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{{task|Routing algorithms}} The [[wp:Floyd–Warshall_algorithm|Floyd–Warshall algorithm]] is an algorithm for finding shortest paths in a weighted graph with positive or negative edge weights.

;Task 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.

[[File:Floyd_warshall_graph.gif|||center]]

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

{{trans|Rexx}}

```*        Floyd-Warshall algorithm - 06/06/2018
FLOYDWAR CSECT
USING  FLOYDWAR,R13       base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
SAVE   (14,12)            save previous context
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 sav
VV       EQU    4
V        DC     A(VV)
A        DC     (VV*VV)F'99999999' a(vv,vv)
PG       DC     CL80'   . ->    .   .'
XDEC     DS     CL12
YREGS
END    FLOYDWAR
```

{{out}}

```
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;

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
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;
}
```

{{out}}

```(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#

{{trans|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

{{trans|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);
}
}
}
}
```

{{out}}

```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))

(init-edges n dist next)
(array-print dist) ;; show init distances
(floyd-with-path n dist next))

```

{{out}}

```
(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])
end
end

edge = [{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}]
Floyd_Warshall.main(4, edge)
```

{{out}}

```
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

{{trans|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 i
End 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 = 4
floydWarshall(weights(), numVertices)
Print
Print "Press any key to quit"
Sleep
```

{{out}}

```
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

```

```
//Floyd's algorithm: Nigel Galloway August 5th 2018
let 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|] fW
List.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))))

```

{{out}}

```
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 vertex
type 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)))
}
}
}
}
```

{{out}}

```
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.Semigroup
import 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
```

{{Out}} 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 graph
0 _1 _2 0
4  0  2 4
5  1  0 2
3 _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)},(\$\$i.@#)y
for_j. i.#y do.
d=. y <. j ({"1 +/ {) y
b=. y~:d
y=. d
n=. (n*-.b)+b * j{"1 n
end.
)

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 graph
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
```

## 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

{{output?|Javascript}}

```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|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
```

{{out}}

```{
"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

{{trans|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

{{trans|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)
}
```

{{out}}

```
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

{{trans|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
end
end

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 = 4
floydWarshall(weights, numVertices)
```

{{out}}

```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
```

```MODULE FloydWarshall;
FROM FormatString IMPORT FormatString;
FROM SpecialReals IMPORT Infinity;

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
END
END 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);

END 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);
```

{{out}}

```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|2016.12}} {{trans|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]]);
```

{{out}}

``` 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 for
end procedure

constant V = 4
constant weights = {{1, 3, -2}, {2, 1, 4}, {2, 3, 3}, {3, 4, 2}, {4, 2, -1}}
FloydWarshall(V,weights)
```

{{out}}

```
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) :-
W #= W1 + 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

{{trans|Ruby}}

```from math import inf
from 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

{{trans|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))
```

{{out}}

```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] + @.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
end
end

n = 4
edge = [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]]
floyd_warshall(n, edge)
```

{{out}}

```
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

{{trans|Go}}

```;
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);
```

{{out}}

```
[[0,-1,-2,0],[4,0,2,4],[5,1,0,2],[3,-1,1,0]]

```

## Sidef

{{trans|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 = 4
var edge = [[1, 3, -2], [2, 1, 4], [2, 3, 3], [3, 4, 2], [4, 2, -1]]
print floyd_warshall(n, edge)
```

{{out}}

```
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

{{tcllib|struct::graph::op}}

The implementation of Floyd-Warshall in tcllib is [https://core.tcl.tk/tcllib/finfo?name=modules/struct/graphops.tcl 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::graph
package 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 first
puts \$paths
```

{{out}}

```{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

{{trans|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
```

{{out}}

```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 Void
foreach i in (V){ dist[i][i] = 0 }	   // zero vertexes

/* Graph from the Wikipedia:
1  2  3  4
d ----------
1| 0  X -2  X
2| 4  0  3  X
3| X  X  0  2
4| 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();
}
```

{{out}}

```
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)

```