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#include <fstream>
using namespace std;
///// DESCRIPTION
// THIS PROGRAM FINDS THE MINIMUM
// PATH BETWEEN ALL NODES IN A WEIGHTED
// UNDIRECTED GRAPH IN O(|V|^3) BY
// APPLYING THE FOLLOWING STEP-BY-STEP APPROXIMATIONS:
// https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm
// shortestPath(i, j, k) -- returns shortest path between i and j by
// going through nodes [1...k]
//
// shortestPath(i, j, 0) -- weight(i, j)
// shortestPath(i, j, k+1) -- min(shortestPath(i, j, k),
// shortestPath(i, k+1, k) + shortestPath(k+1, j, k))
/////
int main(int argc, char **argv)
{
// INPUT
int n;
ifstream indata("royfloyd.in");
indata >> n;
int cost_mat[n][n];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
indata >> cost_mat[i][j];
}
}
indata.close();
// APPLY ROY-FLOYD TO FIND SHORTEST_PATH
for (int k = 0; k < n; k++) { // loop through all possible intermediate nodes
for (int i = 0; i < n; i++) { // loop through all start nodes
for (int j = 0; j < n; j++) { // loop through all end nodes
// if there is a path between [i][k] and [k][j]
if (cost_mat[i][k] != 0 && cost_mat[k][j] != 0) {
// if we are not trying to go back and either 1) there was no path before or 2) the new path is shorter
if((cost_mat[i][j] > cost_mat[i][k] + cost_mat[k][j] || cost_mat[i][j] == 0) && i != j) {
cost_mat[i][j] = cost_mat[i][k] + cost_mat[k][j];
}
}
}
}
}
// OUTPUT
ofstream outdata("royfloyd.out");
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
outdata << cost_mat[i][j] << " ";
}
outdata << "\n";
}
outdata.close();
return 0;
}