题意就是一个组织要杀人,道路是单向的,一个杀人者可以沿着某条路把所经过的点上的人全部杀完,点是可以重复经过的。
问最少需要几个杀人者可以把所有的n个点上的人杀完。。。
这题的难点在于点可以重复经过,而且图中含有环。。。。。
环其实容易想到缩点,,,只是点重复经过怎么处理,因为要用二分图的性质的话,里面的边石不能重复的,所以这里的处理就是添加边进去,如果原图中u到v是可达的,那么u到v就新建一条边。。。。
这样以来就可以用二分图的性质了。。。。
/***************************************** 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 <cstdio> #include <cstring> #include <cmath> #include <cstdlib> #include <climits> using namespace std; #define MEM(x,y) memset(x, y,sizeof x) #define pk push_back typedef long long LL; typedef unsigned long long ULL; typedef pair<int,int> ii; typedef pair<ii,int> iii; const double eps = 1e-10; const int inf = 1 << 30; const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; /**********************Point*****************************/ struct Point{ double x,y; Point(double x=0,double y=0):x(x),y(y){} }; typedef Point Vector; Vector operator + (Vector A,Vector B){ return Vector(A.x + B.x,A.y + B.y); } Vector operator - (Vector A,Vector B){//向量减法 return Vector(A.x - B.x,A.y - B.y); } Vector operator * (Vector A,double p){//向量数乘 return Vector(A.x * p,A.y * p); } Vector operator / (Vector A,double p){//向量除实数 return Vector(A.x / p,A.y / p); } int dcmp(double x){//精度正负、0的判断 if (fabs(x) < eps) return 0; return x < 0?-1:1; } bool operator < (const Point& A,const Point& B){//小于符号的重载 return A.x < B.x || (A.x == B.x && A.y < B.y); } bool operator == (const Point& A,const Point& B){//点重的判断 return dcmp(A.x - B.x) == 0&& dcmp(A.y - B.y) == 0; } double Dot(Vector A,Vector B){//向量的点乘 return A.x * B.x + A.y * B.y; } double Length(Vector A){//向量的模 return sqrt(Dot(A,A)); } double Angle(Vector A,Vector B){//向量的夹角 return acos(Dot(A,B) / Length(A) / Length(B)); } double Cross(Vector A,Vector B){//向量的叉积 return A.x * B.y - A.y * B.x; } double Area2(Point A,Point B,Point C){//三角形面积 return Cross(B - A,C - A); } Vector Rotate(Vector A,double rad){//向量的旋转 return Vector(A.x * cos(rad) - A.y * sin(rad),A.x * sin(rad) + A.y * cos(rad)); } Vector Normal(Vector A){//法向量 int L = Length(A); return Vector(-A.y / L,A.x / L); } double DistanceToLine(Point p,Point A,Point B){//p到直线AB的距离 Vector v1 = B - A,v2 = p - A; return fabs(Cross(v1,v2)) / Length(v1); } double DistanceToSegment(Point p,Point A,Point B){//p到线段AB的距离 if (A == B) return Length(p - A); Vector v1 = B - A, v2 = p - A,v3 = p - B; if (dcmp(Dot(v1,v2) < 0)) return Length(v2); else if (dcmp(Dot(v1,v3)) > 0) return Length(v3); else return DistanceToLine(p,A,B); } bool SegmentProperIntersection(Point A1,Point A2,Point B1,Point B2){//线段相交 double c1 = Cross(A2 - A1,B1 - A1),c2 = Cross(A2 - A1,B2 - A1); double c3 = Cross(B2 - B1,A1 - B1),c4 = Cross(B2 - B1,A2 - B1); return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0; } const int N = 1010; vector<int> G1[N], G2[N], G3[N];//原图,扩张图,缩点后的图。 bool vis[N]; int pre[N], low[N], Belong[N], scc_cnt, Times; int n, m; stack<int> st; void Tarjan(int u) { pre[u] = low[u] = ++Times; st.push(u); for (int i = 0;i < (int)G2[u].size();++i) { int v = G2[u][i]; if (!pre[v]) { Tarjan(v); low[u] = min(low[u], low[v]); }else if (!Belong[v]) low[u] = min(low[u], pre[v]); } if (pre[u] == low[u]) { scc_cnt++; while(true) { int x = st.top(); st.pop(); Belong[x] = scc_cnt; if (x == u) break; } } } void FindSCC() { memset(pre, 0,sizeof pre); memset(Belong, 0,sizeof Belong); Times = scc_cnt = 0; for (int i = 1;i <= n;++i) { if (!pre[i]) Tarjan(i); } } void BFS(int st) { queue<int> que; que.push(st); memset(vis, false,sizeof vis); vis[st] = true; while(!que.empty()) { int u = que.front(); que.pop(); for (int i = 0;i < G1[u].size();++i) { int v = G1[u][i]; if (vis[v]) continue; vis[v] = true; G2[st].push_back(v);//对原图进行这种扩展是不会形成可行环的。 que.push(v); } } } void Initation() { for (int i = 1;i <= n;++i) BFS(i); } void Input() { scanf("%d%d",&n,&m); for (int i = 1;i <= n;++i) G1[i].clear(),G2[i].clear(),G3[i].clear(); int u, v; for (int i = 1;i <= m;++i) { scanf("%d%d",&u,&v); G1[u].push_back(v); } } void Trans() { for (int u = 1;u <= n;++u) { for (int i = 0;i < G2[u].size();++i) { int v = G2[u][i]; if (Belong[u] != Belong[v]) G3[Belong[u]].push_back(Belong[v]); } } } int linker[N]; bool Search(int u) { for (int i = 0;i < G3[u].size();++i) { int v = G3[u][i]; if (vis[v]) continue; vis[v] = true; if (linker[v] == -1 || Search(linker[v])) { linker[v] = u; return true; } } return false; } int Hungary() { int ret = 0; memset(linker, -1,sizeof linker); for (int i = 1;i <= scc_cnt;++i) { memset(vis, false,sizeof vis); if (Search(i)) ret++; } return ret; } int main() { freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); int t, icase = 0; scanf("%d",&t); while(t--) { Input(); Initation(); FindSCC(); // printf("SCC = %d\n", scc_cnt); // for (int i = 1;i <= n;++i) // printf("%d ", Belong[i]); // puts(""); Trans(); // for (int i = 1;i <= n;++i) { // printf("<%d>::", i); // for (int j = 0;j < G2[i].size();++j) // printf("%d ", G2[i][j]); // puts(""); // } // for (int i = 1;i <= scc_cnt;++i) { // printf("i = %d::::", i); // for (int j = 0;j < G3[i].size();++j) // printf("%d ",G3[i][j]); // puts(""); // } printf("Case %d: %d\n", ++icase, scc_cnt - Hungary()); } return 0; }