = %i(oval squiggle diamond)
NUMBERS = %i(one two three)
SHADINGS = %i(solid open striped)
DECK = COLORS.product(SYMBOLS, NUMBERS, SHADINGS)
def get_all_sets(hand)
hand.combination(3).select do |candidate|
grouped_features = candidate.flatten.group_by{|f| f}
grouped_features.values.none?{|v| v.size == 2}
end
end
def get_puzzle_and_answer(hand_size, num_sets_goal)
begin
hand = DECK.sample(hand_size)
sets = get_all_sets(hand)
end until sets.size == num_sets_goal
[hand, sets]
end
def print_cards(cards)
puts cards.map{|card| " %-8s" * 4 % card}
puts
end
def set_puzzle(deal, goal=deal/2)
puzzle, sets = get_puzzle_and_answer(deal, goal)
puts "Dealt #{puzzle.size} cards:"
print_cards(puzzle)
puts "Containing #{sets.size} sets:"
sets.each{|set| print_cards(set)}
end
set_puzzle(9)
set_puzzle(12)
|
http://rosettacode.org/wiki/Set_of_real_numbers
|
Set of real numbers
|
All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:
[a, b]: {x | a ≤ x and x ≤ b }
(a, b): {x | a < x and x < b }
[a, b): {x | a ≤ x and x < b }
(a, b]: {x | a < x and x ≤ b }
Note that if a = b, of the four only [a, a] would be non-empty.
Task
Devise a way to represent any set of real numbers, for the definition of 'any' in the implementation notes below.
Provide methods for these common set operations (x is a real number; A and B are sets):
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
Test your implementation by checking if numbers 0, 1, and 2 are in any of the following sets:
(0, 1] ∪ [0, 2)
[0, 2) ∩ (1, 2]
[0, 3) − (0, 1)
[0, 3) − [0, 1]
Implementation notes
'Any' real set means 'sets that can be expressed as the union of a finite number of convex real sets'. Cantor's set needs not apply.
Infinities should be handled gracefully; indeterminate numbers (NaN) can be ignored.
You can use your machine's native real number representation, which is probably IEEE floating point, and assume it's good enough (it usually is).
Optional work
Create a function to determine if a given set is empty (contains no element).
Define A = {x | 0 < x < 10 and |sin(π x²)| > 1/2 }, B = {x | 0 < x < 10 and |sin(π x)| > 1/2}, calculate the length of the real axis covered by the set A − B. Note that
|sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.
|
#C
|
C
|
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
struct RealSet {
bool(*contains)(struct RealSet*, struct RealSet*, double);
struct RealSet *left;
struct RealSet *right;
double low, high;
};
typedef enum {
CLOSED,
LEFT_OPEN,
RIGHT_OPEN,
BOTH_OPEN,
} RangeType;
double length(struct RealSet *self) {
const double interval = 0.00001;
double p = self->low;
int count = 0;
if (isinf(self->low) || isinf(self->high)) return -1.0;
if (self->high <= self->low) return 0.0;
do {
if (self->contains(self, NULL, p)) count++;
p += interval;
} while (p < self->high);
return count * interval;
}
bool empty(struct RealSet *self) {
if (self->low == self->high) {
return !self->contains(self, NULL, self->low);
}
return length(self) == 0.0;
}
static bool contains_closed(struct RealSet *self, struct RealSet *_, double d) {
return self->low <= d && d <= self->high;
}
static bool contains_left_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low < d && d <= self->high;
}
static bool contains_right_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low <= d && d < self->high;
}
static bool contains_both_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low < d && d < self->high;
}
static bool contains_intersect(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) && self->right->contains(self->right, NULL, d);
}
static bool contains_union(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) || self->right->contains(self->right, NULL, d);
}
static bool contains_subtract(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) && !self->right->contains(self->right, NULL, d);
}
struct RealSet* makeSet(double low, double high, RangeType type) {
bool(*contains)(struct RealSet*, struct RealSet*, double);
struct RealSet *rs;
switch (type) {
case CLOSED:
contains = contains_closed;
break;
case LEFT_OPEN:
contains = contains_left_open;
break;
case RIGHT_OPEN:
contains = contains_right_open;
break;
case BOTH_OPEN:
contains = contains_both_open;
break;
default:
return NULL;
}
rs = malloc(sizeof(struct RealSet));
rs->contains = contains;
rs->left = NULL;
rs->right = NULL;
rs->low = low;
rs->high = high;
return rs;
}
struct RealSet* makeIntersect(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_intersect;
rs->left = left;
rs->right = right;
rs->low = fmin(left->low, right->low);
rs->high = fmin(left->high, right->high);
return rs;
}
struct RealSet* makeUnion(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_union;
rs->left = left;
rs->right = right;
rs->low = fmin(left->low, right->low);
rs->high = fmin(left->high, right->high);
return rs;
}
struct RealSet* makeSubtract(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_subtract;
rs->left = left;
rs->right = right;
rs->low = left->low;
rs->high = left->high;
return rs;
}
int main() {
struct RealSet *a = makeSet(0.0, 1.0, LEFT_OPEN);
struct RealSet *b = makeSet(0.0, 2.0, RIGHT_OPEN);
struct RealSet *c = makeSet(1.0, 2.0, LEFT_OPEN);
struct RealSet *d = makeSet(0.0, 3.0, RIGHT_OPEN);
struct RealSet *e = makeSet(0.0, 1.0, BOTH_OPEN);
struct RealSet *f = makeSet(0.0, 1.0, CLOSED);
struct RealSet *g = makeSet(0.0, 0.0, CLOSED);
int i;
for (i = 0; i < 3; ++i) {
struct RealSet *t;
t = makeUnion(a, b);
printf("(0, 1] union [0, 2) contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeIntersect(b, c);
printf("[0, 2) intersect (1, 2] contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeSubtract(d, e);
printf("[0, 3) - (0, 1) contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeSubtract(d, f);
printf("[0, 3) - [0, 1] contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
printf("\n");
}
printf("[0, 0] is empty %d\n", empty(g));
free(a);
free(b);
free(c);
free(d);
free(e);
free(f);
free(g);
return 0;
}
|
http://rosettacode.org/wiki/Sieve_of_Eratosthenes
|
Sieve of Eratosthenes
|
This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.
The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer.
Task
Implement the Sieve of Eratosthenes algorithm, with the only allowed optimization that the outer loop can stop at the square root of the limit, and the inner loop may start at the square of the prime just found.
That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.
If there's an easy way to add such a wheel based optimization, implement it as an alternative version.
Note
It is important that the sieve algorithm be the actual algorithm used to find prime numbers for the task.
Related tasks
Emirp primes
count in factors
prime decomposition
factors of an integer
extensible prime generator
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#6502_Assembly
|
6502 Assembly
|
ERATOS: STA $D0 ; value of n
LDA #$00
LDX #$00
SETUP: STA $1000,X ; populate array
ADC #$01
INX
CPX $D0
BPL SET
JMP SETUP
SET: LDX #$02
SIEVE: LDA $1000,X ; find non-zero
INX
CPX $D0
BPL SIEVED
CMP #$00
BEQ SIEVE
STA $D1 ; current prime
MARK: CLC
ADC $D1
TAY
LDA #$00
STA $1000,Y
TYA
CMP $D0
BPL SIEVE
JMP MARK
SIEVED: LDX #$01
LDY #$00
COPY: INX
CPX $D0
BPL COPIED
LDA $1000,X
CMP #$00
BEQ COPY
STA $2000,Y
INY
JMP COPY
COPIED: TYA ; how many found
RTS
|
http://rosettacode.org/wiki/Sequence_of_primorial_primes
|
Sequence of primorial primes
|
The sequence of primorial primes is given as the increasing values of n where primorial(n) ± 1 is prime.
Noting that the n'th primorial is defined as the multiplication of the smallest n primes, the sequence is of the number of primes, in order that when multiplied together is one-off being a prime number itself.
Task
Generate and show here the first ten values of the sequence.
Optional extended task
Show the first twenty members of the series.
Notes
This task asks for the primorial indices that create the final primorial prime numbers, so there should be no ten-or-more digit numbers in the program output (although extended precision integers will be needed for intermediate results).
There is some confusion in the references, but for the purposes of this task the sequence begins with n = 1.
Probabilistic primality tests are allowed, as long as they are good enough such that the output shown is correct.
Related tasks
Primorial numbers
Factorial
See also
Primorial prime Wikipedia.
Primorial prime from The Prime Glossary.
Sequence A088411 from The On-Line Encyclopedia of Integer Sequences
|
#C.2B.2B
|
C++
|
#include <cstdint>
#include <iostream>
#include <sstream>
#include <gmpxx.h>
typedef mpz_class integer;
bool is_probably_prime(const integer& n) {
return mpz_probab_prime_p(n.get_mpz_t(), 25) != 0;
}
bool is_prime(unsigned int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (unsigned int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
int main() {
const unsigned int max = 20;
integer primorial = 1;
for (unsigned int p = 0, count = 0, index = 0; count < max; ++p) {
if (!is_prime(p))
continue;
primorial *= p;
++index;
if (is_probably_prime(primorial - 1) || is_probably_prime(primorial + 1)) {
if (count > 0)
std::cout << ' ';
std::cout << index;
++count;
}
}
std::cout << '\n';
return 0;
}
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#Go
|
Go
|
package main
import (
"fmt"
"math"
"math/big"
)
var bi = new(big.Int)
func isPrime(n int) bool {
bi.SetUint64(uint64(n))
return bi.ProbablyPrime(0)
}
func generateSmallPrimes(n int) []int {
primes := make([]int, n)
primes[0] = 2
for i, count := 3, 1; count < n; i += 2 {
if isPrime(i) {
primes[count] = i
count++
}
}
return primes
}
func countDivisors(n int) int {
count := 1
for n%2 == 0 {
n >>= 1
count++
}
for d := 3; d*d <= n; d += 2 {
q, r := n/d, n%d
if r == 0 {
dc := 0
for r == 0 {
dc += count
n = q
q, r = n/d, n%d
}
count += dc
}
}
if n != 1 {
count *= 2
}
return count
}
func main() {
const max = 33
primes := generateSmallPrimes(max)
z := new(big.Int)
p := new(big.Int)
fmt.Println("The first", max, "terms in the sequence are:")
for i := 1; i <= max; i++ {
if isPrime(i) {
z.SetUint64(uint64(primes[i-1]))
p.SetUint64(uint64(i - 1))
z.Exp(z, p, nil)
fmt.Printf("%2d : %d\n", i, z)
} else {
count := 0
for j := 1; ; j++ {
if i%2 == 1 {
sq := int(math.Sqrt(float64(j)))
if sq*sq != j {
continue
}
}
if countDivisors(j) == i {
count++
if count == i {
fmt.Printf("%2d : %d\n", i, j)
break
}
}
}
}
}
}
|
http://rosettacode.org/wiki/Set_consolidation
|
Set consolidation
|
Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:
The two input sets if no common item exists between the two input sets of items.
The single set that is the union of the two input sets if they share a common item.
Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.
Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}
See also
Connected component (graph theory)
Range consolidation
|
#D
|
D
|
import std.stdio, std.algorithm, std.array;
dchar[][] consolidate(dchar[][] sets) @safe {
foreach (set; sets)
set.sort();
foreach (i, ref si; sets[0 .. $ - 1]) {
if (si.empty)
continue;
foreach (ref sj; sets[i + 1 .. $])
if (!sj.empty && !si.setIntersection(sj).empty) {
sj = si.setUnion(sj).uniq.array;
si = null;
}
}
return sets.filter!"!a.empty".array;
}
void main() @safe {
[['A', 'B'], ['C','D']].consolidate.writeln;
[['A','B'], ['B','D']].consolidate.writeln;
[['A','B'], ['C','D'], ['D','B']].consolidate.writeln;
[['H','I','K'], ['A','B'], ['C','D'],
['D','B'], ['F','G','H']].consolidate.writeln;
}
|
http://rosettacode.org/wiki/Sequence:_smallest_number_with_exactly_n_divisors
|
Sequence: smallest number with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: nth number with exactly n divisors
See also
OEIS:A005179
|
#Factor
|
Factor
|
USING: fry kernel lists lists.lazy math math.primes.factors
prettyprint sequences ;
: A005179 ( -- list )
1 lfrom [
1 swap '[ dup divisors length _ = ] [ 1 + ] until
] lmap-lazy ;
15 A005179 ltake list>array .
|
http://rosettacode.org/wiki/Sequence:_smallest_number_with_exactly_n_divisors
|
Sequence: smallest number with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: nth number with exactly n divisors
See also
OEIS:A005179
|
#FreeBASIC
|
FreeBASIC
|
#define UPTO 15
function divisors(byval n as ulongint) as uinteger
'find the number of divisors of an integer
dim as integer r = 2, i
for i = 2 to n\2
if n mod i = 0 then r += 1
next i
return r
end function
dim as ulongint i = 2
dim as integer n, nfound = 1, sfound(UPTO) = {1}
while nfound < UPTO
n = divisors(i)
if n<=UPTO andalso sfound(n)=0 then
nfound += 1
sfound(n) = i
end if
i+=1
wend
print 1;" "; 'special case
for i = 2 to UPTO
print sfound(i);" ";
next i
print
end
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#Lasso
|
Lasso
|
// The following will return a list of all the cipher
// algorithms supported by the installation of Lasso
cipher_list
// With a -digest parameter the method will limit the returned list
// to all of the digest algorithms supported by the installation of Lasso
cipher_list(-digest)
// return the SHA-256 digest. Dependant on SHA-256 being an available digest method
cipher_digest('Rosetta Code', -digest='SHA-256',-hex=true)
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#Lua
|
Lua
|
#!/usr/bin/lua
require "sha2"
print(sha2.sha256hex("Rosetta code"))
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Haskell
|
Haskell
|
import Text.Printf (printf)
sequence_A069654 :: [(Int,Int)]
sequence_A069654 = go 1 $ (,) <*> countDivisors <$> [1..]
where go t ((n,c):xs) | c == t = (t,n):go (succ t) xs
| otherwise = go t xs
countDivisors n = foldr f 0 [1..floor $ sqrt $ realToFrac n]
where f x r | n `mod` x == 0 = if n `div` x == x then r+1 else r+2
| otherwise = r
main :: IO ()
main = mapM_ (uncurry $ printf "a(%2d)=%5d\n") $ take 15 sequence_A069654
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#J
|
J
|
sieve=: 3 :0
NB. sieve y returns a vector of y boxes.
NB. In each box is an array of 2 columns.
NB. The first column is the factor tally
NB. and the second column is a number with
NB. that many factors.
NB. Rather than factoring, the algorithm
NB. counts prime seive cell hits.
NB. The boxes are not ordered by factor tally.
range=. <. + i.@:|@:-
tally=. y#0
for_i.#\tally do.
j=. }:^:(y<:{:)i * 1 range >: <. y % i
tally=. j >:@:{`[`]} tally
end.
(</.~ {."1) (,. i.@:#)tally
)
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#Maple
|
Maple
|
with(StringTools):
Hash("Ars longa, vita brevis",method="SHA1");
# "e640d285242886eb96ab80cbf858389b3df52f43"
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#Mathematica.2FWolfram_Language
|
Mathematica/Wolfram Language
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Hash["Rosetta code","SHA1","HexString"]
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http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
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Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
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#Python
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Python
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from random import randint
def dice5():
return randint(1, 5)
def dice7():
r = dice5() + dice5() * 5 - 6
return (r % 7) + 1 if r < 21 else dice7()
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http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
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Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
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#Quackery
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Quackery
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[ 5 random 1+ ] is dice5 ( --> n )
[ dice5 5 *
dice5 + 6 -
[ table
0 0 0 0 1
1 1 2 2 2
3 3 3 4 4
4 5 5 5 6
6 6 7 7 7 ]
dup 0 = iff
drop again ] is dice7 ( --> n )
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http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
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Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
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#R
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R
|
dice5 <- function(n=1) sample(5, n, replace=TRUE)
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http://rosettacode.org/wiki/Show_ASCII_table
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Show ASCII table
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Task
Show the ASCII character set from values 32 to 127 (decimal) in a table format.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
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#Haskell
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Haskell
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import Data.Char (chr)
import Data.List (transpose)
import Data.List.Split (chunksOf)
import Text.Printf (printf)
----------------------- ASCII TABLE ----------------------
asciiTable :: String
asciiTable =
unlines $
(printf "%-12s" =<<)
<$> transpose
(chunksOf 16 $ asciiEntry <$> [32 .. 127])
asciiEntry :: Int -> String
asciiEntry n
| null k = k
| otherwise = concat [printf "%3d" n, " : ", k]
where
k = asciiName n
asciiName :: Int -> String
asciiName n
| 32 > n = []
| 127 < n = []
| 32 == n = "Spc"
| 127 == n = "Del"
| otherwise = [chr n]
--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn asciiTable
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http://rosettacode.org/wiki/Sierpinski_triangle
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Sierpinski triangle
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Task
Produce an ASCII representation of a Sierpinski triangle of order N.
Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Related tasks
Sierpinski triangle/Graphical for graphics images of this pattern.
Sierpinski carpet
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#Picat
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Picat
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go =>
foreach(N in 1..4)
sierpinski(N),
nl
end,
nl.
sierpinski(N) =>
Size = 2**N,
foreach(Y in Size-1..-1..0)
printf("%s", [' ' : _I in 1..Y]),
foreach(X in 0..Size-Y-1)
printf("%s ", cond(X /\ Y == 0, "*", " "))
end,
nl
end.
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http://rosettacode.org/wiki/Sierpinski_carpet
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Sierpinski carpet
|
Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
Related task
Sierpinski triangle
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#Lua
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Lua
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local function carpet(n, f)
print("n = " .. n)
local function S(x, y)
if x==0 or y==0 then return true
elseif x%3==1 and y%3==1 then return false end
return S(x//3, y//3)
end
for y = 0, 3^n-1 do
for x = 0, 3^n-1 do
io.write(f(S(x, y)))
end
print()
end
print()
end
for n = 0, 4 do
carpet(n, function(b) return b and "■ " or " " end)
end
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http://rosettacode.org/wiki/Short-circuit_evaluation
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Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
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#OCaml
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OCaml
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let a r = print_endline " > function a called"; r
let b r = print_endline " > function b called"; r
let test_and b1 b2 =
Printf.printf "# testing (%b && %b)\n" b1 b2;
ignore (a b1 && b b2)
let test_or b1 b2 =
Printf.printf "# testing (%b || %b)\n" b1 b2;
ignore (a b1 || b b2)
let test_this test =
test true true;
test true false;
test false true;
test false false;
;;
let () =
print_endline "==== Testing and ====";
test_this test_and;
print_endline "==== Testing or ====";
test_this test_or;
;;
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http://rosettacode.org/wiki/Set_puzzle
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Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#Rust
|
Rust
|
use itertools::Itertools;
use rand::Rng;
const DECK_SIZE: usize = 81;
const NUM_ATTRIBUTES: usize = 4;
const ATTRIBUTES: [&[&str]; NUM_ATTRIBUTES] = [
&["red", "green", "purple"],
&["one", "two", "three"],
&["oval", "squiggle", "diamond"],
&["solid", "open", "striped"],
];
fn get_random_card_indexes(num_of_cards: usize) -> Vec<usize> {
let mut selected_cards: Vec<usize> = Vec::with_capacity(num_of_cards);
let mut rng = rand::thread_rng();
loop {
let idx = rng.gen_range(0..DECK_SIZE);
if !selected_cards.contains(&idx) {
selected_cards.push(idx);
}
if selected_cards.len() == num_of_cards {
break;
}
}
selected_cards
}
fn run_game(num_of_cards: usize, minimum_number_of_sets: usize) {
println!(
"\nGAME: # of cards: {} # of sets: {}",
num_of_cards, minimum_number_of_sets
);
// generate the deck with 81 unique cards
let deck = (0..NUM_ATTRIBUTES)
.map(|_| (0..=2_usize))
.multi_cartesian_product()
.collect::<Vec<_>>();
// closure to return true if the three attributes are the same, or each of them is different
let valid_attribute =
|a: usize, b: usize, c: usize| -> bool { a == b && b == c || (a != b && b != c && a != c) };
// closure to test all attributes, each of them should be true to have a valid set
let valid_set = |t: &Vec<&Vec<usize>>| -> bool {
for attr in 0..NUM_ATTRIBUTES {
if !valid_attribute(t[0][attr], t[1][attr], t[2][attr]) {
return false;
}
}
true
};
loop {
// select the required # of cards from the deck randomly
let selected_cards = get_random_card_indexes(num_of_cards)
.iter()
.map(|idx| deck[*idx].clone())
.collect::<Vec<_>>();
// generate all combinations, and filter/keep only which are valid sets
let valid_sets = selected_cards
.iter()
.combinations(3)
.filter(|triplet| valid_set(triplet))
.collect::<Vec<_>>();
// if the # of the sets is matching the requirement, print it and finish
if valid_sets.len() == minimum_number_of_sets {
print!("SELECTED CARDS:");
for card in &selected_cards {
print!("\ncard: ");
for attr in 0..NUM_ATTRIBUTES {
print!("{}, ", ATTRIBUTES[attr][card[attr]]);
}
}
print!("\nSets:");
for triplet in &valid_sets {
print!("\nSet: ");
for card in triplet {
for attr in 0..NUM_ATTRIBUTES {
print!("{}, ", ATTRIBUTES[attr][card[attr]]);
}
print!(" | ");
}
}
break;
}
//otherwise generate again
}
}
fn main() {
run_game(9, 4);
run_game(12, 6);
}
|
http://rosettacode.org/wiki/Set_puzzle
|
Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#Tailspin
|
Tailspin
|
def deck: [ { by 1..3 -> (colour: $),
by 1..3 -> (symbol: $),
by 1..3 -> (number: $),
by 1..3 -> (shading: $)}
];
templates deal
@: $deck;
[ 1..$ -> \($@deal::length -> SYS::randomInt -> ^@deal($ + 1) !\)] !
end deal
templates isSet
def set : $;
[ $(1).colour::raw + $(2).colour::raw + $(3).colour::raw, $(1).symbol::raw + $(2).symbol::raw + $(3).symbol::raw,
$(1).number::raw + $(2).number::raw + $(3).number::raw, $(1).shading::raw + $(2).shading::raw + $(3).shading::raw ] -> #
// if it is an array where all elements of 3, 6 or 9, it is a set
when <[<=3|=6|=9>+ VOID]> do $set !
end isSet
templates findSets
def hand: $;
[ 1..$hand::length - 2 -> \(def a: $;
$a+1..$hand::length - 1 -> \(def b: $;
$b+1..$hand::length -> $hand([$a, $b, $]) !
\) !
\) -> isSet ] !
end findSets
templates setPuzzle
def nCards: $(1);
def nSets: $(2);
{} -> #
when <{sets: <[]($nSets..)>}> do $ !
otherwise
def hand: $nCards -> deal;
{hand: $hand, sets: $hand -> findSets} -> #
end setPuzzle
templates formatCard
def colours: ['red', 'green', 'purple'];
def symbols: ['oval', 'squiggle', 'diamond'];
def numbers: ['one', 'two', 'three'];
def shadings: ['solid', 'open', 'striped'];
$ -> '$colours($.colour);-$symbols($.symbol);-$numbers($.number);-$shadings($.shading);' !
end formatCard
templates formatSets
$ -> 'hand:
$.hand... -> '$ -> formatCard;
';
sets:
$.sets... -> '[$... -> ' $ -> formatCard; ';]
';' !
end formatSets
[9,4] -> setPuzzle -> formatSets -> !OUT::write
|
http://rosettacode.org/wiki/Set_of_real_numbers
|
Set of real numbers
|
All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:
[a, b]: {x | a ≤ x and x ≤ b }
(a, b): {x | a < x and x < b }
[a, b): {x | a ≤ x and x < b }
(a, b]: {x | a < x and x ≤ b }
Note that if a = b, of the four only [a, a] would be non-empty.
Task
Devise a way to represent any set of real numbers, for the definition of 'any' in the implementation notes below.
Provide methods for these common set operations (x is a real number; A and B are sets):
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
Test your implementation by checking if numbers 0, 1, and 2 are in any of the following sets:
(0, 1] ∪ [0, 2)
[0, 2) ∩ (1, 2]
[0, 3) − (0, 1)
[0, 3) − [0, 1]
Implementation notes
'Any' real set means 'sets that can be expressed as the union of a finite number of convex real sets'. Cantor's set needs not apply.
Infinities should be handled gracefully; indeterminate numbers (NaN) can be ignored.
You can use your machine's native real number representation, which is probably IEEE floating point, and assume it's good enough (it usually is).
Optional work
Create a function to determine if a given set is empty (contains no element).
Define A = {x | 0 < x < 10 and |sin(π x²)| > 1/2 }, B = {x | 0 < x < 10 and |sin(π x)| > 1/2}, calculate the length of the real axis covered by the set A − B. Note that
|sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.
|
#C.23
|
C#
|
using System;
namespace RosettaCode.SetOfRealNumbers
{
public class Set<TValue>
{
public Set(Predicate<TValue> contains)
{
Contains = contains;
}
public Predicate<TValue> Contains
{
get;
private set;
}
public Set<TValue> Union(Set<TValue> set)
{
return new Set<TValue>(value => Contains(value) || set.Contains(value));
}
public Set<TValue> Intersection(Set<TValue> set)
{
return new Set<TValue>(value => Contains(value) && set.Contains(value));
}
public Set<TValue> Difference(Set<TValue> set)
{
return new Set<TValue>(value => Contains(value) && !set.Contains(value));
}
}
}
|
http://rosettacode.org/wiki/Sieve_of_Eratosthenes
|
Sieve of Eratosthenes
|
This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.
The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer.
Task
Implement the Sieve of Eratosthenes algorithm, with the only allowed optimization that the outer loop can stop at the square root of the limit, and the inner loop may start at the square of the prime just found.
That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.
If there's an easy way to add such a wheel based optimization, implement it as an alternative version.
Note
It is important that the sieve algorithm be the actual algorithm used to find prime numbers for the task.
Related tasks
Emirp primes
count in factors
prime decomposition
factors of an integer
extensible prime generator
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#68000_Assembly
|
68000 Assembly
|
*-----------------------------------------------------------
* Title : BitSieve
* Written by : G. A. Tippery
* Date : 2014-Feb-24, 2013-Dec-22
* Description: Prime number sieve
*-----------------------------------------------------------
ORG $1000
** ---- Generic macros ---- **
PUSH MACRO
MOVE.L \1,-(SP)
ENDM
POP MACRO
MOVE.L (SP)+,\1
ENDM
DROP MACRO
ADDQ #4,SP
ENDM
PUTS MACRO
** Print a null-terminated string w/o CRLF **
** Usage: PUTS stringaddress
** Returns with D0, A1 modified
MOVEQ #14,D0 ; task number 14 (display null string)
LEA \1,A1 ; address of string
TRAP #15 ; display it
ENDM
GETN MACRO
MOVEQ #4,D0 ; Read a number from the keyboard into D1.L.
TRAP #15
ENDM
** ---- Application-specific macros ---- **
val MACRO ; Used by bit sieve. Converts bit address to the number it represents.
ADD.L \1,\1 ; double it because odd numbers are omitted
ADDQ #3,\1 ; add offset because initial primes (1, 2) are omitted
ENDM
* ** ================================================================================ **
* ** Integer square root routine, bisection method **
* ** IN: D0, should be 0<D0<$10000 (65536) -- higher values MAY work, no guarantee
* ** OUT: D1
*
SquareRoot:
*
MOVEM.L D2-D4,-(SP) ; save registers needed for local variables
* DO == n
* D1 == a
* D2 == b
* D3 == guess
* D4 == temp
*
* a = 1;
* b = n;
MOVEQ #1,D1
MOVE.L D0,D2
* do {
REPEAT
* guess = (a+b)/2;
MOVE.L D1,D3
ADD.L D2,D3
LSR.L #1,D3
* if (guess*guess > n) { // inverse function of sqrt is square
MOVE.L D3,D4
MULU D4,D4 ; guess^2
CMP.L D0,D4
BLS .else
* b = guess;
MOVE.L D3,D2
BRA .endif
* } else {
.else:
* a = guess;
MOVE.L D3,D1
* } //if
.endif:
* } while ((b-a) > 1); ; Same as until (b-a)<=1 or until (a-b)>=1
MOVE.L D2,D4
SUB.L D1,D4 ; b-a
UNTIL.L D4 <LE> #1 DO.S
* return (a) ; Result is in D1
* } //LongSqrt()
MOVEM.L (SP)+,D2-D4 ; restore saved registers
RTS
*
* ** ================================================================================ **
** ======================================================================= **
*
** Prime-number Sieve of Eratosthenes routine using a big bit field for flags **
* Enter with D0 = size of sieve (bit array)
* Prints found primes 10 per line
* Returns # prime found in D6
*
* Register usage:
*
* D0 == n
* D1 == prime
* D2 == sqroot
* D3 == PIndex
* D4 == CIndex
* D5 == MaxIndex
* D6 == PCount
*
* A0 == PMtx[0]
*
* On return, all registers above except D0 are modified. Could add MOVEMs to save and restore D2-D6/A0.
*
** ------------------------ **
GetBit: ** sub-part of Sieve subroutine **
** Entry: bit # is on TOS
** Exit: A6 holds the byte number, D7 holds the bit number within the byte
** Note: Input param is still on TOS after return. Could have passed via a register, but
** wanted to practice with stack. :)
*
MOVE.L (4,SP),D7 ; get value from (pre-call) TOS
ASR.L #3,D7 ; /8
MOVEA D7,A6 ; byte #
MOVE.L (4,SP),D7 ; get value from (pre-call) TOS
AND.L #$7,D7 ; bit #
RTS
** ------------------------ **
Sieve:
MOVE D0,D5
SUBQ #1,D5
JSR SquareRoot ; sqrt D0 => D1
MOVE.L D1,D2
LEA PArray,A0
CLR.L D3
*
PrimeLoop:
MOVE.L D3,D1
val D1
MOVE.L D3,D4
ADD.L D1,D4
*
CxLoop: ; Goes through array marking multiples of d1 as composite numbers
CMP.L D5,D4
BHI ExitCx
PUSH D4 ; set D7 as bit # and A6 as byte pointer for D4'th bit of array
JSR GetBit
DROP
BSET D7,0(A0,A6.L) ; set bit to mark as composite number
ADD.L D1,D4 ; next number to mark
BRA CxLoop
ExitCx:
CLR.L D1 ; Clear new-prime-found flag
ADDQ #1,D3 ; Start just past last prime found
PxLoop: ; Searches for next unmarked (not composite) number
CMP.L D2,D3 ; no point searching past where first unmarked multiple would be past end of array
BHI ExitPx ; if past end of array
TST.L D1
BNE ExitPx ; if flag set, new prime found
PUSH D3 ; check D3'th bit flag
JSR GetBit ; sets D7 as bit # and A6 as byte pointer
DROP ; drop TOS
BTST D7,0(A0,A6.L) ; read bit flag
BNE IsSet ; If already tagged as composite
MOVEQ #-1,D1 ; Set flag that we've found a new prime
IsSet:
ADDQ #1,D3 ; next PIndex
BRA PxLoop
ExitPx:
SUBQ #1,D3 ; back up PIndex
TST.L D1 ; Did we find a new prime #?
BNE PrimeLoop ; If another prime # found, go process it
*
; fall through to print routine
** ------------------------ **
* Print primes found
*
* D4 == Column count
*
* Print header and assumed primes (#1, #2)
PUTS Header ; Print string @ Header, no CR/LF
MOVEQ #2,D6 ; Start counter at 2 because #1 and #2 are assumed primes
MOVEQ #2,D4
*
MOVEQ #0,D3
PrintLoop:
CMP.L D5,D3
BHS ExitPL
PUSH D3
JSR GetBit ; sets D7 as bit # and A6 as byte pointer
DROP ; drop TOS
BTST D7,0(A0,A6.L)
BNE NotPrime
* printf(" %6d", val(PIndex)
MOVE.L D3,D1
val D1
AND.L #$0000FFFF,D1
MOVEQ #6,D2
MOVEQ #20,D0 ; display signed RJ
TRAP #15
ADDQ #1,D4
ADDQ #1,D6
* *** Display formatting ***
* if((PCount % 10) == 0) printf("\n");
CMP #10,D4
BLO NoLF
PUTS CRLF
MOVEQ #0,D4
NoLF:
NotPrime:
ADDQ #1,D3
BRA PrintLoop
ExitPL:
RTS
** ======================================================================= **
N EQU 5000 ; *** Size of boolean (bit) array ***
SizeInBytes EQU (N+7)/8
*
START: ; first instruction of program
MOVE.L #N,D0 ; # to test
JSR Sieve
* printf("\n %d prime numbers found.\n", D6); ***
PUTS Summary1,A1
MOVE #3,D0 ; Display signed number in D1.L in decimal in smallest field.
MOVE.W D6,D1
TRAP #15
PUTS Summary2,A1
SIMHALT ; halt simulator
** ======================================================================= **
* Variables and constants here
ORG $2000
CR EQU 13
LF EQU 10
CRLF DC.B CR,LF,$00
PArray: DCB.B SizeInBytes,0
Header: DC.B CR,LF,LF,' Primes',CR,LF,' ======',CR,LF
DC.B ' 1 2',$00
Summary1: DC.B CR,LF,' ',$00
Summary2: DC.B ' prime numbers found.',CR,LF,$00
END START ; last line of source
|
http://rosettacode.org/wiki/Sequence_of_primorial_primes
|
Sequence of primorial primes
|
The sequence of primorial primes is given as the increasing values of n where primorial(n) ± 1 is prime.
Noting that the n'th primorial is defined as the multiplication of the smallest n primes, the sequence is of the number of primes, in order that when multiplied together is one-off being a prime number itself.
Task
Generate and show here the first ten values of the sequence.
Optional extended task
Show the first twenty members of the series.
Notes
This task asks for the primorial indices that create the final primorial prime numbers, so there should be no ten-or-more digit numbers in the program output (although extended precision integers will be needed for intermediate results).
There is some confusion in the references, but for the purposes of this task the sequence begins with n = 1.
Probabilistic primality tests are allowed, as long as they are good enough such that the output shown is correct.
Related tasks
Primorial numbers
Factorial
See also
Primorial prime Wikipedia.
Primorial prime from The Prime Glossary.
Sequence A088411 from The On-Line Encyclopedia of Integer Sequences
|
#Clojure
|
Clojure
|
(ns example
(:gen-class))
; Lazy Sequence of primes (starting with number 2)
(def primes (iterate #(.nextProbablePrime %) (biginteger 2)))
(defn primorial-prime? [v]
" Test if value is a primorial prime "
(let [a (biginteger (inc v))
b (biginteger (dec v))]
(or (.isProbablePrime a 16)
(.isProbablePrime b 16))))
; Generate indexes for first 20 primorial primes
(println (take 20 (keep-indexed ; take the first 20
#(if (primorial-prime? %2) (inc %1)) ; filters out non-primorials, passing on the index + 1 (since sequence begins with 1 (not 0)
(reductions *' primes)))) ; computes the lazy sequence of product of 1 prime, 2 primes, 3 primes, etc.
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#Haskell
|
Haskell
|
import Control.Monad (guard)
import Math.NumberTheory.ArithmeticFunctions (divisorCount)
import Math.NumberTheory.Primes (Prime, unPrime)
import Math.NumberTheory.Primes.Testing (isPrime)
calc :: Integer -> [(Integer, Integer)]
calc n = do
x <- [1..]
guard (even n || odd n && f x == x)
[(x, divisorCount x)]
where f n = floor (sqrt $ realToFrac n) ^ 2
havingNthDivisors :: Integer -> [(Integer, Integer)]
havingNthDivisors n = filter ((==n) . snd) $ calc n
nths :: [(Integer, Integer)]
nths = do
n <- [1..35] :: [Integer]
if isPrime n then
pure (n, nthPrime (fromIntegral n) ^ pred n)
else
pure (n, f n)
where
f n = fst (havingNthDivisors n !! pred (fromIntegral n))
nthPrime n = unPrime (toEnum n :: Prime Integer)
main :: IO ()
main = mapM_ print nths
|
http://rosettacode.org/wiki/Set_consolidation
|
Set consolidation
|
Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:
The two input sets if no common item exists between the two input sets of items.
The single set that is the union of the two input sets if they share a common item.
Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.
Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}
See also
Connected component (graph theory)
Range consolidation
|
#EchoLisp
|
EchoLisp
|
;; utility : make a set of sets from a list
(define (make-set* s)
(or (when (list? s) (make-set (map make-set* s))) s))
;; union of all sets which intersect - O(n^2)
(define (make-big ss)
(make-set
(for/list ((u ss))
(for/fold (big u) ((v ss)) #:when (set-intersect? big v) (set-union big v)))))
;; remove sets which are subset of another one - O(n^2)
(define (remove-small ss)
(for/list ((keep ss))
#:when (for/and ((v ss)) #:continue (set-equal? keep v) (not (set-subset? v keep)))
keep))
(define (consolidate ss) (make-set (remove-small (make-big ss))))
(define S (make-set* ' ((h i k) ( a b) ( b c) (c d) ( f g h))))
→ { { a b } { b c } { c d } { f g h } { h i k } }
(consolidate S)
→ { { a b c d } { f g h i k } }
|
http://rosettacode.org/wiki/Sequence:_smallest_number_with_exactly_n_divisors
|
Sequence: smallest number with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: nth number with exactly n divisors
See also
OEIS:A005179
|
#Go
|
Go
|
package main
import "fmt"
func countDivisors(n int) int {
count := 0
for i := 1; i*i <= n; i++ {
if n%i == 0 {
if i == n/i {
count++
} else {
count += 2
}
}
}
return count
}
func main() {
const max = 15
seq := make([]int, max)
fmt.Println("The first", max, "terms of the sequence are:")
for i, n := 1, 0; n < max; i++ {
if k := countDivisors(i); k <= max && seq[k-1] == 0 {
seq[k-1] = i
n++
}
}
fmt.Println(seq)
}
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#Mathematica.2FWolfram_Language
|
Mathematica/Wolfram Language
|
Hash["Rosetta code","SHA256","HexString"]
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#min
|
min
|
"Rosetta code" sha256 puts!
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Java
|
Java
|
public class AntiPrimesPlus {
static int count_divisors(int n) {
int count = 0;
for (int i = 1; i * i <= n; ++i) {
if (n % i == 0) {
if (i == n / i)
count++;
else
count += 2;
}
}
return count;
}
public static void main(String[] args) {
final int max = 15;
System.out.printf("The first %d terms of the sequence are:\n", max);
for (int i = 1, next = 1; next <= max; ++i) {
if (next == count_divisors(i)) {
System.out.printf("%d ", i);
next++;
}
}
System.out.println();
}
}
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#min
|
min
|
"Rosetta Code" sha1 puts!
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#Neko
|
Neko
|
/**
SHA-1 in Neko
Tectonics:
nekoc SHA-1.neko
neko SHA-1
*/
var SHA1 = $loader.loadprim("std@make_sha1", 3);
var base_encode = $loader.loadprim("std@base_encode", 2);
var msg = "Rosetta Code";
var result = SHA1(msg, 0, $ssize(msg));
/* Output in lowercase hex */
$print(base_encode(result, "0123456789abcdef"));
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#Racket
|
Racket
|
#lang racket
(define (dice5) (add1 (random 5)))
(define (dice7)
(define res (+ (* 5 (dice5)) (dice5) -6))
(if (< res 21) (+ 1 (modulo res 7)) (dice7)))
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#Raku
|
Raku
|
my $d5 = 1..5;
sub d5() { $d5.roll; } # 1d5
sub d7() {
my $flat = 21;
$flat = 5 * d5() - d5() until $flat < 21;
$flat % 7 + 1;
}
# Testing
my @dist;
my $n = 1_000_000;
my $expect = $n / 7;
loop ($_ = $n; $n; --$n) { @dist[d7()]++; }
say "Expect\t",$expect.fmt("%.3f");
for @dist.kv -> $i, $v {
say "$i\t$v\t" ~ (($v - $expect)/$expect*100).fmt("%+.2f%%") if $v;
}
|
http://rosettacode.org/wiki/Show_ASCII_table
|
Show ASCII table
|
Task
Show the ASCII character set from values 32 to 127 (decimal) in a table format.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
|
#IS-BASIC
|
IS-BASIC
|
100 TEXT 80
110 FOR R=0 TO 15
120 FOR C=32+R TO 112+R STEP 16
130 PRINT USING "###":C;:PRINT ": ";CHR$(C),
140 NEXT
150 PRINT
160 NEXT
|
http://rosettacode.org/wiki/Sierpinski_triangle
|
Sierpinski triangle
|
Task
Produce an ASCII representation of a Sierpinski triangle of order N.
Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Related tasks
Sierpinski triangle/Graphical for graphics images of this pattern.
Sierpinski carpet
|
#PicoLisp
|
PicoLisp
|
(de sierpinski (N)
(let (D '("*") S " ")
(do N
(setq
D (conc
(mapcar '((X) (pack S X S)) D)
(mapcar '((X) (pack X " " X)) D) )
S (pack S S) ) )
D ) )
(mapc prinl (sierpinski 4))
|
http://rosettacode.org/wiki/Sierpinski_carpet
|
Sierpinski carpet
|
Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
Related task
Sierpinski triangle
|
#Liberty_BASIC
|
Liberty BASIC
|
NoMainWin
WindowWidth = 508
WindowHeight = 575
Open "Sierpinski Carpets" For Graphics_nsb_nf As #g
#g "Down; TrapClose [halt]"
'labels
#g "Place 90 15;\Order 0"
#g "Place 340 15;\Order 1"
#g "Place 90 286;\Order 2"
#g "Place 340 286;\Order 3"
'carpets
Call carpet 5, 20, 243, 0
Call carpet 253, 20, 243, 1
Call carpet 5, 293, 243, 2
Call carpet 253, 293, 243, 3
#g "Flush"
Wait
[halt]
Close #g
End
Sub carpet x, y, size, order
#g "Color 0 0 128; BackColor 0 0 128"
#g "Place ";x;" ";y
#g "BoxFilled ";x+size-1;" ";y+size-1
#g "Color white; BackColor white"
side = Int(size/3)
newX = x+side
newY = y+side
#g "Place ";newX;" ";newY
#g "BoxFilled ";newX+side-1;" ";newY+side-1
order = order - 1
If order > -1 Then
Call carpet newX-side, newY-side+1, side, order
Call carpet newX, newY-side+1, side, order
Call carpet newX+side, newY-side+1, side, order
Call carpet newX+side, newY, side, order
Call carpet newX+side, newY+side, side, order
Call carpet newX, newY+side, side, order
Call carpet newX-side, newY+side, side, order
Call carpet newX-side, newY, side, order
End If
End Sub
|
http://rosettacode.org/wiki/Short-circuit_evaluation
|
Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
|
#Ol
|
Ol
|
(define (a x)
(print " (a) => " x)
x)
(define (b x)
(print " (b) => " x)
x)
; and
(print " -- and -- ")
(for-each (lambda (x y)
(print "let's evaluate '(a as " x ") and (b as " y ")':")
(let ((out (and (a x) (b y))))
(print " result is " out)))
'(#t #t #f #f)
'(#t #f #t #f))
; or
(print " -- or -- ")
(for-each (lambda (x y)
(print "let's evaluate '(a as " x ") or (b as " y ")':")
(let ((out (or (a x) (b y))))
(print " result is " out)))
'(#t #t #f #f)
'(#t #f #t #f))
|
http://rosettacode.org/wiki/Set_puzzle
|
Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#Tcl
|
Tcl
|
# Generate random integer uniformly on range [0..$n-1]
proc random n {expr {int(rand() * $n)}}
# Generate a shuffled deck of all cards; the card encoding was stolen from the
# Perl6 solution. This is done once and then used as a constant. Note that the
# rest of the code assumes that all cards in the deck are unique.
set ::AllCards [apply {{} {
set cards {}
foreach color {1 2 4} {
foreach symbol {1 2 4} {
foreach number {1 2 4} {
foreach shading {1 2 4} {
lappend cards [list $color $symbol $number $shading]
}
}
}
}
# Knuth-Morris-Pratt shuffle (not that it matters)
for {set i [llength $cards]} {$i > 0} {} {
set j [random $i]
set tmp [lindex $cards [incr i -1]]
lset cards $i [lindex $cards $j]
lset cards $j $tmp
}
return $cards
}}]
# Randomly pick a hand of cards from the deck (itself in a global for
# convenience).
proc drawCards n {
set cards $::AllCards; # Copies...
for {set i 0} {$i < $n} {incr i} {
set idx [random [llength $cards]]
lappend hand [lindex $cards $idx]
set cards [lreplace $cards $idx $idx]
}
return $hand
}
# Test if a particular group of three cards is a valid set
proc isValidSet {a b c} {
expr {
([lindex $a 0]|[lindex $b 0]|[lindex $c 0]) in {1 2 4 7} &&
([lindex $a 1]|[lindex $b 1]|[lindex $c 1]) in {1 2 4 7} &&
([lindex $a 2]|[lindex $b 2]|[lindex $c 2]) in {1 2 4 7} &&
([lindex $a 3]|[lindex $b 3]|[lindex $c 3]) in {1 2 4 7}
}
}
# Get all unique valid sets of three cards in a hand.
proc allValidSets {hand} {
set sets {}
for {set i 0} {$i < [llength $hand]} {incr i} {
set a [lindex $hand $i]
set hand [set cards2 [lreplace $hand $i $i]]
for {set j 0} {$j < [llength $cards2]} {incr j} {
set b [lindex $cards2 $j]
set cards2 [set cards3 [lreplace $cards2 $j $j]]
foreach c $cards3 {
if {[isValidSet $a $b $c]} {
lappend sets [list $a $b $c]
}
}
}
}
return $sets
}
# Solve a particular version of the set puzzle, by picking random hands until
# one is found that satisfies the constraints. This is usually much faster
# than a systematic search. On success, returns the hand found and the card
# sets within that hand.
proc SetPuzzle {numCards numSets} {
while 1 {
set hand [drawCards $numCards]
set sets [allValidSets $hand]
if {[llength $sets] == $numSets} {
break
}
}
return [list $hand $sets]
}
|
http://rosettacode.org/wiki/Set_of_real_numbers
|
Set of real numbers
|
All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:
[a, b]: {x | a ≤ x and x ≤ b }
(a, b): {x | a < x and x < b }
[a, b): {x | a ≤ x and x < b }
(a, b]: {x | a < x and x ≤ b }
Note that if a = b, of the four only [a, a] would be non-empty.
Task
Devise a way to represent any set of real numbers, for the definition of 'any' in the implementation notes below.
Provide methods for these common set operations (x is a real number; A and B are sets):
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
Test your implementation by checking if numbers 0, 1, and 2 are in any of the following sets:
(0, 1] ∪ [0, 2)
[0, 2) ∩ (1, 2]
[0, 3) − (0, 1)
[0, 3) − [0, 1]
Implementation notes
'Any' real set means 'sets that can be expressed as the union of a finite number of convex real sets'. Cantor's set needs not apply.
Infinities should be handled gracefully; indeterminate numbers (NaN) can be ignored.
You can use your machine's native real number representation, which is probably IEEE floating point, and assume it's good enough (it usually is).
Optional work
Create a function to determine if a given set is empty (contains no element).
Define A = {x | 0 < x < 10 and |sin(π x²)| > 1/2 }, B = {x | 0 < x < 10 and |sin(π x)| > 1/2}, calculate the length of the real axis covered by the set A − B. Note that
|sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.
|
#C.2B.2B
|
C++
|
#include <cassert>
#include <functional>
#include <iostream>
#define _USE_MATH_DEFINES
#include <math.h>
enum RangeType {
CLOSED,
BOTH_OPEN,
LEFT_OPEN,
RIGHT_OPEN
};
class RealSet {
private:
double low, high;
double interval = 0.00001;
std::function<bool(double)> predicate;
public:
RealSet(double low, double high, const std::function<bool(double)>& predicate) {
this->low = low;
this->high = high;
this->predicate = predicate;
}
RealSet(double start, double end, RangeType rangeType) {
low = start;
high = end;
switch (rangeType) {
case CLOSED:
predicate = [start, end](double d) { return start <= d && d <= end; };
break;
case BOTH_OPEN:
predicate = [start, end](double d) { return start < d && d < end; };
break;
case LEFT_OPEN:
predicate = [start, end](double d) { return start < d && d <= end; };
break;
case RIGHT_OPEN:
predicate = [start, end](double d) { return start <= d && d < end; };
break;
default:
assert(!"Unexpected range type encountered.");
}
}
bool contains(double d) const {
return predicate(d);
}
RealSet unionSet(const RealSet& rhs) const {
double low2 = fmin(low, rhs.low);
double high2 = fmax(high, rhs.high);
return RealSet(
low2, high2,
[this, &rhs](double d) { return predicate(d) || rhs.predicate(d); }
);
}
RealSet intersect(const RealSet& rhs) const {
double low2 = fmin(low, rhs.low);
double high2 = fmax(high, rhs.high);
return RealSet(
low2, high2,
[this, &rhs](double d) { return predicate(d) && rhs.predicate(d); }
);
}
RealSet subtract(const RealSet& rhs) const {
return RealSet(
low, high,
[this, &rhs](double d) { return predicate(d) && !rhs.predicate(d); }
);
}
double length() const {
if (isinf(low) || isinf(high)) return -1.0; // error value
if (high <= low) return 0.0;
double p = low;
int count = 0;
do {
if (predicate(p)) count++;
p += interval;
} while (p < high);
return count * interval;
}
bool empty() const {
if (high == low) {
return !predicate(low);
}
return length() == 0.0;
}
};
int main() {
using namespace std;
RealSet a(0.0, 1.0, LEFT_OPEN);
RealSet b(0.0, 2.0, RIGHT_OPEN);
RealSet c(1.0, 2.0, LEFT_OPEN);
RealSet d(0.0, 3.0, RIGHT_OPEN);
RealSet e(0.0, 1.0, BOTH_OPEN);
RealSet f(0.0, 1.0, CLOSED);
RealSet g(0.0, 0.0, CLOSED);
for (int i = 0; i <= 2; ++i) {
cout << "(0, 1] ∪ [0, 2) contains " << i << " is " << boolalpha << a.unionSet(b).contains(i) << "\n";
cout << "[0, 2) ∩ (1, 2] contains " << i << " is " << boolalpha << b.intersect(c).contains(i) << "\n";
cout << "[0, 3) - (0, 1) contains " << i << " is " << boolalpha << d.subtract(e).contains(i) << "\n";
cout << "[0, 3) - [0, 1] contains " << i << " is " << boolalpha << d.subtract(f).contains(i) << "\n";
cout << endl;
}
cout << "[0, 0] is empty is " << boolalpha << g.empty() << "\n";
cout << endl;
RealSet aa(
0.0, 10.0,
[](double x) { return (0.0 < x && x < 10.0) && abs(sin(M_PI * x * x)) > 0.5; }
);
RealSet bb(
0.0, 10.0,
[](double x) { return (0.0 < x && x < 10.0) && abs(sin(M_PI * x)) > 0.5; }
);
auto cc = aa.subtract(bb);
cout << "Approximate length of A - B is " << cc.length() << endl;
return 0;
}
|
http://rosettacode.org/wiki/Sieve_of_Eratosthenes
|
Sieve of Eratosthenes
|
This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.
The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer.
Task
Implement the Sieve of Eratosthenes algorithm, with the only allowed optimization that the outer loop can stop at the square root of the limit, and the inner loop may start at the square of the prime just found.
That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.
If there's an easy way to add such a wheel based optimization, implement it as an alternative version.
Note
It is important that the sieve algorithm be the actual algorithm used to find prime numbers for the task.
Related tasks
Emirp primes
count in factors
prime decomposition
factors of an integer
extensible prime generator
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#8086_Assembly
|
8086 Assembly
|
MAXPRM: equ 5000 ; Change this value for more primes
cpu 8086
bits 16
org 100h
section .text
erato: mov cx,MAXPRM ; Initialize array (set all items to prime)
mov bp,cx ; Keep a copy in BP
mov di,sieve
mov al,1
rep stosb
;;; Sieve
mov bx,sieve ; Set base register to array
inc cx ; CX=1 (CH=0, CL=1); CX was 0 before
mov si,cx ; Start at number 2 (1+1)
.next: inc si ; Next number
cmp cl,[bx+si] ; Is this number marked as prime?
jne .next ; If not, try next number
mov ax,si ; Otherwise, calculate square,
mul si
mov di,ax ; and put it in DI
cmp di,bp ; Check array bounds
ja output ; We're done when SI*SI>MAXPRM
.mark: mov [bx+di],ch ; Mark byte as composite
add di,si ; Next composite
cmp di,bp ; While maximum not reached
jbe .mark
jmp .next
;;; Output
output: mov si,2 ; Start at 2
.test: dec byte [bx+si] ; Prime?
jnz .next ; If not, try next number
mov ax,si ; Otherwise, print number
call prax
.next: inc si
cmp si,MAXPRM
jbe .test
ret
;;; Write number in AX to standard output (using MS-DOS)
prax: push bx ; Save BX
mov bx,numbuf
mov bp,10 ; Divisor
.loop: xor dx,dx ; Divide AX by 10, modulus in DX
div bp
add dl,'0' ; ASCII digit
dec bx
mov [bx],dl ; Store ASCII digit
test ax,ax ; More digits?
jnz .loop
mov dx,bx ; Print number
mov ah,9 ; 9 = MS-DOS syscall to print string
int 21h
pop bx ; Restore BX
ret
section .data
db '*****' ; Room for number
numbuf: db 13,10,'$'
section .bss
sieve: resb MAXPRM
|
http://rosettacode.org/wiki/Sequence_of_primorial_primes
|
Sequence of primorial primes
|
The sequence of primorial primes is given as the increasing values of n where primorial(n) ± 1 is prime.
Noting that the n'th primorial is defined as the multiplication of the smallest n primes, the sequence is of the number of primes, in order that when multiplied together is one-off being a prime number itself.
Task
Generate and show here the first ten values of the sequence.
Optional extended task
Show the first twenty members of the series.
Notes
This task asks for the primorial indices that create the final primorial prime numbers, so there should be no ten-or-more digit numbers in the program output (although extended precision integers will be needed for intermediate results).
There is some confusion in the references, but for the purposes of this task the sequence begins with n = 1.
Probabilistic primality tests are allowed, as long as they are good enough such that the output shown is correct.
Related tasks
Primorial numbers
Factorial
See also
Primorial prime Wikipedia.
Primorial prime from The Prime Glossary.
Sequence A088411 from The On-Line Encyclopedia of Integer Sequences
|
#EchoLisp
|
EchoLisp
|
(lib 'timer) ;; for (every (proc t) interval)
(lib 'bigint)
;; memoize primorial
(define p1000 (cons 1 (primes 1000))) ; remember first 1000 primes
(define (primorial n)
(if(zero? n) 1
(* (list-ref p1000 n) (primorial (1- n)))))
(remember 'primorial)
(define N 0)
;; search one at a time
(define (search t) ;; time parameter, set by (every), not used
(set! N (1+ N))
(if (or (prime? (1+ (primorial N))) (prime? (1- (primorial N))))
(writeln 'HIT N )
(writeln N (date->time-string (current-date )))))
|
http://rosettacode.org/wiki/Sequence_of_primorial_primes
|
Sequence of primorial primes
|
The sequence of primorial primes is given as the increasing values of n where primorial(n) ± 1 is prime.
Noting that the n'th primorial is defined as the multiplication of the smallest n primes, the sequence is of the number of primes, in order that when multiplied together is one-off being a prime number itself.
Task
Generate and show here the first ten values of the sequence.
Optional extended task
Show the first twenty members of the series.
Notes
This task asks for the primorial indices that create the final primorial prime numbers, so there should be no ten-or-more digit numbers in the program output (although extended precision integers will be needed for intermediate results).
There is some confusion in the references, but for the purposes of this task the sequence begins with n = 1.
Probabilistic primality tests are allowed, as long as they are good enough such that the output shown is correct.
Related tasks
Primorial numbers
Factorial
See also
Primorial prime Wikipedia.
Primorial prime from The Prime Glossary.
Sequence A088411 from The On-Line Encyclopedia of Integer Sequences
|
#Factor
|
Factor
|
USING: kernel lists lists.lazy math math.primes prettyprint
sequences ;
: pprime? ( n -- ? )
nprimes product [ 1 + ] [ 1 - ] bi [ prime? ] either? ;
10 1 lfrom [ pprime? ] <lazy-filter> ltake list>array .
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#J
|
J
|
A073916=: {{
if.1 p: y do. (p:^x:)y-1 return.
elseif.1|y do.
f= *:
else.
f=. ]
end. r=.i.0
off=. 1
while. y>#r do.
r=. r,f off+I.y=*/|:1+_ q:f off+i.y
off=. off+y
end.
(y-1){r
}}"0
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#Java
|
Java
|
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
public class SequenceNthNumberWithExactlyNDivisors {
public static void main(String[] args) {
int max = 45;
smallPrimes(max);
for ( int n = 1; n <= max ; n++ ) {
System.out.printf("A073916(%d) = %s%n", n, OEISA073916(n));
}
}
private static List<Integer> smallPrimes = new ArrayList<>();
private static void smallPrimes(int numPrimes) {
smallPrimes.add(2);
for ( int n = 3, count = 0 ; count < numPrimes ; n += 2 ) {
if ( isPrime(n) ) {
smallPrimes.add(n);
count++;
}
}
}
private static final boolean isPrime(long test) {
if ( test == 2 ) {
return true;
}
if ( test % 2 == 0 ) {
return false;
}
for ( long d = 3 ; d*d <= test ; d += 2 ) {
if ( test % d == 0 ) {
return false;
}
}
return true;
}
private static int getDivisorCount(long n) {
int count = 1;
while ( n % 2 == 0 ) {
n /= 2;
count += 1;
}
for ( long d = 3 ; d*d <= n ; d += 2 ) {
long q = n / d;
long r = n % d;
int dc = 0;
while ( r == 0 ) {
dc += count;
n = q;
q = n / d;
r = n % d;
}
count += dc;
}
if ( n != 1 ) {
count *= 2;
}
return count;
}
private static BigInteger OEISA073916(int n) {
if ( isPrime(n) ) {
return BigInteger.valueOf(smallPrimes.get(n-1)).pow(n - 1);
}
int count = 0;
int result = 0;
for ( int i = 1 ; count < n ; i++ ) {
if ( n % 2 == 1 ) {
// The solution for an odd (non-prime) term is always a square number
int sqrt = (int) Math.sqrt(i);
if ( sqrt*sqrt != i ) {
continue;
}
}
if ( getDivisorCount(i) == n ) {
count++;
result = i;
}
}
return BigInteger.valueOf(result);
}
}
|
http://rosettacode.org/wiki/Set_consolidation
|
Set consolidation
|
Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:
The two input sets if no common item exists between the two input sets of items.
The single set that is the union of the two input sets if they share a common item.
Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.
Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}
See also
Connected component (graph theory)
Range consolidation
|
#Egison
|
Egison
|
(define $consolidate
(lambda [$xss]
(match xss (multiset (set char))
{[<cons <cons $m $xs>
<cons <cons ,m $ys>
$rss>>
(consolidate {(unique/m char {m @xs @ys}) @rss})]
[_ xss]})))
(test (consolidate {{'H' 'I' 'K'} {'A' 'B'} {'C' 'D'} {'D' 'B'} {'F' 'G' 'H'}}))
|
http://rosettacode.org/wiki/Set_consolidation
|
Set consolidation
|
Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:
The two input sets if no common item exists between the two input sets of items.
The single set that is the union of the two input sets if they share a common item.
Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.
Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}
See also
Connected component (graph theory)
Range consolidation
|
#Ela
|
Ela
|
open list
merge [] ys = ys
merge (x::xs) ys | x `elem` ys = merge xs ys
| else = merge xs (x::ys)
consolidate (_::[])@xs = xs
consolidate (x::xs) = conso [x] (consolidate xs)
where conso xs [] = xs
conso (x::xs)@r (y::ys) | intersect x y <> [] = conso ((merge x y)::xs) ys
| else = conso (r ++ [y]) ys
|
http://rosettacode.org/wiki/Sequence:_smallest_number_with_exactly_n_divisors
|
Sequence: smallest number with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: nth number with exactly n divisors
See also
OEIS:A005179
|
#Haskell
|
Haskell
|
import Data.List (find, group, sort)
import Data.Maybe (mapMaybe)
import Data.Numbers.Primes (primeFactors)
------------------------- A005179 ------------------------
a005179 :: [Int]
a005179 =
mapMaybe
( \n ->
find
((n ==) . succ . length . properDivisors)
[1 ..]
)
[1 ..]
--------------------------- TEST -------------------------
main :: IO ()
main = print $ take 15 a005179
------------------------- GENERIC ------------------------
properDivisors :: Int -> [Int]
properDivisors =
init
. sort
. foldr
(flip ((<*>) . fmap (*)) . scanl (*) 1)
[1]
. group
. primeFactors
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#NetRexx
|
NetRexx
|
/* NetRexx */
options replace format comments java crossref savelog symbols binary
import java.security.MessageDigest
SHA256('Rosetta code', '764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf')
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method SHA256(messageText, verifyCheck) public static
algorithm = 'SHA-256'
digestSum = getDigest(messageText, algorithm)
say '<Message>'messageText'</Message>'
say Rexx('<'algorithm'>').right(12) || digestSum'</'algorithm'>'
say Rexx('<Verify>').right(12) || verifyCheck'</Verify>'
if digestSum == verifyCheck then say algorithm 'Confirmed'
else say algorithm 'Failed'
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getDigest(messageText = Rexx, algorithm = Rexx 'MD5', encoding = Rexx 'UTF-8', lowercase = boolean 1) public static returns Rexx
algorithm = algorithm.upper
encoding = encoding.upper
message = String(messageText)
messageBytes = byte[]
digestBytes = byte[]
digestSum = Rexx ''
do
messageBytes = message.getBytes(encoding)
md = MessageDigest.getInstance(algorithm)
md.update(messageBytes)
digestBytes = md.digest
loop b_ = 0 to digestBytes.length - 1
bb = Rexx(digestBytes[b_]).d2x(2)
if lowercase then digestSum = digestSum || bb.lower
else digestSum = digestSum || bb.upper
end b_
catch ex = Exception
ex.printStackTrace
end
return digestSum
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#jq
|
jq
|
# The number of prime factors (as in prime factorization)
def numfactors:
. as $num
| reduce range(1; 1 + sqrt|floor) as $i (null;
if ($num % $i) == 0
then ($num / $i) as $r
| if $i == $r then .+1 else .+2 end
else .
end );
# Output: a stream
def A06954:
foreach range(1; infinite) as $i ({k: 0};
.j = .k + 1
| until( $i == (.j | numfactors); .j += 1)
| .k = .j ;
.j ) ;
"First 15 terms of OEIS sequence A069654: ",
[limit(15; A06954)]
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Julia
|
Julia
|
using Primes
function numfactors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, [f*p^j for j in 1:e], init=f)
end
length(f)
end
function A06954(N)
println("First $N terms of OEIS sequence A069654: ")
k = 0
for i in 1:N
j = k
while (j += 1) > 0
if i == numfactors(j)
print("$j ")
k = j
break
end
end
end
end
A06954(15)
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Kotlin
|
Kotlin
|
// Version 1.3.21
const val MAX = 15
fun countDivisors(n: Int): Int {
var count = 0
var i = 1
while (i * i <= n) {
if (n % i == 0) {
count += if (i == n / i) 1 else 2
}
i++
}
return count
}
fun main() {
println("The first $MAX terms of the sequence are:")
var i = 1
var next = 1
while (next <= MAX) {
if (next == countDivisors(i)) {
print("$i ")
next++
}
i++
}
println()
}
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#NetRexx
|
NetRexx
|
/* NetRexx */
options replace format comments java crossref savelog symbols binary
import java.security.MessageDigest
SHA1('Rosetta Code', '48c98f7e5a6e736d790ab740dfc3f51a61abe2b5')
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method SHA1(messageText, verifyCheck) public static
algorithm = 'SHA-1'
digestSum = getDigest(messageText, algorithm)
say '<Message>'messageText'</Message>'
say Rexx('<'algorithm'>').right(12) || digestSum'</'algorithm'>'
say Rexx('<Verify>').right(12) || verifyCheck'</Verify>'
if digestSum == verifyCheck then say algorithm 'Confirmed'
else say algorithm 'Failed'
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method getDigest(messageText = Rexx, algorithm = Rexx 'MD5', encoding = Rexx 'UTF-8', lowercase = boolean 1) public static returns Rexx
algorithm = algorithm.upper
encoding = encoding.upper
message = String(messageText)
messageBytes = byte[]
digestBytes = byte[]
digestSum = Rexx ''
do
messageBytes = message.getBytes(encoding)
md = MessageDigest.getInstance(algorithm)
md.update(messageBytes)
digestBytes = md.digest
loop b_ = 0 to digestBytes.length - 1
bb = Rexx(digestBytes[b_]).d2x(2)
if lowercase then digestSum = digestSum || bb.lower
else digestSum = digestSum || bb.upper
end b_
catch ex = Exception
ex.printStackTrace
end
return digestSum
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#REXX
|
REXX
|
/*REXX program simulates a 7─sided die based on a 5─sided throw for a number of trials. */
parse arg trials sample seed . /*obtain optional arguments from the CL*/
if trials=='' | trials="," then trials= 1 /*Not specified? Then use the default.*/
if sample=='' | sample="," then sample= 1000000 /* " " " " " " */
if datatype(seed, 'W') then call random ,,seed /*Integer? Then use it as a RAND seed.*/
L= length(trials) /* [↑] one million samples to be used.*/
do #=1 for trials; die.= 0 /*performs the number of desired trials*/
k= 0
do until k==sample; r= 5 * random(1, 5) + random(1, 5) - 6
if r>20 then iterate
k= k + 1; r= r // 7 + 1; die.r= die.r + 1
end /*until*/
say
expect= sample % 7
say center('trial:' right(#, L) " " sample 'samples, expect' expect, 80, "─")
do j=1 for 7
say ' side' j "had " die.j ' occurrences',
' difference from expected:'right(die.j - expect, length(sample) )
end /*j*/
end /*#*/ /*stick a fork in it, we're all done. */
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#Ring
|
Ring
|
# Project : Seven-sided dice from five-sided dice
for n = 1 to 20
d = dice7()
see "" + d + " "
next
see nl
func dice7()
x = dice5() * 5 + dice5() - 6
if x > 20
return dice7()
ok
dc = x % 7 + 1
return dc
func dice5()
rnd = random(4) + 1
return rnd
|
http://rosettacode.org/wiki/Show_ASCII_table
|
Show ASCII table
|
Task
Show the ASCII character set from values 32 to 127 (decimal) in a table format.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
|
#J
|
J
|
32}._129}.a.
!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~
NB. A are the decimal ASCII values
[A =: 10 |."1 ] 12 ": |: _16 [\ 32 }. i. 128
32 48 64 80 96 112
33 49 65 81 97 113
34 50 66 82 98 114
35 51 67 83 99 115
36 52 68 84 100 116
37 53 69 85 101 117
38 54 70 86 102 118
39 55 71 87 103 119
40 56 72 88 104 120
41 57 73 89 105 121
42 58 74 90 106 122
43 59 75 91 107 123
44 60 76 92 108 124
45 61 77 93 109 125
46 62 78 94 110 126
47 63 79 95 111 127
NB. B are the corresponding ASCII characters
[B =: |:_16[\32}._128}.a.
0@P`p
!1AQaq
"2BRbr
#3CScs
$4DTdt
%5EUeu
&6FVfv
'7GWgw
(8HXhx
)9IYiy
*:JZjz
+;K[k{
,<L\l|
-=M]m}
.>N^n~
/?O_o�
NB. stuff the characters into the text array of numbers
B [`((4 12 p. i. 6)"_)`]}"1 A
32 48 0 64 @ 80 P 96 ` 112 p
33 ! 49 1 65 A 81 Q 97 a 113 q
34 " 50 2 66 B 82 R 98 b 114 r
35 # 51 3 67 C 83 S 99 c 115 s
36 $ 52 4 68 D 84 T 100 d 116 t
37 % 53 5 69 E 85 U 101 e 117 u
38 & 54 6 70 F 86 V 102 f 118 v
39 ' 55 7 71 G 87 W 103 g 119 w
40 ( 56 8 72 H 88 X 104 h 120 x
41 ) 57 9 73 I 89 Y 105 i 121 y
42 * 58 : 74 J 90 Z 106 j 122 z
43 + 59 ; 75 K 91 [ 107 k 123 {
44 , 60 < 76 L 92 \ 108 l 124 |
45 - 61 = 77 M 93 ] 109 m 125 }
46 . 62 > 78 N 94 ^ 110 n 126 ~
47 / 63 ? 79 O 95 _ 111 o 127 �
|
http://rosettacode.org/wiki/Sierpinski_triangle
|
Sierpinski triangle
|
Task
Produce an ASCII representation of a Sierpinski triangle of order N.
Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Related tasks
Sierpinski triangle/Graphical for graphics images of this pattern.
Sierpinski carpet
|
#PL.2FI
|
PL/I
|
sierpinski: procedure options (main); /* 2010-03-30 */
declare t (79,79) char (1);
declare (i, j, k) fixed binary;
declare (y, xs, ys, xll, xrr, ixrr, limit) fixed binary;
t = ' ';
xs = 40; ys = 1;
/* Make initial triangle */
call make_triangle (xs, ys);
y = ys + 4;
xll = xs-4; xrr = xs+4;
do k = 1 to 3;
limit = 0;
do forever;
ixrr = xrr;
do i = xll to xll+limit by 8;
if t(y-1, i) = ' ' then
do;
call make_triangle (i, y);
if t(y+3,i-5) = '*' then
t(y+3,i-4), t(y+3,ixrr+4) = '*';
call make_triangle (ixrr, y);
end;
ixrr = ixrr - 8;
end;
xll = xll - 4; xrr = xrr + 4;
y = y + 4;
limit = limit + 8;
if xll+limit > xs-1 then leave;
end;
t(y-1,xs) = '*';
end;
/* Finished generation; now print the Sierpinski triangle. */
put edit (t) (skip, (hbound(t,2)) a);
make_triangle: procedure (x, y);
declare (x, y) fixed binary;
declare i fixed binary;
do i = 0 to 3;
t(y+i, x-i), t(y+i, x+i) = '*';
end;
do i = x-2 to x+2; /* The base of the triangle. */
t(y+3, i) = '*';
end;
end make_triangle;
end sierpinski;
|
http://rosettacode.org/wiki/Sierpinski_carpet
|
Sierpinski carpet
|
Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
Related task
Sierpinski triangle
|
#Mathematica.2FWolfram_Language
|
Mathematica/Wolfram Language
|
full={{1,1,1},{1,0,1},{1,1,1}}
empty={{0,0,0},{0,0,0},{0,0,0}}
n=3;
Grid[Nest[ArrayFlatten[#/.{0->empty,1->full}]&,{{1}},n]//.{0->" ",1->"#"}]
|
http://rosettacode.org/wiki/Short-circuit_evaluation
|
Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
|
#ooRexx
|
ooRexx
|
Parse Version v
Say 'Version='v
If a() | b() Then Say 'a and b are true'
If \a() | b() Then Say 'Surprise'
Else Say 'ok'
If a(), b() Then Say 'a is true'
If \a(), b() Then Say 'Surprise'
Else Say 'ok: \a() is false'
Select
When \a(), b() Then Say 'Surprise'
Otherwise Say 'ok: \a() is false (Select)'
End
Exit
a: Say 'a returns .true'; Return .true
b: Say 'b returns 1'; Return 1
|
http://rosettacode.org/wiki/Set_puzzle
|
Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#Wren
|
Wren
|
import "/dynamic" for Enum
import "/trait" for Comparable
import "/fmt" for Fmt
import "/str" for Str
import "/math" for Nums
import "/sort" for Sort
import "random" for Random
var Color = Enum.create("Color", ["RED", "GREEN", "PURPLE"])
var Symbol = Enum.create("Symbol", ["OVAL", "SQUIGGLE", "DIAMOND"])
var Number = Enum.create("Number", ["ONE", "TWO", "THREE"])
var Shading = Enum.create("Shading", ["SOLID", "OPEN", "STRIPED"])
var Degree = Enum.create("Degree", ["BASIC", "ADVANCED"])
class Card is Comparable {
static zero { Card.new(Color.RED, Symbol.OVAL, Number.ONE, Shading.SOLID) }
construct new(color, symbol, number, shading) {
_color = color
_symbol = symbol
_number = number
_shading = shading
_value = color * 27 + symbol * 9 + number * 3 + shading
}
color { _color }
symbol { _symbol }
number { _number }
shading { _shading }
value { _value }
compare(other) { (_value - other.value).sign }
toString {
return Str.lower(Fmt.swrite("$-8s$-10s$-7s$-7s",
Color.members [_color],
Symbol.members [_symbol],
Number.members [_number],
Shading.members[_shading]
))
}
}
var createDeck = Fn.new {
var deck = List.filled(81, null)
for (i in 0...81) {
var col = (i/27).floor
var sym = (i/ 9).floor % 3
var num = (i/ 3).floor % 3
var shd = i % 3
deck[i] = Card.new(col, sym, num, shd)
}
return deck
}
var rand = Random.new()
var isSet = Fn.new { |trio|
var r1 = Nums.sum(trio.map { |c| c.color }) % 3
var r2 = Nums.sum(trio.map { |c| c.symbol }) % 3
var r3 = Nums.sum(trio.map { |c| c.number }) % 3
var r4 = Nums.sum(trio.map { |c| c.shading }) % 3
return r1 + r2 + r3 + r4 == 0
}
var playGame = Fn.new { |degree|
var deck = createDeck.call()
var nCards = (degree == Degree.BASIC) ? 9 : 12
var nSets = (nCards/2).floor
var sets = List.filled(nSets, null)
for (i in 0...nSets) sets[i] = [Card.zero, Card.zero, Card.zero]
var hand = []
while (true) {
rand.shuffle(deck)
hand = deck.take(nCards).toList
var count = 0
var hSize = hand.count
var outer = false
for (i in 0...hSize-2) {
for (j in i+1...hSize-1) {
for (k in j+1...hSize) {
var trio = [hand[i], hand[j], hand[k]]
if (isSet.call(trio)) {
sets[count] = trio
count = count + 1
if (count == nSets) {
outer = true
break
}
}
}
if (outer) break
}
if (outer) break
}
if (outer) break
}
Sort.quick(hand)
System.print("DEALT %(nCards) CARDS:\n")
System.print(hand.join("\n"))
System.print("\nCONTAINING %(nSets) SETS:\n")
for (s in sets) {
Sort.quick(s)
System.print(s.join("\n"))
System.print()
}
}
playGame.call(Degree.BASIC)
System.print()
playGame.call(Degree.ADVANCED)
|
http://rosettacode.org/wiki/Set_of_real_numbers
|
Set of real numbers
|
All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:
[a, b]: {x | a ≤ x and x ≤ b }
(a, b): {x | a < x and x < b }
[a, b): {x | a ≤ x and x < b }
(a, b]: {x | a < x and x ≤ b }
Note that if a = b, of the four only [a, a] would be non-empty.
Task
Devise a way to represent any set of real numbers, for the definition of 'any' in the implementation notes below.
Provide methods for these common set operations (x is a real number; A and B are sets):
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
Test your implementation by checking if numbers 0, 1, and 2 are in any of the following sets:
(0, 1] ∪ [0, 2)
[0, 2) ∩ (1, 2]
[0, 3) − (0, 1)
[0, 3) − [0, 1]
Implementation notes
'Any' real set means 'sets that can be expressed as the union of a finite number of convex real sets'. Cantor's set needs not apply.
Infinities should be handled gracefully; indeterminate numbers (NaN) can be ignored.
You can use your machine's native real number representation, which is probably IEEE floating point, and assume it's good enough (it usually is).
Optional work
Create a function to determine if a given set is empty (contains no element).
Define A = {x | 0 < x < 10 and |sin(π x²)| > 1/2 }, B = {x | 0 < x < 10 and |sin(π x)| > 1/2}, calculate the length of the real axis covered by the set A − B. Note that
|sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.
|
#Clojure
|
Clojure
|
(ns rosettacode.real-set)
(defn >=|<= [lo hi] #(<= lo % hi))
(defn >|< [lo hi] #(< lo % hi))
(defn >=|< [lo hi] #(and (<= lo %) (< % hi)))
(defn >|<= [lo hi] #(and (< lo %) (<= % hi)))
(def ⋃ some-fn)
(def ⋂ every-pred)
(defn ∖
([s1] s1)
([s1 s2]
#(and (s1 %) (not (s2 %))))
([s1 s2 s3]
#(and (s1 %) (not (s2 %)) (not (s3 %))))
([s1 s2 s3 & ss]
(fn [x] (every? #(not (% x)) (list* s1 s2 s3 ss)))))
(clojure.pprint/pprint
(map #(map % [0 1 2])
[(⋃ (>|<= 0 1) (>=|< 0 2))
(⋂ (>=|< 0 2) (>|<= 1 2))
(∖ (>=|< 0 3) (>|< 0 1))
(∖ (>=|< 0 3) (>=|<= 0 1))])
(def ∅ (constantly false))
(def R (constantly true))
(def Z integer?)
(def Q ratio?)
(def I #(∖ R Z Q))
(def N #(∖ Z neg?))
|
http://rosettacode.org/wiki/Set
|
Set
|
Data Structure
This illustrates a data structure, a means of storing data within a program.
You may see other such structures in the Data Structures category.
A set is a collection of elements, without duplicates and without order.
Task
Show each of these set operations:
Set creation
Test m ∈ S -- "m is an element in set S"
A ∪ B -- union; a set of all elements either in set A or in set B.
A ∩ B -- intersection; a set of all elements in both set A and set B.
A ∖ B -- difference; a set of all elements in set A, except those in set B.
A ⊆ B -- subset; true if every element in set A is also in set B.
A = B -- equality; true if every element of set A is in set B and vice versa.
As an option, show some other set operations.
(If A ⊆ B, but A ≠ B, then A is called a true or proper subset of B, written A ⊂ B or A ⊊ B.)
As another option, show how to modify a mutable set.
One might implement a set using an associative array (with set elements as array keys and some dummy value as the values).
One might also implement a set with a binary search tree, or with a hash table, or with an ordered array of binary bits (operated on with bit-wise binary operators).
The basic test, m ∈ S, is O(n) with a sequential list of elements, O(log n) with a balanced binary search tree, or (O(1) average-case, O(n) worst case) with a hash table.
See also
Array
Associative array: Creation, Iteration
Collections
Compound data type
Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
Linked list
Queue: Definition, Usage
Set
Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
Stack
|
#11l
|
11l
|
V s1 = Set([1, 2, 3, 4])
V s2 = Set([3, 4, 5, 6])
print(s1.union(s2))
print(s1.intersection(s2))
print(s1.difference(s2))
print(s1 < s1)
print(Set([3, 1]) < s1)
print(s1 <= s1)
print(Set([3, 1]) <= s1)
print(Set([3, 2, 4, 1]) == s1)
print(s1 == s2)
print(2 C s1)
print(10 !C s1)
print(Set([1, 2, 3, 4, 5]) > s1)
print(Set([1, 2, 3, 4]) > s1)
print(Set([1, 2, 3, 4]) >= s1)
print(s1.symmetric_difference(s2))
print(s1.len)
s1.add(99)
print(s1)
s1.discard(99)
print(s1)
|
http://rosettacode.org/wiki/Send_an_unknown_method_call
|
Send an unknown method call
|
Task
Invoke an object method where the name of the method to be invoked can be generated at run time.
Related tasks
Respond to an unknown method call.
Runtime evaluation
|
#AutoHotkey
|
AutoHotkey
|
obj := {mA: Func("mA"), mB: Func("mB"), mC: Func("mC")}
InputBox, methodToCall, , Which method should I call?
obj[methodToCall].()
mA(){
MsgBox Method A
}
mB(){
MsgBox Method B
}
mC(){
MsgBox Method C
}
|
http://rosettacode.org/wiki/Sieve_of_Eratosthenes
|
Sieve of Eratosthenes
|
This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.
The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer.
Task
Implement the Sieve of Eratosthenes algorithm, with the only allowed optimization that the outer loop can stop at the square root of the limit, and the inner loop may start at the square of the prime just found.
That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.
If there's an easy way to add such a wheel based optimization, implement it as an alternative version.
Note
It is important that the sieve algorithm be the actual algorithm used to find prime numbers for the task.
Related tasks
Emirp primes
count in factors
prime decomposition
factors of an integer
extensible prime generator
primality by trial division
factors of a Mersenne number
trial factoring of a Mersenne number
partition an integer X into N primes
sequence of primes by Trial Division
|
#8th
|
8th
|
with: n
\ create a new buffer which will function as a bit vector
: bit-vec SED: n -- b
dup 3 shr swap 7 band if 1+ then b:new b:clear ;
\ given a buffer, sieving prime, and limit, cross off multiples
\ of the sieving prime.
: +composites SED: b n n -- b
>r dup sqr rot \ want: -- n index b
repeat
over 1- true b:bit!
>r over + r>
over r@ > until!
rdrop nip nip ;
\ SoE algorithm proper
: make-sieve SED: n -- b
dup>r bit-vec 2
repeat
tuck 1- b:bit@ not
if
over r@ +composites
then swap 1+
dup sqr r@ < while!
rdrop drop ;
\ traverse the final buffer, creating an array of primes
: sieve>a SED: b n -- a
>r a:new swap
( 1- b:bit@ not if >r I a:push r> then ) 2 r> loop drop ;
;with
: sieve SED: n -- a
dup make-sieve swap sieve>a ;
|
http://rosettacode.org/wiki/Sequence_of_primorial_primes
|
Sequence of primorial primes
|
The sequence of primorial primes is given as the increasing values of n where primorial(n) ± 1 is prime.
Noting that the n'th primorial is defined as the multiplication of the smallest n primes, the sequence is of the number of primes, in order that when multiplied together is one-off being a prime number itself.
Task
Generate and show here the first ten values of the sequence.
Optional extended task
Show the first twenty members of the series.
Notes
This task asks for the primorial indices that create the final primorial prime numbers, so there should be no ten-or-more digit numbers in the program output (although extended precision integers will be needed for intermediate results).
There is some confusion in the references, but for the purposes of this task the sequence begins with n = 1.
Probabilistic primality tests are allowed, as long as they are good enough such that the output shown is correct.
Related tasks
Primorial numbers
Factorial
See also
Primorial prime Wikipedia.
Primorial prime from The Prime Glossary.
Sequence A088411 from The On-Line Encyclopedia of Integer Sequences
|
#Fortran
|
Fortran
|
PROGRAM PRIMORIALP !Simple enough, with some assistants.
USE PRIMEBAG !Some prime numbers are wanted.
USE BIGNUMBERS !Just so.
TYPE(BIGNUM) B !I'll have one.
INTEGER MAXF !Largest factor to consider by direct division.
PARAMETER (MAXF = 18000000) !Some determination.
INTEGER I !Step stuff.
INTEGER FU,FD !Found factors.
INTEGER NHIT,HIT(666) !A little list.
CHARACTER*4 WOT !A remark.
CHARACTER*66 ALINE !A scratchpad.
REAL T0,T1 !In memory of lost time.
MSG = 6 !Standard output.
WRITE (MSG,1) BIGLIMIT,BIGBASE,HUGE(I) !Announce.
1 FORMAT ('Calculates primorial "primes"',/,
1 "A primorial prime is a value N such that",/,
2 " Primorial(N) - 1 is prime, OR",/,
3 " Primorial(N) + 1 is prime, or both.",/,
4 "and Primorial(N) is the product of the first N prime numbers.",/
5 "Working with up to ",I0," digits in base ",I0,"."/
6 "The integer limit is ",I0,/)
c CALL PREPARE PRIMES !First, catch your rabbit. Via ERATOSTHENES.
IF (.NOT.GRASPPRIMEBAG(66)) STOP "Gan't grab my file!" !Attempt in hope.
WRITE (MSG,2)
2 FORMAT ("Primorial#",3X,"Approx.",8X," -1 Factor +1 Factor Hit")
Commence prime mashing.
100 NHIT = 0 !My list is empty.
B.LAST = 1 !Begin at the beginning.
B.DIGIT(1) = 1 !With one. The same, whatever BIGBASE.
CALL CPU_TIME(T0) !Start the timing.
DO I = 1,30 !69 !Step along the primorials.
CALL BIGMULTN(B,PRIME(I)) !Multiply by the next prime.
c WRITE (MSG,101) I,PRIME(I),I,B.DIGIT(B.LAST:1:-1) !Digits in Arabic/Hindu order.
101 FORMAT ("Prime(",I0,") = ",I0,", Primorial(",I0,") = ", !For a possibly multi-BIGBASE sequence.
1 I0,9I<BIGORDER>.<BIGORDER>,/,(10I<BIGORDER>.<BIGORDER>)) !The first without leading zero digits.
FU = -1 !No factor for up one.
FD = -1 !No factor for down one.
CALL BIGADDN(B,+1) !Go up one.
FU = BIGFACTOR(B,MAXF) !Find a factor, maybe.
CALL BIGADDN(B,-2) !Now test down one.
IF (FU.NE.1) FD = BIGFACTOR(B,MAXF) !But only if FU didn't report "prime".
IF (FU.EQ.1 .OR. FD.EQ.1) THEN !Since if either candidate is a prime,
WOT = "Yes!" !Then a hit.
NHIT = NHIT + 1 !So count up a success.
HIT(NHIT) = I !And append to my list.
ELSE IF (FU.GT.1 .AND. FD.GT.1) THEN !But if both have factors,
WOT = "No." !Then definitely not a hit.
ELSE !Otherwise,
WOT = "?" !I can't decide.
END IF !So much for that candidate.
CALL BIGADDN(B,1) !Recover the original primorial value.
WRITE (ALINE,102) I,BIGVALUE(B),FD,FU,WOT !Prepare a report.
102 FORMAT (I10,1PE18.10,I10,I10,1X,A) !A table.
IF (FD.EQ.-1) ALINE(37:38) = "" !Wasn't looked for, so no remark.
IF (FD.EQ. 0) ALINE(38:38) = "?" !Recode a zero.
IF (FU.EQ. 0) ALINE(48:48) = "?" !Since it represents "Don't know".
WRITE (MSG,"(A)") ALINE !Show the report.
END DO !On to the next prime.
CALL CPU_TIME(T1) !Completed the run.
Cast forth some pearls.
WRITE (MSG,201) HIT(1:NHIT) !The list.
201 FORMAT (/,"Hit list: ",I0,666(",",I0:)) !Don't actually expect so many.
WRITE (MSG,*) "CPU time:",T1 - T0 !The cost.
END !So much for that.
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#jq
|
jq
|
def count(stream): reduce stream as $i (0; .+1);
# To maintain precision:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
def primes: 2, (range(3; infinite; 2) | select(is_prime));
# divisors as an unsorted stream
def divisors:
if . == 1 then 1
else . as $n
| label $out
| range(1; $n) as $i
| ($i * $i) as $i2
| if $i2 > $n then break $out
else if $i2 == $n
then $i
elif ($n % $i) == 0
then $i, ($n/$i)
else empty
end
end
end;
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#Julia
|
Julia
|
using Primes
function countdivisors(n)
f = [one(n)]
for (p, e) in factor(n)
f = reduce(vcat, [f * p ^ j for j in 1:e], init = f)
end
length(f)
end
function nthwithndivisors(N)
parray = findall(primesmask(100 * N))
for i = 1:N
if isprime(i)
println("$i : ", BigInt(parray[i])^(i-1))
else
k = 0
for j in 1:100000000000
if (iseven(i) || Int(floor(sqrt(j)))^2 == j) &&
i == countdivisors(j) && (k += 1) == i
println("$i : $j")
break
end
end
end
end
end
nthwithndivisors(35)
|
http://rosettacode.org/wiki/Sequence:_nth_number_with_exactly_n_divisors
|
Sequence: nth number with exactly n divisors
|
Calculate the sequence where each term an is the nth that has n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A073916
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: smallest number with exactly n divisors
|
#Kotlin
|
Kotlin
|
// Version 1.3.21
import java.math.BigInteger
import kotlin.math.sqrt
const val MAX = 33
fun isPrime(n: Int) = BigInteger.valueOf(n.toLong()).isProbablePrime(10)
fun generateSmallPrimes(n: Int): List<Int> {
val primes = mutableListOf<Int>()
primes.add(2)
var i = 3
while (primes.size < n) {
if (isPrime(i)) {
primes.add(i)
}
i += 2
}
return primes
}
fun countDivisors(n: Int): Int {
var nn = n
var count = 1
while (nn % 2 == 0) {
nn = nn shr 1
count++
}
var d = 3
while (d * d <= nn) {
var q = nn / d
var r = nn % d
if (r == 0) {
var dc = 0
while (r == 0) {
dc += count
nn = q
q = nn / d
r = nn % d
}
count += dc
}
d += 2
}
if (nn != 1) count *= 2
return count
}
fun main() {
var primes = generateSmallPrimes(MAX)
println("The first $MAX terms in the sequence are:")
for (i in 1..MAX) {
if (isPrime(i)) {
var z = BigInteger.valueOf(primes[i - 1].toLong())
z = z.pow(i - 1)
System.out.printf("%2d : %d\n", i, z)
} else {
var count = 0
var j = 1
while (true) {
if (i % 2 == 1) {
val sq = sqrt(j.toDouble()).toInt()
if (sq * sq != j) {
j++
continue
}
}
if (countDivisors(j) == i) {
if (++count == i) {
System.out.printf("%2d : %d\n", i, j)
break
}
}
j++
}
}
}
}
|
http://rosettacode.org/wiki/Set_consolidation
|
Set consolidation
|
Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:
The two input sets if no common item exists between the two input sets of items.
The single set that is the union of the two input sets if they share a common item.
Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.
Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}
See also
Connected component (graph theory)
Range consolidation
|
#Elixir
|
Elixir
|
defmodule RC do
def set_consolidate(sets, result\\[])
def set_consolidate([], result), do: result
def set_consolidate([h|t], result) do
case Enum.find(t, fn set -> not MapSet.disjoint?(h, set) end) do
nil -> set_consolidate(t, [h | result])
set -> set_consolidate([MapSet.union(h, set) | t -- [set]], result)
end
end
end
examples = [[[:A,:B], [:C,:D]],
[[:A,:B], [:B,:D]],
[[:A,:B], [:C,:D], [:D,:B]],
[[:H,:I,:K], [:A,:B], [:C,:D], [:D,:B], [:F,:G,:H]]]
|> Enum.map(fn sets ->
Enum.map(sets, fn set -> MapSet.new(set) end)
end)
Enum.each(examples, fn sets ->
IO.write "#{inspect sets} =>\n\t"
IO.inspect RC.set_consolidate(sets)
end)
|
http://rosettacode.org/wiki/Sequence:_smallest_number_with_exactly_n_divisors
|
Sequence: smallest number with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
Related tasks
Sequence: smallest number greater than previous term with exactly n divisors
Sequence: nth number with exactly n divisors
See also
OEIS:A005179
|
#JavaScript
|
JavaScript
|
(() => {
'use strict';
// a005179 :: () -> [Int]
const a005179 = () =>
fmapGen(
n => find(
compose(
eq(n),
succ,
length,
properDivisors
)
)(enumFrom(1)).Just
)(enumFrom(1));
// ------------------------TEST------------------------
// main :: IO ()
const main = () =>
console.log(
take(15)(
a005179()
)
);
// [1,2,4,6,16,12,64,24,36,48,1024,60,4096,192,144]
// -----------------GENERIC FUNCTIONS------------------
// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});
// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});
// Tuple (,) :: a -> b -> (a, b)
const Tuple = a =>
b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
fs.reduce(
(f, g) => x => f(g(x)),
x => x
);
// enumFrom :: Enum a => a -> [a]
function* enumFrom(x) {
// A non-finite succession of enumerable
// values, starting with the value x.
let v = x;
while (true) {
yield v;
v = succ(v);
}
};
// eq (==) :: Eq a => a -> a -> Bool
const eq = a =>
// True when a and b are equivalent in the terms
// defined below for their shared data type.
b => a === b;
// find :: (a -> Bool) -> Gen [a] -> Maybe a
const find = p => xs => {
const mb = until(tpl => {
const nxt = tpl[0];
return nxt.done || p(nxt.value);
})(
tpl => Tuple(tpl[1].next())(
tpl[1]
)
)(Tuple(xs.next())(xs))[0];
return mb.done ? (
Nothing()
) : Just(mb.value);
}
// fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
const fmapGen = f =>
function*(gen) {
let v = take(1)(gen);
while (0 < v.length) {
yield(f(v[0]))
v = take(1)(gen)
}
};
// group :: [a] -> [[a]]
const group = xs => {
// A list of lists, each containing only equal elements,
// such that the concatenation of these lists is xs.
const go = xs =>
0 < xs.length ? (() => {
const
h = xs[0],
i = xs.findIndex(x => h !== x);
return i !== -1 ? (
[xs.slice(0, i)].concat(go(xs.slice(i)))
) : [xs];
})() : [];
return go(xs);
};
// length :: [a] -> Int
const length = xs =>
// Returns Infinity over objects without finite
// length. This enables zip and zipWith to choose
// the shorter argument when one is non-finite,
// like cycle, repeat etc
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;
// liftA2List :: (a -> b -> c) -> [a] -> [b] -> [c]
const liftA2List = f => xs => ys =>
// The binary operator f lifted to a function over two
// lists. f applied to each pair of arguments in the
// cartesian product of xs and ys.
xs.flatMap(
x => ys.map(f(x))
);
// mul (*) :: Num a => a -> a -> a
const mul = a => b => a * b;
// properDivisors :: Int -> [Int]
const properDivisors = n =>
// The ordered divisors of n,
// excluding n itself.
1 < n ? (
sort(group(primeFactors(n)).reduce(
(a, g) => liftA2List(mul)(a)(
scanl(mul)([1])(g)
),
[1]
)).slice(0, -1)
) : [];
// primeFactors :: Int -> [Int]
const primeFactors = n => {
// A list of the prime factors of n.
const
go = x => {
const
root = Math.floor(Math.sqrt(x)),
m = until(
([q, _]) => (root < q) || (0 === (x % q))
)(
([_, r]) => [step(r), 1 + r]
)(
[0 === x % 2 ? 2 : 3, 1]
)[0];
return m > root ? (
[x]
) : ([m].concat(go(Math.floor(x / m))));
},
step = x => 1 + (x << 2) - ((x >> 1) << 1);
return go(n);
};
// scanl :: (b -> a -> b) -> b -> [a] -> [b]
const scanl = f => startValue => xs =>
xs.reduce((a, x) => {
const v = f(a[0])(x);
return Tuple(v)(a[1].concat(v));
}, Tuple(startValue)([startValue]))[1];
// sort :: Ord a => [a] -> [a]
const sort = xs => xs.slice()
.sort((a, b) => a < b ? -1 : (a > b ? 1 : 0));
// succ :: Enum a => a -> a
const succ = x =>
1 + x;
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n =>
// The first n elements of a list,
// string of characters, or stream.
xs => 'GeneratorFunction' !== xs
.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p => f => x => {
let v = x;
while (!p(v)) v = f(v);
return v;
};
// MAIN ---
return main();
})();
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#NewLISP
|
NewLISP
|
;; using the crypto module from http://www.newlisp.org/code/modules/crypto.lsp.html
;; (import native functions from the crypto library, provided by OpenSSL)
(module "crypto.lsp")
(crypto:sha256 "Rosetta Code")
|
http://rosettacode.org/wiki/SHA-256
|
SHA-256
|
SHA-256 is the recommended stronger alternative to SHA-1. See FIPS PUB 180-4 for implementation details.
Either by using a dedicated library or implementing the algorithm in your language, show that the SHA-256 digest of the string "Rosetta code" is: 764faf5c61ac315f1497f9dfa542713965b785e5cc2f707d6468d7d1124cdfcf
|
#Nim
|
Nim
|
import nimcrypto
echo sha256.digest("Rosetta code")
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Mathematica_.2F_Wolfram_Language
|
Mathematica / Wolfram Language
|
res = {#, DivisorSigma[0, #]} & /@ Range[100000];
highest = 0;
filter = {};
Do[
If[r[[2]] == highest + 1,
AppendTo[filter, r[[1]]];
highest = r[[2]]
]
,
{r, res}
]
Take[filter, 15]
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Nim
|
Nim
|
import strformat
const MAX = 15
func countDivisors(n: int): int =
var i = 1
var count = 0
while i * i <= n:
if n mod i == 0:
if i == n div i:
inc count
else:
inc count, 2
inc i
count
var i, next = 1
echo fmt"The first {MAX} terms of the sequence are:"
while next <= MAX:
if next == countDivisors(i):
write(stdout, fmt"{i} ")
inc next
inc i
write(stdout, "\n")
|
http://rosettacode.org/wiki/Sequence:_smallest_number_greater_than_previous_term_with_exactly_n_divisors
|
Sequence: smallest number greater than previous term with exactly n divisors
|
Calculate the sequence where each term an is the smallest natural number greater than the previous term, that has exactly n divisors.
Task
Show here, on this page, at least the first 15 terms of the sequence.
See also
OEIS:A069654
Related tasks
Sequence: smallest number with exactly n divisors
Sequence: nth number with exactly n divisors
|
#Pascal
|
Pascal
|
program AntiPrimesPlus;
{$IFDEF FPC}
{$MODE Delphi}
{$ELSE}
{$APPTYPE CONSOLE} // delphi
{$ENDIF}
uses
sysutils,math;
const
MAX =32;
function getDividersCnt(n:Uint32):Uint32;
// getDividersCnt by dividing n into its prime factors
// aka n = 2250 = 2^1*3^2*5^3 has (1+1)*(2+1)*(3+1)= 24 dividers
var
divi,quot,deltaRes,rest : Uint32;
begin
result := 1;
//divi := 2; //separat without division
while Not(Odd(n)) do
Begin
n := n SHR 1;
inc(result);
end;
//from now on only odd numbers
divi := 3;
while (sqr(divi)<=n) do
Begin
DivMod(n,divi,quot,rest);
if rest = 0 then
Begin
deltaRes := 0;
repeat
inc(deltaRes,result);
n := quot;
DivMod(n,divi,quot,rest);
until rest <> 0;
inc(result,deltaRes);
end;
inc(divi,2);
end;
//if last factor of n is prime
IF n <> 1 then
result := result*2;
end;
var
T0 : Int64;
i,next,DivCnt: Uint32;
begin
writeln('The first ',MAX,' anti-primes plus are:');
T0:= GetTickCount64;
i := 1;
next := 1;
repeat
DivCnt := getDividersCnt(i);
IF DivCnt= next then
Begin
write(i,' ');
inc(next);
//if next is prime then only prime( => mostly 2 )^(next-1) is solution
IF (next > 4) AND (getDividersCnt(next) = 2) then
i := 1 shl (next-1) -1;// i is incremented afterwards
end;
inc(i);
until Next > MAX;
writeln;
writeln(GetTickCount64-T0,' ms');
end.
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#NewLISP
|
NewLISP
|
;; using the crypto module from http://www.newlisp.org/code/modules/crypto.lsp.html
;; (import native functions from the crypto library, provided by OpenSSL)
(module "crypto.lsp")
(crypto:sha1 "Rosetta Code")
|
http://rosettacode.org/wiki/SHA-1
|
SHA-1
|
SHA-1 or SHA1 is a one-way hash function;
it computes a 160-bit message digest.
SHA-1 often appears in security protocols; for example,
many HTTPS websites use RSA with SHA-1 to secure their connections.
BitTorrent uses SHA-1 to verify downloads.
Git and Mercurial use SHA-1 digests to identify commits.
A US government standard, FIPS 180-1, defines SHA-1.
Find the SHA-1 message digest for a string of octets. You may either call a SHA-1 library, or implement SHA-1 in your language. Both approaches interest Rosetta Code.
Warning: SHA-1 has known weaknesses. Theoretical attacks may find a collision after 252 operations, or perhaps fewer.
This is much faster than a brute force attack of 280 operations. USgovernment deprecated SHA-1.
For production-grade cryptography, users may consider a stronger alternative, such as SHA-256 (from the SHA-2 family) or the upcoming SHA-3.
|
#Nim
|
Nim
|
import std/sha1
echo secureHash("Rosetta Code")
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#Ruby
|
Ruby
|
require './distcheck.rb'
def d5
1 + rand(5)
end
def d7
loop do
d55 = 5*d5 + d5 - 6
return (d55 % 7 + 1) if d55 < 21
end
end
distcheck(1_000_000) {d5}
distcheck(1_000_000) {d7}
|
http://rosettacode.org/wiki/Seven-sided_dice_from_five-sided_dice
|
Seven-sided dice from five-sided dice
|
Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
|
#Scala
|
Scala
|
import scala.util.Random
object SevenSidedDice extends App {
private val rnd = new Random
private def seven = {
var v = 21
def five = 1 + rnd.nextInt(5)
while (v > 20) v = five + five * 5 - 6
1 + v % 7
}
println("Random number from 1 to 7: " + seven)
}
|
http://rosettacode.org/wiki/Show_ASCII_table
|
Show ASCII table
|
Task
Show the ASCII character set from values 32 to 127 (decimal) in a table format.
Other tasks related to string operations:
Metrics
Array length
String length
Copy a string
Empty string (assignment)
Counting
Word frequency
Letter frequency
Jewels and stones
I before E except after C
Bioinformatics/base count
Count occurrences of a substring
Count how many vowels and consonants occur in a string
Remove/replace
XXXX redacted
Conjugate a Latin verb
Remove vowels from a string
String interpolation (included)
Strip block comments
Strip comments from a string
Strip a set of characters from a string
Strip whitespace from a string -- top and tail
Strip control codes and extended characters from a string
Anagrams/Derangements/shuffling
Word wheel
ABC problem
Sattolo cycle
Knuth shuffle
Ordered words
Superpermutation minimisation
Textonyms (using a phone text pad)
Anagrams
Anagrams/Deranged anagrams
Permutations/Derangements
Find/Search/Determine
ABC words
Odd words
Word ladder
Semordnilap
Word search
Wordiff (game)
String matching
Tea cup rim text
Alternade words
Changeable words
State name puzzle
String comparison
Unique characters
Unique characters in each string
Extract file extension
Levenshtein distance
Palindrome detection
Common list elements
Longest common suffix
Longest common prefix
Compare a list of strings
Longest common substring
Find common directory path
Words from neighbour ones
Change e letters to i in words
Non-continuous subsequences
Longest common subsequence
Longest palindromic substrings
Longest increasing subsequence
Words containing "the" substring
Sum of the digits of n is substring of n
Determine if a string is numeric
Determine if a string is collapsible
Determine if a string is squeezable
Determine if a string has all unique characters
Determine if a string has all the same characters
Longest substrings without repeating characters
Find words which contains all the vowels
Find words which contains most consonants
Find words which contains more than 3 vowels
Find words which first and last three letters are equals
Find words which odd letters are consonants and even letters are vowels or vice_versa
Formatting
Substring
Rep-string
Word wrap
String case
Align columns
Literals/String
Repeat a string
Brace expansion
Brace expansion using ranges
Reverse a string
Phrase reversals
Comma quibbling
Special characters
String concatenation
Substring/Top and tail
Commatizing numbers
Reverse words in a string
Suffixation of decimal numbers
Long literals, with continuations
Numerical and alphabetical suffixes
Abbreviations, easy
Abbreviations, simple
Abbreviations, automatic
Song lyrics/poems/Mad Libs/phrases
Mad Libs
Magic 8-ball
99 Bottles of Beer
The Name Game (a song)
The Old lady swallowed a fly
The Twelve Days of Christmas
Tokenize
Text between
Tokenize a string
Word break problem
Tokenize a string with escaping
Split a character string based on change of character
Sequences
Show ASCII table
De Bruijn sequences
Self-referential sequences
Generate lower case ASCII alphabet
|
#Java
|
Java
|
public class ShowAsciiTable {
public static void main(String[] args) {
for ( int i = 32 ; i <= 127 ; i++ ) {
if ( i == 32 || i == 127 ) {
String s = i == 32 ? "Spc" : "Del";
System.out.printf("%3d: %s ", i, s);
}
else {
System.out.printf("%3d: %c ", i, i);
}
if ( (i-1) % 6 == 0 ) {
System.out.println();
}
}
}
}
|
http://rosettacode.org/wiki/Sierpinski_triangle
|
Sierpinski triangle
|
Task
Produce an ASCII representation of a Sierpinski triangle of order N.
Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Related tasks
Sierpinski triangle/Graphical for graphics images of this pattern.
Sierpinski carpet
|
#PL.2FM
|
PL/M
|
100H:
DECLARE ORDER LITERALLY '4';
/* CP/M BDOS CALL */
BDOS: PROCEDURE (FN, ARG);
DECLARE FN BYTE, ARG ADDRESS;
GO TO 5;
END BDOS;
PUT$CHAR: PROCEDURE (CHAR);
DECLARE CHAR BYTE;
CALL BDOS(2, CHAR);
END PUT$CHAR;
/* PRINT SIERPINSKI TRIANGLE */
DECLARE (X, Y, SIZE) BYTE;
SIZE = SHL(1, ORDER);
Y = SIZE - 1;
DO WHILE Y <> -1;
DO X = 0 TO Y;
CALL PUT$CHAR(' ');
END;
DO X = 0 TO SIZE-Y-1;
IF (X AND Y) = 0
THEN CALL PUT$CHAR('*');
ELSE CALL PUT$CHAR(' ');
CALL PUT$CHAR(' ');
END;
Y = Y - 1;
CALL PUT$CHAR(13);
CALL PUT$CHAR(10);
END;
CALL BDOS(0,0);
EOF
|
http://rosettacode.org/wiki/Sierpinski_carpet
|
Sierpinski carpet
|
Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
Related task
Sierpinski triangle
|
#MATLAB
|
MATLAB
|
n = 3;
c = string('#');
for k = 1 : n
c = [c + c + c, c + c.replace('#', ' ') + c, c + c + c];
end
disp(c.join(char(10)))
|
http://rosettacode.org/wiki/Short-circuit_evaluation
|
Short-circuit evaluation
|
Control Structures
These are examples of control structures. You may also be interested in:
Conditional structures
Exceptions
Flow-control structures
Loops
Assume functions a and b return boolean values, and further, the execution of function b takes considerable resources without side effects, and is to be minimized.
If we needed to compute the conjunction (and):
x = a() and b()
Then it would be best to not compute the value of b() if the value of a() is computed as false, as the value of x can then only ever be false.
Similarly, if we needed to compute the disjunction (or):
y = a() or b()
Then it would be best to not compute the value of b() if the value of a() is computed as true, as the value of y can then only ever be true.
Some languages will stop further computation of boolean equations as soon as the result is known, so-called short-circuit evaluation of boolean expressions
Task
Create two functions named a and b, that take and return the same boolean value.
The functions should also print their name whenever they are called.
Calculate and assign the values of the following equations to a variable in such a way that function b is only called when necessary:
x = a(i) and b(j)
y = a(i) or b(j)
If the language does not have short-circuit evaluation, this might be achieved with nested if statements.
|
#Oz
|
Oz
|
declare
fun {A Answer}
AnswerS = {Value.toVirtualString Answer 1 1}
in
{System.showInfo " % Called function {A "#AnswerS#"} -> "#AnswerS}
Answer
end
fun {B Answer}
AnswerS = {Value.toVirtualString Answer 1 1}
in
{System.showInfo " % Called function {B "#AnswerS#"} -> "#AnswerS}
Answer
end
in
for I in [false true] do
for J in [false true] do
X Y
in
{System.showInfo "\nCalculating: X = {A I} andthen {B J}"}
X = {A I} andthen {B J}
{System.showInfo "Calculating: Y = {A I} orelse {B J}"}
Y = {A I} orelse {B J}
end
end
|
http://rosettacode.org/wiki/Set_puzzle
|
Set puzzle
|
Set Puzzles are created with a deck of cards from the Set Game™. The object of the puzzle is to find sets of 3 cards in a rectangle of cards that have been dealt face up.
There are 81 cards in a deck.
Each card contains a unique variation of the following four features: color, symbol, number and shading.
there are three colors:
red, green, purple
there are three symbols:
oval, squiggle, diamond
there is a number of symbols on the card:
one, two, three
there are three shadings:
solid, open, striped
Three cards form a set if each feature is either the same on each card, or is different on each card. For instance: all 3 cards are red, all 3 cards have a different symbol, all 3 cards have a different number of symbols, all 3 cards are striped.
There are two degrees of difficulty: basic and advanced. The basic mode deals 9 cards, that contain exactly 4 sets; the advanced mode deals 12 cards that contain exactly 6 sets.
When creating sets you may use the same card more than once.
Task
Write code that deals the cards (9 or 12, depending on selected mode) from a shuffled deck in which the total number of sets that could be found is 4 (or 6, respectively); and print the contents of the cards and the sets.
For instance:
DEALT 9 CARDS:
green, one, oval, striped
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
red, three, oval, open
red, three, diamond, solid
CONTAINING 4 SETS:
green, one, oval, striped
purple, two, squiggle, open
red, three, diamond, solid
green, one, diamond, open
green, one, diamond, striped
green, one, diamond, solid
green, one, diamond, open
purple, two, squiggle, open
red, three, oval, open
purple, one, diamond, open
purple, two, squiggle, open
purple, three, oval, open
|
#zkl
|
zkl
|
const nDraw=9, nGoal=(nDraw/2); // Basic
var [const] UH=Utils.Helpers; // baked in stash of goodies
deck:=Walker.cproduct("red green purple".split(), // Cartesian product of 4 lists of lists
"one two three".split(), // T(1,2,3) (ie numbers) also works
"oval squiggle diamond".split(),
"solid open striped".split()).walk();
reg draw,sets,N=0;
do{ N+=1;
draw=deck.shuffle()[0,nDraw]; // one draw per shuffle
sets=UH.pickNFrom(3,draw) // 84 sets of 3 cards (each with 4 features)
.filter(fcn(set){ // list of 12 items (== 3 cards)
set[0,4].zip(set[4,4],set[8,4]) // -->4 tuples of 3 features
.pump(List,UH.listUnique,"len", // 1,3 (good) or 2 (bad)
'==(2)) // (F,F,F,F)==good
.sum(0) == 0 // all 4 feature sets good
});
}while(sets.len()!=nGoal);
println("Dealt %d cards %d times:".fmt(draw.len(),N));
draw.pump(Void,fcn(card){ println(("%8s "*4).fmt(card.xplode())) });
println("\nContaining:");
sets.pump(Void,fcn(card){ println((("%8s "*4 + "\n")*3).fmt(card.xplode())) });
|
http://rosettacode.org/wiki/Send_email
|
Send email
|
Task
Write a function to send an email.
The function should have parameters for setting From, To and Cc addresses; the Subject, and the message text, and optionally fields for the server name and login details.
If appropriate, explain what notifications of problems/success are given.
Solutions using libraries or functions from the language are preferred, but failing that, external programs can be used with an explanation.
Note how portable the solution given is between operating systems when multi-OS languages are used.
(Remember to obfuscate any sensitive data used in examples)
|
#Ada
|
Ada
|
with AWS.SMTP, AWS.SMTP.Client, AWS.SMTP.Authentication.Plain;
with Ada.Text_IO;
use Ada, AWS;
procedure Sendmail is
Status : SMTP.Status;
Auth : aliased constant SMTP.Authentication.Plain.Credential :=
SMTP.Authentication.Plain.Initialize ("id", "password");
Isp : SMTP.Receiver;
begin
Isp :=
SMTP.Client.Initialize
("smtp.mail.com",
Port => 5025,
Credential => Auth'Unchecked_Access);
SMTP.Client.Send
(Isp,
From => SMTP.E_Mail ("Me", "[email protected]"),
To => SMTP.E_Mail ("You", "[email protected]"),
Subject => "subject",
Message => "Here is the text",
Status => Status);
if not SMTP.Is_Ok (Status) then
Text_IO.Put_Line
("Can't send message :" & SMTP.Status_Message (Status));
end if;
end Sendmail;
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http://rosettacode.org/wiki/Set_of_real_numbers
|
Set of real numbers
|
All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:
[a, b]: {x | a ≤ x and x ≤ b }
(a, b): {x | a < x and x < b }
[a, b): {x | a ≤ x and x < b }
(a, b]: {x | a < x and x ≤ b }
Note that if a = b, of the four only [a, a] would be non-empty.
Task
Devise a way to represent any set of real numbers, for the definition of 'any' in the implementation notes below.
Provide methods for these common set operations (x is a real number; A and B are sets):
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
Test your implementation by checking if numbers 0, 1, and 2 are in any of the following sets:
(0, 1] ∪ [0, 2)
[0, 2) ∩ (1, 2]
[0, 3) − (0, 1)
[0, 3) − [0, 1]
Implementation notes
'Any' real set means 'sets that can be expressed as the union of a finite number of convex real sets'. Cantor's set needs not apply.
Infinities should be handled gracefully; indeterminate numbers (NaN) can be ignored.
You can use your machine's native real number representation, which is probably IEEE floating point, and assume it's good enough (it usually is).
Optional work
Create a function to determine if a given set is empty (contains no element).
Define A = {x | 0 < x < 10 and |sin(π x²)| > 1/2 }, B = {x | 0 < x < 10 and |sin(π x)| > 1/2}, calculate the length of the real axis covered by the set A − B. Note that
|sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.
|
#Common_Lisp
|
Common Lisp
|
(deftype set== (a b) `(real ,a ,b))
(deftype set<> (a b) `(real (,a) (,b)))
(deftype set=> (a b) `(real ,a (,b)))
(deftype set<= (a b) `(real (,a) ,b))
(deftype set-union (s1 s2) `(or ,s1 ,s2))
(deftype set-intersection (s1 s2) `(and ,s1 ,s2))
(deftype set-diff (s1 s2) `(and ,s1 (not ,s2)))
(defun in-set-p (x set)
(typep x set))
(defun test ()
(let ((set '(set-union (set<= 0 1) (set=> 0 2))))
(assert (in-set-p 0 set))
(assert (in-set-p 1 set))
(assert (not (in-set-p 2 set))))
(let ((set '(set-intersection (set=> 0 2) (set<= 1 2))))
(assert (not (in-set-p 0 set)))
(assert (not (in-set-p 1 set)))
(assert (not (in-set-p 2 set))))
(let ((set '(set-diff (set=> 0 3) (set<> 0 1))))
(assert (in-set-p 0 set))
(assert (in-set-p 1 set))
(assert (in-set-p 2 set)))
(let ((set '(set-diff (set<= 0 3) (set== 0 1))))
(assert (not (in-set-p 0 set)))
(assert (not (in-set-p 1 set)))
(assert (in-set-p 2 set))))
|
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