Floyd-Warshall algorithm: Difference between revisions

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console.log(graph);</lang>
console.log(graph);</lang>

=={{header|Kotlin}}==
{{trans|Java}}
<lang scala>// version 1.0.6

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)
}</lang>

{{out}}
<pre>
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
</pre>


=={{header|Perl 6}}==
=={{header|Perl 6}}==

Revision as of 12:44, 3 January 2017

Task
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.

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.

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



See also



EchoLisp

Transcription of the Floyd-Warshall algorithm, with best path computation. <lang scheme> (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)) </lang>

Output:
(define n 8)
(define next (make-array n n))
(define dist (make-array n n))
(task)

  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

<lang 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)</lang>

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

<lang freebasic>' 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</lang>

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

Go

<lang go>package main

import ( 

   "fmt"
   "math"

)

type arc struct { 

   to int
   wt float64

}

func fw(g [][]arc) [][]float64 { 

   dist := make([][]float64, len(g))
   for i := range dist {
       di := make([]float64, len(g))
       for j := range di {
           di[j] = math.Inf(1)
       }
       di[i] = 0
       dist[i] = di
   }
   for u, arcs := range g {
       for _, v := range arcs {
           dist[u][v.to] = v.wt
       }
   }
   for k, dk := range dist {
       for _, di := range dist {
           for j, dij := range di {
               if d := di[k] + dk[j]; dij > d {
                   di[j] = d
               }
           }
       }
   }
   return dist

}

func main() { 

   g := [][]arc{
       1: Template:3, -2,
       2: {{1, 4}, {3, 3}},
       3: Template:4, 2,
       4: Template:2, -1,
   }
   dist := fw(g)
   for _, d := range dist {
       fmt.Printf("%4g\n", d)
   }

}</lang>

Output:
[   0 +Inf +Inf +Inf +Inf]
[+Inf    0   -1   -2    0]
[+Inf    4    0    2    4]
[+Inf    5    1    0    2]
[+Inf    3   -1    1    0]

Haskell

Necessary imports <lang haskell>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)</lang>

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...)

<lang haskell>data Shortest b a = Shortest { distance :: a, path :: [b] } 

                 deriving Show</lang>

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

<lang haskell>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 }</lang>

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: <lang haskell>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</lang>

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

<lang haskell>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]</lang>

All pre- and postprocessing is done by the main function findMinDistances: <lang haskell>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)</lang>

Examples:

The sample graph: <lang haskell>g = fromList [((2,1), 4) 

            ,((2,3), 3)
            ,((1,3), -2)
            ,((3,4), 2)
            ,((4,2), -1)]</lang>

the helper function <lang haskell>showShortestPaths v g = mapM_ print $ toList $ findMinDistances v g</lang>

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:

<lang haskell>g2 = fromList [(('A','S'), 1) 

            ,(('A','D'), -1)
            ,(('S','E'), 2)
            ,(('D','E'), 4)]</lang>

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

<lang J>floyd=: verb define 

 for_j. i.#y do.
   y=. y <. j ({"1 +/ {) y
 end.

)</lang>

Example use:

<lang J>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</lang>

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:

<lang J>floydrecon=: verb define 

 n=. ((|i.@,~)#y)*1>.y->./(,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

)</lang>

Draft output:

<lang J> 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</lang>

Java

<lang 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);
               }
           }
       }
   }

}</lang> 

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

<lang 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);</lang>

Kotlin

Translation of: Java

<lang scala>// version 1.0.6

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)

}</lang>

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

<lang perl6>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]]);</lang>

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

PHP

<lang 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); ?></lang>

Racket

Translation of: EchoLisp

<lang racket>#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))</lang>
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)

Ruby

<lang 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)</lang>

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

Sidef

Translation of: Ruby

<lang 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
   }

   for k in ^n {
       for i in ^n {
           for j in ^n {
               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 in ^n {
       for j in ^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)</lang>

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:

<lang Tcl>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</lang>

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

zkl

<lang 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()) }</lang> <lang zkl>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();

}</lang>

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)
Retrieved from "https://rosettacode.org/wiki/Floyd-Warshall_algorithm?oldid=261926"