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* All-Pairs Shortest Path Computation
* using Floyd-Warshall O(n**3) method
* CLR 2nd ed p. 632
* Copyright © 2004 Bart Massey.
* All Rights Reserved. See the file COPYING in this directory
* for licensing information.
*/
namespace APSP {
public typedef real distance;
public typedef struct {
distance dist;
int first_hop;
} shortest_path;
public shortest_path[*,*]
compute_paths(distance[*,*] adjacencies) {
int[*] ns = dims(adjacencies);
assert(dim(ns) == 2 && ns[0] == ns[1],
"ill-conditioned adjacencies");
int n = ns[0];
/* set things up */
shortest_path[n,n] path =
{{{.dist = -1, .first_hop = -1}, ...},...};
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i != j && adjacencies[i,j] >= 0) {
path[i,j].dist = adjacencies[i,j];
path[i,j].first_hop = j;
}
}
}
/* do the computation */
for (int k = 0; k < n; k++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j)
continue;
real dik = path[i,k].dist;
real dkj = path[k,j].dist;
if (dik < 0 || dkj < 0)
continue;
real dij = path[i,j].dist;
if (dij < 0 || dik + dkj < dij) {
path[i,j].dist = dik + dkj;
path[i,j].first_hop = path[i,k].first_hop;
}
}
}
}
return path;
}
}
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