Skip to content
Permalink
master
Switch branches/tags
Go to file
 
 
Cannot retrieve contributors at this time
#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
const int INF = 1e9; // INF = 1B, not 2^31-1 to avoid overflow
int main() {
/*
// Graph in Figure 4.18, has negative weight, but no negative cycle
5 5 0
0 1 1
0 2 10
1 3 2
2 3 -10
3 4 3
// Graph in Figure 4.19, negative cycle exists, Bellman Ford's can detect this
6 6 0
0 1 99
0 5 -99
1 2 15
2 3 0
3 1 -42
3 4 2
*/
freopen("bellman_ford_in.txt", "r", stdin);
int V, E, s; scanf("%d %d %d", &V, &E, &s);
vector<vii> AL(V, vii());
while (E--) {
int u, v, w; scanf("%d %d %d", &u, &v, &w);
AL[u].emplace_back(v, w);
}
// Bellman Ford's routine, basically = relax all E edges V-1 times
vi dist(V, INF); dist[s] = 0; // INF = 1e9 here
for (int i = 0; i < V-1; ++i) { // total O(V*E)
bool modified = false; // optimization
for (int u = 0; u < V; ++u) // these two loops = O(E)
if (dist[u] != INF) // important check
for (auto &[v, w] : AL[u]) { // C++17 style
if (dist[u]+w >= dist[v]) continue; // not improving, skip
dist[v] = dist[u]+w; // relax operation
modified = true; // optimization
}
if (!modified) break; // optimization
}
bool hasNegativeCycle = false;
for (int u = 0; u < V; ++u) // one more pass to check
if (dist[u] != INF)
for (auto &[v, w] : AL[u]) // C++17 style
if (dist[v] > dist[u]+w) // should be false
hasNegativeCycle = true; // if true => -ve cycle
printf("Negative Cycle Exist? %s\n", hasNegativeCycle ? "Yes" : "No");
if (!hasNegativeCycle)
for (int u = 0; u < V; ++u)
printf("SSSP(%d, %d) = %d\n", s, u, dist[u]);
return 0;
}