P3387 【模板】缩点

P3387

我的做法就是将原图缩点，得到一个DAG新图，在新图上进行DP求最长路径。

#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
int n, m, t;
int dfn[N], low[N], a[N];
int tot, head[N], to[N], nxt[N];
void add(int x, int y) {
    nxt[++ tot] = head[x]; head[x] = tot, to[tot] = y;
}
int st[N], top, bel[N], vis[N];
int idx, num[N], cnt[N];
void tarjan(int x) {
    dfn[x] = low[x] = ++ t;
    st[++ top] = x, vis[x] = 1;
    for (int i = head[x]; i; i = nxt[i]) {
        int y = to[i];
        if (!dfn[y]) {
            tarjan(y);
            low[x] = min(low[x], low[y]);
        }
        else if (vis[y]) 
            low[x] = min(low[x], dfn[y]);
    }
    if(low[x] == dfn[x]) {
        idx ++;
        int v;
        do {
            v = st[top --];
            cnt[idx] ++;
            num[idx] += a[v];
            bel[v] = idx;
            vis[v] = 0;    
        } while (v != x);
    }
}
vector<int> e[N];
int dp[N];
void dfs(int u, int fa) {
    if (vis[u]) return ;
    vis[u] = 1;
    dp[u] = num[u];
    for (int i = 0; i < e[u].size(); i ++) {
        int v = e[u][i];
        if (v == fa) continue;
        dfs(v, u);
        dp[u] = max(dp[u], num[u] + dp[v]);
    }
}
int main() {
    scanf("%d %d", &n, &m);
    for (int i = 1; i <= n; i ++) scanf("%d", &a[i]);
    for (int i = 1; i <= m; i ++) {
        int u, v; scanf("%d %d", &u, &v);
        add(u, v);
    }    
    for (int i = 1; i <= n; i ++) 
        if (!dfn[i]) tarjan(i);
    for (int i = 1; i <= n; i ++) {
        for (int j = head[i]; j; j = nxt[j]) {
            int v = to[j];
            if (bel[i] != bel[v]) e[bel[i]].push_back(bel[v]);
        }
    }
    memset(vis, 0, sizeof vis);
    for (int i = 1; i <= idx; i ++) {
        if (!vis[i]) dfs(i, 0);
    }
    int ans = 0;
    for (int i = 1; i <= idx; i ++) ans = max(ans, dp[i]);
    printf("%d\n", ans);
    return 0;
}

 

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