# Josephus problem

Josephus problem
You are encouraged to solve this task according to the task description, using any language you may know.

Josephus problem is a math puzzle with a grim description: ${\displaystyle n}$ prisoners are standing on a circle, sequentially numbered from ${\displaystyle 0}$ to ${\displaystyle n-1}$.

An executioner walks along the circle, starting from prisoner ${\displaystyle 0}$, removing every ${\displaystyle k}$-th prisoner and killing him.

As the process goes on, the circle becomes smaller and smaller, until only one prisoner remains, who is then freed. >

For example, if there are ${\displaystyle n=5}$ prisoners and ${\displaystyle k=2}$, the order the prisoners are killed in (let's call it the "killing sequence") will be 1, 3, 0, and 4, and the survivor will be #2.

Given any   ${\displaystyle n,k>0}$,   find out which prisoner will be the final survivor.

In one such incident, there were 41 prisoners and every 3rd prisoner was being killed   (${\displaystyle k=3}$).

Among them was a clever chap name Josephus who worked out the problem, stood at the surviving position, and lived on to tell the tale.

Which number was he?

Extra

The captors may be especially kind and let ${\displaystyle m}$ survivors free,
and Josephus might just have   ${\displaystyle m-1}$   friends to save.

Provide a way to calculate which prisoner is at any given position on the killing sequence.

Notes
1. You can always play the executioner and follow the procedure exactly as described, walking around the circle, counting (and cutting off) heads along the way. This would yield the complete killing sequence and answer the above questions, with a complexity of probably ${\displaystyle O(kn)}$. However, individually it takes no more than ${\displaystyle O(m)}$ to find out which prisoner is the ${\displaystyle m}$-th to die.
2. If it's more convenient, you can number prisoners from   ${\displaystyle 1}$ to ${\displaystyle n}$   instead.   If you choose to do so, please state it clearly.
3. An alternative description has the people committing assisted suicide instead of being executed, and the last person simply walks away. These details are not relevant, at least not mathematically.

## 360 Assembly

Translation of: REXX

The program uses two ASSIST macros (XDECO,XPRNT) to keep the code as short as possible.

`*      Josephus problem               10/02/2017JOSEPH CSECT       USING  JOSEPH,R13              base register       B      72(R15)                 skip savearea       DC     17F'0'                  savearea       STM    R14,R12,12(R13)         prolog       ST     R13,4(R15)              " <-       ST     R15,8(R13)              " ->       LR     R13,R15                 " addressability       LA     R7,1                    m=1       DO WHILE=(C,R7,LE,=A(NPROB))   do m=1 to nprob         LR     R1,R7                   m         MH     R1,=H'6'                *6         LH     R2,PROB-6(R1)         ST     R2,N                    n=prob(m,1)         LH     R2,PROB-4(R1)         ST     R2,W                    w=prob(m,2)         LH     R2,PROB-2(R1)         ST     R2,S                    s=prob(m,3)         MVC    PG,=CL80'josephus'      init buffer         L      R1,N                    n         XDECO  R1,DEC                  edit         MVC    PG+8(4),DEC+8           output         L      R1,W                    w         XDECO  R1,DEC                  edit          MVC    PG+12(4),DEC+8          output         L      R1,S                    s         XDECO  R1,DEC                  edit          MVC    PG+16(4),DEC+8          output         XPRNT  PG,L'PG                 print buffer         MVI    DEAD,X'00'              dead(1)='0'B;         MVC    DEAD+1(255),DEAD        dead(*)='0'B;         L      R11,N                   nx=n         L      R8,=F'-1'               p=-1         DO UNTIL=(C,R11,EQ,S)          do until n=s            SR     R9,R9                   found=0           DO UNTIL=(C,R9,EQ,W)           do until found=w              LA     R8,1(R8)                p=p+1             IF C,R8,EQ,N THEN              if p=nn then               SR     R8,R8                   p=0             ENDIF  ,                       end if             LA     R2,DEAD(R8)             @dead(p+1)             IF CLI,0(R2),EQ,X'00' THEN     if not dead(p+1) then               LA     R9,1(R9)                found=found+1             ENDIF  ,                       end if           ENDDO  ,                       end do           LA     R2,DEAD(R8)             @dead(p+1)           MVI    0(R2),X'01'             dead(p+1)='1'B           BCTR   R11,0                   nx=nx-1         ENDDO  ,                       end do         MVC    PG,=CL80' '             clear buffer         LA     R10,PG                  ipg=0         L      R9,N                    nn         BCTR   R9,0                    nn-1         SR     R6,R6                   i=0         DO WHILE=(CR,R6,LE,R9)         do i=0 to nn-1           LA     R2,DEAD(R6)             @dead(i+1)           IF CLI,0(R2),EQ,X'00' THEN     if not dead(i+1) then             XDECO  R6,DEC                  edit i             MVC    0(4,R10),DEC+8          output             LA     R10,4(R10)              ipg=ipg+4           ENDIF  ,                       end if           LA     R6,1(R6)                i=i+1         ENDDO  ,                       end do         XPRNT  PG,L'PG                 print buffer         LA     R7,1(R7)                m=m+1       ENDDO  ,                       end do       L      R13,4(0,R13)            epilog        LM     R14,R12,12(R13)         " restore       XR     R15,R15                 " rc=0       BR     R14                     exitPROB   DC     H'41',H'3',H'1'         round 1       DC     H'41',H'3',H'3'         round 2NPROB  EQU    (*-PROB)/6              number of roundsN      DS     F                       n number of prisonersW      DS     F                       w killing countS      DS     F                       s number of prisoners to survivePG     DS     CL80                    bufferDEC    DS     CL12                    temp for xdecoDEAD   DS     256X                    n max       YREGS       END    JOSEPH`
Output:
```josephus  41   3   1
30
josephus  41   3   3
15  30  34
```

## 6502 Assembly

This subroutine expects to be called with the value of n in the accumulator and the value of k in index register X. It returns with the index of the survivor in the accumulator, and also leaves an array beginning at address 1000 hex giving the order in which the prisoners died. For example, in the case where n = 5 and k = 2, the values stored in the array are 2, 0, 4, 1, 3. From this we see that prisoner 1 was the first to die, then prisoner 3, and so on. (Note that prisoner 2 in this instance is the survivor.)

`JSEPHS: STA  \$D0        ; n        STX  \$D1        ; k        LDA  #\$FF        LDX  #\$00SETUP:  STA  \$1000,X    ; populate array with hex FF        INX        CPX  \$D0        BEQ  KILL        JMP  SETUPKILL:   LDA  #\$00       ; number killed so far        STA  \$D2        LDX  #\$00       ; position within array        LDY  #\$01       ; counting up to kFIND:   INYSCAN:   INX        CPX  \$D0        BMI  TEST        LDX  #\$00       ; circle back aroundTEST:   LDA  \$1000,X        CMP  #\$FF        BNE  SCAN       ; already been killed        CPY  \$D1        BMI  FIND       ; if y < k keep going round        LDA  \$D2        STA  \$1000,X    ; mark as dead        CLC        ADC  #\$01        STA  \$D2        CMP  \$D0        ; have we killed all but 1?        BPL  RETURN        LDY  #\$00        JMP  FINDRETURN: TXA             ; a <- index of survivor        RTS`

The procedure reads up to 4 parameters from the command line: the number N of prisoners, the step size K, the number M of survivors, and an indicator whether the executions shall be printed ("1") or only surviving prisoners (any other input). The defaults are 41, 3, 1, 1. The prison cells are numbered from 0 to N-1.

`with Ada.Command_Line, Ada.Text_IO; procedure Josephus is    function Arg(Idx, Default: Positive) return Positive is -- read Argument(Idx)      (if Ada.Command_Line.Argument_Count >= Index         then Positive'Value(Ada.Command_Line.Argument(Index)) else Default);    Prisoners:  constant Positive := Arg(Idx => 1, Default => 41);   Steps:      constant Positive := Arg(Idx => 2, Default =>  3);   Survivors:  constant Positive := Arg(Idx => 3, Default =>  1);   Print:               Boolean := (Arg(Idx => 4, Default =>  1) = 1);    subtype Index_Type is Natural range 0 .. Prisoners-1;   Next: array(Index_Type) of Index_Type;   X: Index_Type := (Steps-2) mod Prisoners; begin   Ada.Text_IO.Put_Line     ("N =" & Positive'Image(Prisoners) & ",  K =" & Positive'Image(Steps) &        (if Survivors > 1 then ",  #survivors =" & Positive'Image(Survivors)        else ""));   for Idx in Next'Range loop -- initialize Next      Next(Idx) := (Idx+1) mod Prisoners;   end loop;   if Print then      Ada.Text_IO.Put("Executed: ");   end if;   for Execution in reverse 1 .. Prisoners loop      if Execution = Survivors then         Ada.Text_IO.New_Line;         Ada.Text_IO.Put("Surviving: ");         Print := True;      end if;      if Print then         Ada.Text_IO.Put(Positive'Image(Next(X)));      end if;      Next(X) := Next(Next(X)); -- "delete" a prisoner      for Prisoner in 1 .. Steps-1 loop         X := Next(X);      end loop;   end loop;end Josephus;`
Output:
```\$ ./josephus
N = 41,  K = 3
Executed:  2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Surviving:  30

\$ ./josephus 23482 3343 3 0
N = 23482,  K = 3343,  #survivors = 3

Surviving:  13317 1087 1335```

## ALGOL 68

Translated from the C

`BEGIN   PROC josephus = (INT n, k, m) INT :   CO Return m-th on the reversed kill list; m=0 is final survivor. CO   BEGIN      INT lm := m;			CO Local copy of m CO      FOR a FROM m+1 WHILE a <= n DO lm := (lm+k) %* a OD;      lm   END;   INT n = 41, k=3;   printf ((\$"n = ", g(0), ", k = ", g(0), ", final survivor: ", g(0)l\$,	    n, k, josephus (n, k, 0)))END`
Output:
`n = 41, k = 3, final survivor: 30`

## ANSI Standard BASIC

Translated from ALGOL 68

`100 FUNCTION josephus (n, k, m)110 ! Return m-th on the reversed kill list; m=0 is final survivor.120    LET lm = m  ! Local copy OF m130    FOR a = m+1  TO n 140       LET lm = MOD(lm+k, a) 150    NEXT a160    LET josephus = lm170 END FUNCTION180 LET n = 41190 LET k=3200 PRINT "n =";n, "k =";k,"final survivor =";josephus(n, k, 0)210 END `

## AutoHotkey

`; Since AutoHotkey is 1-based, we're numbering prisoners 1-41.nPrisoners := 41kth        := 3 ; Build a list, purposefully ending with a separatorLoop % nPrisoners	list .= A_Index . "|" ; iterate and remove from listi := 1Loop{	; Step by 2; the third step was done by removing the previous prisoner	i += kth - 1	if (i > nPrisoners)		i := Mod(i, nPrisoners)	; Remove from list	end := InStr(list, "|", 0, 1, i)	bgn := InStr(list, "|", 0, 1, i-1)	list := SubStr(list, 1, bgn) . SubStr(list, end+1)	nPrisoners--}Until (nPrisoners = 1)MsgBox % RegExReplace(list, "\|") ; remove the final separator`
Output:
`31`

Note that since this is one-based, the answer is correct, though it differs with many other examples.

### Using Objects

`nPrisoners := 41kth        := 3list       := [] ; Build a list of 41 itemsLoop % nPrisoners	list.insert(A_Index) ; iterate and remove from listi := 1Loop{	; Step by 3	i += kth - 1	if (i > list.MaxIndex())		i := Mod(i, list.MaxIndex())	list.remove(i)}Until (list.MaxIndex() = 1)MsgBox % list.1 ; there is only 1 element left`

## AWK

` # syntax: GAWK -f JOSEPHUS_PROBLEM.AWK# converted from PL/IBEGIN {    main(5,2,1)    main(41,3,1)    main(41,3,3)    exit(0)}function main(n,k,s,  dead,errors,found,i,killed,nn,p,survived) {# n - number of prisoners# k - kill every k'th prisoner# s - number of survivors    printf("\nn=%d k=%d s=%d\n",n,k,s) # show arguments    if (s > n) { print("s>n"); errors++ }    if (k <= 0) { print("k<=0"); errors++ }    if (errors > 0) { return(0) }    nn = n                             # wrap around boundary    p = -1                             # start here    while (n != s) {                   # until survivor count is met      found = 0                        # start looking      while (found != k) {             # until we have the k-th prisoner        if (++p == nn) { p = 0 }       # wrap around        if (dead[p] != 1) { found++ }  # if prisoner is alive increment found      }      dead[p] = 1                      # kill the unlucky one      killed = killed p " "            # build killed list      n--                              # reduce size of circle    }    for (i=0; i<=nn-1; i++) {      if (dead[i] != 1) {        survived = survived i " "      # build survivor list      }    }    printf("killed: %s\n",killed)    printf("survived: %s\n",survived)    return(1)} `
Output:
```n=5 k=2 s=1
killed: 1 3 0 4
survived: 2

n=41 k=3 s=1
killed: 2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
survived: 30

n=41 k=3 s=3
killed: 2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3
survived: 15 30 34
```

## BASIC

Unstructured implementation: see solutions listed under specific BASIC dialects for structured versions.

`10 N=4120 K=330 M=040 FOR I=M+1 TO N50 M=INT(I*((M+K)/I-INT((M+K)/I))+0.5)60 NEXT I70 PRINT "Survivor is number";M`
Output:
`Survivor is number 30`

### Applesoft BASIC

Translated from the BASIC implementation above and the ANSI Standard BASIC.

`  10  DEF  FN MOD(X) = X - INT (X / A) * A 20  LM = 0: INPUT "GIVE N AND K (N,K): ";N,K 30  IF N < 1 or K < 1 THEN GOTO 20 40  FOR A = 1 TO N: LM =  FN MOD(LM + K): NEXT A 50  PRINT "N = ";N;", K = ";K;", SURVIVOR: ";LM  `
Output:
```GIVE N AND K (N,K): 41,3
N = 41, K = 3, SURVIVOR: 30```

### IS-BASIC

`100 PROGRAM "Josephus.bas"110 INPUT PROMPT "Number of prisoners: ":NP120 INPUT PROMPT "Execution step: ":EX130 INPUT PROMPT "How many survivors:  ":SU140 PRINT "Survivors:";150 FOR S=0 TO SU-1160   PRINT JOSEPHUS(NP,EX,S);170 NEXT180 DEF JOSEPHUS(N,K,M)190   FOR I=M+1 TO N200     LET M=MOD((M+K),I)210   NEXT 220   LET JOSEPHUS=M230 END DEF`

## Batch File

Uses C's `jos()` function.

Translation of: C
`@echo offsetlocal enabledelayedexpansion set "prison=41"		%== Number of prisoners ==%set "step=3"		%== The step... ==%set "survive=1"		%== Number of survivors ==%call :josephus set "prison=41"set "step=3"set "survive=3"call :josephuspauseexit /b 0 	%== The Procedure ==%:josephusset "surv_list="for /l %%S in (!survive!,-1,1) do ( 	set /a "m = %%S - 1"	for /l %%X in (%%S,1,!prison!) do (		set /a "m = (m + step) %% %%X"	)	if defined surv_list (		set "surv_list=!surv_list! !m!"	) else (		set "surv_list=!m!"	))echo !surv_list!goto :EOF`
Output:
```30
34 15 30
Press any key to continue . . .```

## BBC BASIC

`REM >josephusPRINT "Survivor is number "; FNjosephus(41, 3, 0)END:DEF FNjosephus(n%, k%, m%)LOCAL i%FOR i% = m% + 1 TO n%  m% = (m% + k%) MOD i%NEXT= m%`
Output:
`Survivor is number 30`

## Befunge

The number of prisoners and step size are read from stdin.

`>0" :srenosirP">:#,_&>>00p>>vv0p01<&_,#!>#:<"Step size: "<>1+:20p00g`!#v_0"  :rovivru"v^g02%g02+g01<<@.\$_,#!>#:<"S"<`
Output:
```Prisoners: 41
Step size: 3
Survivor:  30```

## C

`#include <stdio.h> // m-th on the reversed kill list; m = 0 is final survivorint jos(int n, int k, int m) {	int a;	for (a = m + 1; a <= n; a++)		m = (m + k) % a;	return m;} typedef unsigned long long xint; // same as jos(), useful if n is large and k is notxint jos_large(xint n, xint k, xint m) {	if (k <= 1) return n - m - 1; 	xint a = m;	while (a < n) {		xint q = (a - m + k - 2) / (k - 1); 		if (a + q > n)	q = n - a;		else if (!q)	q = 1; 		m = (m + q * k) % (a += q);	} 	return m;} int main(void) {	xint n, k, i; 	n = 41;	k = 3;	printf("n = %llu, k = %llu, final survivor: %d\n", n, k, jos(n, k, 0)); 	n = 9876543210987654321ULL;	k = 12031;	printf("n = %llu, k = %llu, three survivors:", n, k); 	for (i = 3; i--; )		printf(" %llu", jos_large(n, k, i));	putchar('\n'); 	return 0;}`
Output:
```n = 41, k = 3, final survivor: 30
n = 9876543210987654321, k = 12031, three survivors: 6892710366467541051 1946357796579138992 3554846299321782413
```

## C#

` namespace Josephus{    using System;    using System.Collections;    using System.Collections.Generic;     public class Program    {        public static int[] JosephusProblem(int n, int m)        {            var circle = new List<int>();            var order = new int[n];             for (var i = 0; i < n; ++i)            {                circle.Add(i);            }             var l = 0;            var j = 0;            var k = 0;             while (circle.Count != 0)            {                j++;                if (j == m)                {                    order[k] = circle[l];                    circle.RemoveAt(l);                     k++;                    l--;                    j = 0;                }                 if (k == n - 1)                {                    order[k] = circle[0];                    circle.RemoveAt(0);                }                 if (l == circle.Count - 1)                {                    l = 0;                }                else                {                    l++;                }            }             return order;        }         static void Main(string[] args)        {            try            {                var n = 7;                var m = 2;                 var result = JosephusProblem(n, m);                for (var i = 0; i < result.Length; i++)               {                   Console.WriteLine(result[i]);//1 3 5 0 4 2 6               }            }            catch (Exception e)            {                Console.WriteLine(e);            }            finally            {                Console.ReadLine();            }        }     }} `

## C++

` #include <iostream>#include <vector> //--------------------------------------------------------------------------------------------------using namespace std;typedef unsigned long long bigint; //--------------------------------------------------------------------------------------------------class josephus{public:    bigint findSurvivors( bigint n, bigint k, bigint s = 0 )    {	bigint i = s + 1;	for( bigint x = i; x <= n; x++, i++ )	    s = ( s + k ) % i; 	return s;    }     void getExecutionList( bigint n, bigint k, bigint s = 1 )    {	cout << endl << endl << "Execution list: " << endl; 	prisoners.clear();	for( bigint x = 0; x < n; x++ )	    prisoners.push_back( x ); 	bigint index = 0;	while( prisoners.size() > s )	{	    index += k - 1;	    if( index >= prisoners.size() ) index %= prisoners.size();	    cout << prisoners[static_cast<unsigned int>( index )] << ", "; 	    vector<bigint>::iterator it = prisoners.begin() + static_cast<unsigned int>( index );	    prisoners.erase( it );	}    } private:    vector<bigint> prisoners;};//--------------------------------------------------------------------------------------------------int main( int argc, char* argv[] ){    josephus jo;    bigint n, k, s;    while( true )    {	system( "cls" );	cout << "Number of prisoners( 0 to QUIT ): "; cin >> n;	if( !n ) return 0;	cout << "Execution step: "; cin >> k;	cout << "How many survivors: "; cin >> s; 	cout << endl << "Survivor";	if( s == 1 )	{	    cout << ": " << jo.findSurvivors( n, k );	    jo.getExecutionList( n, k );	}	else	{	    cout << "s: ";	    for( bigint x = 0; x < s; x++ )		cout << jo.findSurvivors( n, k, x ) << ", "; 	    jo.getExecutionList( n, k, s );	} 	cout << endl << endl;	system( "pause" );    }    return 0;}//-------------------------------------------------------------------------------------------------- `
Output:
```Number of prisoners( 0 to QUIT ): 41
Execution step: 3
How many survivors: 1

Survivor: 30

Execution list:
2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36
, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15,

Number of prisoners( 0 to QUIT ): 41
Execution step: 3
How many survivors: 3

Survivors: 30, 15, 34,

Execution list:
2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36
, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3,

Number of prisoners( 0 to QUIT ): 71
Execution step: 47
How many survivors: 11

Survivors: 29, 58, 41, 14, 39, 28, 35, 45, 64, 49, 27,

Execution list:
46, 22, 70, 48, 26, 5, 56, 36, 17, 0, 54, 38, 23, 9, 66, 55, 43, 33, 25, 16, 11,
6, 2, 69, 68, 1, 4, 10, 15, 24, 32, 42, 53, 65, 20, 40, 60, 19, 47, 8, 44, 13,
52, 31, 12, 62, 57, 50, 51, 61, 7, 30, 59, 34, 18, 3, 21, 37, 67, 63,
```

## Clojure

`(defn rotate [n s] (lazy-cat (drop n s) (take n s))) (defn josephus [n k]    (letfn [(survivor [[ h & r :as l] k]             (cond (empty? r) h                   :else      (survivor (rest (rotate (dec k) l)) k)))]     (survivor (range n) k))) (let [n 41 k 3]   (println (str "Given " n " prisoners in a circle numbered 1.." n                  ", an executioner moving around the"))   (println (str "circle " k " at a time will leave prisoner number "                  (inc (josephus n k)) " as the last survivor.")))`
Output:
```Given 41 prisoners in a circle numbered 1..41, an executioner moving around the
circle 3 at a time will leave prisoner number 31 as the last survivor.```

## Common Lisp

Using a loop:

`(defun kill (n k &aux (m 0))  (loop for a from (1+ m) upto n do        (setf m (mod (+ m k) a)))  m)`

Using a circular list.

`(defun make-circular-list (n)  (let* ((list (loop for i below n                     collect i))         (last (last list)))    (setf (cdr last) list)    list)) (defun kill (n d)  (let ((list (make-circular-list n)))    (flet ((one-element-clist-p (list)             (eq list (cdr list)))           (move-forward ()             (loop repeat (1- d)                   until (eq list (cdr list))                   do (setf list (cdr list))))           (kill-item ()             (setf (car list) (cadr list)                   (cdr list) (cddr list))))      (loop until (one-element-clist-p list) do            (move-forward)            (kill-item))      (first list))))`
Example:
```CL-USER > (kill 41 3)
30
```

## D

Translation of: Python
`import std.stdio, std.algorithm, std.array, std.string, std.range; T pop(T)(ref T[] items, in size_t i) pure /*nothrow*/ @safe /*@nogc*/ {    auto aux = items[i];    items = items.remove(i);    return aux;} string josephus(in int n, in int k) pure /*nothrow*/ @safe {    auto p = n.iota.array;    int i;    immutable(int)[] seq;    while (!p.empty) {        i = (i + k - 1) % p.length;        seq ~= p.pop(i);    }     return format("Prisoner killing order:\n%(%(%d %)\n%)." ~                  "\nSurvivor: %d",                  seq[0 .. \$ - 1].chunks(20), seq[\$ - 1]);} void main() /*@safe*/ {    josephus(5, 2).writeln;    writeln;    josephus(41, 3).writeln;}`
Output:
```Prisoner killing order:
1 3 0 4.
Survivor: 2

Prisoner killing order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27
31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15.
Survivor: 30```

Translation of: Javascript
`import std.stdio, std.algorithm, std.range; int[][] Josephus(in int n, int k, int s=1) {    int[] ks, ps = n.iota.array;    for (int i=--k; ps.length>s; i=(i+k)%ps.length) {        ks ~= ps[i];        ps = remove(ps, i);    }    writefln("Josephus(%d,%d,%d) -> %(%d %) / %(%d %)%s", n, k, s, ps, ks[0..min(\$,45)], ks.length<45 ? "" : " ..." );    return [ps, ks];} void main() {    Josephus(5, 2);    Josephus(41, 3);    Josephus(23482, 3343, 3);}}`
Output:
```Josephus(5,1,1) -> 2 / 1 3 0 4
Josephus(41,2,1) -> 30 / 2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Josephus(23482,3342,3) -> 1087 1335 13317 / 3342 6685 10028 13371 16714 20057 23400 3261 6605 9949 13293 16637 19981 23325 3187 6532 9877 13222 16567 19912 23257 3120 6466 9812 13158 16504 19850 23196 3060 6407 9754 13101 16448 19795 23142 3007 6355 9703 13051 16399 19747 23095 2961 6310 9659 ...```

## EchoLisp

We use a circular list and apply the 'process'. Successive rests are marked 🔫 (killed) or 😥 (remaining). NB: the (mark) function marks lists and sub-lists, not items in lists. The printed mark appears before the first item in the list.

` ;; input(define N 41)(define K 3)(define prisoners (apply circular-list (iota N)))(define last-one prisoners) ; current position ;; kill returns current position = last killed(define (kill lst skip)(cond    ((eq? (mark? lst) '🔫 )(kill (cdr lst) skip)) ;; dead ? goto next    ((zero? skip) (mark lst '🔫)) ;; all skipped ? kill    (else (mark lst '😥 )  ;; relieved face           (kill (cdr lst ) (1- skip))))) ;; skip 1 and goto next `
Output:
` ;; kill N-1    (for ((i (1- N) )) (set! last-one (kill last-one  (1- K))));; look at prisonersprisoners→ ( 🔄 🔫 0 🔫 1 🔫 2 🔫 3 🔫 4 🔫 5 🔫 6 🔫 7 🔫 8 🔫 9 🔫 10 🔫 11 🔫 12 🔫 13 🔫 14 🔫 15 🔫 16 🔫 17 🔫 18 🔫 19 🔫 20 🔫 21 🔫 22 🔫 23 🔫 24 🔫 25 🔫 26 🔫 27 🔫 28 🔫 29 😥 30 🔫 31 🔫 32  🔫 33 🔫 34 🔫 35 🔫 36 🔫 37 🔫 38 🔫 39 🔫 40 🔫 0 🔫 1  … ∞)  ;; #30 seems happy;; kill last(set! last-one (kill last-one (1- K)))last-one  → ( 🔫 30 🔫 31 🔫 32 …🔃 ) ;; #30 was the last ;; extra : we want more survivors(define SURVIVORS 3)(for ((i (- N SURVIVORS) )) (set! last-one (kill last-one  (1- K)))) prisoners→  ( 🔄 🔫 0 🔫 1 🔫 2 🔫 3 🔫 4 🔫 5 🔫 6 🔫 7 🔫 8 🔫 9 🔫 10 🔫 11 🔫 12 🔫 13 🔫 14 😥 15 🔫 16    🔫 17 🔫 18 🔫 19 🔫 20 🔫 21 🔫 22 🔫 23 🔫 24 🔫 25 🔫 26 🔫 27 🔫 28 🔫 29 😥 30 🔫 31 🔫 32    🔫 33 😥 34 🔫 35 🔫 36 🔫 37 🔫 38 🔫 39 🔫 40 🔫 0 🔫 1  🔫 0 … ∞)   `

## Eiffel

` class	APPLICATION create	make feature 	make		do			io.put_string ("Survivor is prisoner: " + execute (12, 4).out)		end 	execute (n, k: INTEGER): INTEGER			-- Survivor of 'n' prisoners, when every 'k'th is executed.		require			n_positive: n > 0			k_positive: k > 0			n_larger: n > k		local			killidx: INTEGER			prisoners: LINKED_LIST [INTEGER]		do			create prisoners.make			across				0 |..| (n - 1) as c			loop				prisoners.extend (c.item)			end			io.put_string ("Prisoners are executed in the order:%N")			killidx := 1			from			until				prisoners.count <= 1			loop				killidx := killidx + k - 1				from				until					killidx <= prisoners.count				loop					killidx := killidx - prisoners.count				end				io.put_string (prisoners.at (killidx).out + "%N")				prisoners.go_i_th (killidx)				prisoners.remove			end			Result := prisoners.at (1)		ensure			Result_in_range: Result >= 0 and Result < n		end end `
Output:
```Prisoners are executed in the order:
3
7
11
4
9
2
10
6
5
8
1
Survivor is prisoner: 0
```

## Elixir

` defmodule Josephus do  def find(n,k) do    find(Enum.to_list(0..n-1),0..k-2,k..n)  end   def find([_|[r|_]],_,_..d) when d < 3 do    IO.inspect r  end   def find(arr,a..c,b..d) when length(arr) >= 3 do    find(Enum.slice(arr,b..d) ++ Enum.slice(arr,a..c),a..c,b..d-1)  endend Josephus.find(41,3) `
Output:
`30`

## Emacs Lisp

` (defun jo(n k)   (if (= 1 n) 1 (1+ (% (+ (1- k) 			  (jo (1- n) k)) n ) ) ))(princ-list (jo 50 2) "\n" (jo 60 3))`
Output:
```37
41```

## Erlang

` -module( josephus_problem ). -export( [general_solution/3, task/0] ). general_solution( Prisoners, Kill, Survive ) -> general_solution( Prisoners, Kill, Survive, erlang:length(Prisoners), [] ). task() -> general_solution( lists:seq(0, 40), 3, 1 ).   general_solution( Prisoners, _Kill, Survive, Survive, Kills ) ->        {Prisoners, lists:reverse(Kills)};general_solution( Prisoners, Kill, Survive, Prisoners_length, Kills ) ->        {Skipped, [Killed | Rest]} = kill( Kill, Prisoners, Prisoners_length ),        general_solution( Rest ++ Skipped, Kill, Survive, Prisoners_length - 1, [Killed | Kills] ). kill( Kill, Prisoners, Prisoners_length ) when Kill < Prisoners_length ->    lists:split( Kill - 1, Prisoners );kill( Kill, Prisoners, Prisoners_length ) ->    kill_few( Kill rem Prisoners_length, Prisoners ). kill_few( 0, Prisoners ) ->    [Last | Rest] = lists:reverse( Prisoners ),    {lists:reverse( Rest ), [Last]};kill_few( Kill, Prisoners ) ->    lists:split( Kill - 1, Prisoners ). `
Output:
```11> josephus_problem:task().
{[30],
[2,5,8,11,14,17,20,23,26,29,32,35,38,0,4,9,13,18,22,27,31,
36,40,6,12,19,25|...]}
```

The general solution can handle other items than numbers.

```12> josephus_problem:general_solution( [joe, jack, william, averell, ratata], 2, 1 ).
{[william],[jack,averell,joe,ratata]}
```

## ERRE

` PROGRAM JOSEPHUS !! for rosettacode.org! !\$INTEGER DIM DEAD[100] PROCEDURE MAIN(N,K,S->ERRORS)! n - number of prisoners! k - kill every k'th prisoner! s - number of survivors    LOCAL KILLED\$,SURVIVED\$,FOUND,P,NN,I    ERRORS=0    FOR I=0 TO 100 DO        DEAD[I]=0    END FOR   ! prepare array    PRINT("N=";N,"K=";K,"S=";S)        ! show arguments    IF S>N THEN PRINT("S>N";) ERRORS+=1 END IF    IF K<=0 THEN PRINT("K<=0";) ERRORS+=1 END IF    IF ERRORS>0 THEN EXIT PROCEDURE END IF    NN=N                               ! wrap around boundary    P=-1                               ! start here    WHILE N<>S DO                      ! until survivor count is met      FOUND=0                          ! start looking      WHILE FOUND<>K DO                ! until we have the k-th prisoner        P+=1        IF P=NN THEN P=0 END IF        ! wrap around        IF DEAD[P]<>1 THEN            FOUND+=1        END IF                         ! if prisoner is alive increment found      END WHILE      DEAD[P]=1                        ! kill the unlucky one      KILLED\$=KILLED\$+STR\$(P)          ! build killed list      N-=1                             ! reduce size of circle    END WHILE    FOR I=0 TO NN-1 DO      IF DEAD[I]<>1 THEN        SURVIVED\$=SURVIVED\$+STR\$(I)    ! build survivor list      END IF    END FOR    PRINT("Killed:";KILLED\$)    PRINT("Survived:";SURVIVED\$)END PROCEDURE BEGIN    ERRORS=0    MAIN(5,2,1->ERRORS)    MAIN(41,3,1->ERRORS)    MAIN(41,3,3->ERRORS)END PROGRAM `

Note: Adapted from AWK version! Output is the same.

## Factor

`USING: kernel locals math math.ranges sequences ;IN: josephus :: josephus ( k n -- m )    n [1,b] 0 [ [ k + ] dip mod ] reduce ;`
```IN: scratchpad 3 41 josephus .
30
```

## Forth

`: josephus  0 1 begin dup 41 <= while  swap 3 + over mod swap  1+ repeat drop ;`
```josephus .
30
```

## Fortran

Naive approach: prisonners are put in a "linked buffer" (implemented as an array giving number of "next living prisonner"). Then we iterate, killing one after each loop, until there is only one left.

`program josephus   implicit none   integer :: n, i, k, p   integer, allocatable :: next(:)   read *, n, k   allocate(next(0:n - 1))   do i = 0, n - 2      next(i) = i + 1   end do   next(n - 1) = 0   p = 0   do while(next(p) /= p)      do i = 1, k - 2         p = next(p)      end do      print *, "Kill", next(p)      next(p) = next(next(p))      p = next(p)   end do   print *, "Alive", p   deallocate(next)end program`

## friendly interactive shell

`function execute    # If the list is empty, don't do anything.    test (count \$argv) -ge 2; or return    # If the list has only one element, return it    if test (count \$argv) -eq 2        echo \$argv[2]        return    end    # Rotate prisoners    for i in (seq 2 \$argv[1])        set argv \$argv[1 3..-1 2]    end    # Mention killed prisoner    echo \$argv[2]    # Kill rest recursively    execute \$argv[1 3..-1]end echo Prisoner (execute 3 (seq 0 40))[-1] survived.`
Output:
`Prisoner 30 survived.`

It's also possible to calculate more than one survivor.

`echo Prisoners (execute 3 (seq 0 40))[-3..-1] survived.`
Output:
`Prisoners 34 15 30 survived.`

Prisoners don't have to be numbers.

`echo Prisoner (execute 2 Joe Jack William Averell Rantanplan)[-1] survived.`
Output:
`Prisoner William survived.`

## Groovy

`int[] Josephus (int size, int kill, int survivors) {    // init user pool    def users = new int[size];     // give initial values such that [0] = 1 (first person) [1] = 2 (second person) etc    users.eachWithIndex() {obj, i -> users[i] = i + 1};     // keep track of which person we are on (ranging from 1 to kill)    def person = 1;     // keep going until we have the desired number of survivors    while (users.size() > survivors)    {        // for each person, if they are the kill'th person, set them to -1 to show eliminated        users.eachWithIndex() {obj, i ->            if (person++ % kill == 0) {                users[i] = -1;            }             // if person overflowed kill then reset back to 1            if (person > kill) {person = 1;}        }         // clear out all eliminated persons        users = users.findAll{w -> w >= 0};    }     // resulting set is the safe positions    return users;} // Run some test cases println "Final survivor for n = 10201 and k = 17: " + Josephus(10201,17,1)[0]; println "4 safe spots for n = 10201 and k = 17: " + Josephus(10201,17,4); `
Output:
```Final survivor for n = 10201 and k = 17: 7450
4 safe spots for n = 10201 and k = 17: [3413, 7244, 7450, 7605]
```

## Go

`package main import "fmt" // basic task functionfunc finalSurvivor(n, k int) int {    // argument validation omitted    circle := make([]int, n)    for i := range circle {        circle[i] = i    }    k--    exPos := 0    for len(circle) > 1 {        exPos = (exPos + k) % len(circle)        circle = append(circle[:exPos], circle[exPos+1:]...)    }    return circle[0]} // extrafunc position(n, k, pos int) int {    // argument validation omitted    circle := make([]int, n)    for i := range circle {        circle[i] = i    }    k--    exPos := 0    for len(circle) > 1 {        exPos = (exPos + k) % len(circle)        if pos == 0 {            return circle[exPos]        }        pos--        circle = append(circle[:exPos], circle[exPos+1:]...)    }    return circle[0]} func main() {    // show basic task function on given test case    fmt.Println(finalSurvivor(41, 3))    // show extra function on all positions of given test case    fmt.Println("Position  Prisoner")    for i := 0; i < 41; i++ {        fmt.Printf("%5d%10d\n", i, position(41, 3, i))    }}`
Output:
```30
Position  Prisoner
0         2
1         5
2         8
3        11
4        14
5        17
6        20
7        23
8        26
9        29
10        32
11        35
12        38
13         0
14         4
15         9
16        13
17        18
18        22
19        27
20        31
21        36
22        40
23         6
24        12
25        19
26        25
27        33
28        39
29         7
30        16
31        28
32        37
33        10
34        24
35         1
36        21
37         3
38        34
39        15
40        30
```

Shows only the surviving prisoners. Change "print \$ snd" to just "print" to show the killed prisoners, too. The arguments to the "main" function are: n = number of prisoners, k = kill every kth prisoner, m = show at most m survivors

`import Data.List ((\\))import System.Environment (getArgs) prisoners :: Int -> [Int]prisoners n = [0 .. n - 1] counter :: Int -> [Int]counter k = cycle [k, k-1 .. 1] killList :: [Int] -> [Int] -> ([Int], [Int], [Int])killList xs cs = (killed, survivors, newCs)    where        (killed, newCs) = kill xs cs []        survivors = xs \\ killed        kill [] cs rs = (rs, cs)        kill (x:xs) (c:cs) rs            | c == 1 =                let ts = rs ++ [x]                in  kill xs cs ts            | otherwise =                kill xs cs rs killRecursive :: [Int] -> [Int] -> Int -> ([Int], [Int])killRecursive xs cs m = killR ([], xs, cs)    where        killR (killed, remaining, counter)            | length remaining <= m = (killed, remaining)            | otherwise =                let (newKilled, newRemaining, newCounter) =                        killList remaining counter                    allKilled = killed ++ newKilled                in  killR (allKilled, newRemaining, newCounter) main :: IO ()main = do    args <- getArgs    case args of        [n, k, m] -> print \$ snd \$ killRecursive (prisoners (read n))                        (counter (read k)) (read m)        _         -> print \$ snd \$ killRecursive (prisoners 41) (counter 3) 1 `

Using modulo and list split, indices are 1-based. This is much faster than cycled list for larger numbers:

`jseq :: Int -> Int -> [Int]jseq n k = f n [1 .. n]  where    f 0 _ = []    f m s = x : f (m - 1) (right ++ left)      where        (left, x:right) = splitAt (mod (k - 1) m) s -- the final survivor is ((k + ...((k + ((k + 0)`mod` 1)) `mod` 2) ... ) `mod` n)jos :: Int -> Int -> Intjos n k = 1 + foldl (mod . (k +)) 0 [2 .. n] main :: IO ()main = do  print \$ jseq 41 3  print \$ jos 10000 100`

## Icon and Unicon

The following works in both languages.

`procedure main(A)   m := integer(A[1]) | 41   c := integer(A[2]) | 3   write("With ",m," men, counting to ",c," last position is: ", j(m,c))end procedure j(m,c)   return if m==1 then 0 else (j(m-1,c)+c)%mend`
Output:
```->josephus
With 41 men, counting to 3 last position is: 30
->
```

Extra 'credit' version:

This is done awkwardly, but I've had this laying around since the late 1980's...

`procedure main(args)   n := total := integer(args[1]) | 41		# Number of people   k := count := integer(args[2]) | 3		# Count   s := integer(args[3])-1 | 0                  # Number to save   write("With ",n," people, counting by ",k,", the ",s+1," safe places are:")   every write("\t",j(n,k,(n-s) to n))end procedure j(n,k,s)   a := k*(n-s) + 1   q := k/(k-1.0)   nk := n*k   olda := a   while a <= nk do {      olda := a      a := ceil(a,q)      }   t := nk - olda   return tend procedure ceil(a,q)  n := a*q  if n = integer(n) then return integer(n)  n ?:= integer(tab(upto('.'))) + 1  return nend`

Sample run:

```->josephus2 41 3 4
With 41 people, counting by 3, the 4 safe places are:
3
34
15
30
->
```

## J

Using the executioner's algorithm.

### Tacit version

`   3 ([ (1 }. <:@[ |. ])^:(1 < #@])^:_ [email protected]]) 4130`

Structured derivation of the fixed tacit code

`   DropNext=. 1 }. <:@[ |. ]   MoreThanOne=. 1 < #@]   WhileMoreThanOne=. (^:MoreThanOne f.) (^:_)   prisoners=. [email protected]]    [ DropNext WhileMoreThanOne prisoners f.[ (1 }. <:@[ |. ])^:(1 < #@])^:_ [email protected]]`

### Explicit version

`Josephus =: dyad define NB. explicit form, assume executioner starts at position 0 NB. use:  SKIP josephus NUMBER_OF_PRISONERS N =: y K =: N | x EXECUTIONER =: 0 PRISONERS =: i. N kill =: ] #~ (~: ([: i. #)) while. 1 (< #) PRISONERS do.  EXECUTIONER =: (# PRISONERS) | <: K + EXECUTIONER  PRISONERS =: EXECUTIONER kill PRISONERS end.)    3 Josephus 4130`

### Explicit version 2

`   NB. this is a direct translation of the algo from C code above.   Josephus2 =: 4 : '(| x&+)/i. - 1+y'     3 Josephus2 4130`

## Java

Works with: Java version 1.5+
`import java.util.ArrayList; public class Josephus {    public static int execute(int n, int k){        int killIdx = 0;        ArrayList<Integer> prisoners = new ArrayList<Integer>(n);        for(int i = 0;i < n;i++){            prisoners.add(i);        }        System.out.println("Prisoners executed in order:");        while(prisoners.size() > 1){            killIdx = (killIdx + k - 1) % prisoners.size();            System.out.print(prisoners.get(killIdx) + " ");            prisoners.remove(killIdx);        }        System.out.println();        return prisoners.get(0);    }     public static ArrayList<Integer> executeAllButM(int n, int k, int m){        int killIdx = 0;        ArrayList<Integer> prisoners = new ArrayList<Integer>(n);        for(int i = 0;i < n;i++){            prisoners.add(i);        }        System.out.println("Prisoners executed in order:");        while(prisoners.size() > m){            killIdx = (killIdx + k - 1) % prisoners.size();            System.out.print(prisoners.get(killIdx) + " ");            prisoners.remove(killIdx);        }        System.out.println();        return prisoners;    }     public static void main(String[] args){        System.out.println("Survivor: " + execute(41, 3));        System.out.println("Survivors: " + executeAllButM(41, 3, 3));    }}`
Output:
```Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Survivor: 30
Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3
Survivors: [15, 30, 34]```
Translation of: Javascript
`import java.util.ArrayList;import java.util.List; public class Josephus { 	public static void main(String[] args) {		execute(5, 1);		execute(41, 2);		execute(23482, 3342, 3);	} 	public static int[][] execute(int n, int k) {		return execute(n, k, 1);	} 	public static int[][] execute(int n, int k, int s) {		List<Integer> ps = new ArrayList<Integer>(n);		for (int i=0; i<n; i+=1) ps.add(i);		List<Integer> ks = new ArrayList<Integer>(n-s);		for (int i=k; ps.size()>s; i=(i+k)%ps.size()) ks.add(ps.remove(i));		System.out.printf("Josephus(%d,%d,%d) -> %s / %s\n", n, k, s, toString(ps), toString(ks));		return new int[][] {			ps.stream().mapToInt(Integer::intValue).toArray(),			ks.stream().mapToInt(Integer::intValue).toArray()		};	} 	private static String toString(List <Integer> ls) {		String dot = "";		if (ls.size() >= 45) {			dot = ", ...";			ls = ls.subList(0, 45);		}		String s = ls.toString();		return s.substring(1, s.length()-1) + dot;	}}`
Output:
```Josephus(5,1,1) -> 2 / 1, 3, 0, 4
Josephus(41,2,1) -> 30 / 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15
Josephus(23482,3342,3) -> 1087, 1335, 13317 / 3342, 6685, 10028, 13371, 16714, 20057, 23400, 3261, 6605, 9949, 13293, 16637, 19981, 23325, 3187, 6532, 9877, 13222, 16567, 19912, 23257, 3120, 6466, 9812, 13158, 16504, 19850, 23196, 3060, 6407, 9754, 13101, 16448, 19795, 23142, 3007, 6355, 9703, 13051, 16399, 19747, 23095, 2961, 6310, 9659, ...
```

## JavaScript

Labels are 1-based, executioner's solution:

`var Josephus = {  init: function(n) {    this.head = {};    var current = this.head;    for (var i = 0; i < n-1; i++) {      current.label = i+1;      current.next = {prev: current};      current = current.next;    }    current.label = n;    current.next = this.head;    this.head.prev = current;    return this;  },  kill: function(spacing) {    var current = this.head;    while (current.next !== current) {      for (var i = 0; i < spacing-1; i++) {        current = current.next;      }      current.prev.next = current.next;      current.next.prev = current.prev;      current = current.next;    }    return current.label;  }}`
Output:
```> Josephus.init(30).kill(2)
29
```

With Array methods:

`function Josephus(n, k, s) {	s = s | 1	for (var ps=[], i=n; i--; ) ps[i]=i	for (var ks=[], i=--k; ps.length>s; i=(i+k)%ps.length) ks.push(ps.splice(i, 1))	document.write((arguments.callee+'').split(/\s|\(/)[1], '(', [].slice.call(arguments, 0), ') -> ', ps, ' / ', ks.length<45?ks:ks.slice(0,45)+',...' , '<br>')	return [ps, ks]}`
Output:
```Josephus(5,1) -> 2 / 1,3,0,4
Josephus(41,2) -> 30 / 2,5,8,11,14,17,20,23,26,29,32,35,38,0,4,9,13,18,22,27,31,36,40,6,12,19,25,33,39,7,16,28,37,10,24,1,21,3,34,15
Josephus(23482,3342,3) -> 1087,1335,13317 / 3342,6685,10028,13371,16714,20057,23400,3261,6605,9949,13293,16637,19981,23325,3187,6532,9877,13222,16567,19912,23257,3120,6466,9812,13158,16504,19850,23196,3060,6407,9754,13101,16448,19795,23142,3007,6355,9703,13051,16399,19747,23095,2961,6310,9659,...
```

## Julia

Works with: Julia version 0.6

Recursive (with Memoize):

`using Memoize@memoize josephus(n::Integer, k::Integer, m::Integer=1) = n == m ? collect(0:m .- 1) : mod.(josephus(n - 1, k, m) + k, n) @show josephus(41, 3)@show josephus(41, 3, 5)`
Output:
```josephus(41, 3) = [30]
josephus(41, 3, 5) = [3, 15, 21, 30, 34]```

Iterative:

`function josephus(n::Integer, k::Integer, m::Integer=1)    p, i, seq = collect(0:n-1), 0, Vector{typeof(n)}(0)    while length(p) > m        i = (i + k - 1) % length(p)        push!(seq, splice!(p, i + 1))    end    return seq, pend seq, surv = josephus(41, 3)println("Prisoner killing in order: \$seq\nSurvivor: \$surv") seq, surv = josephus(41, 3, 3)println("Prisoner killing in order: \$seq\nSurvivor: \$surv")`
Output:
```Prisoner killing in order: [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15]
Survivor: [30]
Prisoner killing in order: [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3]
Survivor: [15, 30, 34]```

## jq

Works with: jq version 1.4

This section illustrates how a simulation can be directly modeled in jq while being fast enough to solve problems such as [n,k,m] = [23482, 3343, 3].

The prisoners are numbered from 0 to (n-1) in keeping with jq's array index origin of 0, but the nature of their labeling is immaterial to the algorithm.

`# A control structure, for convenience:# as soon as "condition" is true, then emit . and stop:def do_until(condition; next):  def u: if condition then . else (next|u) end;  u; # n is the initial number; every k-th prisoner is removed until m remain.# Solution by simulationdef josephus(n;k;m):    reduce range(0;n) as \$i ([]; . + [\$i])    # Number the prisoners from 0 to (n-1)    | do_until( length < k or length <= m; .[k:] + .[0:k-1] )    | do_until( length <= m; (k % length) as \$i | .[\$i:] + .[0:\$i-1] );`

Examples:

`def task(n;k;m):   "Survivors for n=\(n), k=\(k), m=\(m): \( josephus(n;k;m) )"; task(41;3;1),task(23482; 3343; 3)`
Output:
```\$ jq -M -r -n -f josephus.jq
Survivors for n=41, k=3, m=1: [30]
Survivors for n=23482, k=3343, m=3: [13317,1087,1335]
```

## Kotlin

`// version 1.1.3 fun josephus(n: Int, k: Int, m: Int): Pair<List<Int>, List<Int>> {    require(k > 0 && m > 0 && n > k && n > m)    val killed = mutableListOf<Int>()    val survived = MutableList(n) { it }    var start = k - 1    outer@ while (true) {        val end = survived.size - 1        var i = start        var deleted = 0        while (i <= end) {            killed.add(survived.removeAt(i - deleted))            if (survived.size == m) break@outer            deleted++            i += k        }         start = i - end - 1    }    return Pair(survived, killed)} fun main(args: Array<String>) {    val triples = listOf(Triple(5, 2, 1), Triple(41, 3, 1), Triple(41, 3, 3))    for (triple in triples) {        val(n, k, m) = triple         println("Prisoners = \$n, Step = \$m, Survivors = \$m")        val (survived, killed)  = josephus(n, k, m)        println("Survived   : \$survived")        println("Kill order : \$killed")        println()    }}`
Output:
```Prisoners = 5, Step = 1, Survivors = 1
Survived   : [2]
Kill order : [1, 3, 0, 4]

Prisoners = 41, Step = 1, Survivors = 1
Survived   : [30]
Kill order : [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15]

Prisoners = 41, Step = 3, Survivors = 3
Survived   : [15, 30, 34]
Kill order : [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3]
```

## Lua

Lua indexes tables starting at 1. Positions are stored from 0,n-1.

`function josephus(n, k, m)    local positions={}    for i=1,n do        table.insert(positions, i-1)    end    local i,j=1,1    local s='Execution order: '    while #positions>m do        if j==k then            s=s .. positions[i] .. ', '            table.remove(positions, i)            i=i-1        end        i=i+1        j=j+1        if i>#positions then i=1 end        if j>k then j=1 end    end    print(s:sub(1,#s-2) .. '.')    local s='Survivors: '    for _,v in pairs(positions) do s=s .. v .. ', ' end    print(s:sub(1,#s-2) .. '.')endjosephus(41,3, 1) `
Output:
```Execution order: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15.
Survivors: 30.
```

## MATLAB

`function [indAlive] = josephus(numPeople,count)% Josephus: Given a circle of numPeople individuals, with a count of count,% find the index (starting at 1) of the survivor [see Josephus Problem] %% Definitions:%   0 = dead position%   1 = alive position%   index = # of person %% Setting uparrPeople = ones(1, numPeople);currInd = 0; %% Countingwhile (length(arrPeople(arrPeople == 1)) > 1)     % While more than 1 person is alive    counter = 0;    while counter ~= count                       % Counting until we hit the count        currInd = currInd + 1;                  % Move to the next person         if currInd > numPeople                  % If overflow, wraparound            currInd = currInd - numPeople;        end         if arrPeople(currInd)                   % If the current person is alive            counter = counter + 1;                % Add 1 person to the count            %fprintf("Index: %d \t| Counter: %d\n", currInd, counter)           % Uncomment to display index and counter location        end     end     arrPeople(currInd) = 0;                     % Kill the person we reached    %fprintf("Killed person %d \n", currInd)                                   % Uncomment to display order of killing    %disp(arrPeople)                                                           % Uncomment to display current status of peopleend indAlive = find(arrPeople); end `

## Mathematica

`survivor[n_, k_] := Nest[Most[RotateLeft[#, k]] &, Range[0, n - 1], n - 1]survivor[41, 3]`
Output:
```{30}
```

## Modula-2

`MODULE Josephus;FROM FormatString IMPORT FormatString;FROM Terminal IMPORT WriteString,WriteLn,ReadChar; PROCEDURE Josephus(n,k : INTEGER) : INTEGER;VAR a,m : INTEGER;BEGIN    m := 0;    FOR a:=1 TO n DO        m := (m + k) MOD a;    END;    RETURN mEND Josephus; VAR    buf : ARRAY[0..63] OF CHAR;    n,k,i : INTEGER;    nl,kl,il : LONGCARD;BEGIN    n := 41;    k := 3;    FormatString("n = %i, k = %i, final survivor: %i\n", buf, n, k, Josephus(n, k));    WriteString(buf);     ReadCharEND Josephus.`

## NetRexx

Translation of: REXX

Hardly any changes at all...

`/* NetRexx */options replace format comments java crossref symbols nobinary /* REXX *************************************************************** 15.11.2012 Walter Pachl - my own solution* 16.11.2012 Walter Pachl generalized n prisoners + w killing distance*                         and s=number of survivors**********************************************************************/dead = 0                               /* nobody's dead yet          */n = 41                                 /* number of alive prisoners  */nn = n                                 /* wrap around boundary       */w = 3                                  /* killing count              */s = 1                                  /* nuber of survivors         */p = -1                                 /* start here                 */killed = ''                            /* output of killings         */Loop until n = s                       /* until one alive prisoner   */  found = 0                            /* start looking              */  Loop Until found = w                 /* until we have the third    */    p = p + 1                          /* next position              */    If p = nn Then p = 0               /* wrap around                */    If dead[p] = 0 Then                /* a prisoner who is alive    */      found = found + 1                /* increment found count      */    End  dead[p] = 1  n = n - 1                            /* shoot the one on this pos. */  killed = killed p                    /* add to output              */  End                                  /* End of main loop           */Say 'killed:'killed.subword(1, 20)     /* output killing sequence    */Say '       'killed.subword(21)        /* output killing sequence    */Say 'Survivor(s):'                     /* show                       */Loop i = 0 To 40                       /* look for the surviving p's */  If dead[i] = 0 Then Say i            /* found one                  */  End`
Output:
```killed:2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27
31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Survivor(s):
30
```

## Nim

Translation of: Python
`import sequtils, strutils, future proc j(n, k): string =  var    p = toSeq(0 .. < n)    i = 0    s = newSeq[int]()   while p.len > 0:    i = (i + k - 1) mod p.len    s.add p[i]    system.delete(p, i)   result = "Prisoner killing order: "  result.add s.map((x: int) => \$x).join(", ")  result.add ".\nSurvivor: "  result.add(\$s[s.high]) echo j(5,2)echo j(41,3)`
Output:
```Prisoner killing order: 1, 3, 0, 4, 2.
Survivor: 2
Prisoner killing order: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15, 30.
Survivor: 30```

## Objeck

`class Josephus {  function : Execute(n : Int, k : Int) ~ Int {    killIdx := 0;    prisoners := Collection.IntVector->New();    for(i := 0;i < n;i+=1;){      prisoners->AddBack(i);    };     "Prisoners executed in order:"->PrintLine();    while(prisoners->Size() > 1){      killIdx := (killIdx + k - 1) % prisoners->Size();      executed := prisoners->Get(killIdx);      "{\$executed} "->Print();      prisoners->Remove(killIdx);    };    '\n'->Print();        return prisoners->Get(0);  }   function : ExecuteAllButM(n : Int, k : Int, m : Int) ~ Collection.IntVector {    killIdx := 0;    prisoners := Collection.IntVector->New();    for(i := 0;i < n;i+=1;){      prisoners->AddBack(i);    };    "Prisoners executed in order:"->PrintLine();    while(prisoners->Size() > m){      killIdx := (killIdx + k - 1) % prisoners->Size();      executed := prisoners->Get(killIdx);      "{\$executed} "->Print();      prisoners->Remove(killIdx);    };    '\n'->Print();        return prisoners;  }   function : Main(args : String[]) ~ Nil {    result := Execute(41, 3);    "Survivor: {\$result}"->PrintLine();     results := ExecuteAllButM(41, 3, 3);    "Survivors: "->Print();    each(i : results) {    results->Get(i)->Print();      if(i + 1 < results->Size()) {        ' '->Print();      };    };  }} `

## Oforth

Oforth lists are 1-based : prisoners are numbered from 1 to n.

`: josephus(n, k)| prisoners killed i |   n seq asListBuffer ->prisoners   ListBuffer newSize(n) ->killed    0 n 1- loop: i [       k 1- + prisoners size mod dup 1+ prisoners removeAt      killed add       ] drop    System.Out "Killed : " << killed << "\nSurvivor : " << prisoners << cr; `
Output:
```>josephus(41, 3)
Killed : [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 1, 5, 10, 14, 19, 23, 28, 32, 37, 41, 7, 13, 20, 26, 34, 40, 8, 17, 29, 38, 11, 25, 2, 22, 4, 35, 16]
Survivor : [31]
```

## PARI/GP

`Josephus(n, k)=if(n<2, n>0, my(t=(Josephus(n-1, k)+k)%n); if(t, t, n))`

## Perl

Translation of: Perl6
`my @prisoner = 0 .. 40;my \$k = 3;until (@prisoner == 1) {    push @prisoner, shift @prisoner for 1 .. \$k-1;    shift @prisoner;} print "Prisoner @prisoner survived.\n"`
Output:
`Prisoner 30 survived.`

## Perl 6

Works with: rakudo version 2015-11-12

Straightforward implementation of the executioner's algorithm:

`sub Execute(@prisoner, \$k) {    until @prisoner == 1 {	@prisoner.=rotate(\$k - 1);	@prisoner.shift;    }} my @prisoner = ^41;Execute @prisoner, 3;say "Prisoner {@prisoner} survived."; # We don't have to use numbers.  Any list will do: my @dalton = <Joe Jack William Averell Rantanplan>;Execute @dalton, 2;say "{@dalton} survived.";`
Output:
```Prisoner 30 survived.
William survived.```

## Phix

Note indexes and results are 1-based. Prisoners do not have to be numbers. Based on AWK, but replacing killed prisoners in-situ.

`function Josephus(sequence prisoners, integer step, survivors)    integer n = length(prisoners), nn = n    integer p = 0    while n>survivors do        integer found = 0        while found!=step do            p = iff(p=nn?1:p+1)            found += prisoners[p]!=-1        end while        -- (if you want a kill list, build it here!)        prisoners[p] = -1        n -= 1    end while    return remove_all(-1,prisoners)end function ?Josephus(tagset(5),2,1)?Josephus(tagset(41),3,1)?Josephus(tagset(41),3,3)?Josephus({"Joe","Jack","William","John","James"},2,1)`
Output:
```{3}
{31}
{16,31,35}
{"William"}
```

## PHP

`<?php //Josephus.phpfunction Jotapata(\$n=41,\$k=3,\$m=1){\$m--;	\$prisoners=array_fill(0,\$n,false);//make a circle of n prisoners, store false ie: dead=false	\$deadpool=1;//count to next execution	\$order=0;//death order and *dead* flag, ie. deadpool	while((array_sum(array_count_values(\$prisoners))<\$n)){//while sum of count of unique values dead times < n (they start as all false)		foreach(\$prisoners as \$thisPrisoner=>\$dead){			if(!\$dead){//so yeah...if not dead...				if(\$deadpool==\$k){//if their time is up in the deadpool...					\$order++;					//set the deadpool value or enumerate as survivor					\$prisoners[\$thisPrisoner]=(((\$n-\$m)>(\$order)?\$order:((\$n)==\$order?'Call me *Titus Flavius* Josephus':'Joe\'s friend '.((\$order)-(\$n-\$m-1)))));					\$deadpool=1;//reset count to next execution				}else{\$duckpool++;}			}		}	}	return \$prisoners;}echo '<pre>'.print_r(Jotapata(41,3,5),true).'<pre>'; `

## PicoLisp

The counting starts from one instead of zero. The last remaining person is returned.

` #general solution(de jo (N K)   (if (=1 N)      1      (inc         (%            (+ (dec K) (jo (dec N) K))            N ) ) ) ) #special case when K is 2; much faster than general version.(de jo2(N)   (let P 1      (while (<= P N)         (setq P (* 2 P))         (+ (- (* 2 N) P) 1) ) ) ) # find the survivor using an optimal solution(de survivor (N K)   (if (=0 (% N 2))      (jo2 N)      (jo N K) ) )(print (survivor 5 2))(print (survivor 41 3)) `
Output:
```3
31
```

## PL/I

`*process or(!) source attributes xref; joseph: Proc Options(main); /* REXX ************************************************************** * 15.11.2012 Walter Pachl - my own solution * 16.11.2012 Walter Pachl generalized n prisoners + w killing distance *                         and s=number of survivors * 03.05.2013 Walter Pachl Translated From REXX Version 1 **********************************************************************/ Dcl dead(0:100) Bit(1); Dcl (n,nn,w,s,p,found) Bin Fixed(15); Dcl pp Pic'99'; Dcl killed Char(300) Var Init('killed: '); /* output of killings     */ Dcl survived Char(300) Var Init('Survivor(s): '); dead='';                               /* nobody's dead yet          */ n=41;                                  /* number of alive prisoners  */ nn=n;                                  /* wrap around boundary       */ w=3;                                   /* killing count              */ s=1;                                   /* number of survivors         */ p=-1;                                  /* start here                 */ Do Until(n=s);                         /* until one alive prisoner   */   found=0;                             /* start looking              */   Do Until(found=w);                   /* until we have the third    */     p=p+1;                             /* next position              */     If p=nn Then p=0;                  /* wrap around                */     If ^dead(p) Then                   /* a prisoner who is alive    */       found=found+1;                   /* increment found count      */     End;   dead(p)='1'b;                        /* shoot the one on this pos. */   n=n-1;   pp=p;   killed=killed!!' '!!pp;              /* add to output              */   End;                                 /* End of main loop           */ Call o(killed); Do i=0 To nn-1;                        /* look for the surviving p's */   If ^dead(i) Then Do;                 /* found one                  */     pp=i;     survived=survived!!' '!!pp;     End;   End; Call o(survived);  o: Proc(s); /********************************************************************* * Formatted Output of given string: * xxxxxxxxxx xxx xx xx xxx --- *         xx xxx xxx *         xxxxx xxx *********************************************************************/ Dcl s Char(*) Var; Dcl p Bin Fixed(15); Dcl ll Bin Fixed(15) Init(72); Do While(length(s)>ll);   Do p=ll+1 To 10 By -1;     If substr(s,p,1)=' ' Then       Leave;     End;   Put Edit(left(s,p))(Skip,a);   s=repeat(' ',8)!!substr(s,p+1);   End; Put Edit(s)(Skip,a); End;  End;`
Output:
```killed:  02 05 08 11 14 17 20 23 26 29 32 35 38 00 04 09 13 18 22 27 31
36 40 06 12 19 25 33 39 07 16 28 37 10 24 01 21 03 34 15
Survivor(s):  30
```

## PowerShell

Works with: PowerShell version 2

Adapted from the iterative algorithm in Sidef.

Rotating the circle K prisoners is equivalent to the executioner walking around the circle K prisoners. We rotate the circle to bring the next selectee to the "front" of the circle, then "select" him by moving past him to the remaining circle. After repeating through the entire prisoner population, we are left with the prisoners sorted into the order in which they are selected.

The lonely comma in the line where we create the \$Prisoners arraylist is to prevent PowerShell from being too helpful. Normally when we present the PowerShell parser with an array within an array, it treats it as a cast, and

we end up with the single array of elements. In those cases where we need an array to be treated as a single element of a parent array, we can use the unary comma to force PowerShell to treat it as an element.
` <lang PowerShell>function Get-JosephusPrisoners ( [int]\$N, [int]\$K )    {    #  Just for convenience    \$End = \$N - 1     #  Create circle of prisoners    \$Prisoners = New-Object System.Collections.ArrayList ( , (0..\$End) )     #  For each starting point of the reducing circle...    ForEach ( \$Start in 0..(\$End - 1) )        {        #  We subtract one from K for the one we advanced by incrementing \$Start        #  Then take K modulus the length of the remaining circle        \$RoundK = ( \$K - 1 ) % ( \$End - \$Start + 1 )         #  Rotate the remaining prisoners K places around the remaining circle        \$Prisoners.SetRange( \$Start, \$Prisoners[ \$Start..\$End ][ ( \$RoundK + \$Start - \$End - 1 )..( \$RoundK - 1 ) ] )        }    return \$Prisoners    } `
` #  Get the prisoner order for a circle of 41 prisoners, selecting every third\$Prisoners = Get-JosephusPrisoners -N 41 -K 3 #  Display the prisoner order\$Prisoners -join " " #  Display the last remaining prisoner"Last prisoner remmaining: " + \$Prisoners[-1] #  Display the last three remaining prisoners\$S = 3"Last \$S remaining: " + \$Prisoners[-\$S..-1] `
Output:
```2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15 30
Last prisoner remmaining: 30
Last 3 remaining: 34 15 30
```

## PureBasic

`NewList prisoners.i() Procedure f2l(List p.i())  FirstElement(p())    : tmp.i=p()  DeleteElement(p(),1) : LastElement(p())  AddElement(p())      : p()=tmp EndProcedure Procedure l2f(List p.i())  LastElement(p())   : tmp.i=p()  DeleteElement(p()) : FirstElement(p())  InsertElement(p()) : p()=tmp  EndProcedure OpenConsole()Repeat  Print(#LF\$+#LF\$)  Print("Josephus problem - input prisoners : ") : n=Val(Input())  If n=0 : Break : EndIf    Print("                 - input steps     : ") : k=Val(Input())  Print("                 - input survivors : ") : s=Val(Input()) : If s<1 : s=1 : EndIf  ClearList(prisoners()) : For i=0 To n-1 : AddElement(prisoners()) : prisoners()=i : Next  If n<100 : Print("Executed : ") : EndIf  While ListSize(prisoners())>s And n>0 And k>0 And k<n        For j=1 To k : f2l(prisoners()) : Next        l2f(prisoners()) : FirstElement(prisoners()) : If n<100 : Print(Str(prisoners())+Space(2)) : EndIf     DeleteElement(prisoners())      Wend  Print(#LF\$+"Surviving: ")  ForEach prisoners()    Print(Str(prisoners())+Space(2))  Next      ForEverEnd`
Output:
```Josephus problem - input prisoners : 5
- input steps     : 2
- input survivors : 1
Executed : 1  3  0  4
Surviving: 2

Josephus problem - input prisoners : 41
- input steps     : 3
- input survivors : 1
Executed : 2  5  8  11  14  17  20  23  26  29  32  35  38  0  4  9  13  18  22  27  31  36  40  6  12  19  25  33  39  7  16  28  37  10  24  1  21  3  34  15
Surviving: 30

Josephus problem - input prisoners : 41
- input steps     : 3
- input survivors : 3
Executed : 2  5  8  11  14  17  20  23  26  29  32  35  38  0  4  9  13  18  22  27  31  36  40  6  12  19  25  33  39  7  16  28  37  10  24  1  21  3
Surviving: 15  30  34

Josephus problem - input prisoners : 71
- input steps     : 47
- input survivors : 11
Executed : 46  22  70  48  26  5  56  36  17  0  54  38  23  9  66  55  43  33  25  16  11  6  2  69  68  1  4  10  15  24  32  42  53  65  20  40  60  19  47  8  44  13  52  31  12  62  57  50  51  61  7  30  59  34  18  3  21  37  67  63
Surviving: 64  14  27  28  29  35  39  41  45  49  58

Josephus problem - input prisoners :```

## Python

`>>> def j(n, k):	p, i, seq = list(range(n)), 0, []	while p:		i = (i+k-1) % len(p)		seq.append(p.pop(i))	return 'Prisoner killing order: %s.\nSurvivor: %i' % (', '.join(str(i) for i in seq[:-1]), seq[-1]) >>> print(j(5, 2))Prisoner killing order: 1, 3, 0, 4.Survivor: 2>>> print(j(41, 3))Prisoner killing order: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34, 15.Survivor: 30>>> `

Faster way to solve in python, it does not show the killing order.

`>>>def josephus(n, k):        r = 0        for i in xrange(1, n+1):            r = (r+k)%i        return 'Survivor: %d' %r >>> print(josephus(5, 2))Survivor: 2>>> print(josephus(41, 3))Survivor: 30>>> `

### Alternate solution with a circular linked list

The function returns the killing order. The last in the list stays alive. Notice that the result is a permutation of [0, 1, ... n - 1]. In the program, a[p] is the index of the next living prisoner after 'p'. The program stops when p = a[p], that is, when there remains only one living prisoner.

`def josephus(n, k):    a = list(range(1, n + 1))    a[n - 1] = 0    p = 0    v = []    while a[p] != p:        for i in range(k - 2):            p = a[p]        v.append(a[p])        a[p] = a[a[p]]        p = a[p]    v.append(p)    return v josephus(10, 2)[1, 3, 5, 7, 9, 2, 6, 0, 8, 4] josephus(41, 3)[-1]30`

### learning iter in python

`from itertools import compress, cycledef josephus(prisoner, kill, surviver):    p = range(prisoner)    k = [0] * kill    k[kill-1] = 1    s = [1] * kill    s[kill -1] = 0    queue = p     queue = compress(queue, cycle(s))    try:        while True:            p.append(queue.next())            except StopIteration:        pass      kil=[]    killed = compress(p, cycle(k))    try:        while True:            kil.append(killed.next())    except StopIteration:        pass      print 'The surviver is: ', kil[-surviver:]    print 'The kill sequence is ', kil[:prisoner-surviver] josephus(41,3,2)The surviver is:  [15, 30]The kill sequence is  [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34]josephus(5,2,1)The surviver is:  [2]The kill sequence is  [1, 3, 0, 4] `

## R

` jose <-function(s, r,n){y <- 0:(r-1) for (i in (r+1):n)  y <- (y + s) %% i  return(y)}> jose(3,1,41) # r is the number of remained prisoner.[1] 30 `

## Racket

`#lang racket(define (josephus n k (m 0))  (for/fold ((m (add1 m)))    ((a (in-range (add1 m) (add1 n))))    (remainder (+ m k) a))) (josephus 41 3) ; ->30`

## REBOL

Works in Rebol 2 or 3

`rebol [] execute: func [death-list [block!] kill [integer!]] [    assert [not empty? death-list]    until [        loop kill - 1 [append death-list take death-list]        (1 == length? remove death-list)    ]] prisoner: [] for n 0 40 1 [append prisoner n]execute prisoner 3print ["Prisoner" prisoner "survived"]`
Output:
`Prisoner 30 survived`

And any kind of list will do:

`for-the-chop: [Joe Jack William Averell Rantanplan]execute for-the-chop 2print [for-the-chop "survived"]`
Output:
`William survived`

## REXX

### version 1

`/* REXX *************************************************************** 15.11.2012 Walter Pachl - my own solution* 16.11.2012 Walter Pachl generalized n prisoners + w killing distance*                         and s=number of survivors* 09.05.2013 Walter Pachl accept arguments n w s and fix output*                         thanks for the review/test* I see no need for specifying a start count (actually a start number)* This program should work on EVERY REXX. * Pls report if this is not the case and let us know what's a problem.**********************************************************************/Parse Arg n w s .If n='?' Then Do  Say 'Invoke the program with the following arguments:'  Say 'n number of prisoners            (default 41)'  Say 'w killing count                  (default  3)'  Say 's number of prisoners to survive (default  1)'  Exit  EndIf n='' Then n=41                      /* number of alive prisoners  */If w='' Then w=3                       /* killing count              */If s='' Then s=1                       /* nuber of survivors         */dead.=0                                /* nobody's dead yet          */nn=n                                   /* wrap around boundary       */p=-1                                   /* start here                 */killed=''                              /* output of killings         */Do until n=s                           /* until one alive prisoner   */  found=0                              /* start looking              */  Do Until found=w                     /* until we have the third    */    p=p+1                              /* next position              */    If p=nn Then p=0                   /* wrap around                */    If dead.p=0 Then                   /* a prisoner who is alive    */      found=found+1                    /* increment found count      */    End  dead.p=1  /*  Say 'killing' p 'now'  */  n=n-1                                /* shoot the one on this pos. */  killed=killed p                      /* add to output              */  End                                  /* End of main loop           */Say 'killed:'killed                    /* output killing sequence    */s=''Do i=0 To nn-1                            /* look for the surviving p's */  If dead.i=0 Then s=s i               /* found one                  */  EndSay 'Survivor(s):'s                    /* show                       */`
Output:
```killed: 2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Survivor(s): 30```

### version 2

This version allows the user to specify:

•   the number of prisoners
•   the count-off   [every Kth prisoner]
•   the start count   [zero or one]
•   the number of survivors
•   the solving of the extra credit task requirement of multiple survivors

This solution is an   executor's   solution.

`/*REXX program solves  Josephus problem:   N  men standing in a circle,  every Kth kilt.*/parse arg N K Z R .                              /*obtain optional arguments from the CL*/if N=='' | N==","   then  N= 41                  /*    men  not specified?  Use default.*/if K=='' | K==","   then  K=  3                  /*   kilt   "      "        "     "    */if Z=='' | Z==","   then  Z=  0                  /*  start   "      "        "     "    */if R=='' | R==","   then  R=  1                  /*remaining "      "        "     "    */\$=;       do i=Z  for N;  \$=\$ i;  end  /*i*/     /*populate prisoner's circle (with a #)*/x=                                               /*the list of prisoners to be removed. */      do c=k  by k;         p=words(\$)           /*keep removing until  R  are remaining*/      if c>p then do                             /*   [↓] remove (kill) some prisoner(s)*/                    do j=1  for words(x);    \$=delword(\$, word(x, j) + 1 - j,   1)                    if words(\$)==R  then leave c /*The slaying finished? (R people left)*/                    end   /*j*/                  c=(c//p) // words(\$);   x=     /*adjust prisoner count-off and circle.*/                  end      if c\==0  then x=x c                       /*the list of prisoners to be removed. */      end   /*remove*/                           /*remove 'til   R   prisoners are left.*/ say 'removing every '   th(K)   " prisoner out of "    N    ' (starting at'   Z")  with ",                           R    ' survivor's(R)",  leaving prisoner"s(R)':'   \$exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/s:  if arg(1)==1  then return arg(3);            return word( arg(2) 's', 1)   /*plurals*/th: y=arg(1);    return y || word('th st nd rd', 1+ y // 10 * (y//100%10\==1) * (y//10<4))`
output   when using the default inputs:
```removing every  3rd  prisoner out of  41  (starting at 0)  with  1  survivor,  leaving prisoner:  30
```
output   when using the input of:   41   3   1
```removing every  3rd  prisoner out of  41  (starting at 1)  with  1  survivor,  leaving prisoner:  31
```

{{out|output|text=  when using the input of:   41   3   1   2

```removing every  3rd  prisoner out of  41  (starting at 1)  with  2  survivors,  leaving prisoners:  16 31
```

{{out|output|text=  when using the input of:   5   2

```removing every  2nd  prisoner out of  5  (starting at 0)  with  1  survivor,  leaving prisoner:  2
```

## Ring

` n = 41k=3see "n =" + n + " k = " + k + " final survivor = " + josephus(n, k, 0) + nl func josephus (n, k, m)lm = m  for a = m+1  to n      lm = (lm+k) % a nextjosephus = lmreturn josephus `

Output:

```n =41 k = 3 final survivor = 30
```

## Ruby

`n = (ARGV[0] || 41).to_ik = (ARGV[1] || 3).to_i prisoners = (0...n).to_aprisoners.rotate!(k-1).shift  while prisoners.length > 1puts prisoners.first`

## Scala

Executioner's Solution, not Josephus'

(Prisoners labeled 0 to n-1)

`def executed( prisonerCount:Int, step:Int ) = {   val prisoners = ((0 until prisonerCount) map (_.toString)).toList   def behead( dead:Seq[String], alive:Seq[String] )(countOff:Int) : (Seq[String], Seq[String]) = {    val group = if( alive.size < countOff ) countOff - alive.size else countOff     (dead ++ alive.take(group).drop(group-1), alive.drop(group) ++ alive.take(group-1))  }   def beheadN( dead:Seq[String], alive:Seq[String] ) : (Seq[String], Seq[String]) =    behead(dead,alive)(step)   def execute( t:(Seq[String], Seq[String]) ) : (Seq[String], Seq[String]) = t._2 match {    case x :: Nil => (t._1, Seq(x))    case x :: xs => execute(beheadN(t._1,t._2))  }   execute((List(),prisoners))} val (dead,alive) = executed(41,3) println( "Prisoners executed in order:" )print( dead.mkString(" ") ) println( "\n\nJosephus is prisoner " + alive(0) )`
Output:
```Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15

Josephus is prisoner 30```

## Seed7

The main task (find one survivor) is a special case of the extra task (find m survivors). The function executeAllButM solves the extra task and is called with m=1 to solve the main task. The function str converts an array of integer elements to a string. The function enable_output uses str to define everything necessary to write an array of integers. This way the main program can write the survivor array.

`\$ include "seed7_05.s7i"; const func array integer: executeAllButM (in integer: n, in integer: k, in integer: m) is func  result    var array integer: prisoners is [0 .. -1] times 0;  local    var integer: killIdx is 0;    var integer: prisonerNum is 0;  begin    for prisonerNum range 0 to pred(n) do      prisoners &:= prisonerNum;    end for;    writeln("Prisoners executed in order:");    while length(prisoners) > m do      killIdx := (killIdx + k - 1) rem length(prisoners);      write(prisoners[killIdx] <& " ");      ignore(remove(prisoners, killIdx));    end while;    writeln;  end func; const func string: str (in array integer: intArr) is func  result    var string: stri is "";  local    var integer: index is 0;  begin    for key index range intArr do      if index <> minIdx(intArr) then        stri &:= ", ";      end if;      stri &:= str(intArr[index]);    end for;  end func; enable_output(array integer); const proc: main is func  begin    writeln("Survivor: " <& executeAllButM(41, 3, 1));    writeln("Survivors: " <& executeAllButM(41, 3, 3));  end func;`
Output:
```Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Survivor: 30
Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3
Survivors: 15, 30, 34
```

## SequenceL

Translation of: Python
`main := josephus(41, 3); josephus(n, k) := josephusHelper(n, k, 1, 0); josephusHelper(n, k, i, r) :=          r when i > n    else        josephusHelper(n, k, i + 1, (r + k) mod i);`
Output:
```30
```

## Sidef

Iterative:

`func josephus(n, k) {    var prisoners = @^n    while (prisoners.len > 1) {        prisoners.rotate!(k - 1).shift    }    return prisoners[0]}`

Recursive:

`func josephus(n, k) {    n == 1 ? 0 : ((__FUNC__(n-1, k) + k) % n)};`

Calling the function:

`var survivor = josephus(41, 3);say "Prisoner #{survivor} survived.";`
Output:
`Prisoner 30 survived.`

## Swift

`class Josephus {     class func lineUp(#numberOfPeople:Int) -> [Int] {        var people = [Int]()        for (var i = 0; i < numberOfPeople; i++) {            people.append(i)        }        return people    }     class func execute(#numberOfPeople:Int, spacing:Int) -> Int {        var killIndex = 0        var people = self.lineUp(numberOfPeople: numberOfPeople)         println("Prisoners executed in order:")        while (people.count > 1) {            killIndex = (killIndex + spacing - 1) % people.count            executeAndRemove(&people, killIndex: killIndex)        }        println()        return people[0]    }     class func executeAndRemove(inout people:[Int], killIndex:Int) {        print("\(people[killIndex]) ")        people.removeAtIndex(killIndex)    }     class func execucteAllButM(#numberOfPeople:Int, spacing:Int, save:Int) -> [Int] {        var killIndex = 0        var people = self.lineUp(numberOfPeople: numberOfPeople)         println("Prisoners executed in order:")        while (people.count > save) {            killIndex = (killIndex + spacing - 1) % people.count            executeAndRemove(&people, killIndex: killIndex)        }        println()        return people    }} println("Josephus is number: \(Josephus.execute(numberOfPeople: 41, spacing: 3))")println()println("Survivors: \(Josephus.execucteAllButM(numberOfPeople: 41, spacing: 3, save: 3))")`
Output:
```Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15
Josephus is number: 30

Prisoners executed in order:
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3
Survivors: [15, 30, 34]
```

## Tcl

`proc josephus {number step {survivors 1}} {    for {set i 0} {\$i<\$number} {incr i} {lappend l \$i}    for {set i 1} {[llength \$l]} {incr i} {	# If the element is to be killed, append to the kill sequence	if {\$i%\$step == 0} {	    lappend killseq [lindex \$l 0]	    set l [lrange \$l 1 end]	} else {	    # Roll the list	    set l [concat [lrange \$l 1 end] [list [lindex \$l 0]]]	}    }    return [lrange \$killseq end-[expr {\$survivors-1}] end]}`

Demonstrating:

`puts "remaining:   [josephus 41 3]"puts "remaining 4: [join [josephus 41 3 4] ,]"`
Output:
```remaining:   30
remaining 4: 3,34,15,30
```

## VBScript

` Function josephus(n,k,s)	Set prisoner = CreateObject("System.Collections.ArrayList")	For i = 0 To n - 1		prisoner.Add(i)	Next	index = -1	Do Until prisoner.Count = s		step_count = 0		Do Until step_count = k			If index+1 <= prisoner.Count-1 Then				index = index+1			Else				index = (index+1)-(prisoner.Count)			End If			step_count = step_count+1		Loop		prisoner.RemoveAt(index)		index = index-1	Loop	For j = 0 To prisoner.Count-1		If j < prisoner.Count-1 Then			josephus = josephus & prisoner(j) & ","		Else			josephus = josephus & prisoner(j)		End If	NextEnd Function 'testing the functionWScript.StdOut.WriteLine josephus(5,2,1)WScript.StdOut.WriteLine josephus(41,3,1)WScript.StdOut.WriteLine josephus(41,3,3) `
Output:
```2
30
15,30,34
```

## Vedit macro language

This macro first creates a list of prisoners in an edit buffer.
Then the prisoners are deleted in loop until specified number of survivors are left.
When the macro finishes, you can see the list of survivors in the edit buffer.

`#1 = 41		// number of prisoners#2 = 3		// step size#3 = 1		// number of survivors Buf_Switch(Buf_Free)for (#5=0; #5<#1; #5++) {    Ins_Text("prisoner ") Num_Ins(#5, LEFT)} BOF#4=1while (#1 > #3) {    if (#4++ % #2 == 0) {	Del_Line(1)        #1--    } else {	Line(1)    }    if (At_EOF) { BOF }}`
Output:
```prisoner 30
```
Output:
when the number of survivors is set to 3:
```prisoner 15
prisoner 30
prisoner 34
```

## XPL0

`include c:\cxpl\codes; func Prisoner(N, K);            \Return final surviving prisonerint  N, K;                      \number of prisoners, number to skipint  I, J;char A;[A:= Reserve(N);for I:= 0 to N-1 do A(I):= I;I:= 0;repeat  I:= I+K-1;                              \skip to next prisoner        I:= rem(I/N);                           \wrap to start if necessary        IntOut(0, A(I)); ChOut(0, ^ );          \show killed prisoner        for J:= I to N-2 do A(J):= A(J+1);      \shift survivors down        N:= N-1;                                \one less prisoneruntil   N=1;return A(0);]; [IntOut(0, Prisoner(5, 2));  CrLf(0); IntOut(0, Prisoner(41, 3));  CrLf(0);]`
Output:
```1 3 0 4 2
2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25 33 39 7 16 28 37 10 24 1 21 3 34 15 30
```

## zkl

Translation of: Julia
`fcn j(n,k){   reg p=[0..n-1].walk().copy(), i=0, seq=L();   while(p){      i=(i+k-1)%p.len();      seq.append(p.pop(i));   }   "Prisoner killing order: %s.\nSurvivor: %d"   .fmt(seq[0,-1].concat(","),seq[-1]);}`
Output:
```j(41,3).println();
Prisoner killing order: 2,5,8,11,14,17,20,23,26,29,32,35,38,0,4,9,13,18,22,27,31,
36,40,6,12,19,25,33,39,7,16,28,37,10,24,1,21,3,34,15.
Survivor: 30
```
`fcn j2(n,k,m){   reg p=[0..n-1].walk().copy(), i=0, seq=L();   while(p.len()>m){      i=(i+k-1)%p.len();      seq.append(p.pop(i));   }   "Prisoner killing order: %s.\nSurvivors: [%s]"   .fmt(seq.concat(","),p.concat(","))}`
Output:
```j2(41,3,3).println();
Prisoner killing order: 2,5,8,11,14,17,20,23,26,29,32,35,38,0,4,9,13,18,22,27,
31,36,40,6,12,19,25,33,39,7,16,28,37,10,24,1,21,3.
Survivors: [15,30,34]
```

## ZX Spectrum Basic

Translation of: ANSI Standard BASIC
`10 LET n=41: LET k=3: LET m=020 GO SUB 10030 PRINT "n= ";n;TAB (7);"k= ";k;TAB (13);"final survivor= ";lm40 STOP 100 REM Josephus110 REM Return m-th on the reversed kill list; m=0 is final survivor.120 LET lm=m: REM Local copy of m130 FOR a=m+1 TO n140 LET lm=FN m(lm+k,a)150 NEXT a160 RETURN 200 DEF FN m(x,y)=x-INT (x/y)*y: REM MOD function `