校园网(Network of Schools) 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 <algorithm>
using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    if (!(cin >> n)) return 0;
    vector<vector<int>> adj(n + 1);
    for (int i = 1; i <= n; ++i) {
        int x;
        while (cin >> x && x != 0) {
            adj[i].push_back(x);
        }
    }
    vector<int> dfn(n + 1, 0), low(n + 1, 0), in_stk(n + 1, 0), scc(n + 1, 0);
    vector<int> stk, call_u, call_idx;
    int timer = 0, scc_cnt = 0;
    for (int i = 1; i <= n; ++i) {
        if (!dfn[i]) {
            call_u.push_back(i);
            call_idx.push_back(0);
            dfn[i] = low[i] = ++timer;
            stk.push_back(i);
            in_stk[i] = 1;
            while (!call_u.empty()) {
                int u = call_u.back();
                int& idx = call_idx.back();
                if (idx < (int)adj[u].size()) {
                    int v = adj[u][idx++];
                    if (!dfn[v]) {
                        dfn[v] = low[v] = ++timer;
                        stk.push_back(v);
                        in_stk[v] = 1;
                        call_u.push_back(v);
                        call_idx.push_back(0);
                    } else if (in_stk[v]) {
                        low[u] = min(low[u], dfn[v]);
                    }
                } else {
                    if (low[u] == dfn[u]) {
                        ++scc_cnt;
                        while (true) {
                            int x = stk.back();
                            stk.pop_back();
                            in_stk[x] = 0;
                            scc[x] = scc_cnt;
                            if (x == u) break;
                        }
                    }
                    call_u.pop_back();
                    call_idx.pop_back();
                    if (!call_u.empty()) {
                        low[call_u.back()] = min(low[call_u.back()], low[u]);
                    }
                }
            }
        }
    }
    vector<int> indeg(scc_cnt + 1, 0), outdeg(scc_cnt + 1, 0);
    for (int u = 1; u <= n; ++u) {
        for (int v : adj[u]) {
            if (scc[u] != scc[v]) {
                outdeg[scc[u]]++;
                indeg[scc[v]]++;
            }
        }
    }
    int in0 = 0, out0 = 0;
    for (int i = 1; i <= scc_cnt; ++i) {
        if (indeg[i] == 0) in0++;
        if (outdeg[i] == 0) out0++;
    }
    cout << in0 << "\n";
    cout << (scc_cnt == 1 ? 0 : max(in0, out0)) << "\n";
    return 0;
}