# Floyd-Warshall algorithm

Floyd-Warshall algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

The Floyd–Warshall algorithm is an algorithm for finding shortest paths in a weighted graph with positive or negative edge weights.

Find the lengths of the shortest paths between all pairs of vertices of the given directed graph. Your code may assume that the input has already been checked for loops, parallel edges and negative cycles.

Print the pair, the distance and (optionally) the path.

Example
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## 360 Assembly

Translation of: Rexx
`*        Floyd-Warshall algorithm - 06/06/2018FLOYDWAR CSECT         USING  FLOYDWAR,R13       base register         B      72(R15)            skip savearea         DC     17F'0'             savearea         SAVE   (14,12)            save previous context         ST     R13,4(R15)         link backward         ST     R15,8(R13)         link forward         LR     R13,R15            set addressability         MVC    A+8,=F'-2'         a(1,3)=-2         MVC    A+VV*4,=F'4'       a(2,1)= 4         MVC    A+VV*4+8,=F'3'     a(2,3)= 3         MVC    A+VV*8+12,=F'2'    a(3,4)= 2         MVC    A+VV*12+4,=F'-1'   a(4,2)=-1         LA     R8,1               k=1       DO WHILE=(C,R8,LE,V)        do k=1 to v         LA     R10,A                @a         LA     R6,1                 i=1       DO WHILE=(C,R6,LE,V)          do i=1 to v         LA     R7,1                   j=1       DO WHILE=(C,R7,LE,V)            do j=1 to v         LR     R1,R6                    i         BCTR   R1,0         MH     R1,=AL2(VV)         AR     R1,R8                    k         SLA    R1,2         L      R9,A-4(R1)               a(i,k)         LR     R1,R8                    k         BCTR   R1,0         MH     R1,=AL2(VV)         AR     R1,R7                    j         SLA    R1,2         L      R3,A-4(R1)               a(k,j)         AR     R9,R3                    w=a(i,k)+a(k,j)         L      R2,0(R10)                a(i,j)       IF CR,R2,GT,R9 THEN               if a(i,j)>w then         ST     R9,0(R10)                  a(i,j)=w       ENDIF    ,                        endif         LA     R10,4(R10)               next @a         LA     R7,1(R7)                 j++       ENDDO    ,                      enddo j         LA     R6,1(R6)               i++       ENDDO    ,                    enddo i         LA     R8,1(R8)             k++       ENDDO    ,                  enddo k         LA     R10,A              @a         LA     R6,1               f=1       DO WHILE=(C,R6,LE,V)        do f=1 to v         LA     R7,1                 t=1       DO WHILE=(C,R7,LE,V)          do t=1 to v       IF CR,R6,NE,R7 THEN             if f^=t then do         LR     R1,R6                    f         XDECO  R1,XDEC                  edit f         MVC    PG+0(4),XDEC+8           output f         LR     R1,R7                    t         XDECO  R1,XDEC                  edit t         MVC    PG+8(4),XDEC+8           output t         L      R2,0(R10)                a(f,t)         XDECO  R2,XDEC                  edit a(f,t)         MVC    PG+12(4),XDEC+8          output a(f,t)         XPRNT  PG,L'PG                  print       ENDIF    ,                      endif         LA     R10,4(R10)             next @a         LA     R7,1(R7)               t++       ENDDO    ,                    enddo t         LA     R6,1(R6)             f++       ENDDO    ,                  enddo f         L      R13,4(0,R13)       restore previous savearea pointer         RETURN (14,12),RC=0       restore registers from calling savVV       EQU    4V        DC     A(VV)A        DC     (VV*VV)F'99999999' a(vv,vv)PG       DC     CL80'   . ->    .   .'XDEC     DS     CL12         YREGS         END    FLOYDWAR`
Output:
```   1 ->    2  -1
1 ->    3  -2
1 ->    4   0
2 ->    1   4
2 ->    3   2
2 ->    4   4
3 ->    1   5
3 ->    2   1
3 ->    4   2
4 ->    1   3
4 ->    2  -1
4 ->    3   1
```

## C

Reads the graph from a file, prints out usage on incorrect invocation.

` #include<limits.h>#include<stdlib.h>#include<stdio.h> typedef struct{	int sourceVertex, destVertex;	int edgeWeight;}edge; typedef struct{	int vertices, edges;	edge* edgeMatrix;}graph; graph loadGraph(char* fileName){	FILE* fp = fopen(fileName,"r"); 	graph G;	int i; 	fscanf(fp,"%d%d",&G.vertices,&G.edges); 	G.edgeMatrix = (edge*)malloc(G.edges*sizeof(edge)); 	for(i=0;i<G.edges;i++)		fscanf(fp,"%d%d%d",&G.edgeMatrix[i].sourceVertex,&G.edgeMatrix[i].destVertex,&G.edgeMatrix[i].edgeWeight); 	fclose(fp); 	return G;} void floydWarshall(graph g){	int processWeights[g.vertices][g.vertices], processedVertices[g.vertices][g.vertices];	int i,j,k; 	for(i=0;i<g.vertices;i++)		for(j=0;j<g.vertices;j++){			processWeights[i][j] = SHRT_MAX;			processedVertices[i][j] = (i!=j)?j+1:0;		} 	for(i=0;i<g.edges;i++)		processWeights[g.edgeMatrix[i].sourceVertex-1][g.edgeMatrix[i].destVertex-1] = g.edgeMatrix[i].edgeWeight; 	for(i=0;i<g.vertices;i++)		for(j=0;j<g.vertices;j++)			for(k=0;k<g.vertices;k++){				if(processWeights[j][i] + processWeights[i][k] < processWeights[j][k]){					processWeights[j][k] = processWeights[j][i] + processWeights[i][k];					processedVertices[j][k] = processedVertices[j][i];				}			} 	printf("pair    dist   path");	for(i=0;i<g.vertices;i++)		for(j=0;j<g.vertices;j++){			if(i!=j){				printf("\n%d -> %d %3d %5d",i+1,j+1,processWeights[i][j],i+1);				k = i+1;				do{					k = processedVertices[k-1][j];					printf("->%d",k);				}while(k!=j+1);			}		}} int main(int argC,char* argV[]){	if(argC!=2)		printf("Usage : %s <file containing graph data>");	else		floydWarshall(loadGraph(argV[1]));	return 0;} `

Input file, first row specifies number of vertices and edges.

```4 5
1 3 -2
3 4 2
4 2 -1
2 1 4
2 3 3
```

Invocation and output:

```C:\rosettaCode>fwGraph.exe fwGraph.txt
pair    dist   path
1 -> 2  -1     1->3->4->2
1 -> 3  -2     1->3
1 -> 4   0     1->3->4
2 -> 1   4     2->1
2 -> 3   2     2->1->3
2 -> 4   4     2->1->3->4
3 -> 1   5     3->4->2->1
3 -> 2   1     3->4->2
3 -> 4   2     3->4
4 -> 1   3     4->2->1
4 -> 2  -1     4->2
4 -> 3   1     4->2->1->3
```

## C++

`#include <iostream>#include <vector>#include <sstream> void print(std::vector<std::vector<double>> dist, std::vector<std::vector<int>> next) {  std::cout << "(pair, dist, path)" << std::endl;  const auto size = std::size(next);  for (auto i = 0; i < size; ++i) {    for (auto j = 0; j < size; ++j) {      if (i != j) {        auto u = i + 1;        auto v = j + 1;        std::cout << "(" << u << " -> " << v << ", " << dist[i][j]          << ", ";        std::stringstream path;        path << u;        do {          u = next[u - 1][v - 1];          path << " -> " << u;        } while (u != v);        std::cout << path.str() << ")" << std::endl;      }    }  }} void solve(std::vector<std::vector<int>> w_s, const int num_vertices) {  std::vector<std::vector<double>> dist(num_vertices);  for (auto& dim : dist) {    for (auto i = 0; i < num_vertices; ++i) {      dim.push_back(INT_MAX);    }  }  for (auto& w : w_s) {    dist[w[0] - 1][w[1] - 1] = w[2];  }  std::vector<std::vector<int>> next(num_vertices);  for (auto i = 0; i < num_vertices; ++i) {    for (auto j = 0; j < num_vertices; ++j) {      next[i].push_back(0);    }    for (auto j = 0; j < num_vertices; ++j) {      if (i != j) {        next[i][j] = j + 1;      }    }  }  for (auto k = 0; k < num_vertices; ++k) {    for (auto i = 0; i < num_vertices; ++i) {      for (auto j = 0; j < num_vertices; ++j) {        if (dist[i][j] > dist[i][k] + dist[k][j]) {          dist[i][j] = dist[i][k] + dist[k][j];          next[i][j] = next[i][k];        }      }    }  }  print(dist, next);} int main() {  std::vector<std::vector<int>> w = {    { 1, 3, -2 },    { 2, 1, 4 },    { 2, 3, 3 },    { 3, 4, 2 },    { 4, 2, -1 },  };  int num_vertices = 4;  solve(w, num_vertices);  std::cin.ignore();  std::cin.get();  return 0;}`
Output:
```(pair, dist, path)
(1 -> 2, -1, 1 -> 3 -> 4 -> 2)
(1 -> 3, -2, 1 -> 3)
(1 -> 4, 0, 1 -> 3 -> 4)
(2 -> 1, 4, 2 -> 1)
(2 -> 3, 2, 2 -> 1 -> 3)
(2 -> 4, 4, 2 -> 1 -> 3 -> 4)
(3 -> 1, 5, 3 -> 4 -> 2 -> 1)
(3 -> 2, 1, 3 -> 4 -> 2)
(3 -> 4, 2, 3 -> 4)
(4 -> 1, 3, 4 -> 2 -> 1)
(4 -> 2, -1, 4 -> 2)
(4 -> 3, 1, 4 -> 2 -> 1 -> 3)```

## C#

Translation of: Java
`using System; namespace FloydWarshallAlgorithm {    class Program {        static void FloydWarshall(int[,] weights, int numVerticies) {            double[,] dist = new double[numVerticies, numVerticies];            for (int i = 0; i < numVerticies; i++) {                for (int j = 0; j < numVerticies; j++) {                    dist[i, j] = double.PositiveInfinity;                }            }             for (int i = 0; i < weights.GetLength(0); i++) {                dist[weights[i, 0] - 1, weights[i, 1] - 1] = weights[i, 2];            }             int[,] next = new int[numVerticies, numVerticies];            for (int i = 0; i < numVerticies; i++) {                for (int j = 0; j < numVerticies; j++) {                    if (i != j) {                        next[i, j] = j + 1;                    }                }            }             for (int k = 0; k < numVerticies; k++) {                for (int i = 0; i < numVerticies; i++) {                    for (int j = 0; j < numVerticies; j++) {                        if (dist[i, k] + dist[k, j] < dist[i, j]) {                            dist[i, j] = dist[i, k] + dist[k, j];                            next[i, j] = next[i, k];                        }                    }                }            }             PrintResult(dist, next);        }         static void PrintResult(double[,] dist, int[,] next) {            Console.WriteLine("pair     dist    path");            for (int i = 0; i < next.GetLength(0); i++) {                for (int j = 0; j < next.GetLength(1); j++) {                    if (i != j) {                        int u = i + 1;                        int v = j + 1;                        string path = string.Format("{0} -> {1}    {2,2:G}     {3}", u, v, dist[i, j], u);                        do {                            u = next[u - 1, v - 1];                            path += " -> " + u;                        } while (u != v);                        Console.WriteLine(path);                    }                }            }        }         static void Main(string[] args) {            int[,] weights = { { 1, 3, -2 }, { 2, 1, 4 }, { 2, 3, 3 }, { 3, 4, 2 }, { 4, 2, -1 } };            int numVerticies = 4;             FloydWarshall(weights, numVerticies);        }    }}`

## D

Translation of: Java
`import std.stdio; void main() {    int[][] weights = [        [1, 3, -2],        [2, 1, 4],        [2, 3, 3],        [3, 4, 2],        [4, 2, -1]    ];    int numVertices = 4;     floydWarshall(weights, numVertices);} void floydWarshall(int[][] weights, int numVertices) {    import std.array;     real[][] dist = uninitializedArray!(real[][])(numVertices, numVertices);    foreach(dim; dist) {        dim[] = real.infinity;    }     foreach (w; weights) {        dist[w[0]-1][w[1]-1] = w[2];    }     int[][] next = uninitializedArray!(int[][])(numVertices, numVertices);    for (int i=0; i<next.length; i++) {        for (int j=0; j<next.length; j++) {            if (i != j) {                next[i][j] = j+1;            }        }    }     for (int k=0; k<numVertices; k++) {        for (int i=0; i<numVertices; i++) {            for (int j=0; j<numVertices; j++) {                if (dist[i][j] > dist[i][k] + dist[k][j]) {                    dist[i][j] = dist[i][k] + dist[k][j];                    next[i][j] = next[i][k];                }            }        }    }     printResult(dist, next);} void printResult(real[][] dist, int[][] next) {    import std.conv;    import std.format;     writeln("pair     dist    path");    for (int i=0; i<next.length; i++) {        for (int j=0; j<next.length; j++) {            if (i!=j) {                int u = i+1;                int v = j+1;                string path = format("%d -> %d    %2d     %s", u, v, cast(int) dist[i][j], u);                do {                    u = next[u-1][v-1];                    path ~= text(" -> ", u);                } while (u != v);                writeln(path);            }        }    }}`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## EchoLisp

Transcription of the Floyd-Warshall algorithm, with best path computation.

` (lib 'matrix) ;; in : initialized dist and next matrices;; out : dist and next matrices;; O(n^3) (define (floyd-with-path n dist next (d 0)) 	(for* ((k n) (i n) (j n))	 #:break (< (array-ref dist j j) 0) => 'negative-cycle 	(set! d (+ (array-ref dist i k) (array-ref dist k j)))	 (when (< d (array-ref dist i j))		 (array-set! dist i j d)		 (array-set! next i j (array-ref next i k))))) ;; utilities ;; init random edges costs, matrix 66% filled(define (init-edges n dist next)   (for* ((i n) (j n))	(array-set! dist i i 0)   	(array-set! next i j null) 	#:continue (= j i) 	(array-set! dist i j Infinity)	 #:continue (< (random) 0.3)	 (array-set! dist i j (1+ (random 100))) 	(array-set! next i j j))) ;; show path from u to v(define (path u v)	(cond 	 ((= u v) (list u))	 ((null? (array-ref next u v)) null)		 	 (else (cons u (path (array-ref next u v) v))))) (define( mdist u v) ;; show computed distance	  (array-ref dist u v)) (define (task)	 (init-edges n dist next)	 (array-print dist) ;; show init distances	 (floyd-with-path n dist next)) `
Output:
```(define n 8)
(define next (make-array n n))
(define dist (make-array n n))

0    Infinity   Infinity   13         98         Infinity   35         47
8    0          Infinity   Infinity   83         77         16         3
73   3          0          3          76         84         91         Infinity
30   49         Infinity   0          41         Infinity   4          4
22   83         92         Infinity   0          30         27         98
6    Infinity   Infinity   24         59         0          Infinity   Infinity
60   Infinity   45         Infinity   67         100        0          Infinity
72   15         95         21         Infinity   Infinity   27         0

(array-print dist) ;; computed distances

0    32   62   13   54   84   17   17
8    0    61   21   62   77   16   3
11   3    0    3    44   74   7    6
27   19   49   0    41   71   4    4
22   54   72   35   0    30   27   39
6    38   68   19   59   0    23   23
56   48   45   48   67   97   0    51
23   15   70   21   62   92   25   0

(path 1 3)  → (1 0 3)
(mdist 1 0) → 8
(mdist 0 3) → 13
(mdist 1 3) → 21 ;; = 8 + 13
(path 7 6) → (7 3 6)
(path 6 7) → (6 2 1 7)

```

## Elixir

`defmodule Floyd_Warshall do  def main(n, edge) do    {dist, next} = setup(n, edge)    {dist, next} = shortest_path(n, dist, next)    print(n, dist, next)  end   defp setup(n, edge) do    big = 1.0e300    dist = for i <- 1..n, j <- 1..n, into: %{}, do: {{i,j},(if i==j, do: 0, else: big)}    next = for i <- 1..n, j <- 1..n, into: %{}, do: {{i,j}, nil}    Enum.reduce(edge, {dist,next}, fn {u,v,w},{dst,nxt} ->      { Map.put(dst, {u,v}, w), Map.put(nxt, {u,v}, v) }    end)  end   defp shortest_path(n, dist, next) do    (for k <- 1..n, i <- 1..n, j <- 1..n, do: {k,i,j})    |> Enum.reduce({dist,next}, fn {k,i,j},{dst,nxt} ->         if dst[{i,j}] > dst[{i,k}] + dst[{k,j}] do           {Map.put(dst, {i,j}, dst[{i,k}] + dst[{k,j}]), Map.put(nxt, {i,j}, nxt[{i,k}])}         else           {dst, nxt}         end       end)  end   defp print(n, dist, next) do    IO.puts "pair     dist    path"    for i <- 1..n, j <- 1..n, i != j,        do: :io.format "~w -> ~w  ~4w     ~s~n", [i, j, dist[{i,j}], path(next, i, j)]  end   defp path(next, i, j), do: path(next, i, j, [i]) |> Enum.join(" -> ")   defp path(_next, i, i, list), do: Enum.reverse(list)  defp path(next, i, j, list) do    u = next[{i,j}]    path(next, u, j, [u | list])  endend edge = [{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}]Floyd_Warshall.main(4, edge)`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3
```

## FreeBASIC

Translation of: Java
`' FB 1.05.0 Win64 Const POSITIVE_INFINITY As Double = 1.0/0.0 Sub printResult(dist(any, any) As Double, nxt(any, any) As Integer)  Dim As Integer u, v  Print("pair     dist    path")  For i As Integer = 0 To UBound(nxt, 1)    For j As Integer = 0 To UBound(nxt, 1)      If i <> j Then        u = i + 1        v = j + 1        Print Str(u); " -> "; Str(v); "    "; dist(i, j); "     "; Str(u);        Do          u = nxt(u - 1, v - 1)          Print " -> "; Str(u);        Loop While u <> v        Print      End If    Next j  Next iEnd Sub Sub floydWarshall(weights(Any, Any) As Integer, numVertices As Integer)  Dim dist(0 To numVertices - 1, 0 To numVertices - 1) As Double  For i As Integer = 0 To numVertices - 1    For j As Integer = 0 To numVertices - 1      dist(i, j) = POSITIVE_INFINITY    Next j  Next i   For x As Integer = 0 To UBound(weights, 1)    dist(weights(x, 0) - 1, weights(x, 1) - 1) = weights(x, 2)  Next x   Dim nxt(0 To numVertices - 1, 0 To numVertices - 1) As Integer  For i As Integer = 0 To numVertices - 1    For j As Integer = 0 To numVertices - 1      If i <> j Then nxt(i, j) = j + 1    Next j  Next i    For k As Integer = 0 To numVertices - 1    For i As Integer = 0 To numVertices - 1      For j As Integer = 0 To numVertices - 1        If (dist(i, k) + dist(k, j)) < dist(i, j) Then          dist(i, j) = dist(i, k) + dist(k, j)          nxt(i, j) = nxt(i, k)        End If      Next j    Next i  Next k   printResult(dist(), nxt())End Sub Dim weights(4, 2) As Integer = {{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}}Dim numVertices As Integer = 4floydWarshall(weights(), numVertices)PrintPrint "Press any key to quit"Sleep`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3
```

## F#

### Floyd's algorithm

` //Floyd's algorithm: Nigel Galloway August 5th 2018let Floyd (n:'a[]) (g:Map<('a*'a),int>)= //nodes graph(Map of adjacency list)  let ix n g=Seq.init (pown g n) (fun x->List.unfold(fun (a,b)->if a=0 then None else Some(b%g,(a-1,b/g)))(n,x))  let fN w (i,j,k)=match Map.tryFind(i,j) w,Map.tryFind(i,k) w,Map.tryFind(k,j) w with                        |(None  ,Some j,Some k)->Some(j+k)                        |(Some i,Some j,Some k)->if (j+k) < i then Some(j+k) else None                        |_                     ->None  let n,z=ix 3 (Array.length n)|>Seq.choose(fun (i::j::k::_)->if i<>j&&i<>k&&j<>k then Some(n.[i],n.[j],n.[k]) else None)       |>Seq.fold(fun (n,n') ((i,j,k) as g)->match fN n g with |Some g->(Map.add (i,j) g n,Map.add (i,j) k n')|_->(n,n')) (g,Map.empty)  (n,(fun x y->seq{               let rec fN n g=seq{                 match Map.tryFind (n,g) z with                 |Some r->yield! fN n r; yield Some r;yield! fN r g                 |_->yield None}               yield! fN x y |> Seq.choose id; yield y})) `

` let fW=Map[((1,3),-2);((3,4),2);((4,2),-1);((2,1),4);((2,3),3)]let N,G=Floyd [|1..4|] fWList.allPairs [1..4] [1..4]|>List.filter(fun (n,g)->n<>g)|>List.iter(fun (n,g)->printfn "%d->%d %d %A" n g N.[(n,g)] (n::(List.ofSeq (G n g)))) `
Output:
```1->2 -1 [1; 3; 4; 2]
1->3 -2 [1; 3]
1->4 0 [1; 3; 4]
2->1 4 [2; 1]
2->3 2 [2; 1; 3]
2->4 4 [2; 1; 3; 4]
3->1 5 [3; 4; 2; 1]
3->2 1 [3; 4; 2]
3->4 2 [3; 4]
4->1 3 [4; 2; 1]
4->2 -1 [4; 2]
4->3 1 [4; 2; 1; 3]
```

## Go

`package main import (  "fmt"  "strconv") // A Graph is the interface implemented by graphs that// this algorithm can run on.type Graph interface {  Vertices() []Vertex  Neighbors(v Vertex) []Vertex  Weight(u, v Vertex) int} // Nonnegative integer ID of vertextype Vertex int // ig is a graph of integers that satisfies the Graph interface.type ig struct {  vert  []Vertex  edges map[Vertex]map[Vertex]int} func (g ig) edge(u, v Vertex, w int) {  if _, ok := g.edges[u]; !ok {    g.edges[u] = make(map[Vertex]int)  }  g.edges[u][v] = w}func (g ig) Vertices() []Vertex { return g.vert }func (g ig) Neighbors(v Vertex) (vs []Vertex) {  for k := range g.edges[v] {    vs = append(vs, k)  }  return vs}func (g ig) Weight(u, v Vertex) int { return g.edges[u][v] }func (g ig) path(vv []Vertex) (s string) {  if len(vv) == 0 {    return ""  }  s = strconv.Itoa(int(vv[0]))  for _, v := range vv[1:] {    s += " -> " + strconv.Itoa(int(v))  }  return s} const Infinity = int(^uint(0) >> 1) func FloydWarshall(g Graph) (dist map[Vertex]map[Vertex]int, next map[Vertex]map[Vertex]*Vertex) {  vert := g.Vertices()  dist = make(map[Vertex]map[Vertex]int)  next = make(map[Vertex]map[Vertex]*Vertex)  for _, u := range vert {    dist[u] = make(map[Vertex]int)    next[u] = make(map[Vertex]*Vertex)    for _, v := range vert {      dist[u][v] = Infinity    }    dist[u][u] = 0    for _, v := range g.Neighbors(u) {      v := v      dist[u][v] = g.Weight(u, v)      next[u][v] = &v    }  }  for _, k := range vert {    for _, i := range vert {      for _, j := range vert {        if dist[i][k] < Infinity && dist[k][j] < Infinity {          if dist[i][j] > dist[i][k]+dist[k][j] {            dist[i][j] = dist[i][k] + dist[k][j]            next[i][j] = next[i][k]          }        }      }    }  }  return dist, next} func Path(u, v Vertex, next map[Vertex]map[Vertex]*Vertex) (path []Vertex) {  if next[u][v] == nil {    return  }  path = []Vertex{u}  for u != v {    u = *next[u][v]    path = append(path, u)  }  return path} func main() {  g := ig{[]Vertex{1, 2, 3, 4}, make(map[Vertex]map[Vertex]int)}  g.edge(1, 3, -2)  g.edge(3, 4, 2)  g.edge(4, 2, -1)  g.edge(2, 1, 4)  g.edge(2, 3, 3)   dist, next := FloydWarshall(g)  fmt.Println("pair\tdist\tpath")  for u, m := range dist {    for v, d := range m {      if u != v {        fmt.Printf("%d -> %d\t%3d\t%s\n", u, v, d, g.path(Path(u, v, next)))      }    }  }}`
Output:
```pair	dist	path
1 -> 2	 -1	1 -> 3 -> 4 -> 2
1 -> 3	 -2	1 -> 3
1 -> 4	  0	1 -> 3 -> 4
2 -> 1	  4	2 -> 1
2 -> 3	  2	2 -> 1 -> 3
2 -> 4	  4	2 -> 1 -> 3 -> 4
3 -> 1	  5	3 -> 4 -> 2 -> 1
3 -> 2	  1	3 -> 4 -> 2
3 -> 4	  2	3 -> 4
4 -> 1	  3	4 -> 2 -> 1
4 -> 2	 -1	4 -> 2
4 -> 3	  1	4 -> 2 -> 1 -> 3
```

Necessary imports

`import Control.Monad (join)import Data.List (union)import Data.Map hiding (foldr, union)import Data.Maybe (fromJust, isJust)import Data.Semigroupimport Prelude hiding (lookup, filter)`

First we define a general datatype to represent the shortest path. Type `a` represents a distance. It could be a number, in case of weighted graph or boolean value for just a directed graph. Type `b` goes for vertice labels (integers, chars, strings...)

`data Shortest b a = Shortest { distance :: a, path :: [b] }                  deriving Show`

Next we note that shortest paths form a semigroup with following "addition" rule:

`instance (Ord a, Eq b) => Semigroup (Shortest b a) where  a <> b = case distance a `compare` distance b of    GT -> b    LT -> a    EQ -> a { path = path a `union` path b }`

It finds minimal path by `distance`, and in case of equal distances joins both paths. We will lift this semigroup to monoid using `Maybe` wrapper.

Graph is represented as a `Map`, containing pairs of vertices and corresponding weigts. The distance table is a `Map`, containing pairs of joint vertices and corresponding shortest paths.

Now we are ready to define the main part of the Floyd-Warshall algorithm, which processes properly prepared distance table `dist` for given list of vertices `v`:

`floydWarshall v dist = foldr innerCycle (Just <\$> dist) v  where    innerCycle k dist = (newDist <\$> v <*> v) `setTo` dist      where        newDist i j =          ((i,j), do a <- join \$ lookup (i, k) dist                     b <- join \$ lookup (k, j) dist                     return \$ Shortest (distance a <> distance b) (path a))         setTo = unionWith (<>) . fromList`

The `floydWarshall` produces only first steps of shortest paths. Whole paths are build by following function:

`buildPaths d = mapWithKey (\pair s -> s { path = buildPath pair}) d  where    buildPath (i,j)      | i == j    = [[j]]      | otherwise = do k <- path \$ fromJust \$ lookup (i,j) d                       p <- buildPath (k,j)                       [i : p]`

All pre- and postprocessing is done by the main function `findMinDistances`:

`findMinDistances v g =  let weights = mapWithKey (\(_,j) w -> Shortest w [j]) g      trivial = fromList [ ((i,i), Shortest mempty []) | i <- v ]      clean d = fromJust <\$> filter isJust (d \\ trivial)  in buildPaths \$ clean \$ floydWarshall v (weights <> trivial)`

Examples:

The sample graph:

`g = fromList [((2,1), 4)             ,((2,3), 3)             ,((1,3), -2)             ,((3,4), 2)             ,((4,2), -1)]`

the helper function

`showShortestPaths v g = mapM_ print \$ toList \$ findMinDistances v g`
Output:

Weights as distances:

```λ> showShortestPaths [1..4] (Sum <\$> g)
((1,2),Shortest {distance = Sum {getSum = -1}, path = [[1,3,4,2]]})
((1,3),Shortest {distance = Sum {getSum = -2}, path = [[1,3]]})
((1,4),Shortest {distance = Sum {getSum = 0}, path = [[1,3,4]]})
((2,1),Shortest {distance = Sum {getSum = 4}, path = [[2,1]]})
((2,3),Shortest {distance = Sum {getSum = 2}, path = [[2,1,3]]})
((2,4),Shortest {distance = Sum {getSum = 4}, path = [[2,1,3,4]]})
((3,1),Shortest {distance = Sum {getSum = 5}, path = [[3,4,2,1]]})
((3,2),Shortest {distance = Sum {getSum = 1}, path = [[3,4,2]]})
((3,4),Shortest {distance = Sum {getSum = 2}, path = [[3,4]]})
((4,1),Shortest {distance = Sum {getSum = 3}, path = [[4,2,1]]})
((4,2),Shortest {distance = Sum {getSum = -1}, path = [[4,2]]})
((4,3),Shortest {distance = Sum {getSum = 1}, path = [[4,2,1,3]]})```

Unweighted directed graph

```λ> showShortestPaths [1..4] (Any . (/= 0) <\$> g)
((1,2),Shortest {distance = Any {getAny = True}, path = [[1,3,4,2]]})
((1,3),Shortest {distance = Any {getAny = True}, path = [[1,3]]})
((1,4),Shortest {distance = Any {getAny = True}, path = [[1,3,4]]})
((2,1),Shortest {distance = Any {getAny = True}, path = [[2,1]]})
((2,3),Shortest {distance = Any {getAny = True}, path = [[2,1,3],[2,3]]})
((2,4),Shortest {distance = Any {getAny = True}, path = [[2,1,3,4],[2,3,4]]})
((3,1),Shortest {distance = Any {getAny = True}, path = [[3,4,2,1]]})
((3,2),Shortest {distance = Any {getAny = True}, path = [[3,4,2]]})
((3,4),Shortest {distance = Any {getAny = True}, path = [[3,4]]})
((4,1),Shortest {distance = Any {getAny = True}, path = [[4,2,1]]})
((4,2),Shortest {distance = Any {getAny = True}, path = [[4,2]]})
((4,3),Shortest {distance = Any {getAny = True}, path = [[4,2,1,3],[4,2,3]]})```

For some pairs several possible paths are found.

Uniformly weighted graph:

```λ> showShortestPaths [1..4] (const (Sum 1) <\$> g)
((1,2),Shortest {distance = Sum {getSum = 3}, path = [[1,3,4,2]]})
((1,3),Shortest {distance = Sum {getSum = 1}, path = [[1,3]]})
((1,4),Shortest {distance = Sum {getSum = 2}, path = [[1,3,4]]})
((2,1),Shortest {distance = Sum {getSum = 1}, path = [[2,1]]})
((2,3),Shortest {distance = Sum {getSum = 1}, path = [[2,3]]})
((2,4),Shortest {distance = Sum {getSum = 2}, path = [[2,3,4]]})
((3,1),Shortest {distance = Sum {getSum = 3}, path = [[3,4,2,1]]})
((3,2),Shortest {distance = Sum {getSum = 2}, path = [[3,4,2]]})
((3,4),Shortest {distance = Sum {getSum = 1}, path = [[3,4]]})
((4,1),Shortest {distance = Sum {getSum = 2}, path = [[4,2,1]]})
((4,2),Shortest {distance = Sum {getSum = 1}, path = [[4,2]]})
((4,3),Shortest {distance = Sum {getSum = 2}, path = [[4,2,3]]})```

Graph labeled by chars:

`g2 = fromList [(('A','S'), 1)             ,(('A','D'), -1)             ,(('S','E'), 2)             ,(('D','E'), 4)]`
```λ> showShortestPaths "ASDE" (Sum <\$> g2)
(('A','D'),Shortest {distance = Sum {getSum = -1}, path = ["AD"]})
(('A','E'),Shortest {distance = Sum {getSum = 3}, path = ["ASE","ADE"]})
(('A','S'),Shortest {distance = Sum {getSum = 1}, path = ["AS"]})
(('D','E'),Shortest {distance = Sum {getSum = 4}, path = ["DE"]})
(('S','E'),Shortest {distance = Sum {getSum = 2}, path = ["SE"]})```

## J

`floyd=: verb define  for_j. i.#y do.    y=. y <. j ({"1 +/ {) y  end.)`

Example use:

`graph=: ".;._2]0 :0  0  _ _2 _  NB. 1->3 costs _2  4  0  3 _  NB. 2->1 costs 4; 2->3 costs 3  _  _  0 2  NB. 3->4 costs 2  _ _1  _ 0  NB. 4->2 costs _1)    floyd graph0 _1 _2 04  0  2 45  1  0 23 _1  1 0`

The graph matrix holds the costs of each directed node. Row index corresponds to starting node. Column index corresponds to ending node. Unconnected nodes have infinite cost.

This approach turns out to be faster than the more concise <./ .+~^:_ for many relatively small graphs (though `floyd` happens to be slightly slower for the task example).

Path Reconstruction

This draft task currently asks for path reconstruction, which is a different (related) algorithm:

`floydrecon=: verb define  n=. (\$y)\$_(I._=,y)},([email protected]#)y  for_j. i.#y do.    d=. y <. j ({"1 +/ {) y    b=. y~:d    y=. d    n=. (n*-.b)+b * j{"1 n  end.) task=: verb define  dist=. floyd y  next=. floydrecon y  echo 'pair  dist   path'  for_i. i.#y do.    for_k. i.#y do.      ndx=. <i,k      if. (i~:k)*_>ndx{next do.        txt=. (":1+i),'->',(":1+k)        txt=. txt,_5{.":ndx{dist        txt=. txt,'    ',":1+i        j=. i        while. j~:k do.          assert. j~:(<j,k){next          j=. (<j,k){next          txt=. txt,'->',":1+j        end.        echo txt      end.    end.  end.  i.0 0)`

Draft output:

`   task graphpair  dist   path1->2   _1    1->3->4->21->3   _2    1->31->4    0    1->3->42->1    4    2->12->3    2    2->1->32->4    4    2->1->3->43->1    5    3->4->2->13->2    1    3->4->23->4    2    3->44->1    3    4->2->14->2   _1    4->24->3    1    4->2->1->3`

## Java

`import static java.lang.String.format;import java.util.Arrays; public class FloydWarshall {     public static void main(String[] args) {        int[][] weights = {{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}};        int numVertices = 4;         floydWarshall(weights, numVertices);    }     static void floydWarshall(int[][] weights, int numVertices) {         double[][] dist = new double[numVertices][numVertices];        for (double[] row : dist)            Arrays.fill(row, Double.POSITIVE_INFINITY);         for (int[] w : weights)            dist[w[0] - 1][w[1] - 1] = w[2];         int[][] next = new int[numVertices][numVertices];        for (int i = 0; i < next.length; i++) {            for (int j = 0; j < next.length; j++)                if (i != j)                    next[i][j] = j + 1;        }         for (int k = 0; k < numVertices; k++)            for (int i = 0; i < numVertices; i++)                for (int j = 0; j < numVertices; j++)                    if (dist[i][k] + dist[k][j] < dist[i][j]) {                        dist[i][j] = dist[i][k] + dist[k][j];                        next[i][j] = next[i][k];                    }         printResult(dist, next);    }     static void printResult(double[][] dist, int[][] next) {        System.out.println("pair     dist    path");        for (int i = 0; i < next.length; i++) {            for (int j = 0; j < next.length; j++) {                if (i != j) {                    int u = i + 1;                    int v = j + 1;                    String path = format("%d -> %d    %2d     %s", u, v,                            (int) dist[i][j], u);                    do {                        u = next[u - 1][v - 1];                        path += " -> " + u;                    } while (u != v);                    System.out.println(path);                }            }        }    }}`
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## JavaScript

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

`var graph = [];for (i = 0; i < 10; ++i) {  graph.push([]);  for (j = 0; j < 10; ++j)    graph[i].push(i == j ? 0 : 9999999);} for (i = 1; i < 10; ++i) {  graph[0][i] = graph[i][0] = parseInt(Math.random() * 9 + 1);} for (k = 0; k < 10; ++k) {  for (i = 0; i < 10; ++i) {    for (j = 0; j < 10; ++j) {      if (graph[i][j] > graph[i][k] + graph[k][j])        graph[i][j] = graph[i][k] + graph[k][j]    }  }} console.log(graph);`

## jq

Works with: jq version 1.5

In this section, we represent the graph by a JSON object giving the weights: if u and v are the (string) labels of two nodes connected with an arrow from u to v, then .[u][v] is the associated weight:

` def weights: {  "1": {"3": -2},  "2": {"1" : 4, "3": 3},  "3": {"4": 2},  "4": {"2": -1}};`

The algorithm given here is a direct implementation of the definitional algorithm:

`def fwi:  . as \$weights  | keys_unsorted as \$nodes  # construct the dist matrix  | reduce \$nodes[] as \$u ({};      reduce \$nodes[] as \$v (.;        .[\$u][\$v] = infinite))  | reduce \$nodes[] as \$u (.; .[\$u][\$u] = 0 )  | reduce \$nodes[] as \$u (.;      reduce (\$weights[\$u]|keys_unsorted[]) as \$v (.;        .[\$u][\$v] = \$weights[\$u][\$v] ))  | reduce \$nodes[] as \$w (.;      reduce \$nodes[] as \$u (.;        reduce \$nodes[] as \$v (.;	  (.[\$u][\$w] + .[\$w][\$v]) as \$x	  | if .[\$u][\$v] > \$x then .[\$u][\$v] = \$x	    else . end )));  weights | fwi`
Output:
```{
"1": {
"1": 0,
"2": -1,
"3": -2,
"4": 0
},
"2": {
"1": 4,
"2": 0,
"3": 2,
"4": 4
},
"3": {
"1": 5,
"2": 1,
"3": 0,
"4": 2
},
"4": {
"1": 3,
"2": -1,
"3": 1,
"4": 0
}
}```

## Julia

Translation of: Java
`# Floyd-Warshall algorithm: https://rosettacode.org/wiki/Floyd-Warshall_algorithm# v0.6 function floydwarshall(weights::Matrix, nvert::Int)    dist = fill(Inf, nvert, nvert)    for i in 1:size(weights, 1)        dist[weights[i, 1], weights[i, 2]] = weights[i, 3]    end    # return dist    next = collect(j != i ? j : 0 for i in 1:nvert, j in 1:nvert)     for k in 1:nvert, i in 1:nvert, j in 1:nvert        if dist[i, k] + dist[k, j] < dist[i, j]            dist[i, j] = dist[i, k] + dist[k, j]            next[i, j] = next[i, k]        end    end     # return next    function printresult(dist, next)        println("pair     dist    path")        for i in 1:size(next, 1), j in 1:size(next, 2)            if i != j                u = i                path = @sprintf "%d -> %d    %2d     %s" i j dist[i, j] i                while true                    u = next[u, j]                    path *= " -> \$u"                    if u == j break end                end                println(path)            end        end    end    printresult(dist, next)end floydwarshall([1 3 -2; 2 1 4; 2 3 3; 3 4 2; 4 2 -1], 4)`

## Kotlin

Translation of: Java
`// version 1.1 object FloydWarshall {    fun doCalcs(weights: Array<IntArray>, nVertices: Int) {        val dist = Array(nVertices) { DoubleArray(nVertices) { Double.POSITIVE_INFINITY } }        for (w in weights) dist[w[0] - 1][w[1] - 1] = w[2].toDouble()        val next = Array(nVertices) { IntArray(nVertices) }        for (i in 0 until next.size) {            for (j in 0 until next.size) {                if (i != j) next[i][j] = j + 1            }        }        for (k in 0 until nVertices) {            for (i in 0 until nVertices) {                for (j in 0 until nVertices) {                    if (dist[i][k] + dist[k][j] < dist[i][j]) {                        dist[i][j] = dist[i][k] + dist[k][j]                        next[i][j] = next[i][k]                    }                }            }        }        printResult(dist, next)    }     private fun printResult(dist: Array<DoubleArray>, next: Array<IntArray>) {        var u: Int        var v: Int        var path: String        println("pair     dist    path")        for (i in 0 until next.size) {            for (j in 0 until next.size) {                if (i != j) {                    u = i + 1                    v = j + 1                    path = ("%d -> %d    %2d     %s").format(u, v, dist[i][j].toInt(), u)                    do {                        u = next[u - 1][v - 1]                        path += " -> " + u                    } while (u != v)                    println(path)                }            }        }    }} fun main(args: Array<String>) {    val weights = arrayOf(            intArrayOf(1, 3, -2),            intArrayOf(2, 1, 4),            intArrayOf(2, 3, 3),            intArrayOf(3, 4, 2),            intArrayOf(4, 2, -1)    )    val nVertices = 4    FloydWarshall.doCalcs(weights, nVertices)}`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3
```

## Lua

Translation of: D
`function printResult(dist, nxt)    print("pair     dist    path")    for i=0, #nxt do        for j=0, #nxt do            if i ~= j then                u = i + 1                v = j + 1                path = string.format("%d -> %d    %2d     %s", u, v, dist[i][j], u)                repeat                    u = nxt[u-1][v-1]                    path = path .. " -> " .. u                until (u == v)                print(path)            end        end    endend function floydWarshall(weights, numVertices)    dist = {}    for i=0, numVertices-1 do        dist[i] = {}        for j=0, numVertices-1 do            dist[i][j] = math.huge        end    end     for _,w in pairs(weights) do        -- the weights array is one based        dist[w[1]-1][w[2]-1] = w[3]    end     nxt = {}    for i=0, numVertices-1 do        nxt[i] = {}        for j=0, numVertices-1 do            if i ~= j then                nxt[i][j] = j+1            end        end    end     for k=0, numVertices-1 do        for i=0, numVertices-1 do            for j=0, numVertices-1 do                if dist[i][k] + dist[k][j] < dist[i][j] then                    dist[i][j] = dist[i][k] + dist[k][j]                    nxt[i][j] = nxt[i][k]                end            end        end    end     printResult(dist, nxt)end weights = {    {1, 3, -2},    {2, 1, 4},    {2, 3, 3},    {3, 4, 2},    {4, 2, -1}}numVertices = 4floydWarshall(weights, numVertices)`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## Modula-2

`MODULE FloydWarshall;FROM FormatString IMPORT FormatString;FROM SpecialReals IMPORT Infinity;FROM Terminal IMPORT ReadChar,WriteString,WriteLn; CONST NUM_VERTICIES = 4;TYPE    IntArray = ARRAY[0..NUM_VERTICIES-1],[0..NUM_VERTICIES-1] OF INTEGER;    RealArray = ARRAY[0..NUM_VERTICIES-1],[0..NUM_VERTICIES-1] OF REAL; PROCEDURE FloydWarshall(weights : ARRAY OF ARRAY OF INTEGER);VAR    dist : RealArray;    next : IntArray;    i,j,k : INTEGER;BEGIN    FOR i:=0 TO NUM_VERTICIES-1 DO        FOR j:=0 TO NUM_VERTICIES-1 DO            dist[i,j] := Infinity;        END    END;    k := HIGH(weights);    FOR i:=0 TO k DO        dist[weights[i,0]-1,weights[i,1]-1] := FLOAT(weights[i,2]);    END;    FOR i:=0 TO NUM_VERTICIES-1 DO        FOR j:=0 TO NUM_VERTICIES-1 DO            IF i#j THEN                next[i,j] := j+1;            END        END    END;    FOR k:=0 TO NUM_VERTICIES-1 DO        FOR i:=0 TO NUM_VERTICIES-1 DO            FOR j:=0 TO NUM_VERTICIES-1 DO                IF dist[i,j] > dist[i,k] + dist[k,j] THEN                    dist[i,j] := dist[i,k] + dist[k,j];                    next[i,j] := next[i,k];                END            END        END    END;    PrintResult(dist, next);END FloydWarshall; PROCEDURE PrintResult(dist : RealArray; next : IntArray);VAR    i,j,u,v : INTEGER;    buf : ARRAY[0..63] OF CHAR;BEGIN    WriteString("pair     dist    path");    WriteLn;    FOR i:=0 TO NUM_VERTICIES-1 DO        FOR j:=0 TO NUM_VERTICIES-1 DO            IF i#j THEN                u := i + 1;                v := j + 1;                FormatString("%i -> %i    %2i     %i", buf, u, v, TRUNC(dist[i,j]), u);                WriteString(buf);                REPEAT                    u := next[u-1,v-1];                    FormatString(" -> %i", buf, u);                    WriteString(buf);                UNTIL u=v;                WriteLn            END        END    ENDEND PrintResult; TYPE WeightArray = ARRAY[0..4],[0..2] OF INTEGER;VAR weights : WeightArray;BEGIN    weights := WeightArray{        {1,  3, -2},        {2,  1,  4},        {2,  3,  3},        {3,  4,  2},        {4,  2, -1}    };     FloydWarshall(weights);     ReadCharEND FloydWarshall.`

## Perl

`sub FloydWarshall{	my \$edges = shift;	my (@dist, @seq);	my \$num_vert = 0;	# insert given dists into dist matrix	map {		\$dist[\$_->[0] - 1][\$_->[1] - 1] = \$_->[2];		\$num_vert = \$_->[0] if \$num_vert < \$_->[0];		\$num_vert = \$_->[1] if \$num_vert < \$_->[1];	} @\$edges;	my @vertices = 0..(\$num_vert - 1);	# init sequence/"next" table	for my \$i(@vertices){		for my \$j(@vertices){			\$seq[\$i][\$j] = \$j if \$i != \$j;		}	}	# diagonal of dists matrix	#map {\$dist[\$_][\$_] = 0} @vertices;	for my \$k(@vertices){		for my \$i(@vertices){			next unless defined \$dist[\$i][\$k];			for my \$j(@vertices){				next unless defined \$dist[\$k][\$j];				if(\$i != \$j && (!defined(\$dist[\$i][\$j]) 						|| \$dist[\$i][\$j] > \$dist[\$i][\$k] + \$dist[\$k][\$j])){					\$dist[\$i][\$j] = \$dist[\$i][\$k] + \$dist[\$k][\$j];					\$seq[\$i][\$j] = \$seq[\$i][\$k];				}			}		}	}	# print table	print "pair     dist    path\n";	for my \$i(@vertices){		for my \$j(@vertices){			next if \$i == \$j;			my @path = (\$i + 1);			while(\$seq[\$path[-1] - 1][\$j] != \$j){				push @path, \$seq[\$path[-1] - 1][\$j] + 1;			}			push @path, \$j + 1;			printf "%d -> %d  %4d     %s\n", 				\$path[0], \$path[-1], \$dist[\$i][\$j], join(' -> ', @path);		}	}} my \$graph = [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]];FloydWarshall(\$graph);`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## Perl 6

Works with: Rakudo version 2016.12
Translation of: Ruby
`sub Floyd-Warshall (Int \$n, @edge) {    my @dist = [0, |(Inf xx \$n-1)], *.Array.rotate(-1) … !*[*-1];    my @next = [0 xx \$n] xx \$n;     for @edge -> (\$u, \$v, \$w) {        @dist[\$u-1;\$v-1] = \$w;        @next[\$u-1;\$v-1] = \$v-1;    }     for [X] ^\$n xx 3 -> (\$k, \$i, \$j) {        if @dist[\$i;\$j] > my \$sum = @dist[\$i;\$k] + @dist[\$k;\$j] {            @dist[\$i;\$j] = \$sum;            @next[\$i;\$j] = @next[\$i;\$k];        }    }     say ' Pair  Distance     Path';    for [X] ^\$n xx 2 -> (\$i, \$j){        next if \$i == \$j;        my @path = \$i;        @path.push: @next[@path[*-1];\$j] until @path[*-1] == \$j;        printf("%d → %d  %4d       %s\n", \$i+1, \$j+1, @dist[\$i;\$j],          @path.map( *+1 ).join(' → '));    }} Floyd-Warshall(4, [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]]);`
Output:
``` Pair  Distance     Path
1 → 2    -1       1 → 3 → 4 → 2
1 → 3    -2       1 → 3
1 → 4     0       1 → 3 → 4
2 → 1     4       2 → 1
2 → 3     2       2 → 1 → 3
2 → 4     4       2 → 1 → 3 → 4
3 → 1     5       3 → 4 → 2 → 1
3 → 2     1       3 → 4 → 2
3 → 4     2       3 → 4
4 → 1     3       4 → 2 → 1
4 → 2    -1       4 → 2
4 → 3     1       4 → 2 → 1 → 3
```

## Phix

Direct translation of the wikipedia pseudocode

`constant inf = 1e300*1e300 function Path(integer u, integer v, sequence next)    if next[u,v]=null then       return ""    end if    sequence path = {sprintf("%d",u)}    while u!=v do       u = next[u,v]       path = append(path,sprintf("%d",u))    end while    return join(path,"->")end function procedure FloydWarshall(integer V, sequence weights)    sequence dist = repeat(repeat(inf,V),V)    sequence next = repeat(repeat(null,V),V)    for k=1 to length(weights) do      integer {u,v,w} = weights[k]      dist[u,v] := w  -- the weight of the edge (u,v)      next[u,v] := v    end for    -- standard Floyd-Warshall implementation    for k=1 to V do      for i=1 to V do        for j=1 to V do          atom d = dist[i,k] + dist[k,j]          if dist[i,j] > d then            dist[i,j] := d            next[i,j] := next[i,k]          end if        end for      end for    end for    printf(1,"pair  dist  path\n")    for u=1 to V do      for v=1 to V do        if u!=v then          printf(1,"%d->%d   %2d   %s\n",{u,v,dist[u,v],Path(u,v,next)})        end if      end for    end forend procedure    constant V = 4constant weights = {{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}}FloydWarshall(V,weights)`
Output:
```pair  dist  path
1->2   -1   1->3->4->2
1->3   -2   1->3
1->4    0   1->3->4
2->1    4   2->1
2->3    2   2->1->3
2->4    4   2->1->3->4
3->1    5   3->4->2->1
3->2    1   3->4->2
3->4    2   3->4
4->1    3   4->2->1
4->2   -1   4->2
4->3    1   4->2->1->3
```

## PHP

`<?php\$graph = array();for (\$i = 0; \$i < 10; ++\$i) {    \$graph[] = array();    for (\$j = 0; \$j < 10; ++\$j)        \$graph[\$i][] = \$i == \$j ? 0 : 9999999;} for (\$i = 1; \$i < 10; ++\$i) {    \$graph[0][\$i] = \$graph[\$i][0] = rand(1, 9);} for (\$k = 0; \$k < 10; ++\$k) {    for (\$i = 0; \$i < 10; ++\$i) {        for (\$j = 0; \$j < 10; ++\$j) {            if (\$graph[\$i][\$j] > \$graph[\$i][\$k] + \$graph[\$k][\$j])                \$graph[\$i][\$j] = \$graph[\$i][\$k] + \$graph[\$k][\$j];        }    }} print_r(\$graph);?>`

## Prolog

Works with SWI-Prolog as of Jan 2019

`:- use_module(library(clpfd)). path(List, To, From, [From], W) :-    select([To,From,W],List,_).path(List, To, From, [Link|R], W) :-    select([To,Link,W1],List,Rest),    W #= W1 + W2,    path(Rest, Link, From, R, W2). find_path(Din, From, To, [From|Pout], Wout) :-    between(1, 4, From),    between(1, 4, To),    dif(From, To),    findall([W,P], (                path(Din, From, To, P, W),                all_distinct(P)            ), Paths),    sort(Paths, [[Wout,Pout]|_]).  print_all_paths :-    D = [[1, 3, -2], [2, 3, 3], [2, 1, 4], [3, 4, 2], [4, 2, -1]],    format('Pair\t  Dist\tPath~n'),    forall(        find_path(D, From, To, Path, Weight),(            atomic_list_concat(Path, ' -> ', PPath),            format('~p -> ~p\t  ~p\t~w~n', [From, To, Weight, PPath]))).`
Output:
```?- print_all_paths.
Pair      Dist  Path
1 -> 2    -1    1 -> 3 -> 4 -> 2
1 -> 3    -2    1 -> 3
1 -> 4    0     1 -> 3 -> 4
2 -> 1    4     2 -> 1
2 -> 3    2     2 -> 1 -> 3
2 -> 4    4     2 -> 1 -> 3 -> 4
3 -> 1    5     3 -> 4 -> 2 -> 1
3 -> 2    1     3 -> 4 -> 2
3 -> 4    2     3 -> 4
4 -> 1    3     4 -> 2 -> 1
4 -> 2    -1    4 -> 2
4 -> 3    1     4 -> 2 -> 1 -> 3
true.

?- ```

## Python

Translation of: Ruby
`from math import inffrom itertools import product def floyd_warshall(n, edge):    rn = range(n)    dist = [[inf] * n for i in rn]    nxt  = [[0]   * n for i in rn]    for i in rn:        dist[i][i] = 0    for u, v, w in edge:        dist[u-1][v-1] = w        nxt[u-1][v-1] = v-1    for k, i, j in product(rn, repeat=3):        sum_ik_kj = dist[i][k] + dist[k][j]        if dist[i][j] > sum_ik_kj:            dist[i][j] = sum_ik_kj            nxt[i][j]  = nxt[i][k]    print("pair     dist    path")    for i, j in product(rn, repeat=2):        if i != j:            path = [i]            while path[-1] != j:                path.append(nxt[path[-1]][j])            print("%d → %d  %4d       %s"                   % (i + 1, j + 1, dist[i][j],                      ' → '.join(str(p + 1) for p in path))) if __name__ == '__main__':    floyd_warshall(4, [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]])`
Output:
```pair     dist    path
1 → 2    -1       1 → 3 → 4 → 2
1 → 3    -2       1 → 3
1 → 4     0       1 → 3 → 4
2 → 1     4       2 → 1
2 → 3     2       2 → 1 → 3
2 → 4     4       2 → 1 → 3 → 4
3 → 1     5       3 → 4 → 2 → 1
3 → 2     1       3 → 4 → 2
3 → 4     2       3 → 4
4 → 1     3       4 → 2 → 1
4 → 2    -1       4 → 2
4 → 3     1       4 → 2 → 1 → 3```

## Racket

Translation of: EchoLisp
`#lang typed/racket(require math/array) ;; in : initialized dist and next matrices;; out : dist and next matrices;; O(n^3)(define-type Next-T (Option Index))(define-type Dist-T Real)(define-type Dists (Array Dist-T))(define-type Nexts (Array Next-T))(define-type Settable-Dists (Settable-Array Dist-T))(define-type Settable-Nexts (Settable-Array Next-T)) (: floyd-with-path (-> Index Dists Nexts (Values Dists Nexts)))(: init-edges (-> Index (Values Settable-Dists Settable-Nexts))) (define (floyd-with-path n dist-in next-in)  (define dist : Settable-Dists (array->mutable-array dist-in))  (define next : Settable-Nexts (array->mutable-array next-in))  (for* ((k n) (i n) (j n))    (when (negative? (array-ref dist (vector j j)))      (raise 'negative-cycle))    (define i.k (vector i k))    (define i.j (vector i j))    (define d (+ (array-ref dist i.k) (array-ref dist (vector k j))))    (when (< d (array-ref dist i.j))      (array-set! dist i.j d)      (array-set! next i.j (array-ref next i.k))))  (values dist next)) ;; utilities ;; init random edges costs, matrix 66% filled(define (init-edges n)  (define dist : Settable-Dists (array->mutable-array (make-array (vector n n) 0)))  (define next : Settable-Nexts (array->mutable-array (make-array (vector n n) #f)))    (for* ((i n) (j n) #:unless (= i j))    (define i.j (vector i j))    (array-set! dist i.j +Inf.0)    (unless (< (random) 0.3)      (array-set! dist i.j (add1 (random 100)))      (array-set! next i.j j)))  (values dist next)) ;; show path from u to v(: path (-> Nexts Index Index (Listof Index)))(define (path next u v)  (let loop : (Listof Index) ((u : Index u) (rv : (Listof Index) null))    (if (= u v)        (reverse (cons u rv))        (let ((nxt (array-ref next (vector u v))))          (if nxt (loop nxt (cons u rv)) null))))) ;; show computed distance(: mdist (-> Dists Index Index Dist-T))(define (mdist dist u v)  (array-ref dist (vector u v))) (module+ main  (define n 8)  (define-values (dist next) (init-edges n))  (define-values (dist+ next+) (floyd-with-path n dist next))  (displayln "original dist")  dist  (displayln "new dist and next")  dist+  next+  ;; note, these path and dist calls are not as carefully crafted as  ;; the echolisp ones (in fact they're verbatim copied)  (displayln "paths and distances")  (path  next+ 1 3)  (mdist dist+ 1 0)  (mdist dist+ 0 3)  (mdist dist+ 1 3)  (path next+ 7 6)  (path next+ 6 7))`
Output:
```original dist
(mutable-array
#[#[0 51 +inf.0 11 44 13 +inf.0 86]
#[48 0 70 +inf.0 65 78 77 54]
#[29 +inf.0 0 +inf.0 78 14 +inf.0 24]
#[40 79 52 0 +inf.0 99 37 88]
#[71 62 +inf.0 7 0 +inf.0 +inf.0 +inf.0]
#[89 65 83 +inf.0 91 0 41 70]
#[69 34 +inf.0 49 +inf.0 89 0 20]
#[2 56 +inf.0 60 +inf.0 75 +inf.0 0]])
new dist and next
(mutable-array
#[#[0 51 63 11 44 13 48 68]
#[48 0 70 59 65 61 77 54]
#[26 77 0 37 70 14 55 24]
#[40 71 52 0 84 53 37 57]
#[47 62 59 7 0 60 44 64]
#[63 65 83 74 91 0 41 61]
#[22 34 85 33 66 35 0 20]
#[2 53 65 13 46 15 50 0]])
(mutable-array
#[#[#f 1 3 3 4 5 3 3]
#[0 #f 2 0 4 0 6 7]
#[7 7 #f 7 7 5 5 7]
#[0 6 2 #f 0 0 6 6]
#[3 1 3 3 #f 3 3 3]
#[6 1 2 6 4 #f 6 6]
#[7 1 7 7 7 7 #f 7]
#[0 0 0 0 0 0 0 #f]])
paths and distances
'(1 0 3)
48
11
59
'(7 0 3 6)
'(6 7)```

## REXX

`/*REXX program uses Floyd-Warshall algorithm to find shortest distance between vertices.*/v=4              /*███       {1}       ███*/     /*number of vertices in weighted graph.*/@.= 99999999     /*███    4 /   \ -2   ███*/     /*the default distance  (edge weight). */@.1.3=-2         /*███     /  3  \     ███*/     /*the distance (weight) for an edge.   */@.2.1= 4         /*███  {2} ────► {3}  ███*/     /* "     "         "     "   "   "     */@.2.3= 3         /*███     \     /     ███*/     /* "     "         "     "   "   "     */@.3.4= 2         /*███   -1 \   / 2    ███*/     /* "     "         "     "   "   "     */@.4.2=-1         /*███       {4}       ███*/     /* "     "         "     "   "   "     */            do     k=1  for v              do   i=1  for v                do j=1  for v;  [email protected].i.k + @.k.j                if @.i.j>_  then @.i.j=_         /*use a new distance (weight) for edge.*/                end   /*j*/              end     /*i*/            end       /*k*/w=12                                             /*width of the columns for the output. */say center('vertices', w)  center('distance', w) /*display the  1st  line of the title. */say center('pair'    , w)  center('(weight)', w) /*   "     "   2nd    "   "  "    "    */say copies('═'       , w)  copies('═'       , w) /*   "     "   3rd    "   "  "    "    */                                                 /* [↓]  display edge distances (weight)*/   do   f=1  for v                               /*process each of the "from" vertices. */     do t=1  for v;   if f==t  then iterate      /*   "      "   "  "   "to"      "     */     say center(f '─►' t, w)   right(@.f.t, w%2) /*show the distance between 2 vertices.*/     end   /*t*/   end     /*f*/                                 /*stick a fork in it,  we're all done. */`

output   when using the defaults:

```  vertices     distance
pair       (weight)
════════════ ════════════
1 ─► 2        -1
1 ─► 3        -2
1 ─► 4         0
2 ─► 1         4
2 ─► 3         2
2 ─► 4         4
3 ─► 1         5
3 ─► 2         1
3 ─► 4         2
4 ─► 1         3
4 ─► 2        -1
4 ─► 3         1
```

## Ruby

`def floyd_warshall(n, edge)  dist = Array.new(n){|i| Array.new(n){|j| i==j ? 0 : Float::INFINITY}}  nxt = Array.new(n){Array.new(n)}  edge.each do |u,v,w|    dist[u-1][v-1] = w    nxt[u-1][v-1] = v-1  end   n.times do |k|    n.times do |i|      n.times do |j|        if dist[i][j] > dist[i][k] + dist[k][j]          dist[i][j] = dist[i][k] + dist[k][j]          nxt[i][j] = nxt[i][k]        end      end    end  end   puts "pair     dist    path"  n.times do |i|    n.times do |j|      next  if i==j      u = i      path = [u]      path << (u = nxt[u][j])  while u != j      path = path.map{|u| u+1}.join(" -> ")      puts "%d -> %d  %4d     %s" % [i+1, j+1, dist[i][j], path]    end  endend n = 4edge = [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]]floyd_warshall(n, edge)`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3
```

## SequenceL

Translation of: Go
`import <Utilities/Sequence.sl>;import <Utilities/Math.sl>; ARC ::= (To: int, Weight: float);arc(t,w) := (To: t, Weight: w);VERTEX ::= (Label: int, Arcs: ARC(1));vertex(l,arcs(1)) := (Label: l, Arcs: arcs); getArcsFrom(vertex, graph(1)) :=    let        index := firstIndexOf(graph.Label, vertex);    in        [] when index = 0    else        graph[index].Arcs; getWeightTo(vertex, arcs(1)) :=    let        index := firstIndexOf(arcs.To, vertex);    in        0 when index = 0    else        arcs[index].Weight; throughK(k, dist(2)) :=    let        newDist[i, j] := min(dist[i][k] + dist[k][j], dist[i][j]);    in        dist when k > size(dist)    else        throughK(k + 1, newDist); floydWarshall(graph(1)) :=    let        initialResult[i,j] := 1.79769e308 when i /= j else 0                              foreach i within 1 ... size(graph),                                      j within 1 ... size(graph);         singleResult[i,j] := getWeightTo(j, getArcsFrom(i, graph))                             foreach i within 1 ... size(graph),                                     j within 1 ... size(graph);         start[i,j] :=                 initialResult[i,j] when singleResult[i,j] = 0            else                singleResult[i,j];        in        throughK(1, start); main() :=    let        graph := [vertex(1, [arc(3,-2)]),                  vertex(2, [arc(1,4), arc(3,3)]),                  vertex(3, [arc(4,2)]),                  vertex(4, [arc(2,-1)])];    in        floydWarshall(graph);`
Output:
```[[0,-1,-2,0],[4,0,2,4],[5,1,0,2],[3,-1,1,0]]
```

## Sidef

Translation of: Ruby
`func floyd_warshall(n, edge) {    var dist = n.of {|i| n.of { |j| i == j ? 0 : Inf }}    var nxt  = n.of { n.of(nil) }    for u,v,w in edge {        dist[u-1][v-1] = w         nxt[u-1][v-1] = v-1    }     [^n] * 3 -> cartesian { |k, i, j|        if (dist[i][j] > dist[i][k]+dist[k][j]) {            dist[i][j] = dist[i][k]+dist[k][j]            nxt[i][j] = nxt[i][k]        }    }     var summary = "pair     dist    path\n"    for i,j (^n ~X ^n) {        i==j && next        var u = i        var path = [u]        while (u != j) {            path << (u = nxt[u][j])        }        path.map!{|u| u+1 }.join!(" -> ")        summary += ("%d -> %d  %4d     %s\n" % (i+1, j+1, dist[i][j], path))    }     return summary} var n = 4var edge = [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]]print floyd_warshall(n, edge)`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3
```

## Tcl

Library: Tcllib (Package: struct::graph::op)

The implementation of Floyd-Warshall in tcllib is quite readable; this example merely initialises a graph from an adjacency list then calls the tcllib code:

`package require Tcl 8.5     ;# for {*} and [dict]package require struct::graphpackage require struct::graph::op struct::graph g set arclist {    a b    a p    b m    b c    c d    d e    e f    f q    f g} g node insert {*}\$arclist foreach {from to} \$arclist {    set a [g arc insert \$from \$to]    g arc setweight \$a 1.0} set paths [::struct::graph::op::FloydWarshall g] set paths [dict filter \$paths key {a *}]        ;# filter for paths starting at "a"set paths [dict filter \$paths value {[0-9]*}]   ;# whose cost is not "Inf"set paths [lsort -stride 2 -index 1 -real -decreasing \$paths]   ;# and print the longest firstputs \$paths`
Output:
`{a q} 6.0 {a g} 6.0 {a f} 5.0 {a e} 4.0 {a d} 3.0 {a m} 2.0 {a c} 2.0 {a p} 1.0 {a b} 1.0 {a a} 0`

## Visual Basic .NET

Translation of: C#
`Module Module1     Sub PrintResult(dist As Double(,), nxt As Integer(,))        Console.WriteLine("pair     dist    path")        For i = 1 To nxt.GetLength(0)            For j = 1 To nxt.GetLength(1)                If i <> j Then                    Dim u = i                    Dim v = j                    Dim path = String.Format("{0} -> {1}    {2,2:G}     {3}", u, v, dist(i - 1, j - 1), u)                    Do                        u = nxt(u - 1, v - 1)                        path += String.Format(" -> {0}", u)                    Loop While u <> v                    Console.WriteLine(path)                End If            Next        Next    End Sub     Sub FloydWarshall(weights As Integer(,), numVerticies As Integer)        Dim dist(numVerticies - 1, numVerticies - 1) As Double        For i = 1 To numVerticies            For j = 1 To numVerticies                dist(i - 1, j - 1) = Double.PositiveInfinity            Next        Next         For i = 1 To weights.GetLength(0)            dist(weights(i - 1, 0) - 1, weights(i - 1, 1) - 1) = weights(i - 1, 2)        Next         Dim nxt(numVerticies - 1, numVerticies - 1) As Integer        For i = 1 To numVerticies            For j = 1 To numVerticies                If i <> j Then                    nxt(i - 1, j - 1) = j                End If            Next        Next         For k = 1 To numVerticies            For i = 1 To numVerticies                For j = 1 To numVerticies                    If dist(i - 1, k - 1) + dist(k - 1, j - 1) < dist(i - 1, j - 1) Then                        dist(i - 1, j - 1) = dist(i - 1, k - 1) + dist(k - 1, j - 1)                        nxt(i - 1, j - 1) = nxt(i - 1, k - 1)                    End If                Next            Next        Next         PrintResult(dist, nxt)    End Sub     Sub Main()        Dim weights = {{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}}        Dim numVeritices = 4         FloydWarshall(weights, numVeritices)    End Sub End Module`
Output:
```pair     dist    path
1 -> 2    -1     1 -> 3 -> 4 -> 2
1 -> 3    -2     1 -> 3
1 -> 4     0     1 -> 3 -> 4
2 -> 1     4     2 -> 1
2 -> 3     2     2 -> 1 -> 3
2 -> 4     4     2 -> 1 -> 3 -> 4
3 -> 1     5     3 -> 4 -> 2 -> 1
3 -> 2     1     3 -> 4 -> 2
3 -> 4     2     3 -> 4
4 -> 1     3     4 -> 2 -> 1
4 -> 2    -1     4 -> 2
4 -> 3     1     4 -> 2 -> 1 -> 3```

## zkl

`fcn FloydWarshallWithPathReconstruction(dist){ // dist is munged   V:=dist[0].len();   next:=V.pump(List,V.pump(List,Void.copy).copy);  // VxV matrix of Void   foreach u,v in (V,V){ if(dist[u][v]!=Void and u!=v) next[u][v] = v }   foreach k,i,j in (V,V,V){      a,b,c:=dist[i][j],dist[i][k],dist[k][j];      if( (a!=Void and b!=Void and c!=Void and a>b+c) or  // Inf math	  (a==Void and b!=Void and c!=Void) ){	 dist[i][j] = b+c;	 next[i][j] = next[i][k];      }   }   return(dist,next)} fcn path(next,u,v){   if(Void==next[u][v]) return(T);   path:=List(u);   while(u!=v){ path.append(u = next[u][v]) }   path}fcn printM(m){ m.pump(Console.println,rowFmt) }fcn rowFmt(row){ ("%5s "*row.len()).fmt(row.xplode()) }`
`const V=4;dist:=V.pump(List,V.pump(List,Void.copy).copy);  // VxV matrix of Voidforeach i in (V){ dist[i][i] = 0 }	   // zero vertexes /* Graph from the Wikipedia:   1  2  3  4 d ----------1| 0  X -2  X2| 4  0  3  X3| X  X  0  24| X -1  X  0*/dist[0][2]=-2; dist[1][0]=4; dist[1][2]=3; dist[2][3]=2; dist[3][1]=-1;  dist,next:=FloydWarshallWithPathReconstruction(dist);println("Shortest distance array:"); printM(dist);println("\nPath array:");	     printM(next);println("\nAll paths:");foreach u,v in (V,V){   if(p:=path(next,u,v)) p.println();}`
Output:
```Shortest distance array:
0    -1    -2     0
4     0     2     4
5     1     0     2
3    -1     1     0

Path array:
Void     2     2     2
0  Void     0     0
3     3  Void     3
1     1     1  Void

All paths:
L(0,2,3,1)
L(0,2)
L(0,2,3)
L(1,0)
L(1,0,2)
L(1,0,2,3)
L(2,3,1,0)
L(2,3,1)
L(2,3)
L(3,1,0)
L(3,1)
L(3,1,0,2)
```