洛谷P1807 最长路

题目传送门：https://www.luogu.com.cn/problem/P1807

解法一：拓扑排序

#include <bits/stdc++.h>
using i64 = long long;
using namespace std;
typedef pair<int, int> pii;
constexpr int N = 1505, M = 5e4 + 5;
// mt19937_64 rng(random_device{}());
int n, m;
int ver[M], edge[M], nxt[M], head[N], tot, in[N];
i64 d[N];
void add(int x, int y, int z) {
    ver[++tot] = y, edge[tot] = z, nxt[tot] = head[x], head[x] = tot;
}
void topsort() {
    queue<int> q;
    for (int x = 2; x <= n; ++x) {
        if (in[x] == 0) {
            q.push(x);
        }
    }
    while (!q.empty()) {
        int x = q.front(); q.pop();
        for (int i = head[x]; i ; i = nxt[i]) {
            int y = ver[i];
            if (--in[y] == 0) {
                q.push(y);
            }
        }
    }
    d[1] = 0;
    q.push(1);
    while (!q.empty()) {
        int x = q.front(); q.pop();
        for (int i = head[x]; i ; i = nxt[i]) {
            int y = ver[i], z = edge[i];
            d[y] = max(d[y], d[x] + z);
            if (--in[y] == 0) {
                q.push(y);
            }
        }
    }
}
const i64 inf = 1e18;
void solve() {
    cin >> n >> m;
    fill(d, d + 1 + n, -inf);
    for (int i = 0; i < m; ++i) {
        int x, y, z;
        cin >> x >> y >> z;
        add(x, y, z);
        ++in[y];
    }
    topsort();
    cout << (d[n] ==-inf ? -1 : d[n]) << '\n';
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    solve();
    return 0;
}

解法二：边权取负，用spfa跑最短路

#include <bits/stdc++.h>
using i64 = long long;
using namespace std;
typedef pair<int, int> pii;
constexpr int N = 1500 + 5, M = 5e4 + 10;
mt19937_64 rng(random_device{}());
int ver[M], edge[M], nxt[M], head[N], tot, vis[N];
i64 d[N];
void add(int x, int y, int z) {
    ver[++tot] = y, edge[tot] = z, nxt[tot] = head[x], head[x] = tot;
}
void spfa(int st) {
    memset(d, 0x3f, sizeof d);
    queue<int> q;
    q.push(st);
    vis[st] = 1;
    d[st] = 0;
    while (!q.empty()) {
        int x = q.front(); q.pop();
        vis[x] = 0;
        for (int i = head[x]; i ; i = nxt[i]) {
            int y = ver[i], z = edge[i];
            if (d[x] + z < d[y]) {
                d[y] = d[x] + z;
                if (!vis[y]) {
                    q.push(y);
                    vis[y] = 1;
                }
            }
        }
    }
}
void solve(){
    int n,m;
    cin >> n >> m;
    for (int i = 0; i < m; ++i) {
        int x, y, z;
        cin >> x >> y >> z;
        add(x, y, -z); // 加负边
    }
    spfa(1);
    if (d[n] == 0x3f3f3f3f3f3f3f3f) {
        cout << "-1\n";
    } else {
        cout << -d[n] << '\n';
    }

}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    solve();
    return 0;
}