UvaLive 4287 Proving Equivalences 强连通缩点
原题链接:https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2288
题意:
给你一个有向图,问你至少需要添加多少条边,使得整个图强连通。
题解:
就。。直接缩点,令缩点后入度为0的点有a个,出度为0的点有b个,答案就是max(a,b)
代码:
#include<iostream> #include<cstring> #include<vector> #include<algorithm> #include<stack> #define MAX_N 20004 using namespace std; vector<int> G[MAX_N]; int dfn[MAX_N],low[MAX_N],ind; bool vis[MAX_N]; stack<int> st; bool inStack[MAX_N]; int id[MAX_N],tot=0; vector<int> newG[MAX_N]; vector<int> newrG[MAX_N]; int n,m; void init() { for (int i = 0; i <= n; i++) { G[i].clear(); newG[i].clear(); newrG[i].clear(); } memset(dfn, 0, sizeof(dfn)); memset(low, 0, sizeof(low)); ind = tot = 0; memset(vis, 0, sizeof(vis)); while (st.size())st.pop(); memset(inStack, 0, sizeof(inStack)); memset(id, 0, sizeof(id)); } void Tarjan(int u) { dfn[u] = low[u] = ++ind; st.push(u); inStack[u] = 1; vis[u] = 1; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (!vis[v]) { Tarjan(v); low[u] = min(low[u], low[v]); } else if (inStack[v]) low[u] = min(low[u], dfn[v]); } if (low[u] == dfn[u]) { tot++; int t; do { t = st.top(); st.pop(); inStack[t] = 0; id[t] = tot; } while (t != u); } } int main() { int T; cin.sync_with_stdio(false); cin >> T; while (T--) { cin >> n >> m; int ans = 0; init(); for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; G[u].push_back(v); } for (int i = 1; i <= n; i++) if (!vis[i])Tarjan(i); for (int u = 1; u <= n; u++) for (int i = 0; i < G[u].size(); i++) if (id[u] != id[G[u][i]]) { newG[id[u]].push_back(id[G[u][i]]); newrG[id[G[u][i]]].push_back(id[u]); } if (tot == 1) { cout << 0 << endl; continue; } int a = 0, b = 0; for (int u = 1; u <= tot; u++) { if (newG[u].size() == 0)a++; if (newrG[u].size() == 0)b++; } cout << max(a, b) << endl; } return 0; }