Luogu3119 草鉴定-Tarjan+Topsort

Solution

简单的$Tarjan$题。

有大佬现成博客 就不写了 → 传送门

Code

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define rd read()
using namespace std;

const int N = 1e5 + 5;
const int inf = ~0U >> 2;

int n, m;
int head[N], tot, Head[N], Tot;
int low[N], dfn[N], cnt;
int st[N], tp, col, c[N], val[N], subsz[N], upsz[N], deg[N], bvis[N];
bool vis[N];

struct edge {
    int nxt, fr, to;
}e[N], E[N];

queue<int> q;

int read() {
    int X = 0, p = 1; char c = getchar();
    for (; c > '9' || c < '0'; c = getchar())
        if (c == '-') p = -1;
    for (; c >= '0' && c <= '9'; c = getchar())
        X = X * 10 + c - '0';
    return X * p;
}

void add(int u, int v) {
    e[++tot].to = v;
    e[tot].fr = u;
    e[tot].nxt = head[u];
    head[u] = tot;
}

void Add(int u, int v) {
    E[++Tot].to = v;
    E[Tot].fr = u;
    E[Tot].nxt = Head[u];
    Head[u] = Tot;
}

void cmin(int &A, int B) {
    if (A > B) A = B;
}

void cmax(int &A, int B) {
    if (A < B) A = B;
}

void tarjan(int u) {
    dfn[u] = low[u] = ++cnt;
    vis[u] = 1; st[++tp] = u;
    for (int i = head[u]; i; i = e[i].nxt) {
        int nt = e[i].to;
        if (!dfn[nt]) {
            tarjan(nt);
            cmin(low[u], low[nt]);
        }
        else if (vis[nt]) cmin(low[u], dfn[nt]);
    }
    if (low[u] == dfn[u]) {
        col++;
        for (; tp;) {
            int z = st[tp--];
            c[z] = col;
            vis[z] = 0;
            val[col]++;
            if (z == u) break;
        }
    }
}

void dfs(int u) {
    vis[u] = 1;
    for (int i = Head[u]; i; i = E[i].nxt) {
        int nt = E[i].to;
        dfs(nt);
    }
}

int dfs2(int u) {
    if (bvis[u] == 1) return 1;
    if (bvis[u] == -1) return 0;
    if (u == c[1]) return 1;
    bool flag = false;
    for (int i = Head[u]; i; i = E[i].nxt) {
        int nt = E[i].to;
        if (dfs2(nt)) {
            flag = true;
            cmax(upsz[u], upsz[nt] + val[u]);
        }
    }
    bvis[u] = flag ? 1 : -1;
    return flag;
}

void Topsort() {
    subsz[c[1]] = val[c[1]];
    for (int i = 1; i <= col; ++i)
        if (!deg[i]) q.push(i);
    for (int u; !q.empty(); ) {
        u = q.front(); q.pop();
        for (int i = Head[u]; i; i = E[i].nxt) {
            int nt = E[i].to;
            if (subsz[u] != -inf)
                cmax(subsz[nt], subsz[u] + val[nt]);
            deg[nt]--;
            if (!deg[nt]) q.push(nt);
        }
    }
}

int main()
{
    n = rd; m = rd;
    for (int i = 1; i <= m; ++i) {
        int u = rd, v = rd;
        add(u, v);
    }
    for (int i = 1; i <= n; ++i)
        if (!dfn[i]) tarjan(i);
    for (int i = 1; i <= m; ++i) {
        int u = e[i].fr, v = e[i].to;
        u = c[u], v = c[v];
        if (u == v) continue;
        Add(u, v);
        deg[v]++;
    }
    memset(vis, 0, sizeof(vis));
    for (int i = 1; i <= col; ++i) subsz[i] = -inf;
    dfs(c[1]);
    Topsort();
    bvis[c[1]] = 1;
    upsz[c[1]] = val[c[1]];
    for (int i = 1; i <= col; ++i) 
        if (!vis[i]) dfs2(i);
    int ans = val[c[1]];
    for (int i = 1; i <= m; ++i) {
        int u = e[i].fr, v = e[i].to;
        u = c[u]; v = c[v];
        if (u == v) continue;
        if (!vis[v] || !(bvis[u] == 1)) continue;
        cmax(ans, subsz[v] + upsz[u] - val[c[1]]);
    }
    printf("%d
", ans);
}