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// Belmann-Ford Algorithm
//
// Given a graph where all edges have a (possibly negative) weight, compute the
// shortest distances from a given source vertex s to all other vertices.
//
// Idea: Do N - 1 rounds of relaxations. After these rounds, every node will
// store the stortest path to the starting node.
//
// Shortest Path Faster Algorithm (SPFA)
// - faster algorithm on average
// - keep a queue of nodes that can be relaxed; perform relaxations until you
// can't
//
// Complexity: O(N * M)
#include <bits/stdc++.h>
using namespace std;
int n, m;
vector<vector<pair<int, int>>> adj;
vector<int> parent;
vector<int> dist;
bool spfa(int start)
{
queue<int> q;
vector<int> relaxed(n, 0);
vector<int> inqueue(n, false);
dist[start] = 0;
inqueue[start] = true;
q.push(start);
while (!q.empty()) {
int node = q.front();
q.pop();
inqueue[node] = false;
for (auto [next, weight] : adj[node]) {
int next_dist = dist[node] + weight;
if (next_dist < dist[next]) {
parent[next] = node;
dist[next] = next_dist;
if (!inqueue[next]) {
if (++relaxed[next] >= n)
return false; // Negative cycle found
inqueue[next] = true;
q.push(next);
}
}
}
}
return true;
}
int main()
{
freopen("bellmanford.in", "r", stdin);
freopen("bellmanford.out", "w", stdout);
cin >> n >> m;
adj.resize(n);
parent.resize(n, -1);
dist.resize(n, INT_MAX);
for (int i = 0; i < m; i++) {
int x, y, w;
cin >> x >> y >> w;
adj[--x].push_back({--y, w});
}
if (!spfa(0)) {
cout << "Ciclu negativ!\n";
return 0;
}
for (int i = 1; i < n; i++)
cout << dist[i] << ' ';
cout << '\n';
return 0;
}