The King’s Problem

1
3 2
1 2
1 3

2

2、一个州内的两点至少要有一方能到达还有一方。3、一个点仅仅能划分到一个州内。问他至少要建多少州

思路：先把能相互两两到达的点用强连通归为一个州，然后再进行缩点。建立新图。然后用匈牙利算法求出最大匹配，答案=强连通求出的联通块-最大匹配（最小路径覆盖=结点数-最大匹配）。

#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
#include <queue>
#define maxn 50000+100
#define maxm 200000+100
using namespace std;
int n, m;

struct node {
    int u, v, next;
};

node edge[maxm];
int head[maxn], cnt;
int low[maxn], dfn[maxn];
int dfs_clock;
int Stack[maxn], top;
bool Instack[maxn];
int Belong[maxn];
int scc_clock;
vector<int>Map[maxn];

void init(){
    cnt = 0;
    memset(head, -1, sizeof(head));
}

void addedge(int u, int v){
    edge[cnt] = {u, v, head[u]};
    head[u] = cnt++;
}

void getmap(){
    scanf("%d%d", &n, &m);
    while(m--){
        int a, b;
        scanf("%d%d", &a, &b);
        addedge(a, b);
    }
}

void Tarjan(int u, int per){
    int v;
    low[u] = dfn[u] = ++dfs_clock;
    Stack[top++] = u;
    Instack[u] = true;
    for(int i = head[u]; i != -1; i = edge[i].next){
        int v = edge[i].v;
        if(!dfn[v]){
            Tarjan(v, u);
            low[u] = min(low[u], low[v]);
        }
        else if(Instack[v])
            low[u] = min(low[u], dfn[v]);
    }
    if(dfn[u] == low[u]){
        scc_clock++;
        do{
            v = Stack[--top];
            Instack[v] = false;
            Belong[v] = scc_clock;
        }
        while( v != u);
    }
}

void find(){
    memset(low, 0, sizeof(low));
    memset(dfn, 0, sizeof(dfn));
    memset(Belong, 0, sizeof(Belong));
    memset(Stack, 0, sizeof(Stack));
    memset(Instack, false, sizeof(false));
    dfs_clock = scc_clock = top = 0;
    for(int i = 1; i <= n ; ++i){
        if(!dfn[i])
            Tarjan(i, i);
    }
}

void suodian(){
    for(int i = 1; i <= scc_clock; ++i)
        Map[i].clear();
    for(int i = 0; i < cnt; ++i){
        int u = Belong[edge[i].u];
        int v = Belong[edge[i].v];
        if(u != v){
            Map[u].push_back(v);
        }
    }
}

int used[maxn], link[maxn];

bool dfs(int x){
    for(int i = 0; i < Map[x].size(); ++i){
        int y = Map[x][i];
        if(!used[y]){
            used[y] = 1;
            if(link[y] == -1 || dfs(link[y])){
                link[y] = x;
                return true;
            }
        }
    }
    return false;
}

void hungary(){
    int ans = 0;
    memset(link, -1, sizeof(link));
    for(int j = 1; j <= scc_clock; ++j){
        memset(used, 0, sizeof(used));
        if(dfs(j))
            ans++;
    }
    printf("%d\n", scc_clock - ans);
}

int main (){
    int T;
    scanf("%d", &T);
    while(T--){
        init();
        getmap();
        find();
        suodian();
        hungary();
    }
    return 0;
}