题意:给出一张有向图,要求你将这些点进行划分,划分依据如下
1.如果两个点互相可达,那么这两个点必须在同一个集合中;
2.同一个集合中的两个点u,v要满足要么u->v || v->u;
3.一个点只能被划分到同一个集合;
问最少能划分成几个集合
思路:对于条件一就是强联通分量;对于条件2,3得话就要球出来最小路径覆盖,所以可以将所有的强联通分量进行缩点,桥作为连接,然后匈牙利一下,求出最大匹配数目,最后的结果就是强联通分量数- 最大匹配数;
/***************************************** Author :Crazy_AC(JamesQi) Time :2015 File Name : *****************************************/ // #pragma comment(linker, "/STACK:1024000000,1024000000") #include <iostream> #include <algorithm> #include <iomanip> #include <sstream> #include <string> #include <stack> #include <queue> #include <deque> #include <vector> #include <map> #include <set> #include <stdio.h> #include <string.h> #include <math.h> #include <stdlib.h> #include <limits.h> using namespace std; #define MEM(a,b) memset(a,b,sizeof a) #define pk push_back template<class T> inline T Get_Max(const T&a,const T&b){return a < b?b:a;} template<class T> inline T Get_Min(const T&a,const T&b){return a < b?a:b;} typedef long long ll; typedef pair<int,int> ii; const int inf = 1 << 30; const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; struct Edge{ int to,nxt; }E[100010]; struct node{ int x,y; }node[100010]; int head[5010],sccno[5010],pre[5010],lowlink[5010],st[5010],link[5010]; int n,m,tot,scc_tot,dfs_clock,top; bool vis[5010]; void Addedge(int u,int v){ E[tot].to = v; E[tot].nxt = head[u]; head[u] = tot++; } void Init(){ scanf("%d%d",&n,&m); MEM(head, -1); tot = 0; for (int i = 1;i <= m;i++){ scanf("%d%d",&node[i].x,&node[i].y); Addedge(node[i].x,node[i].y); } } void DFS(int u){ pre[u] = lowlink[u] = ++dfs_clock; st[++top] = u; for (int i = head[u];i != -1;i = E[i].nxt){ int v = E[i].to; if (!pre[v]){ DFS(v); lowlink[u] = Get_Min(lowlink[v],lowlink[u]); } else if (!sccno[v]){ lowlink[u] = Get_Min(lowlink[u],pre[v]); } } int x; if (lowlink[u] == pre[u]){ ++scc_tot; while(true){ x = st[top--]; sccno[x] = scc_tot; if (x == u) break; } } } bool dfs2(int u){ for (int i = head[u];i != -1;i = E[i].nxt){ int v = E[i].to; if (!vis[v]){ vis[v] = true; if (link[v] == -1 || dfs2(link[v])){ link[v] = u; return true; } } } return false; } void solve(){ MEM(pre, 0); MEM(sccno, 0); scc_tot = top = dfs_clock = 0; for (int i = 1;i <= n;i++){ if (!pre[i]) DFS(i); } MEM(head, -1); tot = 0; int u,v; for (int i = 1;i <= m;i++){ u = sccno[node[i].x]; v = sccno[node[i].y]; if (u != v) Addedge(u,v);//去掉自环; } int ans = 0; MEM(link, -1); for (int i = 1;i <= scc_tot;i++){ MEM(vis, false); if (dfs2(i)) ans++; } printf("%d\n",scc_tot - ans); } int main() { // ios::sync_with_stdio(false); // freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); int test; scanf("%d",&test); while(test--){ Init(); solve(); } return 0; }