# Floyd-Warshall algorithm

```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)
```

#### 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
```


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