P2764 最小路径覆盖问题 (最小点覆盖=顶点数-最大匹配)

题意:最小路径覆盖

题解:对于一个有向图,最小点覆盖 = 顶点数 - 最大匹配

　　 这里的最大匹配指的是将原图中每一个点拆成入点、出点, 每条边连接起点的出点和终点的入点

　　 源点S连接每个点的出点,汇点T连接每个点的入点,这样建出来的二分图的最大匹配

　　 然后输出路径被坑了很久 因为自己拆点的标号问题吧

　　 我的拆点方式入点是偶数 出点是奇数 然后特判哪里就要写清楚

 

#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
int n, m, s, t, cnt, maxflow;

struct node {
    int to, nex, val;
}E[20005];
int head[305];
int cur[305];

void addedge(int x, int y, int va) {
    E[++cnt].to = y; E[cnt].nex = head[x]; head[x] = cnt; E[cnt].val = va;
    E[++cnt].to = x; E[cnt].nex = head[y]; head[y] = cnt; E[cnt].val = 0;
}

int inque[305];
int dep[305];
int to[305];
bool bfs() {
    for(int i = 0; i <= n * 2 + 1; i++) cur[i] = head[i], inque[i] = 0, dep[i] = INF;
    queue<int> que;
    dep[s] = 0; inque[s] = 1;
    que.push(s);

    while(!que.empty()) {
        int u = que.front();
        que.pop();
        inque[u] = 0;

        for(int i = head[u]; i; i = E[i].nex) {
            int v = E[i].to;
            if(E[i].val > 0 && dep[v] > dep[u] + 1) {
                dep[v] = dep[u] + 1;
                if(!inque[v]) {
                    inque[v] = 1;
                    que.push(v);
                }
            }
        }
    }
    if(dep[t] != INF) return true;
    return false;
}

int vis;
int viss[155];
int dfs(int x, int flow) {
    if(x == t) {
        vis = 1;
        maxflow += flow;
        return flow;
    }

    int used = 0;
    int rflow = 0;
    for(int i = cur[x]; i; i = E[i].nex) {
        cur[x] = i;
        int v = E[i].to;
        if(E[i].val > 0 && dep[v] == dep[x] + 1) {
            if(rflow = dfs(v, min(flow - used, E[i].val))) {
                if(v != t && x != s && (x % 2 == 0) && (v % 2 == 1)) to[x / 2] = v / 2, viss[v / 2] = 1;
                used += rflow;
                E[i].val -= rflow;
                E[i ^ 1].val += rflow;
                if(used == flow) break;
            }
        }
    }
    return used;
}

void dinic() {
    maxflow = 0;
    while(bfs()) {
        vis = 1;
        while(vis) {
            vis = 0;
            dfs(s, INF);
        }
    }
}

int main() {
    scanf("%d%d", &n, &m);
    s = 0, t = 1;
    cnt = 1;
    for(int i = 1; i <= n; i++) {
        addedge(s, i << 1, 1);
        addedge(i << 1 | 1, t, 1);
    }

    for(int i = 1; i <= m; i++) {
        int a, b;
        scanf("%d%d", &a, &b);
        addedge(a << 1, b << 1 | 1, INF);
    }
    dinic();
    int ans = n - maxflow;
    for(int i = 1; i <= n; i++) {
        if(!viss[i]) {
            printf("%d", i);
            for(int j = to[i]; j; j = to[j]) printf(" %d", j);
            puts("");
        }
    }
    printf("%d\n", ans);
    return 0;
}