task_url
stringlengths 30
116
| task_name
stringlengths 2
86
| task_description
stringlengths 0
14.4k
| language_url
stringlengths 2
53
| language_name
stringlengths 1
52
| code
stringlengths 0
61.9k
|
|---|---|---|---|---|---|
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Simula | Simula | BEGIN
END |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Slate | Slate | |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | primes = Prime[Range[10^7]];
gaps = {Differences[primes], Most[primes]} // Transpose;
tmp = GatherBy[gaps, First][[All, 1]];
tmp = SortBy[tmp, First];
starts = Association[Rule @@@ tmp];
set = {Most[tmp[[All, 1]]], Abs@Differences[tmp[[All, 2]]]} // Transpose;
data = Table[{n, k} = SelectFirst[set, Last/*GreaterThan[10^i]];
{10^i, n, starts[n], n + 2, starts[n + 2], k}, {i, 1, 7}];
StringTemplate["Earliest difference > `` between adjacent prime gap starting primes:
Gap `` starts at ``, gap `` starts at ``, difference is ``."]/*Print @@@ data; |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Pascal | Pascal | program primesieve;
// sieving small ranges of 65536
//{$O+,R+}
{$IFDEF FPC}
{$MODE DELPHI}{$OPTIMIZATION ON,ALL}{$CODEALIGN proc=32}
uses
sysutils;
{$ENDIF}
{$IFDEF WINDOWS}
{$APPTYPE CONSOLE}
{$ENDIF}
const
smlPrimes :array [0..10] of Byte = (2,3,5,7,11,13,17,19,23,29,31);
maxPreSievePrime = 17;
sieveSize = 1 shl 15;//32768*2 ->max count of FoundPrimes = 6542
type
tSievePrim = record
svdeltaPrime:word;//diff between actual and new prime
svSivOfs:word;//-> sieveSize< 1 shl 16
svSivNum:LongWord;// 1 shl (16+32) = 2.8e14
end;
var
{$Align 16}
//primes up to 1E6-> sieving to 1E12
sievePrimes : array[0..78497] of tSievePrim;
{$Align 16}
preSieve :array[0..3*5*7*11*13*17-1] of Byte;
{$Align 16}
Sieve :array[0..sieveSize-1] of Byte;
{$Align 16}
FoundPrimes : array[0..6542] of LongWord;
{$Align 16}
Gaps : array[0..255] Of Uint64;
{$Align 16}
Limit,OffSet : Uint64;
SieveMaxIdx,
preSieveOffset,
SieveNum,
FoundPrimesCnt,
PrimPos,
LastInsertedSievePrime :NativeUInt;
procedure CopyPreSieveInSieve;forward;
procedure CollectPrimes;forward;
procedure sieveOneSieve;forward;
procedure preSieveInit;
var
i,pr,j,umf : NativeInt;
Begin
fillchar(preSieve[0],SizeOf(preSieve),#1);
i := 1;// starts with pr = 3
umf := 1;
repeat
IF preSieve[i] <> 0 then
Begin
pr := 2*i+1;
j := i;
repeat
preSieve[j] := 0;
inc(j,pr);
until j> High(preSieve);
umf := umf*pr;
end;
inc(i);
until umf>High(preSieve);
preSieveOffset := 0;
end;
procedure CalcSievePrimOfs(lmt:NativeUint);
var
i,pr : NativeUInt;
sq : Uint64;
begin
pr := 0;
i := 0;
repeat
with sievePrimes[i] do
Begin
pr := pr+svdeltaPrime;
IF sqr(pr) < (SieveSize*2) then
Begin
svSivNum := 0;
svSivOfs := (pr*pr-1) DIV 2;
end
else
Begin
SieveMaxIdx := i;
pr := pr-svdeltaPrime;
BREAK;
end;
end;
inc(i);
until i > lmt;
for i := i to lmt do
begin
with sievePrimes[i] do
Begin
pr := pr+svdeltaPrime;
sq := sqr(pr);
svSivNum := sq DIV (2*SieveSize);
svSivOfs := ( (sq - Uint64(svSivNum)*(2*SieveSize))-1)DIV 2;
end;
end;
end;
procedure InitSieve;
begin
preSieveOffset := 0;
SieveNum :=0;
CalcSievePrimOfs(PrimPos-1);
end;
procedure InsertSievePrimes;
var
j :NativeUINt;
i,pr : NativeUInt;
begin
i := 0;
//ignore first primes already sieved with
if SieveNum = 0 then
repeat
inc(i);
until FoundPrimes[i] > maxPreSievePrime;
pr :=0;
j := Uint64(SieveNum)*SieveSize*2-LastInsertedSievePrime;
with sievePrimes[PrimPos] do
Begin
pr := FoundPrimes[i];
svdeltaPrime := pr+j;
j := pr;
end;
inc(PrimPos);
for i := i+1 to FoundPrimesCnt-1 do
Begin
IF PrimPos > High(sievePrimes) then
BREAK;
with sievePrimes[PrimPos] do
Begin
pr := FoundPrimes[i];
svdeltaPrime := (pr-j);
j := pr;
end;
inc(PrimPos);
end;
LastInsertedSievePrime :=Uint64(SieveNum)*(SieveSize*2)+pr;
end;
procedure sievePrimesInit;
var
i,j,pr:NativeInt;
Begin
LastInsertedSievePrime := 0;
PrimPos := 0;
preSieveOffset := 0;
SieveNum :=0;
CopyPreSieveInSieve;
i := 1; // start with 3
repeat
while Sieve[i] = 0 do
inc(i);
pr := 2*i+1;
inc(i);
j := ((pr*pr)-1) DIV 2;
if j > High(Sieve) then
BREAK;
repeat
Sieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
until false;
CollectPrimes;
InsertSievePrimes;
IF PrimPos < High(sievePrimes) then
Begin
InitSieve;
//Erste Sieb nochmals, aber ohne Eintrag
CopyPreSieveInSieve;
sieveOneSieve;
repeat
inc(SieveNum);
CopyPreSieveInSieve;
sieveOneSieve;
CollectPrimes;
InsertSievePrimes;
until PrimPos > High(sievePrimes);
end;
end;
procedure OutGaps(g1,g2,delta:NativeUint);
begin
if g2= 0 then
writeln(2*g1:4,2*g1+2:4,delta:13,Gaps[g1]:13,Gaps[g1+1]:13)
else
writeln(2*g2-1:4,2*g1:4,delta:13,Gaps[g1-1]:13,Gaps[g1]:13);
end;
function GetDiffval(val1,val2: NativeInt): NativeInt;
begin
if val1*val2 = 0 then
EXIT(0);
dec(val1,val2);
if val1<0 then
val1 :=-val1;
GetDiffval := val1;
end;
procedure CheckGaps;
var
val1,val2,val3,i,DekaLimit : NativeInt;
Begin
writeln('Gap1 Gap2 difference first second prime');
dekaLimit := 10;
i := 1;
repeat
val1 := Gaps[i];
if val1 <> 0 then
Begin
val2 := GetDiffval(val1,Gaps[i-1]);
val3 := GetDiffval(val1,Gaps[i+1]);
while (val2>DekaLimit) or (val3>DekaLimit) do
begin
writeln(DekaLimit:21,'<');
if val2 = 0 then
begin
if val3 > 0 then
OutGaps(i,0,val3);
end
else
begin
if val3 = 0 then
OutGaps(i,1,val2)
else
Begin
if val3 > val2 then
OutGaps(i,0,val3)
else
OutGaps(i,1,val2);
end;
end;
DekaLimit := 10*DekaLimit;
end;
end;
inc(i);
until i>=254;
end;
procedure CopyPreSieveInSieve;
var
lmt : NativeInt;
Begin
lmt := preSieveOffset+sieveSize;
lmt := lmt-(High(preSieve)+1);
IF lmt<= 0 then
begin
Move(preSieve[preSieveOffset],Sieve[0],sieveSize);
if lmt <> 0 then
inc(preSieveOffset,sieveSize)
else
preSieveOffset := 0;
end
else
begin
Move(preSieve[preSieveOffset],Sieve[0],sieveSize-lmt);
Move(preSieve[0],Sieve[sieveSize-lmt],lmt);
preSieveOffset := lmt
end;
end;
procedure CollectPrimes;
var
pSieve : pbyte;
pFound : pLongWord;
i,idx : NativeInt;
Begin
pFound := @FoundPrimes[0];
idx := 0;
i := 0;
IF SieveNum = 0 then
Begin
repeat
pFound[idx] := smlPrimes[idx];
inc(idx);
until smlPrimes[idx]>maxPreSievePrime;
i := (smlPrimes[idx] -1) DIV 2;
end;
pSieve := @Sieve[0];
repeat
pFound[idx]:= 2*i+1;
inc(idx,pSieve[i]);
inc(i);
until i>High(Sieve);
FoundPrimesCnt:= idx;
end;
procedure sieveOneSieve;
var
i,j,pr,dSievNum :NativeUint;
Begin
pr := 0;
For i := 0 to SieveMaxIdx do
with sievePrimes[i] do
begin
pr := pr+svdeltaPrime;
IF svSivNum = sieveNum then
Begin
j := svSivOfs;
repeat
Sieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
dSievNum := j DIV SieveSize;
svSivOfs := j-dSievNum*SieveSize;
inc(svSivNum,dSievNum);
end;
end;
i := SieveMaxIdx+1;
repeat
if i > High(SievePrimes) then
BREAK;
with sievePrimes[i] do
begin
if svSivNum > sieveNum then
Begin
SieveMaxIdx := I-1;
Break;
end;
pr := pr+svdeltaPrime;
j := svSivOfs;
repeat
Sieve[j] := 0;
inc(j,pr);
until j > High(Sieve);
dSievNum := j DIV SieveSize;
svSivOfs := j-dSievNum*SieveSize;
inc(svSivNum,dSievNum);
inc(i);
end;
until false;
end;
var
T1,T0,CNT,ActPrime,LastPrime,delta : Int64;
i: Int32;
begin
T0 := GetTickCount64;
Limit := 10*1000*1000*1000;//158*1000*1000*1000;
preSieveInit;
sievePrimesInit;
InitSieve;
offset := 0;
Cnt := 1;//==2
LastPrime := 2;
repeat
CopyPreSieveInSieve;sieveOneSieve;CollectPrimes;
inc(Cnt,FoundPrimesCnt);
//collect first occurrence of gap
i := 0;
repeat
ActPrime := Offset+FoundPrimes[i];
delta := (ActPrime - LastPrime) shr 1;
If Gaps[delta] = 0 then
Gaps[delta] := LastPrime;
LastPrime := ActPrime;
inc(i);
until (i >= FoundPrimesCnt);
inc(SieveNum);
inc(offset,2*SieveSize);
until SieveNum > (Limit DIV (2*SieveSize));
CheckGaps;
T1 := GetTickCount64;
OffSet := Uint64(SieveNum-1)*(2*SieveSize);
i := FoundPrimesCnt;
repeat
dec(i);
dec(cnt);
until (i = 0) OR (OffSet+FoundPrimes[i]<Limit);
writeln;
writeln(cnt,' in ',Limit,' takes ',T1-T0,' ms');
{$IFDEF WINDOWS}
writeln('Press <Enter>');readln;
{$ENDIF}
end. |
http://rosettacode.org/wiki/Element-wise_operations | Element-wise operations | This task is similar to:
Matrix multiplication
Matrix transposition
Task
Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.
Implement:
addition
subtraction
multiplication
division
exponentiation
Extend the task if necessary to include additional basic operations, which should not require their own specialised task.
| #C.23 | C# | using System;
using System.Collections.Generic;
using System.Linq;
public static class ElementWiseOperations
{
private static readonly Dictionary<string, Func<double, double, double>> operations =
new Dictionary<string, Func<double, double, double>> {
{ "add", (a, b) => a + b },
{ "sub", (a, b) => a - b },
{ "mul", (a, b) => a * b },
{ "div", (a, b) => a / b },
{ "pow", (a, b) => Math.Pow(a, b) }
};
private static readonly Func<double, double, double> nothing = (a, b) => a;
public static double[,] DoOperation(this double[,] m, string name, double[,] other) =>
DoOperation(m, operations.TryGetValue(name, out var operation) ? operation : nothing, other);
public static double[,] DoOperation(this double[,] m, Func<double, double, double> operation, double[,] other) {
if (m == null || other == null) throw new ArgumentNullException();
int rows = m.GetLength(0), columns = m.GetLength(1);
if (rows != other.GetLength(0) || columns != other.GetLength(1)) {
throw new ArgumentException("Matrices have different dimensions.");
}
double[,] result = new double[rows, columns];
for (int r = 0; r < rows; r++) {
for (int c = 0; c < columns; c++) {
result[r, c] = operation(m[r, c], other[r, c]);
}
}
return result;
}
public static double[,] DoOperation(this double[,] m, string name, double number) =>
DoOperation(m, operations.TryGetValue(name, out var operation) ? operation : nothing, number);
public static double[,] DoOperation(this double[,] m, Func<double, double, double> operation, double number) {
if (m == null) throw new ArgumentNullException();
int rows = m.GetLength(0), columns = m.GetLength(1);
double[,] result = new double[rows, columns];
for (int r = 0; r < rows; r++) {
for (int c = 0; c < columns; c++) {
result[r, c] = operation(m[r, c], number);
}
}
return result;
}
public static void Print(this double[,] m) {
if (m == null) throw new ArgumentNullException();
int rows = m.GetLength(0), columns = m.GetLength(1);
for (int r = 0; r < rows; r++) {
Console.WriteLine("[ " + string.Join(", ", Enumerable.Range(0, columns).Select(c => m[r, c])) + " ]");
}
}
}
public class Program
{
public static void Main() {
double[,] matrix = {
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 }
};
double[,] tens = {
{ 10, 10, 10, 10 },
{ 20, 20, 20, 20 },
{ 30, 30, 30, 30 }
};
matrix.Print();
WriteLine();
(matrix = matrix.DoOperation("add", tens)).Print();
WriteLine();
matrix.DoOperation((a, b) => b - a, 100).Print();
}
} |
http://rosettacode.org/wiki/Egyptian_division | Egyptian division | Egyptian division is a method of dividing integers using addition and
doubling that is similar to the algorithm of Ethiopian multiplication
Algorithm:
Given two numbers where the dividend is to be divided by the divisor:
Start the construction of a table of two columns: powers_of_2, and doublings; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
Continue with successive i’th rows of 2^i and 2^i * divisor.
Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
We now assemble two separate sums that both start as zero, called here answer and accumulator
Consider each row of the table, in the reverse order of its construction.
If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).
Example: 580 / 34
Table creation:
powers_of_2
doublings
1
34
2
68
4
136
8
272
16
544
Initialization of sums:
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
0
0
Considering table rows, bottom-up:
When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
16
544
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
16
544
4
136
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
17
578
2
68
4
136
8
272
16
544
Answer
So 580 divided by 34 using the Egyptian method is 17 remainder (578 - 580) or 2.
Task
The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.
Functions should be clear interpretations of the algorithm.
Use the function to divide 580 by 34 and show the answer here, on this page.
Related tasks
Egyptian fractions
References
Egyptian Number System
| #AutoHotkey | AutoHotkey | divident := 580
divisor := 34
answer := accumulator := 0
obj := [] , div := divisor
while (div < divident)
{
obj[2**(A_Index-1)] := div ; obj[powers_of_2] := doublings
div *= 2 ; double up
}
while obj.MaxIndex() ; iterate rows "in the reverse order"
{
if (accumulator + obj[obj.MaxIndex()] <= divident) ; If (accumulator + current doubling) <= dividend
{
accumulator += obj[obj.MaxIndex()] ; add current doubling to the accumulator
answer += obj.MaxIndex() ; add the powers_of_2 value to the answer.
}
obj.pop() ; remove current row
}
MsgBox % divident "/" divisor " = " answer ( divident-accumulator > 0 ? " r" divident-accumulator : "") |
http://rosettacode.org/wiki/Egyptian_fractions | Egyptian fractions | An Egyptian fraction is the sum of distinct unit fractions such as:
1
2
+
1
3
+
1
16
(
=
43
48
)
{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{16}}\,(={\tfrac {43}{48}})}
Each fraction in the expression has a numerator equal to 1 (unity) and a denominator that is a positive integer, and all the denominators are distinct (i.e., no repetitions).
Fibonacci's Greedy algorithm for Egyptian fractions expands the fraction
x
y
{\displaystyle {\tfrac {x}{y}}}
to be represented by repeatedly performing the replacement
x
y
=
1
⌈
y
/
x
⌉
+
(
−
y
)
mod
x
y
⌈
y
/
x
⌉
{\displaystyle {\frac {x}{y}}={\frac {1}{\lceil y/x\rceil }}+{\frac {(-y)\!\!\!\!\mod x}{y\lceil y/x\rceil }}}
(simplifying the 2nd term in this replacement as necessary, and where
⌈
x
⌉
{\displaystyle \lceil x\rceil }
is the ceiling function).
For this task, Proper and improper fractions must be able to be expressed.
Proper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that
a
<
b
{\displaystyle a<b}
, and
improper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that a ≥ b.
(See the REXX programming example to view one method of expressing the whole number part of an improper fraction.)
For improper fractions, the integer part of any improper fraction should be first isolated and shown preceding the Egyptian unit fractions, and be surrounded by square brackets [n].
Task requirements
show the Egyptian fractions for:
43
48
{\displaystyle {\tfrac {43}{48}}}
and
5
121
{\displaystyle {\tfrac {5}{121}}}
and
2014
59
{\displaystyle {\tfrac {2014}{59}}}
for all proper fractions,
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive one-or two-digit (decimal) integers, find and show an Egyptian fraction that has:
the largest number of terms,
the largest denominator.
for all one-, two-, and three-digit integers, find and show (as above). {extra credit}
Also see
Wolfram MathWorld™ entry: Egyptian fraction
| #C.23 | C# | using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
namespace EgyptianFractions {
class Program {
class Rational : IComparable<Rational>, IComparable<int> {
public BigInteger Num { get; }
public BigInteger Den { get; }
public Rational(BigInteger n, BigInteger d) {
var c = Gcd(n, d);
Num = n / c;
Den = d / c;
if (Den < 0) {
Num = -Num;
Den = -Den;
}
}
public Rational(BigInteger n) {
Num = n;
Den = 1;
}
public override string ToString() {
if (Den == 1) {
return Num.ToString();
} else {
return string.Format("{0}/{1}", Num, Den);
}
}
public Rational Add(Rational rhs) {
return new Rational(Num * rhs.Den + rhs.Num * Den, Den * rhs.Den);
}
public Rational Sub(Rational rhs) {
return new Rational(Num * rhs.Den - rhs.Num * Den, Den * rhs.Den);
}
public int CompareTo(Rational rhs) {
var ad = Num * rhs.Den;
var bc = Den * rhs.Num;
return ad.CompareTo(bc);
}
public int CompareTo(int rhs) {
var ad = Num * rhs;
var bc = Den * rhs;
return ad.CompareTo(bc);
}
}
static BigInteger Gcd(BigInteger a, BigInteger b) {
if (b == 0) {
if (a < 0) {
return -a;
} else {
return a;
}
} else {
return Gcd(b, a % b);
}
}
static List<Rational> Egyptian(Rational r) {
List<Rational> result = new List<Rational>();
if (r.CompareTo(1) >= 0) {
if (r.Den == 1) {
result.Add(r);
result.Add(new Rational(0));
return result;
}
result.Add(new Rational(r.Num / r.Den));
r = r.Sub(result[0]);
}
BigInteger modFunc(BigInteger m, BigInteger n) {
return ((m % n) + n) % n;
}
while (r.Num != 1) {
var q = (r.Den + r.Num - 1) / r.Num;
result.Add(new Rational(1, q));
r = new Rational(modFunc(-r.Den, r.Num), r.Den * q);
}
result.Add(r);
return result;
}
static string FormatList<T>(IEnumerable<T> col) {
StringBuilder sb = new StringBuilder();
var iter = col.GetEnumerator();
sb.Append('[');
if (iter.MoveNext()) {
sb.Append(iter.Current);
}
while (iter.MoveNext()) {
sb.AppendFormat(", {0}", iter.Current);
}
sb.Append(']');
return sb.ToString();
}
static void Main() {
List<Rational> rs = new List<Rational> {
new Rational(43, 48),
new Rational(5, 121),
new Rational(2014, 59)
};
foreach (var r in rs) {
Console.WriteLine("{0} => {1}", r, FormatList(Egyptian(r)));
}
var lenMax = Tuple.Create(0UL, new Rational(0));
var denomMax = Tuple.Create(BigInteger.Zero, new Rational(0));
var query = (from i in Enumerable.Range(1, 100)
from j in Enumerable.Range(1, 100)
select new Rational(i, j))
.Distinct()
.ToList();
foreach (var r in query) {
var e = Egyptian(r);
ulong eLen = (ulong) e.Count;
var eDenom = e.Last().Den;
if (eLen > lenMax.Item1) {
lenMax = Tuple.Create(eLen, r);
}
if (eDenom > denomMax.Item1) {
denomMax = Tuple.Create(eDenom, r);
}
}
Console.WriteLine("Term max is {0} with {1} terms", lenMax.Item2, lenMax.Item1);
var dStr = denomMax.Item1.ToString();
Console.WriteLine("Denominator max is {0} with {1} digits {2}...{3}", denomMax.Item2, dStr.Length, dStr.Substring(0, 5), dStr.Substring(dStr.Length - 5, 5));
}
}
} |
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Perl | Perl | $str = "eertree";
for $n (1 .. length($str)) {
for $m (1 .. length($str)) {
$strrev = "";
$strpal = substr($str, $n-1, $m);
if ($strpal ne "") {
for $p (reverse 1 .. length($strpal)) {
$strrev .= substr($strpal, $p-1, 1);
}
($strpal eq $strrev) and push @pal, $strpal;
}
}
}
print join ' ', grep {not $seen{$_}++} @pal, "\n"; |
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #Quackery | Quackery | [ 1 & not ] is even ( n --> b )
[ 1 << ] is double ( n --> n )
[ 1 >> ] is halve ( n --> n )
[ dup 0 < unrot abs
[ dup 0 = iff nip done
over double over halve
recurse
swap even
iff nip else + ]
swap if negate ] is e* ( n n --> n ) |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #EchoLisp | EchoLisp |
(lib 'types) ;; int32 vectors
(lib 'plot)
(define-constant BIT0 0)
(define-constant BIT1 (rgb 0.8 0.9 0.7)) ;; colored bit 1
;; integer to pattern
(define ( n->pat n)
(for/vector ((i 8))
#:when (bitwise-bit-set? n i)
(for/vector ((j (in-range 2 -1 -1)))
(if (bitwise-bit-set? i j) BIT1 BIT0 ))))
;; test if three pixels match a pattern
(define (pmatch a b c pat)
(for/or ((v pat))
(and (= a (vector-ref v 0)) (= b (vector-ref v 1)) (= c (vector-ref v 2)) )))
;; next generation = next row
(define (generate x0 width PAT PIX (x))
(for ((dx (in-range 0 width)))
(set! x (+ x0 dx))
(vector-set! PIX (+ x width) ;; next row
(if
(pmatch
(vector-ref PIX (if (zero? dx) (+ x0 width) (1- x))) ;; let's wrap
(vector-ref PIX x)
(vector-ref PIX (if (= dx (1- width)) x0 (1+ x)))
PAT)
BIT1 BIT0))))
;; n is the pattern, starters in the number of set pixels at generation 0
(define (task n (starters 1))
(define width (first (plot-size)))
(define height (rest (plot-size)))
(define PAT (n->pat n))
(plot-clear)
(define PIX (pixels->int32-vector))
(init-pix starters width height PIX)
(for ((y (1- height)))
(generate (* y width) width PAT into: PIX))
(vector->pixels PIX))
;; put n starters on first row
(define (init-pix starters width height PIX)
(define dw (floor (/ width (1+ starters))))
(for ((x (in-range dw width (1+ dw))))
(vector-set! PIX x BIT1)))
;; usage
(task 99 3) → 672400 ;; ESC to see it
(task 22) → 672400
;; check pattern generator
(n->pat 13)
→ #( #( 0 0 0) #( 0 -5052980 0) #( 0 -5052980 -5052980))
|
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #Tcl | Tcl | proc ifact n {
for {set i $n; set sum 1} {$i >= 2} {incr i -1} {
set sum [expr {$sum * $i}]
}
return $sum
} |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #.E0.AE.89.E0.AE.AF.E0.AE.BF.E0.AE.B0.E0.AF.8D.2FUyir | உயிர்/Uyir | முதன்மை என்பதின் வகை எண் பணி {{
எ இன் வகை எண்{$5} = 0;
படை வகை சரம்;
"எண்ணைக் கொடுங்கள்? ") ஐ திரை.இடு;
எ = எண்{$5} ஐ விசை.எடு;
ஒருக்கால் (எ.இருமம்(0) == 1) ஆகில் {
படை = "ஒற்றை";
} இல்லையேல் {
படை = "இரட்டை ";
}
{எ, " ஒரு ", படை, "ப்படை எண் ஆகும்"} என்பதை திரை.இடு;
முதன்மை = 0;
}}; |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #VBA | VBA | 4 ways = 4 Functions :
IsEven ==> Use the even and odd predicates
IsEven2 ==> Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even
IsEven3 ==> Divide i by 2. The remainder equals 0 if i is even.
IsEven4 ==> Use modular congruences |
http://rosettacode.org/wiki/Echo_server | Echo server | Create a network service that sits on TCP port 12321, which accepts connections on that port, and which echoes complete lines (using a carriage-return/line-feed sequence as line separator) back to clients. No error handling is required. For the purposes of testing, it is only necessary to support connections from localhost (127.0.0.1 or perhaps ::1). Logging of connection information to standard output is recommended.
The implementation must be able to handle simultaneous connections from multiple clients. A multi-threaded or multi-process solution may be used. Each connection must be able to echo more than a single line.
The implementation must not stop responding to other clients if one client sends a partial line or stops reading responses.
| #Factor | Factor | USING: accessors io io.encodings.utf8 io.servers io.sockets threads ;
IN: rosetta.echo
CONSTANT: echo-port 12321
: handle-client ( -- )
[ print flush ] each-line ;
: <echo-server> ( -- threaded-server )
utf8 <threaded-server>
"echo server" >>name
echo-port >>insecure
[ handle-client ] >>handler ;
: start-echo-server ( -- )
<echo-server> [ start-server ] in-thread start-server drop ;
|
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #XPL0 | XPL0 | code Text=12;
string 0; \use zero-terminated convention, instead of MSb set
char S;
[S:= ""; \assign an empty string
if S(0) = 0 then Text(0, "empty
");
S:= "Hello";
if S(0) # 0 then Text(0, "not empty
");
] |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #Z80_Assembly | Z80 Assembly | EmptyString:
byte 0 |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Smalltalk | Smalltalk | [] |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #SNOBOL4 | SNOBOL4 | end |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #SNUSP | SNUSP | $#
|
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Perl | Perl | #!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Earliest_difference_between_prime_gaps
use warnings;
use ntheory qw( primes );
my @gaps;
my $primeref = primes( 1e9 );
for my $i ( 2 .. $#$primeref )
{
my $diff = $primeref->[$i] - $primeref->[$i - 1];
$gaps[ $diff >> 1 ] //= $primeref->[$i - 1];
}
my %first;
for my $i ( 1 .. $#gaps )
{
defined $gaps[$i] && defined $gaps[$i-1] or next;
my $diff = abs $gaps[$i] - $gaps[$i-1];
for my $m ( map 10 ** $_, 1 .. 10 )
{
$diff > $m and !$first{$m}++ and
print "above $m gap @{[$i * 2 - 2 ]} abs( $gaps[$i-1] - $gaps[$i] )\n";
}
} |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Phix | Phix | with javascript_semantics
constant limit = iff(platform()=JS?1e7:1e8),
gslim = 250
sequence primes = get_primes_le(limit*4),
gapstarts = repeat(0,gslim)
for i=2 to length(primes) do
integer gap = primes[i]-primes[i-1]
if gapstarts[gap]=0 then
gapstarts[gap] = primes[i-1]
end if
end for
integer pm = 10, gap1 = 2
while true do
while gapstarts[gap1]=0 do gap1 += 2 end while
integer start1 = gapstarts[gap1],
gap2 = gap1 + 2
if gapstarts[gap2]=0 then
gap1 = gap2 + 2
else
integer start2 = gapstarts[gap2],
diff = abs(start2 - start1)
if diff>pm then
printf(1,"Earliest difference >%,d between adjacent prime gap starting primes:\n",{pm})
printf(1,"Gap %d starts at %,d, gap %d starts at %,d, difference is %,d.\n\n",
{gap1, start1, gap2, start2, diff})
if pm=limit then exit end if
pm *= 10
else
gap1 = gap2
end if
end if
end while
|
http://rosettacode.org/wiki/Element-wise_operations | Element-wise operations | This task is similar to:
Matrix multiplication
Matrix transposition
Task
Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.
Implement:
addition
subtraction
multiplication
division
exponentiation
Extend the task if necessary to include additional basic operations, which should not require their own specialised task.
| #C.2B.2B | C++ | #include <cassert>
#include <cmath>
#include <iostream>
#include <valarray>
template <typename scalar_type> class matrix {
public:
matrix(size_t rows, size_t columns) : rows_(rows), columns_(columns) {
elements_.resize(rows * columns);
}
matrix(size_t rows, size_t columns, scalar_type value)
: rows_(rows), columns_(columns), elements_(value, rows * columns) {}
size_t rows() const { return rows_; }
size_t columns() const { return columns_; }
const scalar_type& at(size_t row, size_t column) const {
assert(row < rows_);
assert(column < columns_);
return elements_[index(row, column)];
}
scalar_type& at(size_t row, size_t column) {
assert(row < rows_);
assert(column < columns_);
return elements_[index(row, column)];
}
matrix& operator+=(scalar_type e) {
elements_ += e;
return *this;
}
matrix& operator-=(scalar_type e) {
elements_ -= e;
return *this;
}
matrix& operator*=(scalar_type e) {
elements_ *= e;
return *this;
}
matrix& operator/=(scalar_type e) {
elements_ /= e;
return *this;
}
matrix& operator+=(const matrix& other) {
assert(rows_ == other.rows_);
assert(columns_ == other.columns_);
elements_ += other.elements_;
return *this;
}
matrix& operator-=(const matrix& other) {
assert(rows_ == other.rows_);
assert(columns_ == other.columns_);
elements_ -= other.elements_;
return *this;
}
matrix& operator*=(const matrix& other) {
assert(rows_ == other.rows_);
assert(columns_ == other.columns_);
elements_ *= other.elements_;
return *this;
}
matrix& operator/=(const matrix& other) {
assert(rows_ == other.rows_);
assert(columns_ == other.columns_);
elements_ /= other.elements_;
return *this;
}
matrix& negate() {
for (scalar_type& element : elements_)
element = -element;
return *this;
}
matrix& invert() {
for (scalar_type& element : elements_)
element = 1 / element;
return *this;
}
friend matrix pow(const matrix& a, scalar_type b) {
return matrix(a.rows_, a.columns_, std::pow(a.elements_, b));
}
friend matrix pow(const matrix& a, const matrix& b) {
assert(a.rows_ == b.rows_);
assert(a.columns_ == b.columns_);
return matrix(a.rows_, a.columns_, std::pow(a.elements_, b.elements_));
}
private:
matrix(size_t rows, size_t columns, std::valarray<scalar_type>&& values)
: rows_(rows), columns_(columns), elements_(std::move(values)) {}
size_t index(size_t row, size_t column) const {
return row * columns_ + column;
}
size_t rows_;
size_t columns_;
std::valarray<scalar_type> elements_;
};
template <typename scalar_type>
matrix<scalar_type> operator+(const matrix<scalar_type>& a, scalar_type b) {
matrix<scalar_type> c(a);
c += b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator-(const matrix<scalar_type>& a, scalar_type b) {
matrix<scalar_type> c(a);
c -= b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator*(const matrix<scalar_type>& a, scalar_type b) {
matrix<scalar_type> c(a);
c *= b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator/(const matrix<scalar_type>& a, scalar_type b) {
matrix<scalar_type> c(a);
c /= b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator+(scalar_type a, const matrix<scalar_type>& b) {
matrix<scalar_type> c(b);
c += a;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator-(scalar_type a, const matrix<scalar_type>& b) {
matrix<scalar_type> c(b);
c.negate() += a;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator*(scalar_type a, const matrix<scalar_type>& b) {
matrix<scalar_type> c(b);
c *= a;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator/(scalar_type a, const matrix<scalar_type>& b) {
matrix<scalar_type> c(b);
c.invert() *= a;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator+(const matrix<scalar_type>& a,
const matrix<scalar_type>& b) {
matrix<scalar_type> c(a);
c += b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator-(const matrix<scalar_type>& a,
const matrix<scalar_type>& b) {
matrix<scalar_type> c(a);
c -= b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator*(const matrix<scalar_type>& a,
const matrix<scalar_type>& b) {
matrix<scalar_type> c(a);
c *= b;
return c;
}
template <typename scalar_type>
matrix<scalar_type> operator/(const matrix<scalar_type>& a,
const matrix<scalar_type>& b) {
matrix<scalar_type> c(a);
c /= b;
return c;
}
template <typename scalar_type>
void print(std::ostream& out, const matrix<scalar_type>& matrix) {
out << '[';
size_t rows = matrix.rows(), columns = matrix.columns();
for (size_t row = 0; row < rows; ++row) {
if (row > 0)
out << ", ";
out << '[';
for (size_t column = 0; column < columns; ++column) {
if (column > 0)
out << ", ";
out << matrix.at(row, column);
}
out << ']';
}
out << "]\n";
}
void test_matrix_matrix() {
const size_t rows = 3, columns = 2;
matrix<double> a(rows, columns);
for (size_t i = 0; i < rows; ++i) {
for (size_t j = 0; j < columns; ++j)
a.at(i, j) = double(columns * i + j + 1);
}
matrix<double> b(a);
std::cout << "a + b:\n";
print(std::cout, a + b);
std::cout << "\na - b:\n";
print(std::cout, a - b);
std::cout << "\na * b:\n";
print(std::cout, a * b);
std::cout << "\na / b:\n";
print(std::cout, a / b);
std::cout << "\npow(a, b):\n";
print(std::cout, pow(a, b));
}
void test_matrix_scalar() {
const size_t rows = 3, columns = 4;
matrix<double> a(rows, columns);
for (size_t i = 0; i < rows; ++i) {
for (size_t j = 0; j < columns; ++j)
a.at(i, j) = double(columns * i + j + 1);
}
std::cout << "a + 10:\n";
print(std::cout, a + 10.0);
std::cout << "\na - 10:\n";
print(std::cout, a - 10.0);
std::cout << "\n10 - a:\n";
print(std::cout, 10.0 - a);
std::cout << "\na * 10:\n";
print(std::cout, a * 10.0);
std::cout << "\na / 10:\n";
print(std::cout, a / 10.0);
std::cout << "\npow(a, 0.5):\n";
print(std::cout, pow(a, 0.5));
}
int main() {
test_matrix_matrix();
std::cout << '\n';
test_matrix_scalar();
return 0;
} |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #APL | APL |
is←{ t←⍵ ⋄ ⎕this⍎⍺,'←t' } ⍝⍝ the 'Slick Willie' function ;)
'test' is ⍳2 3
test
1 1 1 2 1 3
2 1 2 2 2 3
|
http://rosettacode.org/wiki/Egyptian_division | Egyptian division | Egyptian division is a method of dividing integers using addition and
doubling that is similar to the algorithm of Ethiopian multiplication
Algorithm:
Given two numbers where the dividend is to be divided by the divisor:
Start the construction of a table of two columns: powers_of_2, and doublings; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
Continue with successive i’th rows of 2^i and 2^i * divisor.
Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
We now assemble two separate sums that both start as zero, called here answer and accumulator
Consider each row of the table, in the reverse order of its construction.
If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).
Example: 580 / 34
Table creation:
powers_of_2
doublings
1
34
2
68
4
136
8
272
16
544
Initialization of sums:
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
0
0
Considering table rows, bottom-up:
When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
16
544
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
16
544
4
136
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
17
578
2
68
4
136
8
272
16
544
Answer
So 580 divided by 34 using the Egyptian method is 17 remainder (578 - 580) or 2.
Task
The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.
Functions should be clear interpretations of the algorithm.
Use the function to divide 580 by 34 and show the answer here, on this page.
Related tasks
Egyptian fractions
References
Egyptian Number System
| #BaCon | BaCon |
'---Ported from the c code example to BaCon by bigbass
'==================================================================================
FUNCTION EGYPTIAN_DIVISION(long dividend, long divisor, long remainder) TYPE long
'==================================================================================
'--- remainder is the third parameter, pass 0 if you do not need the remainder
DECLARE powers[64] TYPE long
DECLARE doublings[64] TYPE long
LOCAL i TYPE long
FOR i = 0 TO 63 STEP 1
powers[i] = 1 << i
doublings[i] = divisor << i
IF (doublings[i] > dividend) THEN
BREAK
ENDIF
NEXT
LOCAL answer TYPE long
LOCAL accumulator TYPE long
answer = 0
accumulator = 0
WHILE i >= 0
'--- If the current value of the accumulator added to the
'--- doublings cell would be less than or equal to the
'--- dividend then add it to the accumulator
IF (accumulator + doublings[i] <= dividend) THEN
accumulator = accumulator + doublings[i]
answer = answer + powers[i]
ENDIF
DECR i
WEND
IF remainder THEN
remainder = dividend - accumulator
PRINT dividend ," / ", divisor, " = " , answer ," remainder " , remainder
PRINT "Decoded the answer to a standard fraction"
PRINT (remainder + 0.0 )/ (divisor + 0.0) + answer
PRINT
ELSE
PRINT dividend ," / ", divisor , " = " , answer
ENDIF
RETURN answer
ENDFUNCTION
'--- the large number divided by the smaller number
'--- the third argument is 1 if you want to have a remainder
'--- and 0 if you dont want to have a remainder
EGYPTIAN_DIVISION(580,34,1)
EGYPTIAN_DIVISION(580,34,0)
EGYPTIAN_DIVISION(580,34,1)
|
http://rosettacode.org/wiki/Egyptian_fractions | Egyptian fractions | An Egyptian fraction is the sum of distinct unit fractions such as:
1
2
+
1
3
+
1
16
(
=
43
48
)
{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{16}}\,(={\tfrac {43}{48}})}
Each fraction in the expression has a numerator equal to 1 (unity) and a denominator that is a positive integer, and all the denominators are distinct (i.e., no repetitions).
Fibonacci's Greedy algorithm for Egyptian fractions expands the fraction
x
y
{\displaystyle {\tfrac {x}{y}}}
to be represented by repeatedly performing the replacement
x
y
=
1
⌈
y
/
x
⌉
+
(
−
y
)
mod
x
y
⌈
y
/
x
⌉
{\displaystyle {\frac {x}{y}}={\frac {1}{\lceil y/x\rceil }}+{\frac {(-y)\!\!\!\!\mod x}{y\lceil y/x\rceil }}}
(simplifying the 2nd term in this replacement as necessary, and where
⌈
x
⌉
{\displaystyle \lceil x\rceil }
is the ceiling function).
For this task, Proper and improper fractions must be able to be expressed.
Proper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that
a
<
b
{\displaystyle a<b}
, and
improper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that a ≥ b.
(See the REXX programming example to view one method of expressing the whole number part of an improper fraction.)
For improper fractions, the integer part of any improper fraction should be first isolated and shown preceding the Egyptian unit fractions, and be surrounded by square brackets [n].
Task requirements
show the Egyptian fractions for:
43
48
{\displaystyle {\tfrac {43}{48}}}
and
5
121
{\displaystyle {\tfrac {5}{121}}}
and
2014
59
{\displaystyle {\tfrac {2014}{59}}}
for all proper fractions,
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive one-or two-digit (decimal) integers, find and show an Egyptian fraction that has:
the largest number of terms,
the largest denominator.
for all one-, two-, and three-digit integers, find and show (as above). {extra credit}
Also see
Wolfram MathWorld™ entry: Egyptian fraction
| #C.2B.2B | C++ | #include <iostream>
#include <optional>
#include <vector>
#include <string>
#include <sstream>
#include <boost/multiprecision/cpp_int.hpp>
typedef boost::multiprecision::cpp_int integer;
struct fraction {
fraction(const integer& n, const integer& d) : numerator(n), denominator(d) {}
integer numerator;
integer denominator;
};
integer mod(const integer& x, const integer& y) {
return ((x % y) + y) % y;
}
size_t count_digits(const integer& i) {
std::ostringstream os;
os << i;
return os.str().length();
}
std::string to_string(const integer& i) {
const int max_digits = 20;
std::ostringstream os;
os << i;
std::string s = os.str();
if (s.length() > max_digits) {
s = s.substr(0, max_digits/2) + "..." + s.substr(s.length()-max_digits/2);
}
return s;
}
std::ostream& operator<<(std::ostream& out, const fraction& f) {
return out << to_string(f.numerator) << '/' << to_string(f.denominator);
}
void egyptian(const fraction& f, std::vector<fraction>& result) {
result.clear();
integer x = f.numerator, y = f.denominator;
while (x > 0) {
integer z = (y + x - 1)/x;
result.emplace_back(1, z);
x = mod(-y, x);
y = y * z;
}
}
void print_egyptian(const std::vector<fraction>& result) {
if (result.empty())
return;
auto i = result.begin();
std::cout << *i++;
for (; i != result.end(); ++i)
std::cout << " + " << *i;
std::cout << '\n';
}
void print_egyptian(const fraction& f) {
std::cout << "Egyptian fraction for " << f << ": ";
integer x = f.numerator, y = f.denominator;
if (x > y) {
std::cout << "[" << x/y << "] ";
x = x % y;
}
std::vector<fraction> result;
egyptian(fraction(x, y), result);
print_egyptian(result);
std::cout << '\n';
}
void show_max_terms_and_max_denominator(const integer& limit) {
size_t max_terms = 0;
std::optional<fraction> max_terms_fraction, max_denominator_fraction;
std::vector<fraction> max_terms_result;
integer max_denominator = 0;
std::vector<fraction> max_denominator_result;
std::vector<fraction> result;
for (integer b = 2; b < limit; ++b) {
for (integer a = 1; a < b; ++a) {
fraction f(a, b);
egyptian(f, result);
if (result.size() > max_terms) {
max_terms = result.size();
max_terms_result = result;
max_terms_fraction = f;
}
const integer& denominator = result.back().denominator;
if (denominator > max_denominator) {
max_denominator = denominator;
max_denominator_result = result;
max_denominator_fraction = f;
}
}
}
std::cout << "Proper fractions with most terms and largest denominator, limit = " << limit << ":\n\n";
std::cout << "Most terms (" << max_terms << "): " << max_terms_fraction.value() << " = ";
print_egyptian(max_terms_result);
std::cout << "\nLargest denominator (" << count_digits(max_denominator_result.back().denominator)
<< " digits): " << max_denominator_fraction.value() << " = ";
print_egyptian(max_denominator_result);
}
int main() {
print_egyptian(fraction(43, 48));
print_egyptian(fraction(5, 121));
print_egyptian(fraction(2014, 59));
show_max_terms_and_max_denominator(100);
show_max_terms_and_max_denominator(1000);
return 0;
} |
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Phix | Phix | with javascript_semantics
enum LEN,SUFF,CHARS,NEXT
function node(integer len, suffix=1, string chars="", sequence next={})
return {len,suffix,chars,next} -- must match above enum!
end function
function eertree(string s)
sequence tree = {node(-1), -- odd lengths
node(0)} -- even lengths
integer suff = 2 -- max suffix palindrome
for i=1 to length(s) do
integer cur = suff, curlen, ch = s[i], k
while (true) do
curlen = tree[cur][LEN]
k = i-1-curlen
if k>=1 and s[k]==ch then
exit
end if
cur = tree[cur][SUFF]
end while
k = find(ch,tree[cur][CHARS])
if k then
suff = tree[cur][NEXT][k]
else
tree = append(tree,node(curlen+2))
suff = length(tree)
tree[cur][CHARS] &= ch
tree[cur][NEXT] = deep_copy(tree[cur][NEXT])&suff
if tree[suff][LEN]==1 then
tree[suff][SUFF] = 2
else
while (true) do
cur = tree[cur][SUFF]
curlen = tree[cur][LEN]
k = i-1-curlen
if k>=0 and s[k]==ch then
k = find(ch,tree[cur][CHARS])
if k then
tree[suff][SUFF] = tree[cur][NEXT][k]
end if
exit
end if
end while
end if
end if
end for
return tree
end function
function children(sequence s, tree, integer n, string root="")
for i=1 to length(tree[n][CHARS]) do
integer c = tree[n][CHARS][i],
nxt = tree[n][NEXT][i]
string p = iff(n=1 ? c&""
: c&root&c)
s = append(s, p)
s = children(s, tree, nxt, p)
end for
return s
end function
procedure main()
sequence tree = eertree("eertree")
puts(1,"tree:\n")
for i=1 to length(tree) do
sequence ti = deep_copy(tree[i])
ti[NEXT] = sprint(ti[NEXT])
ti = i&ti
printf(1,"[%d]: len:%2d suffix:%d chars:%-5s next:%s\n",ti)
end for
puts(1,"\n")
-- odd then even lengths:
?children(children({},tree,1), tree, 2)
end procedure
main()
|
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #R | R | halve <- function(a) floor(a/2)
double <- function(a) a*2
iseven <- function(a) (a%%2)==0
ethiopicmult <- function(plier, plicand, tutor=FALSE) {
if (tutor) { cat("ethiopic multiplication of", plier, "and", plicand, "\n") }
result <- 0
while(plier >= 1) {
if (!iseven(plier)) { result <- result + plicand }
if (tutor) {
cat(plier, ", ", plicand, " ", ifelse(iseven(plier), "struck", "kept"), "\n", sep="")
}
plier <- halve(plier)
plicand <- double(plicand)
}
result
}
print(ethiopicmult(17, 34, TRUE)) |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #Elixir | Elixir | defmodule Elementary_cellular_automaton do
def run(start_str, rule, times) do
IO.puts "rule : #{rule}"
each(start_str, rule_pattern(rule), times)
end
defp rule_pattern(rule) do
list = Integer.to_string(rule, 2) |> String.pad_leading(8, "0")
|> String.codepoints |> Enum.reverse
Enum.map(0..7, fn i -> Integer.to_string(i, 2) |> String.pad_leading(3, "0") end)
|> Enum.zip(list) |> Map.new
end
defp each(_, _, 0), do: :ok
defp each(str, patterns, times) do
IO.puts String.replace(str, "0", ".") |> String.replace("1", "#")
str2 = String.last(str) <> str <> String.first(str)
next_str = Enum.map_join(0..String.length(str)-1, fn i ->
Map.get(patterns, String.slice(str2, i, 3))
end)
each(next_str, patterns, times-1)
end
end
pad = String.duplicate("0", 14)
str = pad <> "1" <> pad
Elementary_cellular_automaton.run(str, 18, 25) |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #F.23 | F# |
// Elementary Cellular Automaton . Nigel Galloway: July 31st., 2019
let eca N=
let N=Array.init 8 (fun n->(N>>>n)%2)
Seq.unfold(fun G->Some(G,[|yield Array.last G; yield! G; yield Array.head G|]|>Array.windowed 3|>Array.map(fun n->N.[n.[2]+2*n.[1]+4*n.[0]])))
|
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #TI-83_BASIC | TI-83 BASIC | 10→N
N! ---> 362880
prod(seq(I,I,1,N)) ---> 362880 |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #VBScript | VBScript |
Function odd_or_even(n)
If n Mod 2 = 0 Then
odd_or_even = "Even"
Else
odd_or_even = "Odd"
End If
End Function
WScript.StdOut.Write "Please enter a number: "
n = WScript.StdIn.ReadLine
WScript.StdOut.Write n & " is " & odd_or_even(CInt(n))
WScript.StdOut.WriteLine
|
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Verilog | Verilog | module main;
integer i;
initial begin
for (i = 1; i <= 10; i = i+1) begin
if (i % 2 == 0) $display(i, " is even");
else $display(i, " is odd");
end
$finish ;
end
endmodule |
http://rosettacode.org/wiki/Echo_server | Echo server | Create a network service that sits on TCP port 12321, which accepts connections on that port, and which echoes complete lines (using a carriage-return/line-feed sequence as line separator) back to clients. No error handling is required. For the purposes of testing, it is only necessary to support connections from localhost (127.0.0.1 or perhaps ::1). Logging of connection information to standard output is recommended.
The implementation must be able to handle simultaneous connections from multiple clients. A multi-threaded or multi-process solution may be used. Each connection must be able to echo more than a single line.
The implementation must not stop responding to other clients if one client sends a partial line or stops reading responses.
| #Forth | Forth | include unix/socket.fs
128 constant size
: (echo) ( sock buf -- sock buf )
begin
cr ." waiting..."
2dup 2dup size read-socket nip
dup 0>
while
." got: " 2dup type
rot write-socket
repeat
drop drop drop ;
create buf size allot
: echo-server ( port -- )
cr ." Listening on " dup .
create-server
dup 4 listen
begin
dup accept-socket
cr ." Connection!"
buf ['] (echo) catch
cr ." Disconnected (" . ." )"
drop close-socket
again ;
12321 echo-server |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #zkl | zkl | s:=""; // or s:=String, String is the object ""
s.toBool() //-->False
if (s) println("not empty") |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #Zoomscript | Zoomscript | var string
string = ""
if eq string ""
print "The string is empty."
else
print "The string is not empty."
endif |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Sparkling | Sparkling | |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #SQL_PL | SQL PL |
SELECT 1 FROM sysibm.sysdummy1;
|
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #SSEM | SSEM | 00000000000000000000000000000000 0. 0 to CI jump to store(0) + 1
00000000000000000000000000000000 1. 0 to CI jump to store(0) + 1 |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Python | Python | """ https://rosettacode.org/wiki/Earliest_difference_between_prime_gaps """
from primesieve import primes
LIMIT = 10**9
pri = primes(LIMIT * 5)
gapstarts = {}
for i in range(1, len(pri)):
if pri[i] - pri[i - 1] not in gapstarts:
gapstarts[pri[i] - pri[i - 1]] = pri[i - 1]
PM, GAP1, = 10, 2
while True:
while GAP1 not in gapstarts:
GAP1 += 2
start1 = gapstarts[GAP1]
GAP2 = GAP1 + 2
if GAP2 not in gapstarts:
GAP1 = GAP2 + 2
continue
start2 = gapstarts[GAP2]
diff = abs(start2 - start1)
if diff > PM:
print(f"Earliest difference >{PM: ,} between adjacent prime gap starting primes:")
print(f"Gap {GAP1} starts at{start1: ,}, gap {GAP2} starts at{start2: ,}, difference is{diff: ,}.\n")
if PM == LIMIT:
break
PM *= 10
else:
GAP1 = GAP2
|
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Raku | Raku | use Math::Primesieve;
use Lingua::EN::Numbers;
my $iterator = Math::Primesieve::iterator.new;
my @gaps;
my $last = 2;
for 1..9 {
my $m = exp $_, 10;
my $this;
loop {
$this = (my $p = $iterator.next) - $last;
if !@gaps[$this].defined {
@gaps[$this]= $last;
check-gap($m, $this, @gaps) && last
if $this > 2 and @gaps[$this - 2].defined and (abs($last - @gaps[$this - 2]) > $m);
}
$last = $p;
}
}
sub check-gap ($n, $this, @p) {
my %upto = @p[^$this].pairs.grep: *.value;
my @upto = (1..$this).map: { last unless %upto{$_ * 2}; %upto{$_ * 2} }
my $key = @upto.rotor(2=>-1).first( {.sink; abs(.[0] - .[1]) > $n}, :k );
return False unless $key;
say "Earliest difference > {comma $n} between adjacent prime gap starting primes:";
printf "Gap %s starts at %s, gap %s starts at %s, difference is %s\n\n",
|(2 * $key + 2, @upto[$key], 2 * $key + 4, @upto[$key+1], abs(@upto[$key] - @upto[$key+1]))».,
True
} |
http://rosettacode.org/wiki/Eban_numbers | Eban numbers |
Definition
An eban number is a number that has no letter e in it when the number is spelled in English.
Or more literally, spelled numbers that contain the letter e are banned.
The American version of spelling numbers will be used here (as opposed to the British).
2,000,000,000 is two billion, not two milliard.
Only numbers less than one sextillion (1021) will be considered in/for this task.
This will allow optimizations to be used.
Task
show all eban numbers ≤ 1,000 (in a horizontal format), and a count
show all eban numbers between 1,000 and 4,000 (inclusive), and a count
show a count of all eban numbers up and including 10,000
show a count of all eban numbers up and including 100,000
show a count of all eban numbers up and including 1,000,000
show a count of all eban numbers up and including 10,000,000
show all output here.
See also
The MathWorld entry: eban numbers.
The OEIS entry: A6933, eban numbers.
| #11l | 11l | F iseban(n)
I n == 0
R 0B
V (b, r) = divmod(n, 1'000'000'000)
(V m, r) = divmod(r, 1'000'000)
(V t, r) = divmod(r, 1'000)
m = I m C 30..66 {m % 10} E m
t = I t C 30..66 {t % 10} E t
r = I r C 30..66 {r % 10} E r
R Set([b, m, t, r]) <= Set([0, 2, 4, 6])
print(‘eban numbers up to and including 1000:’)
L(i) 0..100
I iseban(i)
print(i, end' ‘ ’)
print("\n\neban numbers between 1000 and 4000 (inclusive):")
L(i) 1000..4000
I iseban(i)
print(i, end' ‘ ’)
print()
L(maxn) (10'000, 100'000, 1'000'000, 10'000'000)
V count = 0
L(i) 0..maxn
I iseban(i)
count++
print("\nNumber of eban numbers up to and including #8: #4".format(maxn, count)) |
http://rosettacode.org/wiki/Duffinian_numbers | Duffinian numbers | A Duffinian number is a composite number k that is relatively prime to its sigma sum σ.
The sigma sum of k is the sum of the divisors of k.
E.G.
161 is a Duffinian number.
It is composite. (7 × 23)
The sigma sum 192 (1 + 7 + 23 + 161) is relatively prime to 161.
Duffinian numbers are very common.
It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.
Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.
Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).
It is not possible to have six consecutive Duffinian numbers
Task
Find and show the first 50 Duffinian numbers.
Find and show at least the first 15 Duffinian triplets.
See also
Numbers Aplenty - Duffinian numbers
OEIS:A003624 - Duffinian numbers: composite numbers k relatively prime to sigma(k)
| #ALGOL_68 | ALGOL 68 | BEGIN # find Duffinian numbers: non-primes relatively prime to their divisor count #
INT max number := 500 000; # largest number we will consider #
# iterative Greatest Common Divisor routine, returns the gcd of m and n #
PROC gcd = ( INT m, n )INT:
BEGIN
INT a := ABS m, b := ABS n;
WHILE b /= 0 DO
INT new a = b;
b := a MOD b;
a := new a
OD;
a
END # gcd # ;
# construct a table of the divisor counts #
[ 1 : max number ]INT ds; FOR i TO UPB ds DO ds[ i ] := 1 OD;
FOR i FROM 2 TO UPB ds
DO FOR j FROM i BY i TO UPB ds DO ds[ j ] +:= i OD
OD;
# set the divisor counts of non-Duffinian numbers to 0 #
ds[ 1 ] := 0; # 1 is not Duffinian #
FOR n FROM 2 TO UPB ds DO
IF INT nds = ds[ n ];
IF nds = n + 1 THEN TRUE ELSE gcd( n, nds ) /= 1 FI
THEN
# n is prime or is not relatively prime to its divisor sum #
ds[ n ] := 0
FI
OD;
# show the first 50 Duffinian numbers #
print( ( "The first 50 Duffinian numbers:", newline ) );
INT dcount := 0;
FOR n WHILE dcount < 50 DO
IF ds[ n ] /= 0
THEN # found a Duffinian number #
print( ( " ", whole( n, -3) ) );
IF ( dcount +:= 1 ) MOD 25 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline ) );
# show the duffinian triplets below UPB ds #
print( ( "The Duffinian triplets up to ", whole( UPB ds, 0 ), ":", newline ) );
dcount := 0;
FOR n FROM 3 TO UPB ds DO
IF ds[ n - 2 ] /= 0 AND ds[ n - 1 ] /= 0 AND ds[ n ] /= 0
THEN # found a Duffinian triplet #
print( ( " (", whole( n - 2, -7 ), " ", whole( n - 1, -7 ), " ", whole( n, -7 ), ")" ) );
IF ( dcount +:= 1 ) MOD 4 = 0 THEN print( ( newline ) ) FI
FI
OD
END |
http://rosettacode.org/wiki/Element-wise_operations | Element-wise operations | This task is similar to:
Matrix multiplication
Matrix transposition
Task
Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.
Implement:
addition
subtraction
multiplication
division
exponentiation
Extend the task if necessary to include additional basic operations, which should not require their own specialised task.
| #Clojure | Clojure | (defn initial-mtx [i1 i2 value]
(vec (repeat i1 (vec (repeat i2 value)))))
(defn operation [f mtx1 mtx2]
(if (vector? mtx1)
(vec (map #(vec (map f %1 %2)) mtx1 mtx2)))
(recur f (initial-mtx (count mtx2) (count (first mtx2)) mtx1) mtx2)
)) |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #Arturo | Arturo | name: strip input "enter a variable name: "
value: strip input "enter a variable value: "
let name value
print ["the value of variable" name "is:" var name] |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #AutoHotkey | AutoHotkey | InputBox, Dynamic, Variable Name
%Dynamic% = hello
ListVars
MsgBox % %dynamic% ; says hello |
http://rosettacode.org/wiki/Egyptian_division | Egyptian division | Egyptian division is a method of dividing integers using addition and
doubling that is similar to the algorithm of Ethiopian multiplication
Algorithm:
Given two numbers where the dividend is to be divided by the divisor:
Start the construction of a table of two columns: powers_of_2, and doublings; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
Continue with successive i’th rows of 2^i and 2^i * divisor.
Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
We now assemble two separate sums that both start as zero, called here answer and accumulator
Consider each row of the table, in the reverse order of its construction.
If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).
Example: 580 / 34
Table creation:
powers_of_2
doublings
1
34
2
68
4
136
8
272
16
544
Initialization of sums:
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
0
0
Considering table rows, bottom-up:
When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
16
544
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
16
544
4
136
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
17
578
2
68
4
136
8
272
16
544
Answer
So 580 divided by 34 using the Egyptian method is 17 remainder (578 - 580) or 2.
Task
The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.
Functions should be clear interpretations of the algorithm.
Use the function to divide 580 by 34 and show the answer here, on this page.
Related tasks
Egyptian fractions
References
Egyptian Number System
| #C | C |
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <assert.h>
uint64_t egyptian_division(uint64_t dividend, uint64_t divisor, uint64_t *remainder) {
// remainder is an out parameter, pass NULL if you do not need the remainder
static uint64_t powers[64];
static uint64_t doublings[64];
int i;
for(i = 0; i < 64; i++) {
powers[i] = 1 << i;
doublings[i] = divisor << i;
if(doublings[i] > dividend)
break;
}
uint64_t answer = 0;
uint64_t accumulator = 0;
for(i = i - 1; i >= 0; i--) {
// If the current value of the accumulator added to the
// doublings cell would be less than or equal to the
// dividend then add it to the accumulator
if(accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
answer += powers[i];
}
}
if(remainder)
*remainder = dividend - accumulator;
return answer;
}
void go(uint64_t a, uint64_t b) {
uint64_t x, y;
x = egyptian_division(a, b, &y);
printf("%llu / %llu = %llu remainder %llu\n", a, b, x, y);
assert(a == b * x + y);
}
int main(void) {
go(580, 32);
}
|
http://rosettacode.org/wiki/Egyptian_fractions | Egyptian fractions | An Egyptian fraction is the sum of distinct unit fractions such as:
1
2
+
1
3
+
1
16
(
=
43
48
)
{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{16}}\,(={\tfrac {43}{48}})}
Each fraction in the expression has a numerator equal to 1 (unity) and a denominator that is a positive integer, and all the denominators are distinct (i.e., no repetitions).
Fibonacci's Greedy algorithm for Egyptian fractions expands the fraction
x
y
{\displaystyle {\tfrac {x}{y}}}
to be represented by repeatedly performing the replacement
x
y
=
1
⌈
y
/
x
⌉
+
(
−
y
)
mod
x
y
⌈
y
/
x
⌉
{\displaystyle {\frac {x}{y}}={\frac {1}{\lceil y/x\rceil }}+{\frac {(-y)\!\!\!\!\mod x}{y\lceil y/x\rceil }}}
(simplifying the 2nd term in this replacement as necessary, and where
⌈
x
⌉
{\displaystyle \lceil x\rceil }
is the ceiling function).
For this task, Proper and improper fractions must be able to be expressed.
Proper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that
a
<
b
{\displaystyle a<b}
, and
improper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that a ≥ b.
(See the REXX programming example to view one method of expressing the whole number part of an improper fraction.)
For improper fractions, the integer part of any improper fraction should be first isolated and shown preceding the Egyptian unit fractions, and be surrounded by square brackets [n].
Task requirements
show the Egyptian fractions for:
43
48
{\displaystyle {\tfrac {43}{48}}}
and
5
121
{\displaystyle {\tfrac {5}{121}}}
and
2014
59
{\displaystyle {\tfrac {2014}{59}}}
for all proper fractions,
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive one-or two-digit (decimal) integers, find and show an Egyptian fraction that has:
the largest number of terms,
the largest denominator.
for all one-, two-, and three-digit integers, find and show (as above). {extra credit}
Also see
Wolfram MathWorld™ entry: Egyptian fraction
| #Common_Lisp | Common Lisp | (defun egyption-fractions (x y &optional acc)
(let* ((a (/ x y)))
(cond
((> (numerator a) (denominator a))
(multiple-value-bind (q r) (floor x y)
(if (zerop r)
(cons q acc)
(egyption-fractions r y (cons q acc)))))
((= (numerator a) 1) (reverse (cons a acc)))
(t (let ((b (ceiling y x)))
(egyption-fractions (mod (- y) x) (* y b) (cons (/ b) acc)))))))
(defun test (n fn)
(car (sort (loop for i from 1 to n append
(loop for j from 2 to n collect
(cons (/ i j) (funcall fn (egyption-fractions i j)))))
#'>
:key #'cdr)))
|
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Python | Python | #!/bin/python
from __future__ import print_function
class Node(object):
def __init__(self):
self.edges = {} # edges (or forward links)
self.link = None # suffix link (backward links)
self.len = 0 # the length of the node
class Eertree(object):
def __init__(self):
self.nodes = []
# two initial root nodes
self.rto = Node() #odd length root node, or node -1
self.rte = Node() #even length root node, or node 0
# Initialize empty tree
self.rto.link = self.rte.link = self.rto;
self.rto.len = -1
self.rte.len = 0
self.S = [0] # accumulated input string, T=S[1..i]
self.maxSufT = self.rte # maximum suffix of tree T
def get_max_suffix_pal(self, startNode, a):
# We traverse the suffix-palindromes of T in the order of decreasing length.
# For each palindrome we read its length k and compare T[i-k] against a
# until we get an equality or arrive at the -1 node.
u = startNode
i = len(self.S)
k = u.len
while id(u) != id(self.rto) and self.S[i - k - 1] != a:
assert id(u) != id(u.link) #Prevent infinte loop
u = u.link
k = u.len
return u
def add(self, a):
# We need to find the maximum suffix-palindrome P of Ta
# Start by finding maximum suffix-palindrome Q of T.
# To do this, we traverse the suffix-palindromes of T
# in the order of decreasing length, starting with maxSuf(T)
Q = self.get_max_suffix_pal(self.maxSufT, a)
# We check Q to see whether it has an outgoing edge labeled by a.
createANewNode = not a in Q.edges
if createANewNode:
# We create the node P of length Q+2
P = Node()
self.nodes.append(P)
P.len = Q.len + 2
if P.len == 1:
# if P = a, create the suffix link (P,0)
P.link = self.rte
else:
# It remains to create the suffix link from P if |P|>1. Just
# continue traversing suffix-palindromes of T starting with the suffix
# link of Q.
P.link = self.get_max_suffix_pal(Q.link, a).edges[a]
# create the edge (Q,P)
Q.edges[a] = P
#P becomes the new maxSufT
self.maxSufT = Q.edges[a]
#Store accumulated input string
self.S.append(a)
return createANewNode
def get_sub_palindromes(self, nd, nodesToHere, charsToHere, result):
#Each node represents a palindrome, which can be reconstructed
#by the path from the root node to each non-root node.
#Traverse all edges, since they represent other palindromes
for lnkName in nd.edges:
nd2 = nd.edges[lnkName] #The lnkName is the character used for this edge
self.get_sub_palindromes(nd2, nodesToHere+[nd2], charsToHere+[lnkName], result)
#Reconstruct based on charsToHere characters.
if id(nd) != id(self.rto) and id(nd) != id(self.rte): #Don't print for root nodes
tmp = "".join(charsToHere)
if id(nodesToHere[0]) == id(self.rte): #Even string
assembled = tmp[::-1] + tmp
else: #Odd string
assembled = tmp[::-1] + tmp[1:]
result.append(assembled)
if __name__=="__main__":
st = "eertree"
print ("Processing string", st)
eertree = Eertree()
for ch in st:
eertree.add(ch)
print ("Number of sub-palindromes:", len(eertree.nodes))
#Traverse tree to find sub-palindromes
result = []
eertree.get_sub_palindromes(eertree.rto, [eertree.rto], [], result) #Odd length words
eertree.get_sub_palindromes(eertree.rte, [eertree.rte], [], result) #Even length words
print ("Sub-palindromes:", result) |
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #Racket | Racket | #lang racket
(define (halve i) (quotient i 2))
(define (double i) (* i 2))
;; `even?' is built-in
(define (ethiopian-multiply x y)
(cond [(zero? x) 0]
[(even? x) (ethiopian-multiply (halve x) (double y))]
[else (+ y (ethiopian-multiply (halve x) (double y)))]))
(ethiopian-multiply 17 34) ; -> 578 |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #Factor | Factor | USING: assocs formatting grouping io kernel math math.bits
math.combinatorics sequences sequences.extras ;
: make-rules ( n -- assoc )
{ f t } 3 selections swap make-bits 8 f pad-tail zip ;
: next-state ( assoc seq -- assoc seq' )
dupd 3 circular-clump -1 rotate [ of ] with map ;
: first-state ( -- seq ) 15 f <repetition> dup { t } glue ;
: show-state ( seq -- ) [ "#" "." ? write ] each nl ;
: show-automaton ( rule -- )
dup "Rule %d:\n" printf make-rules first-state 16
[ dup show-state next-state ] times 2drop ;
90 show-automaton |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #FreeBASIC | FreeBASIC |
#define NCELLS 400
#define border 16
dim as ubyte rule = 110
sub evolve( row as uinteger, rule as ubyte, pattern() as ubyte )
dim as ubyte newp(NCELLS)
dim as uinteger i
dim as ubyte lookup
for i = 0 to NCELLS-1
pset (i + border, row + border ), pattern(i)*15
lookup = 4*pattern((i-1) mod NCELLS) + 2*pattern(i) + pattern( (i+1) mod NCELLS )
newp(i)=0
if ( 2^lookup and rule )<>0 then newp(i) = 1
next i
for i = 0 to NCELLS-1
pattern(i) = newp(i)
next i
end sub
sub perform_simulation( rule as ubyte, pattern() as ubyte )
dim as integer i
for i = 1 to NCELLS
evolve(i, rule, pattern())
next i
end sub
sub reseed( pattern() as ubyte )
dim as integer i
for i = 0 to NCELLS-1
pattern(i) = int(rnd+0.5)
next i
end sub
sub display_text( rule as ubyte )
locate 4,58 : print using "Rule ###";rule
locate 6,53 : print " R: reshuffle seed "
locate 8,53 : print " <,>: change rule "
locate 10,53 : print " Q: quit "
end sub
screen 12
randomize timer
dim as boolean pattern(0 to NCELLS-1)
dim as string key="R"
do
if key = "R" then
cls
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
if key="<" then
cls
rule = (rule-1) mod 256
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
if key=">" then
cls
rule = (rule+1) mod 256
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
key = ucase(inkey)
loop until ucase(key) = "Q" |
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #TI-89_BASIC | TI-89 BASIC | factorial(x)
Func
Return Π(y,y,1,x)
EndFunc |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Visual_Basic_.NET | Visual Basic .NET | Module Module1
Sub Main()
Dim str As String
Dim num As Integer
While True
Console.Write("Enter an integer or 0 to finish: ")
str = Console.ReadLine()
If Integer.TryParse(str, num) Then
If num = 0 Then
Exit While
End If
If num Mod 2 = 0 Then
Console.WriteLine("Even")
Else
Console.WriteLine("Odd")
End If
Else
Console.WriteLine("Bad input.")
End If
End While
End Sub
End Module |
http://rosettacode.org/wiki/Echo_server | Echo server | Create a network service that sits on TCP port 12321, which accepts connections on that port, and which echoes complete lines (using a carriage-return/line-feed sequence as line separator) back to clients. No error handling is required. For the purposes of testing, it is only necessary to support connections from localhost (127.0.0.1 or perhaps ::1). Logging of connection information to standard output is recommended.
The implementation must be able to handle simultaneous connections from multiple clients. A multi-threaded or multi-process solution may be used. Each connection must be able to echo more than a single line.
The implementation must not stop responding to other clients if one client sends a partial line or stops reading responses.
| #Go | Go | package main
import (
"fmt"
"net"
"bufio"
)
func echo(s net.Conn, i int) {
defer s.Close();
fmt.Printf("%d: %v <-> %v\n", i, s.LocalAddr(), s.RemoteAddr())
b := bufio.NewReader(s)
for {
line, e := b.ReadBytes('\n')
if e != nil {
break
}
s.Write(line)
}
fmt.Printf("%d: closed\n", i)
}
func main() {
l, e := net.Listen("tcp", ":12321")
for i := 0; e == nil; i++ {
var s net.Conn
s, e = l.Accept()
go echo(s, i)
}
} |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #ZX_Spectrum_Basic | ZX Spectrum Basic | const std = @import("std");
pub fn main() !void {
// default is [:0]const u8, which is a 0-terminated string with len field
const str = "";
if (str.len == 0) {
std.debug.print("string empty\n", .{});
}
if (str.len != 0) {
std.debug.print("string empty\n", .{});
}
} |
http://rosettacode.org/wiki/Empty_string | Empty string | Languages may have features for dealing specifically with empty strings
(those containing no characters).
Task
Demonstrate how to assign an empty string to a variable.
Demonstrate how to check that a string is empty.
Demonstrate how to check that a string is not empty.
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
| #Zig | Zig | const std = @import("std");
pub fn main() !void {
// default is [:0]const u8, which is a 0-terminated string with len field
const str = "";
if (str.len == 0) {
std.debug.print("string empty\n", .{});
}
if (str.len != 0) {
std.debug.print("string empty\n", .{});
}
} |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Standard_ML | Standard ML | ; |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Stata | Stata | program define nop
version 15
end |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Suneido | Suneido | function () { } |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Rust | Rust | // [dependencies]
// primal = "0.3"
fn main() {
use std::collections::HashMap;
let mut primes = primal::Primes::all();
let mut last_prime = primes.next().unwrap();
let mut gap_starts = HashMap::new();
let mut find_gap_start = move |gap: usize| -> usize {
if let Some(start) = gap_starts.get(&gap) {
return *start;
}
loop {
let prev = last_prime;
last_prime = primes.next().unwrap();
let diff = last_prime - prev;
if !gap_starts.contains_key(&diff) {
gap_starts.insert(diff, prev);
}
if gap == diff {
return prev;
}
}
};
let limit = 100000000000;
let mut pm = 10;
let mut gap1 = 2;
loop {
let start1 = find_gap_start(gap1);
let gap2 = gap1 + 2;
let start2 = find_gap_start(gap2);
let diff = if start2 > start1 {
start2 - start1
} else {
start1 - start2
};
if diff > pm {
println!(
"Earliest difference > {} between adjacent prime gap starting primes:\n\
Gap {} starts at {}, gap {} starts at {}, difference is {}.\n",
pm, gap1, start1, gap2, start2, diff
);
if pm == limit {
break;
}
pm *= 10;
} else {
gap1 = gap2;
}
}
} |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Sidef | Sidef | func prime_gap_records(upto) {
var gaps = []
var p = 3
each_prime(p.next_prime, upto, {|q|
gaps[q-p] := p
p = q
})
gaps.grep { defined(_) }
}
var gaps = prime_gap_records(1e8)
for m in (1 .. gaps.max.len) {
gaps.each_cons(2, {|p,q|
if (abs(q-p) > 10**m) {
say "10^#{m} -> (#{p}, #{q}) with gaps (#{
p.next_prime-p}, #{q.next_prime-q}) and difference #{abs(q-p)}"
break
}
})
} |
http://rosettacode.org/wiki/Earliest_difference_between_prime_gaps | Earliest difference between prime gaps | When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
gap
minimal
starting
prime
ending
prime
2
3
5
4
7
11
6
23
29
8
89
97
10
139
149
12
199
211
14
113
127
16
1831
1847
18
523
541
20
887
907
22
1129
1151
24
1669
1693
26
2477
2503
28
2971
2999
30
4297
4327
This task involves locating the minimal primes corresponding to those gaps.
Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
Task
For each order of magnitude m from 10¹ through 10⁶:
Find the first two sets of adjacent minimum prime gaps where the absolute value of the difference between the prime gap start values is greater than m.
E.G.
For an m of 10¹;
The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < 10¹ so keep going.
The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > 10¹ so this the earliest adjacent gap difference > 10¹.
Stretch goal
Do the same for 10⁷ and 10⁸ (and higher?) orders of magnitude
Note: the earliest value found for each order of magnitude may not be unique, in fact, is not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
| #Wren | Wren | import "./math" for Int
import "/fmt" for Fmt
var limit = 1e9
var gapStarts = {}
var primes = Int.segmentedSieve(limit * 5, 8 * 1024 * 1024) // 8 MB cache
for (i in 1...primes.count) {
var gap = primes[i] - primes[i-1]
if (!gapStarts[gap]) gapStarts[gap] = primes[i-1]
}
var pm = 10
var gap1 = 2
while (true) {
while (!gapStarts[gap1]) gap1 = gap1 + 2
var start1 = gapStarts[gap1]
var gap2 = gap1 + 2
if (!gapStarts[gap2]) {
gap1 = gap2 + 2
continue
}
var start2 = gapStarts[gap2]
var diff = (start2 - start1).abs
if (diff > pm) {
Fmt.print("Earliest difference > $,d between adjacent prime gap starting primes:", pm)
Fmt.print("Gap $d starts at $,d, gap $d starts at $,d, difference is $,d.\n", gap1, start1, gap2, start2, diff)
if (pm == limit) break
pm = pm * 10
} else {
gap1 = gap2
}
} |
http://rosettacode.org/wiki/Eban_numbers | Eban numbers |
Definition
An eban number is a number that has no letter e in it when the number is spelled in English.
Or more literally, spelled numbers that contain the letter e are banned.
The American version of spelling numbers will be used here (as opposed to the British).
2,000,000,000 is two billion, not two milliard.
Only numbers less than one sextillion (1021) will be considered in/for this task.
This will allow optimizations to be used.
Task
show all eban numbers ≤ 1,000 (in a horizontal format), and a count
show all eban numbers between 1,000 and 4,000 (inclusive), and a count
show a count of all eban numbers up and including 10,000
show a count of all eban numbers up and including 100,000
show a count of all eban numbers up and including 1,000,000
show a count of all eban numbers up and including 10,000,000
show all output here.
See also
The MathWorld entry: eban numbers.
The OEIS entry: A6933, eban numbers.
| #AppleScript | AppleScript | (*
Quickly generate all the (positive) eban numbers up to and including the
specified end number, then lose those before the start number.
0 is taken as "zero" rather than as "nought" or "nil".
WARNING: The getEbans() handler returns a potentially very long list of numbers.
Don't let such a list get assigned to a persistent variable or be the end result displayed in an editor!
*)
on getEbans(startNumber, endNumber)
script o
property output : {}
property listCollector : missing value
property temp : missing value
end script
if (startNumber > endNumber) then set {startNumber, endNumber} to {endNumber, startNumber}
-- The range is limited to between 0 and 10^15 to keep within AppleScript's current number precision.
-- Even so, some of the numbers may not /look/ right when displayed in a editor.
set limit to 10 ^ 15 - 1
if (endNumber > limit) then set endNumber to limit
if (startNumber > limit) then set startNumber to limit
-- Initialise the output list with 0 and the sub-1000 ebans, stopping if the end number's reached.
-- The 0's needed for rest of the process, but is removed at the end.
repeat with tens in {0, 30, 40, 50, 60}
repeat with units in {0, 2, 4, 6}
set thisEban to tens + units
if (thisEban ≤ endNumber) then set end of o's output to thisEban
end repeat
end repeat
-- Repeatedly sweep the output list, adding new ebans formed from the addition of those found previously
-- to a suitable power of 1000 times each one. Stop when the end number's reached or exceeded.
-- The output list may become very long and appending items to it individually take forever, so results are
-- collected in short, 1000-item lists, which are concatenated to the output at the end of each sweep.
set sweepLength to (count o's output)
set multiplier to 1000
repeat while (thisEban < endNumber) -- Per sweep.
set o's temp to {}
set o's listCollector to {o's temp}
repeat with i from 2 to sweepLength -- Per eban found already. (Not the 0.)
set baseAmount to (item i of o's output) * multiplier
repeat with j from 1 to sweepLength by 1000 -- Per 1000-item list.
set z to j + 999
if (z > sweepLength) then set z to sweepLength
repeat with k from j to z -- Per new eban.
set thisEban to baseAmount + (item k of o's output)
if (thisEban ≤ endNumber) then set end of o's temp to thisEban
if (thisEban ≥ endNumber) then exit repeat
end repeat
if (thisEban ≥ endNumber) then exit repeat
set o's temp to {}
set end of o's listCollector to o's temp
end repeat
if (thisEban ≥ endNumber) then exit repeat
end repeat
-- Concatentate this sweep's new lists together
set listCount to (count o's listCollector)
repeat until (listCount is 1)
set o's temp to {}
repeat with i from 2 to listCount by 2
set end of o's temp to (item (i - 1) of o's listCollector) & (item i of o's listCollector)
end repeat
if (listCount mod 2 is 1) then set item -1 of o's temp to (end of o's temp) & (end of o's listCollector)
set o's listCollector to o's temp
set o's temp to {}
set listCount to (count o's listCollector)
end repeat
-- Concatenate the result to the output list and prepare to go round again.
set o's output to o's output & (beginning of o's listCollector)
set sweepLength to sweepLength * sweepLength
set multiplier to multiplier * multiplier
end repeat
-- Lose the initial 0 and any ebans before the specified start number.
set resultCount to (count o's output)
if (resultCount is 1) then
set o's output to {}
else
repeat with i from 2 to resultCount
if (item i of o's output ≥ startNumber) then exit repeat
end repeat
set o's output to items i thru resultCount of o's output
end if
if (endNumber = limit) then set end of o's output to "(Limit of AppleScript's number precision.)"
return o's output
end getEbans
-- Task code:
on runTask()
set output to {}
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ", "
set ebans to getEbans(0, 1000)
set end of output to ((count ebans) as text) & " eban numbers between 0 and 1,000:" & (linefeed & " " & ebans)
set ebans to getEbans(1000, 4000)
set end of output to ((count ebans) as text) & " between 1,000 and 4,000:" & (linefeed & " " & ebans)
set end of output to ((count getEbans(0, 10000)) as text) & " up to and including 10,000"
set end of output to ((count getEbans(0, 100000)) as text) & " up to and including 100,000"
set end of output to ((count getEbans(0, 1000000)) as text) & " up to and including 1,000,000"
set end of output to ((count getEbans(0, 10000000)) as text) & " up to and including 10,000,000"
set ebans to getEbans(6.606606602E+10, 1.0E+12)
set end of output to ((count ebans) as text) & " between 66,066,066,020 and 1,000,000,000,000:" & (linefeed & " " & ebans)
set AppleScript's text item delimiters to linefeed
set output to output as text
set AppleScript's text item delimiters to astid
return output
end runTask
runTask() |
http://rosettacode.org/wiki/Duffinian_numbers | Duffinian numbers | A Duffinian number is a composite number k that is relatively prime to its sigma sum σ.
The sigma sum of k is the sum of the divisors of k.
E.G.
161 is a Duffinian number.
It is composite. (7 × 23)
The sigma sum 192 (1 + 7 + 23 + 161) is relatively prime to 161.
Duffinian numbers are very common.
It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.
Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.
Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).
It is not possible to have six consecutive Duffinian numbers
Task
Find and show the first 50 Duffinian numbers.
Find and show at least the first 15 Duffinian triplets.
See also
Numbers Aplenty - Duffinian numbers
OEIS:A003624 - Duffinian numbers: composite numbers k relatively prime to sigma(k)
| #AppleScript | AppleScript | on aliquotSum(n)
if (n < 2) then return 0
set sum to 1
set sqrt to n ^ 0.5
set limit to sqrt div 1
if (limit = sqrt) then
set sum to sum + limit
set limit to limit - 1
end if
repeat with i from 2 to limit
if (n mod i is 0) then set sum to sum + i + n div i
end repeat
return sum
end aliquotSum
on hcf(a, b)
repeat until (b = 0)
set x to a
set a to b
set b to x mod b
end repeat
if (a < 0) then return -a
return a
end hcf
on isDuffinian(n)
set aliquot to aliquotSum(n) -- = sigma sum - n. = 1 if n's prime.
return ((aliquot > 1) and (hcf(n, aliquot + n) = 1))
end isDuffinian
-- Task code:
on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script
set o's matrix to matrix
set padding to " "
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat
return join(o's matrix, linefeed)
end matrixToText
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
on task(duffTarget, tupTarget, tupSize)
if ((duffTarget < 1) or (tupTarget < 1) or (tupSize < 2)) then error "Duff parameter(s)."
script o
property duffinians : {}
property tuplets : {}
end script
-- Populate o's duffinians and tuplets lists.
set n to 1
set tuplet to {}
repeat while (((count o's tuplets) < tupTarget) or ((count o's duffinians) < duffTarget))
if (isDuffinian(n)) then
if ((count o's duffinians) < duffTarget) then set end of o's duffinians to n
if (tuplet ends with n - 1) then
set end of tuplet to n
else
if ((count tuplet) = tupSize) then set end of o's tuplets to tuplet
set tuplet to {n}
end if
end if
set n to n + 1
end repeat
-- Format for output.
set duffinians to {}
repeat with i from 1 to duffTarget by 20
set j to i + 19
if (j > duffTarget) then set j to duffTarget
set end of duffinians to items i thru j of o's duffinians
end repeat
set part1 to "First " & duffTarget & " Duffinian numbers:" & linefeed & ¬
matrixToText(duffinians, (count (end of o's duffinians as text)) + 2)
set tupletTypes to {missing value, "twins", "triplets:", "quadruplets:", "quintuplets:"}
set part2 to "First " & tupTarget & " Duffinian " & item tupSize of tupletTypes & linefeed & ¬
matrixToText(o's tuplets, (count (end of end of o's tuplets as text)) + 2)
return part1 & (linefeed & linefeed & part2)
end task
return task(50, 20, 3) -- First 50 Duffinians, first 20 3-item tuplets. |
http://rosettacode.org/wiki/Element-wise_operations | Element-wise operations | This task is similar to:
Matrix multiplication
Matrix transposition
Task
Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.
Implement:
addition
subtraction
multiplication
division
exponentiation
Extend the task if necessary to include additional basic operations, which should not require their own specialised task.
| #Common_Lisp | Common Lisp | (defun element-wise-matrix (fn A B)
(let* ((len (array-total-size A))
(m (car (array-dimensions A)))
(n (cadr (array-dimensions A)))
(C (make-array `(,m ,n) :initial-element 0.0d0)))
(loop for i from 0 to (1- len) do
(setf (row-major-aref C i)
(funcall fn
(row-major-aref A i)
(row-major-aref B i))))
C))
;; A.+B, A.-B, A.*B, A./B, A.^B.
(defun m+ (A B) (element-wise-matrix #'+ A B))
(defun m- (A B) (element-wise-matrix #'- A B))
(defun m* (A B) (element-wise-matrix #'* A B))
(defun m/ (A B) (element-wise-matrix #'/ A B))
(defun m^ (A B) (element-wise-matrix #'expt A B)) |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #AWK | AWK |
# syntax: GAWK -f DYNAMIC_VARIABLE_NAMES.AWK
# Variables created in GAWK's internal SYMTAB (symbol table) can only be accessed via SYMTAB[name]
BEGIN {
PROCINFO["sorted_in"] = "@ind_str_asc"
show_symbol_table()
while (1) {
printf("enter variable name? ")
getline v_name
if (v_name in SYMTAB) {
printf("name already exists with a value of '%s'\n",SYMTAB[v_name])
continue
}
if (v_name ~ /^$/) {
printf("name is null\n")
continue
}
if (v_name !~ /^[A-Za-z][A-Za-z0-9_]*$/) {
printf("name illegally constructed\n")
continue
}
break
}
printf("enter value? ")
getline v_value
SYMTAB[v_name] = v_value
printf("variable '%s' has been created and assigned the value '%s'\n\n",v_name,v_value)
show_symbol_table()
exit(0)
}
function show_symbol_table( count,i) {
for (i in SYMTAB) {
printf("%s ",i)
if (isarray(SYMTAB[i])) { count++ }
}
printf("\nsymbol table contains %d names of which %d are arrays\n\n",length(SYMTAB),count)
}
|
http://rosettacode.org/wiki/Egyptian_division | Egyptian division | Egyptian division is a method of dividing integers using addition and
doubling that is similar to the algorithm of Ethiopian multiplication
Algorithm:
Given two numbers where the dividend is to be divided by the divisor:
Start the construction of a table of two columns: powers_of_2, and doublings; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
Continue with successive i’th rows of 2^i and 2^i * divisor.
Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
We now assemble two separate sums that both start as zero, called here answer and accumulator
Consider each row of the table, in the reverse order of its construction.
If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).
Example: 580 / 34
Table creation:
powers_of_2
doublings
1
34
2
68
4
136
8
272
16
544
Initialization of sums:
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
0
0
Considering table rows, bottom-up:
When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
16
544
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
16
544
4
136
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
17
578
2
68
4
136
8
272
16
544
Answer
So 580 divided by 34 using the Egyptian method is 17 remainder (578 - 580) or 2.
Task
The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.
Functions should be clear interpretations of the algorithm.
Use the function to divide 580 by 34 and show the answer here, on this page.
Related tasks
Egyptian fractions
References
Egyptian Number System
| #C.23 | C# |
using System;
using System.Collections;
namespace Egyptian_division
{
class Program
{
public static void Main(string[] args)
{
Console.Clear();
Console.WriteLine();
Console.WriteLine(" Egyptian division ");
Console.WriteLine();
Console.Write(" Enter value of dividend : ");
int dividend = int.Parse(Console.ReadLine());
Console.Write(" Enter value of divisor : ");
int divisor = int.Parse(Console.ReadLine());
Divide(dividend, divisor);
Console.WriteLine();
Console.Write("Press any key to continue . . . ");
Console.ReadKey(true);
}
static void Divide(int dividend, int divisor)
{
//
// Local variable declaration and initialization
//
int result = 0;
int reminder = 0;
int powers_of_two = 0;
int doublings = 0;
int answer = 0;
int accumulator = 0;
int two = 2;
int pow = 0;
int row = 0;
//
// Tables declaration
//
ArrayList table_powers_of_two = new ArrayList();
ArrayList table_doublings = new ArrayList();
//
// Fill and Show table values
//
Console.WriteLine(" ");
Console.WriteLine(" powers_of_2 doublings ");
Console.WriteLine(" ");
// Set initial values
powers_of_two = 1;
doublings = divisor;
while( doublings <= dividend )
{
// Set table value
table_powers_of_two.Add( powers_of_two );
table_doublings.Add( doublings );
// Show new table row
Console.WriteLine("{0,8}{1,16}",powers_of_two, doublings);
pow++;
powers_of_two = (int)Math.Pow( two, pow );
doublings = powers_of_two * divisor;
}
Console.WriteLine(" ");
//
// Calculate division and Show table values
//
row = pow - 1;
Console.WriteLine(" ");
Console.WriteLine(" powers_of_2 doublings answer accumulator");
Console.WriteLine(" ");
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row);
pow--;
while( pow >= 0 && accumulator < dividend )
{
// Get values from tables
doublings = int.Parse(table_doublings[pow].ToString());
powers_of_two = int.Parse(table_powers_of_two[pow].ToString());
if(accumulator + int.Parse(table_doublings[pow].ToString()) <= dividend )
{
// Set new values
accumulator += doublings;
answer += powers_of_two;
// Show accumulated row values in different collor
Console.ForegroundColor = ConsoleColor.Green;
Console.Write("{0,8}{1,16}",powers_of_two, doublings);
Console.ForegroundColor = ConsoleColor.Green;
Console.WriteLine("{0,10}{1,12}", answer, accumulator);
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
}
else
{
// Show not accumulated row walues
Console.ForegroundColor = ConsoleColor.DarkGray;
Console.Write("{0,8}{1,16}",powers_of_two, doublings);
Console.ForegroundColor = ConsoleColor.Gray;
Console.WriteLine("{0,10}{1,12}", answer, accumulator);
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop - 2);
}
pow--;
}
Console.WriteLine();
Console.SetCursorPosition(Console.CursorLeft, Console.CursorTop + row + 2);
Console.ResetColor();
// Set result and reminder
result = answer;
if( accumulator < dividend )
{
reminder = dividend - accumulator;
Console.WriteLine(" So " + dividend +
" divided by " + divisor +
" using the Egyptian method is \n " + result +
" remainder (" + dividend + " - " + accumulator +
") or " + reminder);
Console.WriteLine();
}
else
{
reminder = 0;
Console.WriteLine(" So " + dividend +
" divided by " + divisor +
" using the Egyptian method is \n " + result +
" remainder " + reminder);
Console.WriteLine();
}
}
}
}
|
http://rosettacode.org/wiki/Egyptian_fractions | Egyptian fractions | An Egyptian fraction is the sum of distinct unit fractions such as:
1
2
+
1
3
+
1
16
(
=
43
48
)
{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{16}}\,(={\tfrac {43}{48}})}
Each fraction in the expression has a numerator equal to 1 (unity) and a denominator that is a positive integer, and all the denominators are distinct (i.e., no repetitions).
Fibonacci's Greedy algorithm for Egyptian fractions expands the fraction
x
y
{\displaystyle {\tfrac {x}{y}}}
to be represented by repeatedly performing the replacement
x
y
=
1
⌈
y
/
x
⌉
+
(
−
y
)
mod
x
y
⌈
y
/
x
⌉
{\displaystyle {\frac {x}{y}}={\frac {1}{\lceil y/x\rceil }}+{\frac {(-y)\!\!\!\!\mod x}{y\lceil y/x\rceil }}}
(simplifying the 2nd term in this replacement as necessary, and where
⌈
x
⌉
{\displaystyle \lceil x\rceil }
is the ceiling function).
For this task, Proper and improper fractions must be able to be expressed.
Proper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that
a
<
b
{\displaystyle a<b}
, and
improper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that a ≥ b.
(See the REXX programming example to view one method of expressing the whole number part of an improper fraction.)
For improper fractions, the integer part of any improper fraction should be first isolated and shown preceding the Egyptian unit fractions, and be surrounded by square brackets [n].
Task requirements
show the Egyptian fractions for:
43
48
{\displaystyle {\tfrac {43}{48}}}
and
5
121
{\displaystyle {\tfrac {5}{121}}}
and
2014
59
{\displaystyle {\tfrac {2014}{59}}}
for all proper fractions,
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive one-or two-digit (decimal) integers, find and show an Egyptian fraction that has:
the largest number of terms,
the largest denominator.
for all one-, two-, and three-digit integers, find and show (as above). {extra credit}
Also see
Wolfram MathWorld™ entry: Egyptian fraction
| #D | D | import std.stdio, std.bigint, std.algorithm, std.range, std.conv, std.typecons,
arithmetic_rational: Rat = Rational;
Rat[] egyptian(Rat r) pure nothrow {
typeof(return) result;
if (r >= 1) {
if (r.denominator == 1)
return [r, Rat(0, 1)];
result = [Rat(r.numerator / r.denominator, 1)];
r -= result[0];
}
static enum mod = (in BigInt m, in BigInt n) pure nothrow =>
((m % n) + n) % n;
while (r.numerator != 1) {
immutable q = (r.denominator + r.numerator - 1) / r.numerator;
result ~= Rat(1, q);
r = Rat(mod(-r.denominator, r.numerator), r.denominator * q);
}
result ~= r;
return result;
}
void main() {
foreach (immutable r; [Rat(43, 48), Rat(5, 121), Rat(2014, 59)])
writefln("%s => %(%s %)", r, r.egyptian);
Tuple!(size_t, Rat) lenMax;
Tuple!(BigInt, Rat) denomMax;
foreach (immutable r; iota(1, 100).cartesianProduct(iota(1, 100))
.map!(nd => nd[].Rat).array.sort().uniq) {
immutable e = r.egyptian;
immutable eLen = e.length;
immutable eDenom = e.back.denominator;
if (eLen > lenMax[0])
lenMax = tuple(eLen, r);
if (eDenom > denomMax[0])
denomMax = tuple(eDenom, r);
}
writefln("Term max is %s with %d terms", lenMax[1], lenMax[0]);
immutable dStr = denomMax[0].text;
writefln("Denominator max is %s with %d digits %s...%s",
denomMax[1], dStr.length, dStr[0 .. 5], dStr[$ - 5 .. $]);
} |
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Racket | Racket | #lang racket
(struct node (edges ; edges (or forward links)
link ; suffix link (backward links)
len) ; the length of the node
#:mutable)
(define (new-node link len) (node (make-hash) link len))
(struct eertree (nodes
rto ; odd length root node, or node -1
rte ; even length root node, or node 0
S ; accumulated input string, T=S[1..i]
max-suf-t) ; maximum suffix of tree T
#:mutable)
(define (new-eertree)
(let* ((rto (new-node #f -1))
(rte (new-node rto 0)))
(eertree null rto rte (list 0) rte)))
(define (eertree-get-max-suffix-pal et start-node a)
#| We traverse the suffix-palindromes of T in the order of decreasing length.
For each palindrome we read its length k and compare T[i-k] against a
until we get an equality or arrive at the -1 node. |#
(match et
[(eertree nodes rto rte (and S (app length i)) max-suf-t)
(let loop ((u start-node))
(let ((k (node-len u)))
(if (or (eq? u rto) (= (list-ref S (- i k 1)) a))
u
(let ((u→ (node-link u)))
(when (eq? u u→) (error 'eertree-get-max-suffix-pal "infinite loop"))
(loop u→)))))]))
(define (eertree-add! et a)
#| We need to find the maximum suffix-palindrome P of Ta
Start by finding maximum suffix-palindrome Q of T.
To do this, we traverse the suffix-palindromes of T
in the order of decreasing length, starting with maxSuf(T) |#
(match (eertree-get-max-suffix-pal et (eertree-max-suf-t et) a)
[(node Q.edges Q.→ Q.len)
;; We check Q to see whether it has an outgoing edge labeled by a.
(define new-node? (not (hash-has-key? Q.edges a)))
(when new-node?
(define P (new-node #f (+ Q.len 2))) ; We create the node P of length Q+2
(set-eertree-nodes! et (append (eertree-nodes et) (list P)))
(define P→
(if (= (node-len P) 1)
(eertree-rte et) ; if P = a, create the suffix link (P,0)
;; It remains to c reate the suffix link from P if |P|>1.
;; Just continue traversing suffix-palindromes of T starting with the suffix link of Q.
(hash-ref (node-edges (eertree-get-max-suffix-pal et Q.→ a)) a)))
(set-node-link! P P→)
(hash-set! Q.edges a P)) ; create the edge (Q,P)
(set-eertree-max-suf-t! et (hash-ref Q.edges a)) ; P becomes the new maxSufT
(set-eertree-S! et (append (eertree-S et) (list a))) ; Store accumulated input string
new-node?]))
(define (eertree-get-sub-palindromes et)
(define (inr nd (node-path (list nd)) (char-path/rev null))
;; Each node represents a palindrome, which can be reconstructed by the path from the root node to
;; each non-root node.
(let ((deeper ; Traverse all edges, since they represent other palindromes
(for/fold ((result null)) (([→-name nd2] (in-hash (node-edges nd))))
; The lnk-name is the character used for this edge
(append result (inr nd2 (append node-path (list nd2)) (cons →-name char-path/rev)))))
(root-node? (or (eq? (eertree-rto et) nd) (eq? (eertree-rte et) nd))))
(if root-node? ; Don't add root nodes
deeper
(let ((even-string? (eq? (car node-path) (eertree-rte et)))
(char-path (reverse char-path/rev)))
(cons (append char-path/rev (if even-string? char-path (cdr char-path))) deeper)))))
inr)
(define (eertree-get-palindromes et)
(define sub (eertree-get-sub-palindromes et))
(append (sub (eertree-rto et))
(sub (eertree-rte et))))
(module+ main
(define et (new-eertree))
;; eertree works in integer space, so we'll map to/from char space here
(for ((c "eertree")) (eertree-add! et (char->integer c)))
(map (compose list->string (curry map integer->char)) (eertree-get-palindromes et)))
|
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Raku | Raku | my $str = "eertree";
my @pal = ();
my ($strrev,$strpal);
for (1 .. $str.chars) -> $n {
for (1 .. $str.chars) -> $m {
$strrev = "";
$strpal = $str.substr($n-1, $m);
if ($strpal ne "") {
for ($strpal.chars ... 1) -> $p {
$strrev ~= $strpal.substr($p-1,1);
}
($strpal eq $strrev) and @pal.push($strpal);
}
}
}
say @pal.unique;
|
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #Raku | Raku | sub halve (Int $n is rw) { $n div= 2 }
sub double (Int $n is rw) { $n *= 2 }
sub even (Int $n --> Bool) { $n %% 2 }
sub ethiopic-mult (Int $a is copy, Int $b is copy --> Int) {
my Int $r = 0;
while $a {
even $a or $r += $b;
halve $a;
double $b;
}
return $r;
}
say ethiopic-mult(17,34); |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #F.C5.8Drmul.C3.A6 | Fōrmulæ |
argc 4 < { ."Usage: " 0 argv sprint SPACE 1 argv sprint SPACE ."rule size\n"
."The \"rule\" and \"size\" are numbers.\n"
."0<=rule<=255\n" end }
zero gen
3 argv #s (#g) sto maxcell
2 argv (#g) sto rule
#g argc 5 >= { 4 argv #s (#g) sto gen }
@maxcell mem !maximize sto livingspace
@maxcell mem sto originallivingspace
@maxcell {| @livingspace {} 0 [^] |} @livingspace @maxcell #g 2 / 1 [^]
infi: {...
originallivingspace @livingspace #s =
@livingspace {~ #k @@ { '* }{ '. } print |} NL
#g
@livingspace~ lsp: {|
zero a
@originallivingspace {} ? @maxcell -- [] { 4 sto a }
@originallivingspace {} [] { @a 2 | sto a }
@originallivingspace {+} @maxcell == { 0 }{ {+} } [] { @a 1 | sto a }
8 {| @rule 1 {} << & {
{} @a == { @livingspace {}§lsp 1 [^] {<}§lsp }
}
|}
z: @livingspace {} 0 [^] {<}
|}
#s @originallivingspace @livingspace == { {.>.} }
@gen { {...} @gen #g == { {.>.} } }
...}
."Generations: " {...}§infi #g printnl
@livingspace free
@originallivingspace free
end
{ „maxcell” }
{ „rule” }
{ „state” }
{ „livingspace” }
{ „originallivingspace” }
{ „a” }
{ „gen” }
// =================================================
|
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #Furor | Furor |
argc 4 < { ."Usage: " 0 argv sprint SPACE 1 argv sprint SPACE ."rule size\n"
."The \"rule\" and \"size\" are numbers.\n"
."0<=rule<=255\n" end }
zero gen
3 argv #s (#g) sto maxcell
2 argv (#g) sto rule
#g argc 5 >= { 4 argv #s (#g) sto gen }
@maxcell mem !maximize sto livingspace
@maxcell mem sto originallivingspace
@maxcell {| @livingspace {} 0 [^] |} @livingspace @maxcell #g 2 / 1 [^]
infi: {...
originallivingspace @livingspace #s =
@livingspace {~ #k @@ { '* }{ '. } print |} NL
#g
@livingspace~ lsp: {|
zero a
@originallivingspace {} ? @maxcell -- [] { 4 sto a }
@originallivingspace {} [] { @a 2 | sto a }
@originallivingspace {+} @maxcell == { 0 }{ {+} } [] { @a 1 | sto a }
8 {| @rule 1 {} << & {
{} @a == { @livingspace {}§lsp 1 [^] {<}§lsp }
}
|}
z: @livingspace {} 0 [^] {<}
|}
#s @originallivingspace @livingspace == { {.>.} }
@gen { {...} @gen #g == { {.>.} } }
...}
."Generations: " {...}§infi #g printnl
@livingspace free
@originallivingspace free
end
{ „maxcell” }
{ „rule” }
{ „state” }
{ „livingspace” }
{ „originallivingspace” }
{ „a” }
{ „gen” }
// =================================================
|
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #TorqueScript | TorqueScript | function Factorial(%num)
{
if(%num < 2)
return 1;
for(%a = %num-1; %a > 1; %a--)
%num *= %a;
return %num;
} |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Vlang | Vlang | fn test(n i64) {
print('Testing integer $n')
if n&1 == 0 {
print(' even')
}else{
print(' odd')
}
if n%2 == 0 {
println(' even')
}else{
println(' odd')
}
}
fn main(){
test(-2)
test(-1)
test(0)
test(1)
test(2)
} |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #WDTE | WDTE | let s => import 'stream';
let str => import 'strings';
let evenOrOdd n => (
let even n => == (% n 2) 0;
switch n {
even => 'even';
default => 'odd';
};
);
s.range 10
-> s.map (@ s n => str.format '{} is {}.' n (evenOrOdd n))
-> s.map (io.writeln io.stdout)
-> s.drain; |
http://rosettacode.org/wiki/Echo_server | Echo server | Create a network service that sits on TCP port 12321, which accepts connections on that port, and which echoes complete lines (using a carriage-return/line-feed sequence as line separator) back to clients. No error handling is required. For the purposes of testing, it is only necessary to support connections from localhost (127.0.0.1 or perhaps ::1). Logging of connection information to standard output is recommended.
The implementation must be able to handle simultaneous connections from multiple clients. A multi-threaded or multi-process solution may be used. Each connection must be able to echo more than a single line.
The implementation must not stop responding to other clients if one client sends a partial line or stops reading responses.
| #Haskell | Haskell | module Main where
import Network (withSocketsDo, accept, listenOn, sClose, PortID(PortNumber))
import Control.Monad (forever)
import System.IO (hGetLine, hPutStrLn, hFlush, hClose)
import System.IO.Error (isEOFError)
import Control.Concurrent (forkIO)
import Control.Exception (bracket)
-- For convenience in testing, ensure that the listen socket is closed if the main loop is aborted
withListenOn port body = bracket (listenOn port) sClose body
echo (handle, host, port) = catch (forever doOneLine) stop where
doOneLine = do line <- hGetLine handle
print (host, port, init line)
hPutStrLn handle line
hFlush handle
stop error = do putStrLn $ "Closed connection from " ++ show (host, port) ++ " due to " ++ show error
hClose handle
main = withSocketsDo $
withListenOn (PortNumber 12321) $ \listener ->
forever $ do
acc@(_, host, port) <- accept listener
putStrLn $ "Accepted connection from " ++ show (host, port)
forkIO (echo acc) |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Swift | Swift | |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Symsyn | Symsyn | |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #Tcl | Tcl | |
http://rosettacode.org/wiki/Eban_numbers | Eban numbers |
Definition
An eban number is a number that has no letter e in it when the number is spelled in English.
Or more literally, spelled numbers that contain the letter e are banned.
The American version of spelling numbers will be used here (as opposed to the British).
2,000,000,000 is two billion, not two milliard.
Only numbers less than one sextillion (1021) will be considered in/for this task.
This will allow optimizations to be used.
Task
show all eban numbers ≤ 1,000 (in a horizontal format), and a count
show all eban numbers between 1,000 and 4,000 (inclusive), and a count
show a count of all eban numbers up and including 10,000
show a count of all eban numbers up and including 100,000
show a count of all eban numbers up and including 1,000,000
show a count of all eban numbers up and including 10,000,000
show all output here.
See also
The MathWorld entry: eban numbers.
The OEIS entry: A6933, eban numbers.
| #AutoHotkey | AutoHotkey | eban_numbers(min, max, show:=0){
counter := 0, output := ""
i := min
while ((i+=2) <= max)
{
b := floor(i / 1000000000)
r := Mod(i, 1000000000)
m := floor(r / 1000000)
r := Mod(i, 1000000)
t := floor(r / 1000)
r := Mod(r, 1000)
if (m >= 30 && m <= 66)
m := Mod(m, 10)
if (t >= 30 && t <= 66)
t := Mod(t, 10)
if (r >= 30 && r <= 66)
r := Mod(r, 10)
if (b = 0 || b = 2 || b = 4 || b = 6)
&& (m = 0 || m = 2 || m = 4 || m = 6)
&& (t = 0 || t = 2 || t = 4 || t = 6)
&& (r = 0 || r = 2 || r = 4 || r = 6)
counter++, (show ? output .= i " " : "")
}
return min "-" max " : " output " Count = " counter
} |
http://rosettacode.org/wiki/Duffinian_numbers | Duffinian numbers | A Duffinian number is a composite number k that is relatively prime to its sigma sum σ.
The sigma sum of k is the sum of the divisors of k.
E.G.
161 is a Duffinian number.
It is composite. (7 × 23)
The sigma sum 192 (1 + 7 + 23 + 161) is relatively prime to 161.
Duffinian numbers are very common.
It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.
Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.
Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).
It is not possible to have six consecutive Duffinian numbers
Task
Find and show the first 50 Duffinian numbers.
Find and show at least the first 15 Duffinian triplets.
See also
Numbers Aplenty - Duffinian numbers
OEIS:A003624 - Duffinian numbers: composite numbers k relatively prime to sigma(k)
| #Arturo | Arturo | duffinian?: function [n]->
and? [not? prime? n]
[
fn: factors n
[1] = intersection factors sum fn fn
]
first50: new []
i: 0
while [50 > size first50][
if duffinian? i -> 'first50 ++ i
i: i + 1
]
print "The first 50 Duffinian numbers:"
loop split.every: 10 first50 'row [
print map to [:string] row 'item -> pad item 3
]
first15: new []
i: 0
while [15 > size first15][
if every? i..i+2 => duffinian? [
'first15 ++ @[@[i, i+1, i+2]]
i: i+2
]
i: i + 1
]
print ""
print "The first 15 Duffinian triplets:"
loop split.every: 5 first15 'row [
print map row 'item -> pad.right as.code item 17
] |
http://rosettacode.org/wiki/Duffinian_numbers | Duffinian numbers | A Duffinian number is a composite number k that is relatively prime to its sigma sum σ.
The sigma sum of k is the sum of the divisors of k.
E.G.
161 is a Duffinian number.
It is composite. (7 × 23)
The sigma sum 192 (1 + 7 + 23 + 161) is relatively prime to 161.
Duffinian numbers are very common.
It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.
Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.
Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).
It is not possible to have six consecutive Duffinian numbers
Task
Find and show the first 50 Duffinian numbers.
Find and show at least the first 15 Duffinian triplets.
See also
Numbers Aplenty - Duffinian numbers
OEIS:A003624 - Duffinian numbers: composite numbers k relatively prime to sigma(k)
| #C.2B.2B | C++ | #include <iomanip>
#include <iostream>
#include <numeric>
#include <sstream>
bool duffinian(int n) {
if (n == 2)
return false;
int total = 1, power = 2, m = n;
for (; (n & 1) == 0; power <<= 1, n >>= 1)
total += power;
for (int p = 3; p * p <= n; p += 2) {
int sum = 1;
for (power = p; n % p == 0; power *= p, n /= p)
sum += power;
total *= sum;
}
if (m == n)
return false;
if (n > 1)
total *= n + 1;
return std::gcd(total, m) == 1;
}
int main() {
std::cout << "First 50 Duffinian numbers:\n";
for (int n = 1, count = 0; count < 50; ++n) {
if (duffinian(n))
std::cout << std::setw(3) << n << (++count % 10 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 50 Duffinian triplets:\n";
for (int n = 1, m = 0, count = 0; count < 50; ++n) {
if (duffinian(n))
++m;
else
m = 0;
if (m == 3) {
std::ostringstream os;
os << '(' << n - 2 << ", " << n - 1 << ", " << n << ')';
std::cout << std::left << std::setw(24) << os.str()
<< (++count % 3 == 0 ? '\n' : ' ');
}
}
std::cout << '\n';
} |
http://rosettacode.org/wiki/Element-wise_operations | Element-wise operations | This task is similar to:
Matrix multiplication
Matrix transposition
Task
Implement basic element-wise matrix-matrix and scalar-matrix operations, which can be referred to in other, higher-order tasks.
Implement:
addition
subtraction
multiplication
division
exponentiation
Extend the task if necessary to include additional basic operations, which should not require their own specialised task.
| #D | D | import std.stdio, std.typetuple, std.traits;
T[][] elementwise(string op, T, U)(in T[][] A, in U B) {
auto R = new typeof(return)(A.length, A[0].length);
foreach (r, row; A)
R[r][] = mixin("row[] " ~ op ~ (isNumeric!U ? "B" : "B[r][]"));
return R;
}
void main() {
const M = [[3, 5, 7], [1, 2, 3], [2, 4, 6]];
foreach (op; TypeTuple!("+", "-", "*", "/", "^^"))
writefln("%s:\n[%([%(%d, %)],\n %)]]\n\n[%([%(%d, %)],\n %)]]\n",
op, elementwise!op(M, 2), elementwise!op(M, M));
} |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #BASIC | BASIC | 10 INPUT "Enter a variable name", v$
20 KEYIN "LET "+v$+"=42" |
http://rosettacode.org/wiki/Dynamic_variable_names | Dynamic variable names | Task
Create a variable with a user-defined name.
The variable name should not be written in the program text, but should be taken from the user dynamically.
See also
Eval in environment is a similar task.
| #Batch_File | Batch File | @echo off
setlocal enableDelayedExpansion
set /p "name=Enter a variable name: "
set /p "value=Enter a value: "
::Create the variable and set its value
set "%name%=%value%"
::Display the value without delayed expansion
call echo %name%=%%%name%%%
::Display the value using delayed expansion
echo %name%=!%name%! |
http://rosettacode.org/wiki/Egyptian_division | Egyptian division | Egyptian division is a method of dividing integers using addition and
doubling that is similar to the algorithm of Ethiopian multiplication
Algorithm:
Given two numbers where the dividend is to be divided by the divisor:
Start the construction of a table of two columns: powers_of_2, and doublings; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
Continue with successive i’th rows of 2^i and 2^i * divisor.
Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
We now assemble two separate sums that both start as zero, called here answer and accumulator
Consider each row of the table, in the reverse order of its construction.
If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
(And the remainder is given by the absolute value of accumulator - dividend).
Example: 580 / 34
Table creation:
powers_of_2
doublings
1
34
2
68
4
136
8
272
16
544
Initialization of sums:
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
0
0
Considering table rows, bottom-up:
When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
8
272
16
544
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
4
136
16
544
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
2
68
16
544
4
136
8
272
16
544
powers_of_2
doublings
answer
accumulator
1
34
17
578
2
68
4
136
8
272
16
544
Answer
So 580 divided by 34 using the Egyptian method is 17 remainder (578 - 580) or 2.
Task
The task is to create a function that does Egyptian division. The function should
closely follow the description above in using a list/array of powers of two, and
another of doublings.
Functions should be clear interpretations of the algorithm.
Use the function to divide 580 by 34 and show the answer here, on this page.
Related tasks
Egyptian fractions
References
Egyptian Number System
| #C.2B.2B | C++ | #include <cassert>
#include <iostream>
typedef unsigned long ulong;
/*
* Remainder is an out paramerter. Use nullptr if the remainder is not needed.
*/
ulong egyptian_division(ulong dividend, ulong divisor, ulong* remainder) {
constexpr int SIZE = 64;
ulong powers[SIZE];
ulong doublings[SIZE];
int i = 0;
for (; i < SIZE; ++i) {
powers[i] = 1 << i;
doublings[i] = divisor << i;
if (doublings[i] > dividend) {
break;
}
}
ulong answer = 0;
ulong accumulator = 0;
for (i = i - 1; i >= 0; --i) {
/*
* If the current value of the accumulator added to the
* doublings cell would be less than or equal to the
* dividend then add it to the accumulator
*/
if (accumulator + doublings[i] <= dividend) {
accumulator += doublings[i];
answer += powers[i];
}
}
if (remainder) {
*remainder = dividend - accumulator;
}
return answer;
}
void print(ulong a, ulong b) {
using namespace std;
ulong x, y;
x = egyptian_division(a, b, &y);
cout << a << " / " << b << " = " << x << " remainder " << y << endl;
assert(a == b * x + y);
}
int main() {
print(580, 34);
return 0;
} |
http://rosettacode.org/wiki/Egyptian_fractions | Egyptian fractions | An Egyptian fraction is the sum of distinct unit fractions such as:
1
2
+
1
3
+
1
16
(
=
43
48
)
{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{16}}\,(={\tfrac {43}{48}})}
Each fraction in the expression has a numerator equal to 1 (unity) and a denominator that is a positive integer, and all the denominators are distinct (i.e., no repetitions).
Fibonacci's Greedy algorithm for Egyptian fractions expands the fraction
x
y
{\displaystyle {\tfrac {x}{y}}}
to be represented by repeatedly performing the replacement
x
y
=
1
⌈
y
/
x
⌉
+
(
−
y
)
mod
x
y
⌈
y
/
x
⌉
{\displaystyle {\frac {x}{y}}={\frac {1}{\lceil y/x\rceil }}+{\frac {(-y)\!\!\!\!\mod x}{y\lceil y/x\rceil }}}
(simplifying the 2nd term in this replacement as necessary, and where
⌈
x
⌉
{\displaystyle \lceil x\rceil }
is the ceiling function).
For this task, Proper and improper fractions must be able to be expressed.
Proper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that
a
<
b
{\displaystyle a<b}
, and
improper fractions are of the form
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive integers, such that a ≥ b.
(See the REXX programming example to view one method of expressing the whole number part of an improper fraction.)
For improper fractions, the integer part of any improper fraction should be first isolated and shown preceding the Egyptian unit fractions, and be surrounded by square brackets [n].
Task requirements
show the Egyptian fractions for:
43
48
{\displaystyle {\tfrac {43}{48}}}
and
5
121
{\displaystyle {\tfrac {5}{121}}}
and
2014
59
{\displaystyle {\tfrac {2014}{59}}}
for all proper fractions,
a
b
{\displaystyle {\tfrac {a}{b}}}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are positive one-or two-digit (decimal) integers, find and show an Egyptian fraction that has:
the largest number of terms,
the largest denominator.
for all one-, two-, and three-digit integers, find and show (as above). {extra credit}
Also see
Wolfram MathWorld™ entry: Egyptian fraction
| #Erlang | Erlang | -module(egypt).
-import(lists, [reverse/1, seq/2]).
-export([frac/2, show/2, rosetta/0]).
rosetta() ->
Fractions = [{N, D, second(frac(N, D))} || N <- seq(2,99), D <- seq(N+1, 99)],
{Longest, A1, B1} = findmax(fun length/1, Fractions),
io:format("~b/~b has ~b terms.~n", [A1, B1, Longest]),
{Largest, A2, B2} = findmax(fun (L) -> hd(reverse(L)) end, Fractions),
io:format("~b/~b has a really long denominator. (~b)~n", [A2, B2, Largest]).
second({_, B}) -> B.
findmax(Fn, L) -> findmax(Fn, L, 0, 0, 0).
findmax(_, [], M, A, B) -> {M, A, B};
findmax(Fn, [{A,B,Frac}|Fracs], M, A0, B0) ->
Val = Fn(Frac),
case Val > M of
true -> findmax(Fn, Fracs, Val, A, B);
false -> findmax(Fn, Fracs, M, A0, B0)
end.
show(A, B) ->
{W, R} = frac(A, B),
case W of
0 -> ok;
_ -> io:format("[~b] ", [W])
end,
case R of
[] -> ok;
[D0|Ds] ->
io:format("1/~b ", [D0]),
[io:format("+ 1/~b ", [D]) || D <- Ds],
ok
end.
frac(A, B) ->
{A div B, reverse(proper(A rem B, B, []))}.
proper(0, _, L) -> L;
proper(1, Y, L) -> [Y|L];
proper(X, Y, L) ->
D = ceildiv(Y, X),
X2 = mod(-Y, X),
Y2 = Y*ceildiv(Y, X),
proper(X2, Y2, [D|L]).
ceildiv(A, B) ->
Q = A div B,
case A rem B of
0 -> Q;
_ -> Q+1
end.
mod(A, M) ->
B = A rem M,
if
B < 0 -> B + M;
true -> B
end.
|
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #REXX | REXX | /*REXX program creates a list of (unique) sub─palindromes that exist in an input string.*/
parse arg x . /*obtain optional input string from CL.*/
if x=='' | x=="," then x= 'eertree' /*Not specified? Then use the default.*/
L= length(x) /*the length (in chars) of input string*/
@.= . /*@ tree indicates uniqueness of pals. */
$= /*list of unsorted & unique palindromes*/
do j=1 for L /*start at the left side of the string.*/
do k=1 for L /*traverse from left to right of string*/
parse var x =(j) y +(k) /*extract a substring from the string. */
if reverse(y)\==y | @.y\==. then iterate /*Partial string a palindrome? Skip it*/
@.y= y /*indicate a sub─palindrome was found. */
$= $' ' y /*append the sub─palindrome to the list*/
end /*k*/ /* [↑] an extra blank is inserted. */
end /*j*/
say '──────── The input string that is being used: ' space(x)
say '──────── The number of sub─palindromes found: ' words($)
say '──────── The list of sub─palindromes found: ' strip($)
/*stick a fork in it, we're all done. */ |
http://rosettacode.org/wiki/Eertree | Eertree | An eertree is a data structure designed for efficient processing of certain palindrome tasks, for instance counting the number of sub-palindromes in an input string.
The data structure has commonalities to both tries and suffix trees.
See links below.
Task
Construct an eertree for the string "eertree", then output all sub-palindromes by traversing the tree.
See also
Wikipedia entry: trie.
Wikipedia entry: suffix tree
Cornell University Library, Computer Science, Data Structures and Algorithms ───► EERTREE: An Efficient Data Structure for Processing Palindromes in Strings.
| #Ring | Ring |
# Project : Eertree
str = "eertree"
pal = []
for n=1 to len(str)
for m=1 to len(str)
strrev = ""
strpal = substr(str, n, m)
if strpal != ""
for p=len(strpal) to 1 step -1
strrev = strrev + strpal[p]
next
if strpal = strrev
add(pal, strpal)
ok
ok
next
next
sortpal = sort(pal)
for n=len(sortpal) to 2 step -1
if sortpal[n] = sortpal[n-1]
del(sortpal, n)
ok
next
see sortpal + nl
|
http://rosettacode.org/wiki/Ethiopian_multiplication | Ethiopian multiplication | Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.
Method:
Take two numbers to be multiplied and write them down at the top of two columns.
In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
Examine the table produced and discard any row where the value in the left column is even.
Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 × 34
17 34
Halving the first column:
17 34
8
4
2
1
Doubling the second column:
17 34
8 68
4 136
2 272
1 544
Strike-out rows whose first cell is even:
17 34
8 68
4 136
2 272
1 544
Sum the remaining numbers in the right-hand column:
17 34
8 --
4 ---
2 ---
1 544
====
578
So 17 multiplied by 34, by the Ethiopian method is 578.
Task
The task is to define three named functions/methods/procedures/subroutines:
one to halve an integer,
one to double an integer, and
one to state if an integer is even.
Use these functions to create a function that does Ethiopian multiplication.
References
Ethiopian multiplication explained (BBC Video clip)
A Night Of Numbers - Go Forth And Multiply (Video)
Russian Peasant Multiplication
Programming Praxis: Russian Peasant Multiplication
| #Rascal | Rascal | import IO;
public int halve(int n) = n/2;
public int double(int n) = n*2;
public bool uneven(int n) = (n % 2) != 0);
public int ethiopianMul(int n, int m) {
result = 0;
while(n >= 1) {
if(uneven(n))
result += m;
n = halve(n);
m = double(m);
}
return result;
} |
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #GFA_Basic | GFA Basic |
'
' Elementary One-Dimensional Cellular Automaton
'
' World is cyclic, and rules are defined by a parameter
'
' start$="01110110101010100100" ! start state for world
' rules%=104 ! number defining rule-set to use
start$="00000000000000000000100000000000000000000"
rules%=18
max_cycles%=20 ! give a maximum depth to world
'
' Global variables hold the world, with two rows
' world! is treated as cyclical
' cur% gives the row for current world,
' new% gives the row for the next world.
'
size%=LEN(start$)
DIM world!(size%,2)
cur%=0
new%=1
clock%=0
'
@setup_world(start$)
OPENW 1
CLEARW 1
DO
@display_world
@update_world
EXIT IF @same_state
clock%=clock%+1
EXIT IF clock%>max_cycles% ! safety net
LOOP
~INP(2)
CLOSEW 1
'
' parse given string to set up initial states in world
' -- assumes world! is of correct size
'
PROCEDURE setup_world(defn$)
LOCAL i%
' clear out the array
ARRAYFILL world!(),FALSE
' for each 1 in string, set cell to true
FOR i%=1 TO LEN(defn$)
IF MID$(defn$,i%,1)="1"
world!(i%-1,0)=TRUE
ENDIF
NEXT i%
' set references to cur and new
cur%=0
new%=1
RETURN
'
' Display the world
'
PROCEDURE display_world
LOCAL i%
FOR i%=1 TO size%
IF world!(i%-1,cur%)
PRINT "#";
ELSE
PRINT ".";
ENDIF
NEXT i%
PRINT ""
RETURN
'
' Create new version of world
'
PROCEDURE update_world
LOCAL i%
FOR i%=1 TO size%
world!(i%-1,new%)=@new_state(@get_value(i%-1))
NEXT i%
' reverse cur/new
cur%=1-cur%
new%=1-new%
RETURN
'
' Test if cur/new states are the same
'
FUNCTION same_state
LOCAL i%
FOR i%=1 TO size%
IF world!(i%-1,cur%)<>world!(i%-1,new%)
RETURN FALSE
ENDIF
NEXT i%
RETURN TRUE
ENDFUNC
'
' Return new state of cell given value
'
FUNCTION new_state(value%)
RETURN BTST(rules%,value%)
ENDFUNC
'
' Compute value for cell + neighbours
'
FUNCTION get_value(cell%)
LOCAL result%
result%=0
IF cell%-1<0 ! check for wrapping at left
IF world!(size%-1,cur%)
result%=result%+4
ENDIF
ELSE ! no wrapping
IF world!(cell%-1,cur%)
result%=result%+4
ENDIF
ENDIF
IF world!(cell%,cur%)
result%=result%+2
ENDIF
IF cell%+1>size% ! check for wrapping at right
IF world!(0,cur%)
result%=result%+1
ENDIF
ELSE ! no wrapping
IF world!(cell%+1,cur%)
result%=result%+1
ENDIF
ENDIF
RETURN result%
ENDFUNC
|
http://rosettacode.org/wiki/Elementary_cellular_automaton | Elementary cellular automaton | An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
See also
Cellular automata (natureofcode.com)
| #Go | Go | package main
import (
"fmt"
"math/big"
"math/rand"
"strings"
)
func main() {
const cells = 20
const generations = 9
fmt.Println("Single 1, rule 90:")
a := big.NewInt(1)
a.Lsh(a, cells/2)
elem(90, cells, generations, a)
fmt.Println("Random intial state, rule 30:")
a = big.NewInt(1)
a.Rand(rand.New(rand.NewSource(3)), a.Lsh(a, cells))
elem(30, cells, generations, a)
}
func elem(rule uint, cells, generations int, a *big.Int) {
output := func() {
fmt.Println(strings.Replace(strings.Replace(
fmt.Sprintf("%0*b", cells, a), "0", " ", -1), "1", "#", -1))
}
output()
a1 := new(big.Int)
set := func(cell int, k uint) {
a1.SetBit(a1, cell, rule>>k&1)
}
last := cells - 1
for r := 0; r < generations; r++ {
k := a.Bit(last) | a.Bit(0)<<1 | a.Bit(1)<<2
set(0, k)
for c := 1; c < last; c++ {
k = k>>1 | a.Bit(c+1)<<2
set(c, k)
}
set(last, k>>1|a.Bit(0)<<2)
a, a1 = a1, a
output()
}
} |
http://rosettacode.org/wiki/Factorial | Factorial | Definitions
The factorial of 0 (zero) is defined as being 1 (unity).
The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
Related task
Primorial numbers
| #TransFORTH | TransFORTH | : FACTORIAL
1 SWAP
1 + 1 DO
I * LOOP ; |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #WebAssembly | WebAssembly | (module
;; function isOdd: returns 1 if its argument is odd, 0 if it is even.
(func $isOdd (param $n i32) (result i32)
get_local $n
i32.const 1
i32.and ;; computes (n & 1), i.e. returns low bit of n
)
(export "isOdd" (func $isOdd))
) |
http://rosettacode.org/wiki/Even_or_odd | Even or odd | Task
Test whether an integer is even or odd.
There is more than one way to solve this task:
Use the even and odd predicates, if the language provides them.
Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd.
Divide i by 2. The remainder equals 0 iff i is even. The remainder equals +1 or -1 iff i is odd.
Use modular congruences:
i ≡ 0 (mod 2) iff i is even.
i ≡ 1 (mod 2) iff i is odd.
| #Wren | Wren | import "/fmt" for Fmt
var isEven1 = Fn.new { |i| i & 1 == 0 }
var isEven2 = Fn.new { |i| i % 2 == 0 }
var tests = [10, 11, 0, 57, 34, -23, -42]
System.print("Tests : %(Fmt.v("s", -4, tests, 0, " ", ""))")
var res1 = tests.map { |t| isEven1.call(t) ? "even" : "odd" }.toList
System.print("Method 1 : %(Fmt.v("s", -4, res1, 0, " ", ""))")
var res2 = tests.map { |t| isEven2.call(t) ? "even" : "odd" }.toList
System.print("Method 2 : %(Fmt.v("s", -4, res2, 0, " ", ""))") |
http://rosettacode.org/wiki/Echo_server | Echo server | Create a network service that sits on TCP port 12321, which accepts connections on that port, and which echoes complete lines (using a carriage-return/line-feed sequence as line separator) back to clients. No error handling is required. For the purposes of testing, it is only necessary to support connections from localhost (127.0.0.1 or perhaps ::1). Logging of connection information to standard output is recommended.
The implementation must be able to handle simultaneous connections from multiple clients. A multi-threaded or multi-process solution may be used. Each connection must be able to echo more than a single line.
The implementation must not stop responding to other clients if one client sends a partial line or stops reading responses.
| #Icon_and_Unicon | Icon and Unicon | global mlck, nCons
procedure main()
mlck := mutex()
nCons := 0
while f := open(":12321","na") do {
handle_client(f)
critical mlck: if nCons <= 0 then close(f)
}
end
procedure handle_client(f)
critical mlck: nCons +:= 1
thread {
select(f,1000) & repeat writes(f,reads(f))
critical mlck: nCons -:= 1
}
end |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #TI-83_BASIC | TI-83 BASIC | |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #TI-83_Hex_Assembly | TI-83 Hex Assembly | PROGRAM:EMPTY
:AsmPrgmC9 |
http://rosettacode.org/wiki/Empty_program | Empty program | Task
Create the simplest possible program that is still considered "correct."
| #TI-89_BASIC | TI-89 BASIC | Prgm
EndPrgm
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.