# 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.

## 11l

Translation of: Python
```F j(n, k)
V p = Array(0 .< n)
V i = 0
[Int] seq
L !p.empty
i = (i + k - 1) % p.len
seq.append(p.pop(i))
R "Prisoner killing order: #..\nSurvivor: #.".format(seq[0 .< (len)-1].join(‘, ’), seq.last)

print(j(5, 2))
print(j(41, 3))```
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
```

## 360 Assembly

Translation of: REXX

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

```*      Josephus problem               10/02/2017
JOSEPH 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)              " ->
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
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
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
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
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                     exit
PROB   DC     H'41',H'3',H'1'         round 1
DC     H'41',H'3',H'3'         round 2
NPROB  EQU    (*-PROB)/6              number of rounds
N      DS     F                       n number of prisoners
W      DS     F                       w killing count
S      DS     F                       s number of prisoners to survive
PG     DS     CL80                    buffer
DEC    DS     CL12                    temp for xdeco
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  #\$00
SETUP:  STA  \$1000,X    ; populate array with hex FF
INX
CPX  \$D0
BEQ  KILL
JMP  SETUP
KILL:   LDA  #\$00       ; number killed so far
STA  \$D2
LDX  #\$00       ; position within array
LDY  #\$01       ; counting up to k
FIND:   INY
SCAN:   INX
CPX  \$D0
BMI  TEST
LDX  #\$00       ; circle back around
TEST:   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
STA  \$D2
CMP  \$D0        ; have we killed all but 1?
BPL  RETURN
LDY  #\$00
JMP  FIND
RETURN: TXA             ; a <- index of survivor
RTS```

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
```/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program josephus64.s   */
/* run with josephus64 maxi intervalle */
/* example : josephus64 41 3

/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"

.equ FIRSTNODE,        0              //identification first node

/*******************************************/
/* Structures                               */
/********************************************/
.struct  0
llist_next:                            // next element
.struct  llist_next + 8
llist_value:                           // element value
.struct  llist_value + 8
llist_fin:
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessDebutPgm:          .asciz "Start program.\n"
szMessFinPgm:            .asciz "Program End ok.\n"
szRetourLigne:            .asciz "\n"
szMessValElement:        .asciz "Value : @ \n"
szMessListeVide:         .asciz "List empty.\n"
szMessImpElement:        .asciz "Node display: @ Value : @ Next @ \n"
szMessErrComm:           .asciz "Incomplete Command line  : josephus64 <maxi> <intervalle>\n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:         .skip 100
.align 4
qDebutListe1:       .skip llist_fin
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                   // entry of program
mov fp,sp                           // copy stack address  register x29 fp
bl affichageMess
ldr x0,[fp]                         // parameter number command line
cmp x0,#2                           // correct ?
ble erreurCommande                  // error

ldr x0,[x0]
bl conversionAtoD
ldr x0,[x0]
bl conversionAtoD
mov x21,x0                          // save gap

mov x0,FIRSTNODE                    // create first node
mov x1,0
bl createNode
mov x25,x0                          // first node address
mov x26,x0
mov x24,FIRSTNODE + 1
mov x23,1
1:                                      // loop create others nodes
mov x0,x24                          // key value
mov x1,0
bl createNode
str x0,[x26,llist_next]             // store current node address in prev node
mov x26,x0
cmp x23,x22                         // maxi ?
blt 1b
str x25,[x26,llist_next]            // store first node address in last pointer
mov x24,x26
2:
mov x20,1                           // counter for gap
3:
ldr x24,[x24,llist_next]
cmp x20,x21                         // intervalle ?
blt 3b
ldr x25,[x24,llist_next]            // removing the node from the list
ldr x22,[x25,llist_value]
ldr x27,[x25,llist_next]            // load pointer next
str x27,[x24,llist_next]            // ans store in prev node
//mov x0,x25
//bl displayNode
cmp x27,x24
csel x24,x24,x27,ne                 // next node address
bne 2b                              // and loop

mov x0,x24
bl displayNode                      // display last node

b 100f
erreurCommande:
bl affichageMess
mov x0,#1                          // error code
b 100f
100:                                   // program end standard
bl affichageMess
mov x0,0                          // return code Ok
mov x8,EXIT                       // system call "Exit"
svc #0

/******************************************************************/
/*     create node                                             */
/******************************************************************/
/* x0 contains key   */
/* x1 contains zero or address next node */
/* x0 returns address heap node  */
createNode:
stp x20,lr,[sp,-16]!        // save  registres
stp x21,x22,[sp,-16]!       // save  registres
mov x20,x0                  // save key
mov x21,x1                  // save key
mov x0,#0                   // allocation place heap
mov x8,BRK                  // call system 'brk'
svc #0
mov x22,x0                  // save address heap for node
add x0,x0,llist_fin         // reservation place node length
mov x8,BRK                  // call system 'brk'
svc #0
cmp x0,#-1                  // allocation error
beq 100f

str x20,[x22,llist_value]
str x21,[x22,llist_next]
mov x0,x22
100:
ldp x21,x22,[sp],16         // restaur des  2 registres
ldp x20,lr,[sp],16          // restaur des  2 registres
ret                         // retour adresse lr x30

/******************************************************************/
/*     display infos node                                     */
/******************************************************************/
/* x0 contains node address */
displayNode:
stp x1,lr,[sp,-16]!        // save  registres
stp x2,x3,[sp,-16]!        // save  registres
mov x2,x0
bl conversion16
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,llist_value]
bl conversion10S
mov x0,x3
bl strInsertAtCharInc
mov x3,x0
ldr x0,[x2,llist_next]
bl conversion16
mov x0,x3
bl strInsertAtCharInc
bl affichageMess

100:
ldp x2,x3,[sp],16          // restaur des  2 registres
ldp x1,lr,[sp],16          // restaur des  2 registres
ret                        // retour adresse lr x30
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"```
Output:
```pi@debian-buster-64:~/asm64/rosetta/asm5 \$ josephus64 41 3
Start program.
Node display: 000000000FFCB1E0 Value : +30 Next 000000000FFCB1E0
Program End ok.
pi@debian-buster-64:~/asm64/rosetta/asm5 \$ josephus64 5 2
Start program.
Node display: 000000002BDF7020 Value : +2 Next 000000002BDF7020
Program End ok.
```

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(Index, Default: Positive) return Natural is -- read Argument(Index)

Prisoners:  constant Positive := Arg(Index => 1, Default => 41);
Steps:      constant Positive := Arg(Index => 2, Default =>  3);
Survivors:  constant Positive := Arg(Index => 3, Default =>  1);
Print:               Boolean := (Arg(Index => 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
("N =" & Positive'Image(Prisoners) & ",  K =" & Positive'Image(Steps) &
(if Survivors > 1 then ",  #survivors =" & Positive'Image(Survivors)
else ""));
for Index in Next'Range loop -- initialize Next
Next(Index) := (Index+1) mod Prisoners;
end loop;
if Print then
end if;
for Execution in reverse 1 .. Prisoners loop
if Execution = Survivors then
Print := True;
end if;
if Print then
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`

## AppleScript

### Straightforward

Both scripts here use 1-based numbering.

Translation of: BBC BASIC
```on josephus(n, k)
set m to 0
repeat with i from 2 to n
set m to (m + k) mod i
end repeat

return m + 1
end josephus

josephus(41, 3) --> 31
```

Or with an option to specify the number of survivors:

```on josephus(n, k, s)
script o
property living : {}
end script

repeat with i from 1 to n
set end of o's living to i
end repeat

set startPosition to k
repeat until (n = s) -- Keep going round the circle until only s prisoners remain.
set circleSize to n
if (n < k) then
set i to (startPosition - 1) mod circleSize + 1
set item i of o's living to missing value
set n to n - 1
else
repeat with i from startPosition to circleSize by k
set item i of o's living to missing value
set n to n - 1
if (n = s) then exit repeat
end repeat
end if
set startPosition to i + k - circleSize
set o's living to o's living's integers
end repeat

return o's living
end josephus

josephus(41, 3, 1) --> {31}
josephus(41, 3, 6) --> {2, 4, 16, 22, 31, 35}
```

### Composition of pure functions

Composing a solution from generic and reusable (pure) functions, and using the zero-based notation of the problem statement:

```-- josephusSurvivor :: Int -> Int -> Int
on josephusSurvivor(n, k)
script go
on |λ|(x, a)
(k + x) mod a
end |λ|
end script

foldl(go, 0, enumFromTo(1, n))
end josephusSurvivor

-- josephusSequence :: Int -> Int -> [Int]
on josephusSequence(n, k)
script josephus
on |λ|(m, xs)
if 0 ≠ m then
set {l, r} to splitAt((k - 1) mod m, xs)
{item 1 of r} & |λ|(m - 1, rest of r & l)
else
{}
end if
end |λ|
end script

|λ|(n, enumFromTo(0, n - 1)) of josephus
end josephusSequence

--------------------------- TEST ---------------------------
on run
unlines({"Josephus survivor -> " & str(josephusSurvivor(41, 3)), ¬
"Josephus sequence ->" & linefeed & tab & ¬
showList(josephusSequence(41, 3))})
end run

---------------- REUSABLE GENERIC FUNCTIONS ----------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
lst
else
{}
end if
end enumFromTo

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set str to xs as text
set my text item delimiters to dlm
str
end intercalate

-- showList :: [a] -> String
on showList(xs)
script show
on |λ|(x)
x as text
end |λ|
end script
"[" & intercalate(",", map(show, xs)) & "]"
end showList

-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
if class of xs is text then
{items 1 thru n of xs as text, ¬
items (n + 1) thru -1 of xs as text}
else
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
end if
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt

-- str :: a -> String
on str(x)
x as string
end str

-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
```
Output:
```Josephus survivor -> 30
Josephus sequence ->
[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]```

## ARM Assembly

Works with: as version Raspberry Pi
```/* ARM assembly AARCH64 Raspberry PI 3B */
/* ARM assembly Raspberry PI  */
/*  program josephus.s   */

/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */

/*******************************************/
/* Constantes                              */
/*******************************************/
.equ STDOUT, 1           @ Linux output console
.equ EXIT,   1           @ Linux syscall
.equ WRITE,  4           @ Linux syscall
.equ BRK,    0x2d        @ Linux syscall
.equ CHARPOS,     '@'

.equ FIRSTNODE,        0              //identification first node

/*******************************************/
/* Structures                               */
/********************************************/
.struct  0
llist_next:                            // next element
.struct  llist_next + 4
llist_value:                           // element value
.struct  llist_value + 4
llist_fin:
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessDebutPgm:          .asciz "Start program.\n"
szMessFinPgm:            .asciz "Program End ok.\n"
szRetourLigne:            .asciz "\n"
szMessValElement:        .asciz "Value : @ \n"
szMessListeVide:         .asciz "List empty.\n"
szMessImpElement:        .asciz "Node display: @ Value : @ Next @ \n"
szMessErrComm:           .asciz "Incomplete Command line  : josephus <maxi> <intervalle>\n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:         .skip 24
.align 4
qDebutListe1:      .skip llist_fin
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                   // entry of program
mov fp,sp                           // copy stack address  register r29 fp
bl affichageMess
ldr r0,[fp]                        // parameter number command line
cmp r0,#2                          // correct ?
ble erreurCommande                 // error

ldr r0,[r0]
bl conversionAtoD
ldr r0,[r0]
bl conversionAtoD
mov r8,r0                          // save gap

mov r0,#FIRSTNODE                  // create first node
mov r1,#0
bl createNode
mov r5,r0                          // first node address
mov r6,r0
mov r4,#FIRSTNODE + 1
mov r3,#1
1:                                     // loop create others nodes
mov r0,r4                          // key value
mov r1,#0
bl createNode
str r0,[r6,#llist_next]             // store current node address in prev node
mov r6,r0
cmp r3,r2                          // maxi ?
blt 1b
str r5,[r6,#llist_next]            // store first node address in last pointer
mov r4,r6
2:
mov r2,#1                          // counter for gap
3:
ldr r4,[r4,#llist_next]
cmp r2,r8                          // intervalle ?
blt 3b
ldr r5,[r4,#llist_next]            // removing the node from the list
ldr r2,[r5,#llist_value]
ldr r7,[r5,#llist_next]            // load pointer next
str r7,[r4,#llist_next]            // ans store in prev node
//mov r0,r25
//bl displayNode
cmp r7,r4
moveq r4,r7
bne 2b                              // and loop

mov r0,r4
bl displayNode                      // display last node

b 100f
erreurCommande:
bl affichageMess
mov r0,#1                          // error code
b 100f
100:                                   // program end standard
bl affichageMess
mov r0,#0                          // return code Ok
mov r7,#EXIT                       // system call "Exit"
svc #0

/******************************************************************/
/*     create node                                             */
/******************************************************************/
/* r0 contains key   */
/* r1 contains zero or address next node */
/* r0 returns address heap node  */
createNode:
push {r1-r11,lr}            // save  registers
mov r9,r0                   // save key
mov r10,r1                  // save key
mov r0,#0                   // allocation place heap
mov r7,#BRK                 // call system 'brk'
svc #0
mov r11,r0                  // save address heap for node
add r0,r0,#llist_fin        // reservation place node length
mov r7,#BRK                 // call system 'brk'
svc #0
cmp r0,#-1                  // allocation error
beq 100f

str r9,[r11,#llist_value]
str r10,[r11,#llist_next]
mov r0,r11
100:
pop {r1-r11,lr}            // restaur registers
bx lr                      // return

/******************************************************************/
/*     display infos node                                     */
/******************************************************************/
/* r0 contains node address */
displayNode:
push {r1-r4,lr}           // save  registers
mov r2,r0
bl conversion16
mov r4,#0
strb r4,[r1,r0]           // store zero final
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#llist_value]
bl conversion10S
mov r4,#0
strb r4,[r1,r0]           // store zero final
mov r0,r3
bl strInsertAtCharInc
mov r3,r0
ldr r0,[r2,#llist_next]
bl conversion16
mov r4,#0
strb r4,[r1,#8]           // store zero final
mov r0,r3
bl strInsertAtCharInc
bl affichageMess

100:
pop {r1-r4,lr}            // restaur registers
bx lr                     // return
/***************************************************/
/*      ROUTINES INCLUDE                 */
/***************************************************/
.include "../affichage.inc"```
```pi@raspberrypi:~/asm32/rosetta32/ass6 \$ josephus 41 3
Start program.
Node display: 00F880F0 Value :         +30 Next 00F880F0
Program End ok.
```

## Arturo

```josephus: function [n,k][
p: new 0..n-1
i: 0
seq: []

while [0 < size p][
i: (i+k-1) % size p
append 'seq p\[i]
remove 'p .index i
]
print ["Prisoner killing order:" chop seq]
print ["Survivor:" last seq]
print ""
]

print "josephus 5 2 =>"
josephus 5 2

print "josephus 41 3 =>"
josephus 41 3
```
Output:
```josephus 5 2 =>
Prisoner killing order: [1 3 0 4]
Survivor: 2

josephus 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```

## AutoHotkey

```; Since AutoHotkey is 1-based, we're numbering prisoners 1-41.
nPrisoners := 41
kth        := 3

; Build a list, purposefully ending with a separator
Loop % nPrisoners
list .= A_Index . "|"

; iterate and remove from list
i := 1
Loop
{
; 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 := 41
kth        := 3
list       := []

; Build a list of 41 items
Loop % nPrisoners
list.insert(A_Index)

; iterate and remove from list
i := 1
Loop
{
; 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/I
BEGIN {
main(5,2,1)
main(41,3,1)
main(41,3,3)
exit(0)
}
# 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++) {
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=41
20 K=3
30 M=0
40 FOR I=M+1 TO N
50 M=INT(I*((M+K)/I-INT((M+K)/I))+0.5)
60 NEXT I
70 PRINT "Survivor is number";M
```
Output:
`Survivor is number 30`

### ANSI BASIC

Translation of: ALGOL 68
Works with: Decimal BASIC
```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 m
130    FOR a = m+1  TO n
140       LET lm = MOD(lm+k, a)
150    NEXT a
160    LET josephus = lm
170 END FUNCTION
180 LET n = 41
190 LET k=3
200 PRINT "n =";n, "k =";k,"final survivor =";josephus(n, k, 0)
210 END
```
Output:
```n = 41                  k = 3                   final survivor = 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```

### BASIC256

```n = 41 #prisoners
k = 3  #order of execution

print "n = "; n, "k = "; k, "final survivor = "; Josephus(n, k, 0)
end

function Josephus(n, k, m)
lm = m
for i = m + 1 to n
lm = (lm + k) mod i
next
return lm
end function```
Output:
`Same as FreeBASIC entry.`

### BBC BASIC

```REM >josephus
PRINT "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`

### Chipmunk Basic

Works with: Chipmunk Basic version 3.6.4
Works with: QBasic
```100 n = 41
110 k = 3
120 print "n = ";n,"k = ";k,"final survivor = ";josephus(n,k,0)
130 end
140 function josephus(n,k,m)
150 lm = m
160 for i = m+1 to n
170 lm = (lm+k) mod i
180 next
190 josephus = lm
200 end function
```
Output:
`Same as FreeBASIC entry.`

### Craft Basic

```'using 1 to n

define prisoners = 0, step = 0, killcount = 0, survivor = 0
define fn (josephus) as ( survivor + step ) % killcount

do

input "Prisoners", prisoners
input "Step", step

gosub executioner

loop

sub executioner

let killcount = 1

do

let killcount = killcount + 1
let survivor = (josephus)

loop killcount < prisoners

print "survivor = ", survivor

return
```
Output:
```prisoners? 41
step? 3

survivor = 30```

### FreeBASIC

```Function Josephus (n As Integer, k As Integer, m As Integer) As Integer
Dim As Integer lm = m
For i As Integer = m + 1  To n
lm = (lm + k) Mod i
Next i
Josephus = lm
End Function

Dim As Integer n = 41 'prisioneros
Dim As Integer k = 3  'orden de ejecución

Print "n ="; n, "k ="; k, "superviviente = "; Josephus(n, k, 0)```
Output:
```n = 41        k = 3         superviviente =  30
```

### FTCBASIC

```define prisoners = 0, step = 0, killcount = 0
define survivor = 0, remainder = 0

do

print "Prisoners: " \
input prisoners

print "Step: " \
input step

gosub executioner

loop

sub executioner

let killcount = 1

do

let killcount = killcount + 1
let survivor = survivor + step
let survivor = survivor / killcount
carry survivor

loop killcount < prisoners

print "survivor = " \
print survivor

return
```

### Gambas

```Public Sub Main()

Dim n As Integer = 41 'prisoners
Dim k As Integer = 3  'order of execution

Print "n = "; n, "k = "; k, "final survivor = "; Josephus(n, k, 0)

End

Function Josephus(n As Integer, k As Integer, m As Integer) As Integer

Dim lm As Integer = m

For i As Integer = m + 1 To n
lm = (lm + k) Mod i
Next
Return lm

End Function
```
Output:
`Same as FreeBASIC entry.`

### GW-BASIC

Works with: Chipmunk Basic
Works with: PC-BASIC version any
Works with: MSX Basic
Works with: QBasic
```10 LET N = 41
20 LET K = 3
30 LET M = 0
40 GOSUB 100
50 PRINT "n ="; N, "k ="; K, "final survivor ="; LM
60 END
100 REM Josephus
110 REM Return m-th on the reversed kill list; m=0 is final survivor.
120 LET LM = M : REM Local copy of m
130 FOR A = M+1 TO N
140   LET LM = (LM+K) MOD A: REM MOD function
150 NEXT A
160 RETURN
```

### IS-BASIC

```100 PROGRAM "Josephus.bas"
110 INPUT PROMPT "Number of prisoners: ":NP
120 INPUT PROMPT "Execution step: ":EX
130 INPUT PROMPT "How many survivors:  ":SU
140 PRINT "Survivors:";
150 FOR S=0 TO SU-1
160   PRINT JOSEPHUS(NP,EX,S);
170 NEXT
180 DEF JOSEPHUS(N,K,M)
190   FOR I=M+1 TO N
200     LET M=MOD((M+K),I)
210   NEXT
220   LET JOSEPHUS=M
230 END DEF```

### Minimal BASIC

Works with: QBasic
Works with: QuickBasic
Works with: Applesoft BASIC
Works with: BASICA
Works with: Chipmunk Basic
Works with: GW-BASIC
Works with: MSX BASIC
Works with: Just BASIC
Works with: Liberty BASIC
Works with: Run BASIC
```10 LET N = 41
20 LET K = 3
30 LET M = 0
40 GOSUB 100
50 PRINT "N ="; N, "K ="; K, "FINAL SURVIVOR ="; S
60 GOTO 150
100 LET S = M
110 FOR A = M+1  TO N
120   LET S = INT(A * ((S+K) / A - INT((S+K) / A)) + 0.5)
130 NEXT A
140 RETURN
150 END
```

### MSX Basic

The GW-BASIC solution works without any changes.

### Palo Alto Tiny BASIC

Translation of: ANSI BASIC
```10 REM JOSEPHUS PROBLEM
20 LET N=41,K=3,M=0
30 GOSUB 100
40 PRINT #1,"N =",N,", K =",K,", FINAL SURVIVOR =",L
50 STOP
90 REM ** JOSEPHUS
100 LET L=M
110 FOR A=M+1 TO N
120 LET L=L+K-((L+K)/A)*A
130 NEXT A
140 RETURN
```
Output:
```N = 41, K = 3, FINAL SURVIVOR = 30
```

### PureBasic

```NewList prisoners.i()

Procedure f2l(List p.i())
FirstElement(p())    : tmp.i=p()
DeleteElement(p(),1) : LastElement(p())
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
ForEver
End```
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 :```

### QBasic

Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
```FUNCTION josephus (n, k, m)
lm = m
FOR i = m + 1 TO n
lm = (lm + k) MOD i
NEXT i
josephus = lm
END FUNCTION

n = 41
k = 3
PRINT "n = "; n, "k = "; k, "final survivor = "; josephus(n, k, 0)
END
```
Output:
`Same as FreeBASIC entry.`

### Quite BASIC

```10 LET N = 41
20 LET K = 3
30 LET M = 0
40 GOSUB 100
50 PRINT "N = " ; N; "  K = "; K; "  FINAL SURVIVOR  ="; S
60 END
100 LET S = M
110 FOR A = M+1  TO N
120   LET S = INT(A * ((S+K) / A - INT((S+K) / A)) + 0.5)
130 NEXT A
140 RETURN
```

### Tiny BASIC

```    REM Josephus problem

LET N = 41
LET K = 3
LET M = 0
GOSUB 10
PRINT "N = ", N
PRINT "K = ", K
PRINT "FINAL SURVIVOR = ", S
END
REM ** JOSEPHUS
10  LET S = M
LET I = M + 1
20  IF I = N  THEN GOTO 30
LET S = S + K - ((S + K) / I) * I
LET I = I + 1
GOTO 20
30  RETURN
```

### True BASIC

```FUNCTION josephus(n, k, m)
LET lm = m
FOR i = m+1 TO n
LET lm = REMAINDER(lm+k,i)
NEXT i
LET josephus = lm
END FUNCTION

LET n = 41
LET k = 3
PRINT "n = "; n, "k = "; k, "final survivor = "; josephus(n, k, 0)
END
```
Output:
`Same as QBasic entry.`

### VBScript

```Function josephus(n,k,s)
Set prisoner = CreateObject("System.Collections.ArrayList")
For i = 0 To n - 1
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
Next
End Function

'testing the function
WScript.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
```

### Visual Basic .NET

Translation of: D
```Module Module1

'Determines the killing order numbering prisoners 1 to n
Sub Josephus(n As Integer, k As Integer, m As Integer)
Dim p = Enumerable.Range(1, n).ToList()
Dim i = 0

Console.Write("Prisoner killing order:")
While p.Count > 1
i = (i + k - 1) Mod p.Count
Console.Write(" {0}", p(i))
p.RemoveAt(i)
End While
Console.WriteLine()

Console.WriteLine("Survivor: {0}", p(0))
End Sub

Sub Main()
Josephus(5, 2, 1)
Console.WriteLine()
Josephus(41, 3, 1)
End Sub

End Module
```
Output:
```Prisoner killing order: 2 4 1 5
Survivor: 3

Prisoner killing order: 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```

### Yabasic

```n = 41 //prisoners
k = 3  //order of execution

print "n = ", n, "\tk = ", k, "\tfinal survivor = ", Josephus(n, k, 0)
end

sub Josephus(n, k, m)
local lm

lm = m
for i = m + 1 to n
lm = mod(lm + k, i)
next
return lm
end sub```
Output:
`Same as FreeBASIC entry.`

### ZX Spectrum Basic

Translation of: ANSI BASIC
```10 LET n=41: LET k=3: LET m=0
20 GO SUB 100
30 PRINT "n= ";n;TAB (7);"k= ";k;TAB (13);"final survivor= ";lm
40 STOP
100 REM Josephus
110 REM Return m-th on the reversed kill list; m=0 is final survivor.
120 LET lm=m: REM Local copy of m
130 FOR a=m+1 TO n
140 LET lm=FN m(lm+k,a)
150 NEXT a
160 RETURN
200 DEF FN m(x,y)=x-INT (x/y)*y: REM MOD function```

## Batch File

Uses C's `jos()` function.

Translation of: C
```@echo off
setlocal 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 :josephus
pause
exit /b 0

%== The Procedure ==%
:josephus
set "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 . . .```

## Befunge

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

```>0" :srenosirP">:#,_&>>00p>>v
v0p01<&_,#!>#:<"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 survivor
int 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 not
xint 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)
{
}

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
{
}
}

}
}
```

## 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 ()
(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
```

## Crystal

Translation of: Ruby
```n = ARGV.fetch(0, 41).to_i  # n default is 41 or ARGV[0]
k = ARGV.fetch(1,  3).to_i  # k default is 3 or ARGV[1]

prisoners = (0...n).to_a
while prisoners.size > 1; prisoners.rotate!(k-1).shift end
puts "From #{n} prisoners, eliminating each prisoner #{k} leaves prisoner #{prisoners.first}."
```
Output:
```\$ crystal josephus.cr
From 41 prisoners, eliminating each prisoner 3 leaves prisoner 30.

\$ crystal josephus.cr 123
From 123 prisoners, eliminating each prisoner 3 leaves prisoner 54.

\$ crystal josephus.cr 123 47
From 123 prisoners, eliminating each prisoner 47 leaves prisoner 101.
```

## 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```

## Delphi

Works with: Delphi version 6.0

Uses standard Delphi TList to hold and delete numbers as it analyzes the data.

```type TIntArray = array of integer;

procedure GetJosephusSequence(N,K: integer; var IA: TIntArray);
{Analyze sequence of deleting every K of N numbers}
{Retrun result in Integer Array}
var LS: TList;
var I,J: integer;
begin
SetLength(IA,N);
LS:=TList.Create;
try
{Store number 0..N-1 in list}
for I:=0 to N-1 do LS.Add(Pointer(I));
J:=0;
for I:=0 to N-1 do
begin
{Advance J by K-1 because iterms are deleted}
{And wrapping around if it J exceed the count }
J:=(J+K-1) mod LS.Count;
{Caption the sequence}
IA[I]:=Integer(LS[J]);
{Delete (kill) one item}
LS.Delete(J);
end;
finally LS.Free; end;
end;

procedure ShowJosephusProblem(Memo: TMemo; N,K: integer);
{Analyze and display one Josephus Problem}
var IA: TIntArray;
var I: integer;
var S: string;
const CRLF = #\$0D#\$0A;
begin
GetJosephusSequence(N,K,IA);
S:='';
for I:=0 to High(IA) do
begin
if I>0 then S:=S+',';
if (I mod 12)=11 then S:=S+CRLF+'           ';
S:=S+IntToStr(IA[I]);
end;
end;

procedure TestJosephusProblem(Memo: TMemo);
{Test suite of Josephus Problems}
begin
ShowJosephusProblem(Memo,5,2);
ShowJosephusProblem(Memo,41,3);
end;
```
Output:
```N=5 K=2
Sequence: [1,3,0,4,2]
Survivor: 2

N=41 K=3
Sequence: [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
```
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 ...```

## EasyLang

```n = 41
k = 3
print "prisoners: " & n
print "step size: " & k
for i = 1 to n
lm = (lm + k) mod i
.
print "final survivor: " & lm```

## 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 prisoners
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  … ∞)

;; #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 … ∞)
```

## EDSAC order code

The algorithm is of the "increasing modulus" type. Though written independently of the Ring solution, it seems to be essentially the same. The (n,k) pairs used by the demo program are taken from solutions on this page. Running time totals 1.2 EDSAC minutes for the first eight examples, and 12.5 for the last two.

```[Jospehus problem - Rosetta Code
EDSAC program (Initial Orders 2)]

[Arrange the storage]
T45K P56F       [H parameter: library subroutine R4 to read integer]
T46K P80F       [N parameter: subroutine to print 17-bit non-neg integer]
T47K P160F      [M parameter: main routine]
T51K P128F      [G parameter: subroutine to find last survivor]

[Library subroutine M3, runs at load time and is then overwritten.
Prints header; here, last character sets teleprinter to figures.]
PF GK IF AF RD LF UF OF E@ A6F G@ E8F EZ PF
*!!!!N!!!!!K!!!!SURVIVOR@&#..PZ

[============== G parameter: Subroutine to find last survivor ==============
Input:  4F = n = number of prisoners
5F = k = executioner's step
Output: 0F = 0-based index of last survivor]

[Pascal equivalent:
z := 0; // solution when n = 1
for j := 2 to n do z := (z + k) mod j;
result := z;]
E25K TG GK
A3F T22@        [plant return link as usual]
T23@            [z := 0]
A2F T24@        [j := 2]
[6]   TF              [clear acc]
A23@ A5F        [acc := z + k]
[Get residue modulo j by repeatedly subtracting j.
The number of subtractions is usually small.]
[9]   S24@ E9@        [subtract j till result < 0]
A24@            [add back the last j]
T23@            [update z]
A24@ A25@ T24@  [inc(j)]
[16]   A4F S24@        [acc := n - j]
E6@             [loop back if j <= n]
TF              [done: clear acc]
A23@ TF         [return z (last survivor) to caller in 0F]
[22]   ZF              [(planted) jump back to caller]
[Storage]
[23]   PF              [Pascal z]
[24]   PF              [Pascal j]
[25]   PD              [constant 1]

[====================== M parameter: Main routine ======================]
E25K TM GK
[0]   PF              [negative data count]
[1]   PF              [number of prisoners]
[2]   PF              [executioner's step]
[3]   !F              [space]
[4]   @F              [carriage return]
[5]   &F              [line feed]
[6]   K4096F          [null character]
[Enter with acc = 0]
[7]   A7@ GH          [call subroutine R4, sets 0D := count of (n,k) pairs]
SF              [acc := count negated; it's assumed that count < 2^16]
E46@            [exit if count = 0]
LD              [shift count into address field]
[12]   T@              [update negative loop counter]
A13@ GH         [call library subroutine R4, 0D := number of prisoners]
AF T1@          [store number of prisoners, assumed < 2^16]
A17@ GH         [call library subroutine R4, 0D := executioner's step]
AF T2@          [store executioner's step, assumed < 2^16]
A3@ T1F         [to print leading 0's as spaces]
A1@ TF          [pass number of prisoners to print subroutine]
A25@ GN O3@     [print number of prisoners, plus space]
A2@ TF          [same for executioner's step]
A30@ GN O3@
A1@ T4F         [pass number of prisoners to "last survivor" subroutine]
A2@ T5F         [same for executioner's step]
A37@ GG         [call subroutine, 0F := 0-based index of last survivor]
A39@ GN O4@ O5@ [print last survivor, plus CR,LF]
A@ A2F          [increment negative counter]
G12@            [loop back if still negative]
[46]   O6@             [print null to flush printer buffer]
ZF              [halt the machine]

[The next 3 lines put the entry address into location 50,
so that it can be accessed via the X parameter (see end of program).]
T50K
P7@
T7Z

[================== H parameter: Library subroutine R4 ==================
Input of one signed integer, returned in 0D.
22 locations.]
E25K TH GK
GKA3FT21@T4DH6@E11@P5DJFT6FVDL4FA4DTDI4FA4FS5@G7@S5@G20@SDTDT6FEF

[============================= N parameter ==============================
Subroutine to print non-negative 17-bit integer.
Input: 0F = integer to be printed (not preserved)
1F = character for leading zero (preserved)
Workspace: 4F..7F, 38 locations]
E25K TN
GKA3FT34@A1FT7FS35@T6FT4#FAFT4FH36@V4FRDA4#FR1024FH37@E23@O7FA2F
T6FT5FV4#FYFL8FT4#FA5FL1024FUFA6FG16@OFTFT7FA6FG17@ZFP4FZ219DTF

[==========================================================================
On the original EDSAC, the following (without the whitespace and comments)
might have been input on a separate tape.]
E25K TX GK
EZ              [define entry point]
PF              [acc = 0 on entry]
[Count of (n,k) pairs, then the pairs, to be read by library subroutine R4.
Note that sign comes *after* value.]
10+5+2+12+4+41+3+50+2+60+3+71+47+123+3+123+47+10201+17+23482+3343+```
Output:
```    N     K    SURVIVOR
5     2     2
12     4     0
41     3    30
50     2    36
60     3    40
71    47    29
123     3    54
123    47   101
10201    17  7449
23482  3343  1335
```

## 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
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)
end
end

Josephus.find(41,3)
```
Output:
`30`

## Emacs Lisp

```(defun jo (n k)
(if (= 1 n)
1
(1+ (% (+ (1- k)
(jo (1- n) k))
n))))

(message "%d" (jo 50 2))
(message "%d" (jo 60 3))
```
Output:
```37
41
```

## Erlang

```-module( josephus_problem ).

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

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
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
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
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(:)
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.`

## Frink

```killingCycle[prisonerCount,killStep = 2] :=
{
i = 0
killed = new array
prisoners = array[0 to prisonerCount - 1]
while length[prisoners] > 1
{
i = (i + killStep - 1) mod length[prisoners]
killed.push[prisoners.remove[i]] // Remove the killed prisoner from the prisoners array and add it to the killed array.
}
killedResult = "Killed:"
for kill = killed // Loop through the killed array to format it nicely.
{
killedResult = killedResult + " " + kill
}
aliveResult = "Alive: " + prisoners@0 // Get the only item left in the array
return """\$killedResult
\$aliveResult"""
}

println[killingCycle[41,3]] // Enter in total number of prisoners and the number to skip each cycle```
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
Alive: 30
```

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution:

We start with two lists. The first one contains initially the prisoners (their number), and the second one contains the kills, and it is initially empty.

On every kill, the number of the killed prisoner is deleted from the first list, and it is (striked out) appended to the second one, in order to show the order of kills.

In order to leave more than one survivor, the cycle is repeated n-s times, where n is the number of prisoners and s is the number of survivors.

At the end, the two lists are retrieved.

Even when Fōrmulæ is 1-based, the list is filled starting with the 0 prisoner, in order to the results can be compared with other languages (mostly 0-based).

Case 1. 5 prisoners, killing every 2:

Case 2. 41 prisoners, killing every 3:

Case 3. The captors may be especially kind and let m survivors free, and Josephus might just have m - 1 friends to save.:

Case 4. Larger example. 23,482 prisoners, killing every 3,343, leaving 3 survivors. Only the survivors are shown (the first element of the resulting list is extracted):

Drawing history

The following function creates a raster graphics of size n squares width, and n + 1 squares height, where n is the number of prisoners. The size of the square is defines as pixels.

The horizontal axis (right to left) is the number of the prisoner. The vertical axis (top to bottom) is the number of cycle.

An alive prisoner is drawn as green, a dead one is drawn as black.

Example 1. Drawing for the case 41 prisoners, killing every 3 (cell size is 5x5 pixels)::

Example 2. Drawing for the case 500 prisoners, killing every 6 (cell size is 1x1 pixel)::

## Go

```package main

import "fmt"

func 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]
}

// extra
func 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
```

## 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]
```

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))
_         -> 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 -> Int
jos 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)%m
end
```
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 t
end

procedure ceil(a,q)
n := a*q
if n = integer(n) then return integer(n)
n ?:= integer(tab(upto('.'))) + 1
return n
end
```

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 < #@])^:_ i.@]) 41
30
```

Structured derivation of the fixed tacit code

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

[ DropNext WhileMoreThanOne prisoners f.
[ (1 }. <:@[ |. ])^:(1 < #@])^:_ i.@]
```

### 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 41
30
```

### Explicit version 2

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

3 Josephus2 41
30
```

## 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++){
}
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++){
}
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) {
for (var i = 0; i < n-1; i++) {
current.label = i+1;
current.next = {prev: current};
current = current.next;
}
current.label = n;
return this;
},
kill: function(spacing) {
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,...
```

## 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 simulation
def 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) )";

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]
```

## 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, p
end

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]```

## 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) {
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) .. '.')
end
josephus(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.
```

## Mathematica/Wolfram Language

```survivor[n_, k_] := Nest[Most[RotateLeft[#, k]] &, Range[0, n - 1], n - 1]
survivor[41, 3]
```
Output:
`{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:
%   1 = alive position
%   index = # of person

%% Setting up
arrPeople = ones(1, numPeople);
currInd = 0;

%% Counting
while (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 people
end

indAlive = find(arrPeople);

end
```

## Maxima

```josephus_list(n,k):=(result:[],pos:1,ref:makelist(i,i,n),while ref#[] do (pos:mod(pos+k-2,length(ref))+1,push(ref[pos],result),ref:delete(ref[pos],ref)),
reverse(result));
/* Example */
/* last_survivor:last(josephus_list(41,3));
31
*/
```

## Modula-2

```MODULE Josephus;
FROM FormatString IMPORT FormatString;

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 m
END 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);

END Josephus.
```

## Nanoquery

Translation of: Python
```def j(n, k)
p = list(range(0, n-1))
i = 0
seq = {}
while len(p) > 0
i = (i+k-1) % len(p)
seq.append(p[i])
p.remove(i)
end
sur = seq[len(seq) - 1]; seq.remove(len(seq) - 1)
return format("Prisoner killing order: %s\nSurvivor: %d", seq, sur)
end

println j(5,2)
println
println j(41,3)```
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```

## 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
**********************************************************************/
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
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

### Simulating

Translation of: Python
```import sequtils, strutils, sugar

proc j(n, k: int): string =
var
p = toSeq(0 ..< n)
i = 0
s = newSeq[int]()

while p.len > 0:
i = (i + k - 1) mod p.len
system.delete(p, i)

result = "Prisoner killing order: "
result.add s.map((x: int) => \$x).join(", ")

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```

### Processing backwards

Another more efficient way but without the killing order:

```func prisonerPos(n, k: Positive): int =
## The result is computed backwards. We start from the winner at
## position 0 on last round and compute its position on previous rounds.
var pos = 0
for i in 2..n:
pos = (pos + k) mod i
result = pos

echo "Survivor: ", prisonerPos(5, 2)
echo "Survivor: ", prisonerPos(41, 3)
```
Output:
```Survivor: 2
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 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 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
] 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]
```

## Oz

### data-driven concurrent version

Figure 7.35 from "Concepts, Techniques, and Models of Computer Programming" indexes from 1 instead of 0. It was modified to report indexes from 0 and also report the killed list:

```declare
fun {Pipe Xs L H F}
if L=<H then {Pipe {F Xs L} L+1 H F} else Xs end
end
fun {Josephus N K}
fun {Victim Xs I}
case Xs of kill(X S)|Xr then
if S==1 then Last=I nil
elseif X mod K==0 then
Killed:=I-1|@Killed
kill(X+1 S-1)|Xr
else
kill(X+1 S)|{Victim Xr I}
end
[] nil then nil end
end
Last Zs Killed={NewCell nil}
in
Zs={Pipe kill(1 N)|Zs 1 N
fun {\$ Is I} thread {Victim Is I} end end}
result(survivor: Last-1 killed: {Reverse @Killed})
end
{Show {Josephus 41 3}}```
Output:
`result(killed:2|5|8|11|14|17|20|23|...|... survivor:30)`

## 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: Raku
```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.`

## Phix

I managed to identify eight algorithms in use on this page, so I translated all of them. Kill ordering lists omitted for sanity.
Unclassified: Haskell, Python[4 aka learning iter in python], REXX[version 2], RPL (plus Befunge, J, and Mathematica, which I'm happy to ignore)
Note all indexes and results are 1-based. For skipping/linked_list/sliding_queue, prisoners do not have to be numbers, the same would be true for contractacycle and contractalot with the tiniest of tweaks. For recursive/iterative, prisoners are implicitly numbers, not that it would be difficult to use the result(s) to subscript a list of string names.

### skipping

360 assembly, 6502 Assembly, AWK, EchoLisp, ERRE, MATLAB, NetRexx, PHP, PL/I, REXX[version 1].
Method: all prisoners stay where they are, executioner walks round and round, skipping over ever increasing numbers of dead bodies (slowest of the lot, by quite some margin)

```function skipping(sequence prisoners, integer step, survivors=1)
integer n = length(prisoners), nn = n, 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
prisoners[p] = -1
n -= 1
end while
return remove_all(-1,prisoners)
end function
--?skipping({"Joe","Jack","William","John","James"},2,1) --> {"William"}
```

AArch64 Assembly, Ada, ARM Assembly, Common Lisp[2, probably], Fortran, JavaScript[1] (albeit dbl-lnk), Python[3].
Method: like skipping, all prisoners stay where they are, but the executioner uses the links to speed things up a bit.

```function linked_list(sequence prisoners, integer step, survivors)
integer n = length(prisoners)
integer p = n, prvp
while n>survivors do
for i=1 to step do
prvp = p
end for
prisoners[p] = -1
n -= 1
end while
return remove_all(-1,prisoners)
end function
```

### sliding queue

Clojure, Crystal, D (both), Eiffel, Elixir, Erlang, friendly interactive shell, Go, jq, Perl, PowerShell, PureBasic (albeit one at a time), Quackery, Raku, REBOL, Ruby, Scala, Sidef[1], Tcl, Vlang. Method: all skipped prisoners rejoin the end of the queue which sidles left, executioner stays put until the queue gets too short.

```function sliding_queue(sequence prisoners, integer step, survivors)
integer n = length(prisoners)
while n>survivors do
integer k = remainder(step-1,n)+1                   -- (mostly k==step)
prisoners = prisoners[k+1..\$]&prisoners[1..k-1]     -- rotate, dropping one.
n -= 1
end while
return prisoners
end function
```

### contractacycle

AppleScript[2], Groovy
Method: executioner walks along killing every k'th prisoner; while he walks back the queue contracts to remove gaps. (once the queue gets too small it obviously reverts to one at a time, a bit more like contractalot below)

```function contractacycle(integer n, integer k, s)
sequence living = tagset(n)
integer startPosition = k, i, lasti
while n!=s do -- Keep going round the circle until only s prisoners remain.
integer circleSize = n
if (n < k) then
i = mod(startPosition-1,circleSize) + 1
living = living[1..i-1]&living[i+1..\$]
n -= 1
lasti = i
else
for i=startPosition to circleSize by k do
living[i] = -1
n -= 1
if (n = s) then exit end if -- Not Groovy, see note
lasti = i
end for
living = remove_all(-1,living)
end if
startPosition = lasti + k - circleSize
end while
return living
end function
```

Groovy does not have a n=s test, it probably is entirely unnecessary. The Groovy code is also somewhat neater, always using a loop and remove_all() - while not probihitively expensive, it may check lots of things for -1 that the slicing won't.

### contractalot

11L, Arturo, AutoHotkey, C#, C++, Delphi, Frink, Formulae, Java (both), JavaScript[2], Julia[2], Kotlin, Lua, NanoQuery, Nim, Objeck, Oforth, Processing, Python[1], R[2], Rust, Seed7, Swift, VBScript, Vedit, VisualBasic.NET, XPL0, zkl.
Method: executioner walks round and round, queue contracts after every kill. Often implemented as execute all prisoners then release last one killed.

```function contractalot(integer n, integer k, s)
sequence list = tagset(n)
integer i = 1
while n>s do
i += k - 1
if (i > n) then i := mod(i-1, n)+1 end if
list [i..i] = {}
n -= 1
end while
return list
end function
```

### recursive

Emacs Lisp, Icon, Julia[1], PARI/GP, PicoLisp (less the optms.n), Sidef[2]
Method: recursive mod maths madness - only handles the lone survivor case.

```function recursive(integer n, k)
return iff(n=1?1:1+mod(k-1+(recursive(n-1, k)),n))
end function
```

### iterative

ALGOL 68, ANSI Standard BASIC, AppleScript[1,3(!!)], BASIC(*11), Batch File, C (but not ULL), Common Lisp[1], Craft Basic, Easylang, EDSAC (allegedly), Factor, Forth, FreeBASIC, FTCBASIC, Modula-2, Python[2], R, Racket, Ring, SequenceL, ZX Spectrum Basic
Method: iterative mod maths madness - but hey, it will be extremely fast. Unlike recursive, it can also deliver >1 survivor, one at a time.

```function iterative(integer n, k, m=0)
-- Return m-th on the reversed kill list; m=0 is final survivor.
for a = m+1 to n do
m = mod(m+k, a)
end for
return m + 1     -- (make result 1-based)
end function
```

### iterative2

Icon[2]

```function iterative2(integer n,k,s)
integer a = k*(n-s) + 1,
olda = a
atom q = k/(k-1),
nk = n*k
while a <= nk do
olda = a
a = ceil(a*q)
end while
return nk - olda + 1 -- (make result 1-based)
end function
```

### test driver

```--demo/rosetta/Josephus.exw
constant show_all = true,
show_slow = false,
show_skipping = false,
show_sliding_queue = false,
show_contractacycle = false,
show_contractalot = false,
show_recursive = false,
show_iterative = false,
show_iterative2 = true

constant TAGSET = #01,
ITER   = #02,
ITER2  = #04,
SLOW   = #08,
ONES   = #10

constant tests = {{41,3,1,false},
{41,3,3,false},
{5,2,1,false},
{5,4,1,false},
{50,2,1,false},
{60,3,1,false},
{23482,3343,3,true},
{23482,3343,1,true},
{41,3,6,false}}

procedure test(string name, integer flags)
atom t0 = time()
integer rid = routine_id(name)
for i=1 to length(tests) do
integer {prisoners, step, survivors, slow} = tests[i]
if (not and_bits(flags,ONES) or survivors=1)
and (not slow or show_slow or not and_bits(flags,SLOW)) then
sequence res
if and_bits(flags,ONES) then
-- (recursive does not take a 3rd param)
res = {rid(prisoners,step)}
elsif and_bits(flags,TAGSET) then
res = rid(tagset(prisoners),step,survivors)
elsif and_bits(flags,ITER) then
res = {}
for s=0 to survivors-1 do
res &= rid(prisoners,step,s)
end for
elsif and_bits(flags,ITER2) then
res = {}
for s=prisoners-survivors+1 to prisoners do
res &= rid(prisoners,step,s)
end for
else
res = rid(prisoners,step,survivors)
end if
printf(1,"%s(%d,%d,%d) = %v\n",{name,prisoners,step,survivors,res})
end if
end for
?elapsed(time()-t0)
end procedure
if show_all or show_skipping        then test("skipping",TAGSET+SLOW)       end if
if show_all or show_sliding_queue   then test("sliding_queue",TAGSET+SLOW)  end if
if show_all or show_contractacycle  then test("contractacycle",SLOW)        end if
if show_all or show_contractalot    then test("contractalot",NULL)          end if
if show_all or show_recursive       then test("recursive",ONES)             end if
if show_all or show_iterative       then test("iterative",ITER)             end if
if show_all or show_iterative2      then test("iterative2",ITER2)           end if
```
Output:

As shown for sliding_queue, some of the result sets are in a slightly different order, sometimes, otherwise matching output replaced by "...".

```skipping(41,3,1) = {31}
skipping(41,3,3) = {16,31,35}
skipping(5,2,1) = {3}
skipping(5,4,1) = {1}
skipping(50,2,1) = {37}
skipping(60,3,1) = {41}
skipping(23482,3343,3) = {1088,1336,13318}
skipping(23482,3343,1) = {1336}
skipping(41,3,6) = {2,4,16,22,31,35}
"17s"
"0.6s"
sliding_queue(41,3,1) = {31}...
sliding_queue(23482,3343,3) = {13318,1088,1336}
sliding_queue(41,3,6) = {31,35,2,4,16,22}
"1.0s"
contractacycle(41,3,1) = {31}...
"1.5s"
contractalot(41,3,1) = {31}...
"0.9s"
recursive(41,3,1) = {31}...
"0.0s"
iterative(41,3,1) = {31}...
"0.0s"
iterative2(41,3,1) = {31}...
"0.0s"
```

## PHP

```<?php //Josephus.php
function 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
while((array_sum(array_count_values(\$prisoners))<\$n)){//while sum of count of unique values dead times < n (they start as all false)
\$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)))));
}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 (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): ');
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.

```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
```

## Processing

Translation of Java example.

```void setup() {
println("Survivor: " + execute(41, 3));
println("Survivors: " + executeAllButM(41, 3, 3));
}

int execute(int n, int k) {
int killIdx = 0;
IntList prisoners = new IntList(n);
for (int i = 0; i < n; i++) {
prisoners.append(i);
}
println("Prisoners executed in order:");
while (prisoners.size() > 1) {
killIdx = (killIdx + k - 1) % prisoners.size();
print(prisoners.get(killIdx) + " ");
prisoners.remove(killIdx);
}
println();
return prisoners.get(0);
}

IntList executeAllButM(int n, int k, int m) {
int killIdx = 0;
IntList prisoners = new IntList(n);
for (int i = 0; i < n; i++) {
prisoners.append(i);
}
println("Prisoners executed in order:");
while (prisoners.size() > m) {
killIdx = (killIdx + k - 1) % prisoners.size();
print(prisoners.get(killIdx) + " ");
prisoners.remove(killIdx);
}
println();
return 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

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, cycle
def 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]
```

## Quackery

Not the fastest method, but illustrates use of ancillary stacks, and using nests as queues.

```[ stack ]                      is survivors           (     --> s   )

[ stack ]                      is prisoners           (     --> s   )

[ stack ]                      is executioner-actions (     --> s   )

[ [] swap times [ i^ join ]
prisoners put ]              is make-prisoners      (   n -->     )

[ prisoners take
prisoners put ]              is walk                (     -->     )

[ prisoners take
prisoners put ]              is kill                (     -->     )

[ [] swap 1 - times
[ ' walk nested join ]
' kill nested join
executioner-actions put ]    is make-executioner    (   n -->     )

[ executioner-actions take
executioner-actions put ]    is execute-kth         (     -->     )

[ survivors put
make-executioner
make-prisoners
[ execute-kth
prisoners share
size
survivors share = until ]
survivors release
executioner-actions release
prisoners take ]             is josephus             ( n n n --> n )```

Testing in Quackery shell:

```/O> 41 3 1 josephus
... 41 3 3 josephus
...

Stack: [ 30 ] [ 15 30 34 ]```

## R

### Growing circle solution

```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```

### Iterative solution

I hope to be proven wrong, but R seems to be the wrong tool for this problem:

• It is 1-indexed, meaning that we will have a tough time using most solutions that exploit modular arithmetic.
• It lacks any concept of a linked list, meaning that we can't take a circular list approach.
• The idiomatic way to roll an array in R (e.g. as the Ruby solution has) is to exploit the head and tail functions, but those break if we are rolling by more than the length of the array (see https://stackoverflow.com/q/18791212 for a few tricks for this).

Regardless, it is still solvable. The following adapts a great deal of the Lua solution. The arguments n, k, and m are as in the task description.

```josephusProblem <- function(n, k, m)
{
prisoners <- 0:(n - 1)
exPos <- countToK <- 1
while(length(prisoners) > m)
{
if(countToK == k)
{
prisoners <- prisoners[-exPos]
exPos <- exPos - 1
}
exPos <- exPos + 1
countToK <- countToK + 1
if(exPos > length(prisoners)) exPos <- 1
if(countToK > k) countToK <- 1
}
print(paste0("Execution order: ", paste0(dead, collapse = ", "), "."))
paste0("Survivors: ", paste0(prisoners, collapse = ", "), ".")
}```
Output:
```> josephusProblem(5, 2, 1)
[1] "Execution order: 1, 3, 0, 4."
[1] "Survivors: 2."
> josephusProblem(41, 3, 1)
[1] "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."
[1] "Survivors: 30."
> josephusProblem(41, 3, 3)
[1] "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."
[1] "Survivors: 15, 30, 34."```

## Racket

```#lang racket
(define (josephus n k (m 0))
(remainder (+ m k) a)))

(josephus 41 3) ; ->30
```

## Raku

(formerly 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.```

## 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 3
print ["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 2
print [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 task states:      n    prisoners are standing on a circle,
*    sequentially numbered from  0  to  n-1.    The 1st prisoner is  0.
* 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
End
If n='' Then n=41                      /* number of alive prisoners  */
If w='' Then w=3                       /* killing count              */
If s='' Then s=1                       /* nuber of survivors         */
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
/*
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                  */
End
Say '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 REXX 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   /*c*/                                /*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 = 41
k=3
see "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
next
josephus = lm
return josephus```

Output:

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

## RPL

Works with: Halcyon Calc version 4.2.7

### Last survivor

We use here the recursive approach.

```≪ IF OVER 1 - THEN LAST OVER JPHUS SWAP + SWAP MOD ELSE DROP2 0 END
≫
'JPHUS' STO
```
```5 2 JPHUS
41 3 JPHUS
```
Output:
```2: 2
1: 30
```

### m survivors + ordered list of executed prisoners

Program execution mimics prisoners' execution ;-)

```≪ OVER SIZE → list idx len
≪ {}
1 len 1 - FOR j
list
j idx + 1 - len MOD 1 +
GET +
NEXT
≫ ≫
'RnDL' STO

≪ → n k m
≪ {} DUP
1 n FOR j j 1 - + NEXT
m n 1 - START
k 1 - OVER SIZE MOD 1 +
DUP2 GET 4 ROLL SWAP + 3 ROLLD
RnDL
NEXT
≫ ≫
'JPHUL' STO
```
```41 3 2 JPHUL
```
Output:
```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 }
1: { 15 30 }
```

## Ruby

```n = (ARGV[0] || 41).to_i
k = (ARGV[1] || 3).to_i

prisoners = (0...n).to_a
prisoners.rotate!(k-1).shift  while prisoners.length > 1
puts prisoners.first
```

## Rust

```const N: usize = 41;
const K: usize = 3;
const M: usize = 3;
const POSITION: usize = 5;

fn main() {
let mut prisoners: Vec<usize> = Vec::new();
let mut executed: Vec<usize> = Vec::new();
for pos in 0..N {
prisoners.push(pos);
}

let mut to_kill: usize = 0;
let mut len: usize = prisoners.len();

while len > M {
to_kill = (to_kill + K - 1) % len;
executed.push(prisoners.remove(to_kill));
len -= 1;
}

println!("JOSEPHUS n={}, k={}, m={}", N, K, M);
println!("Executed: {:?}", executed);
println!("Executed position number {}: {}", POSITION, executed[POSITION - 1]);
println!("Survivors: {:?}", prisoners);
}
```
Output:
```JOSEPHUS n=41, k=3, m=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]
Executed position number 5: 14
Survivors: [15, 30, 34]
```

## 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

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 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))
}

println( "Prisoners executed in order:" )

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]
```

## TypeScript

```function josephus(n: number, k: number): number {
if (!n) {
return 1;
}

return ((josephus(n - 1, k) + k - 1) % n) + 1;
}
```
Output:
```> josephus(41, 3);
31
```

## 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
```

## 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=1
while (#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
```

## V (Vlang)

Translation of: Go
```// basic task fntion
fn final_survivor(n int, kk int) int {
// argument validation omitted
mut circle := []int{len: n, init: it}
k := kk-1
mut ex_pos := 0
for circle.len > 1 {
ex_pos = (ex_pos + k) % circle.len
circle.delete(ex_pos)
}
return circle[0]
}

// extra
fn position(n int, kk int, p int) int {
// argument validation omitted
mut circle := []int{len: n, init: it}
k := kk-1
mut pos := p
mut ex_pos := 0
for circle.len > 1 {
ex_pos = (ex_pos + k) % circle.len
if pos == 0 {
return circle[ex_pos]
}
pos--
circle.delete(ex_pos)
}
return circle[0]
}

fn main() {
// show basic task fntion on given test case
println(final_survivor(41, 3))
// show extra fntion on all positions of given test case
println("Position  Prisoner")
for i in 0..41 {
println("\${i:5}\${position(41, 3, i):10}")
}
}```
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
```

## Wren

Translation of: Kotlin
```var josephus = Fn.new { |n, k, m|
if (k <= 0 || m <= 0 || n <= k || n <= m) Fiber.abort("One or more parameters are invalid.")
var killed = []
var survived = List.filled(n, 0)
for (i in 0...n) survived[i] = i
var start = k - 1
while (true) {
var end = survived.count - 1
var i = start
var deleted = 0
while (i <= end) {
if (survived.count == m) return [survived, killed]
deleted = deleted + 1
i = i + k
}
start = i - end - 1
}
return [survived, killed]
}

var triples = [ [5, 2, 1], [41, 3, 1], [41, 3, 3] ]
for (triple in triples) {
var n = triple[0]
var k = triple[1]
var m = triple[2]
System.print("Prisoners = %(n), Step = %(m), Survivors = %(m)")
var sk = josephus.call(n, k, m)
System.print("Survived   : %(sk[0])")
System.print("Kill order : %(sk[1])")
System.print()
}
```
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]
```

## XPL0

```include c:\cxpl\codes;

func Prisoner(N, K);            \Return final surviving prisoner
int  N, K;                      \number of prisoners, number to skip
int  I, J;
char A;
[A:= Reserve(N);
for I:= 0 to N-1 do A(I):= I;
I:= 0;
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 prisoner
until   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]
```