Task: Floyd-Warshall algorithm




Go: package main
 
import (
  "fmt"
  "strconv"
)
 


type Graph interface {
  Vertices() []Vertex
  Neighbors(v Vertex) []Vertex
  Weight(u, v Vertex) int
}
 

type Vertex int
 

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)))
      }
    }
  }
}




Python: 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]])