【模板】差分约束(Difference Constraints) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <iostream>
#include <vector>
#include <queue>
using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, m;
    if (!(cin >> n >> m)) return 0;
    vector<vector<pair<int, long long>>> adj(n + 1);
    for (int i = 0; i < m; ++i) {
        int c, cp;
        long long y;
        cin >> c >> cp >> y;
        adj[cp].push_back({c, y});
    }
    vector<long long> dist(n + 1, 5);
    vector<int> in_q(n + 1, 1), cnt(n + 1, 0);
    queue<int> q;
    for (int i = 1; i <= n; ++i) q.push(i);
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        in_q[u] = 0;
        for (auto& edge : adj[u]) {
            int v = edge.first;
            long long w = edge.second;
            if (dist[u] + w < dist[v]) {
                dist[v] = dist[u] + w;
                cnt[v] = cnt[u] + 1;
                if (cnt[v] >= n) {
                    cout << "NO\n";
                    return 0;
                }
                if (!in_q[v]) {
                    in_q[v] = 1;
                    q.push(v);
                }
            }
        }
    }
    for (int i = 1; i <= n; ++i) {
        cout << dist[i] << (i == n ? "\n" : " ");
    }
    return 0;
}