【网络流24题 #03】最小路径覆盖问题

题目链接：最小路径覆盖问题

哇 卡在输出也是醉了

重要结论：最小路径覆盖数 = 结点数（拆成边之前） -  最大流

本题也是点拆边

与【网络流24题 #04】魔术球问题 

有异曲同工之妙

void output(int x){
    if(x >= S) return ;
    printf("%d ", x >> 1);
    for(int i = head[x]; i != -1; i = edge[i].next)
        if(!edge[i].w && edge[i].v < S) output(edge[i].v - 1);
}   

……


 for(int i = 1; i <= n; i++) fa[i] = i;
    for(int i = 0; i <= esize; i += 2) {
        if(!edge[i].w && edge[i].v < S && edge[i].u < S){
            fa[find(edge[i].v >> 1)] = find(edge[i].u >> 1);        
        }
    }
    for(int i = 1; i <= n; i++){
        if(find(i) == i){
            output(i << 1);
            printf("
");
        }

内心戏：(╯‵□′)╯︵┻━┻

悄咪咪：居然还打扰H神吃饭…

#include <cstdio>
#include <algorithm>
#include <queue>
#include <cstring>
#include <cmath>
using namespace std;
const int N = 4e4 + 5;
const int inf = 0x3f3f3f3f;
int n, m;
struct Edge{
    int u, v, w, next;
}edge[N << 1];
int head[N], esize = -1;
bool vis[N];
int next[N], fa[N];
inline void addedge(int x, int y, int z){
    edge[++esize] = (Edge){x, y, z, head[x]};
    head[x] = esize;
    edge[++esize] = (Edge){y, x, 0, head[y]};
    head[y] = esize;
}
queue<int> q;
int dep[N];
int S, T;

bool bfs(){
    int fro;
    q.push(S); 
    memset(dep, 0, sizeof(dep));
    dep[S] = 1;
    while(!q.empty()){
        fro = q.front(); q.pop();
        for(int i = head[fro]; i != -1; i = edge[i].next){
            int vv = edge[i].v;
            if(!dep[vv] && edge[i].w > 0){
                dep[vv] = dep[fro] + 1;
                q.push(vv);
            }
        }
    }
    return dep[T];
}

int dfs(int x, int rest){
    if(x == T || !rest) return rest;
    for(int i = head[x], vv, ww, d; i != -1; i = edge[i].next){
        vv = edge[i].v, ww = edge[i].w;
        if(dep[vv] != dep[x] + 1) continue;
        d = dfs(vv, min(rest, ww));
        if(d > 0){
            edge[i].w -= d;
            edge[i ^ 1].w += d;
            return d;
        }
    }
    return 0;
}

int dinic(){
    int ret = 0;
    while(bfs()){
        ret += dfs(S, inf);
    }
    return ret;
}

int find(int x){
    return x == fa[x] ? x : fa[x] = find(fa[x]);
}

void output(int x){
    if(x >= S) return ;
    printf("%d ", x >> 1);
    for(int i = head[x]; i != -1; i = edge[i].next)
        if(!edge[i].w && edge[i].v < S) output(edge[i].v - 1);
}

int main(){
    scanf("%d%d", &n, &m);
    memset(head, -1, sizeof(head));
    memset(next, -1, sizeof(next));
    S = N - 3, T = N - 2;
    for(int i = 1; i <= n; i++){
        addedge(S, i << 1, 1);
        addedge(i << 1 | 1, T, 1);
    }
    for(int i = 1, x, y; i <= m; i++){
        addedge(x << 1, y << 1 | 1, 1);
    }
    int cnt = n - dinic();
    for(int i = 1; i <= n; i++) fa[i] = i;
    for(int i = 0; i <= esize; i += 2) {
        if(!edge[i].w && edge[i].v < S && edge[i].u < S){
            fa[find(edge[i].v >> 1)] = find(edge[i].u >> 1);
        }
    }
    for(int i = 1; i <= n; i++){
        if(find(i) == i){
            output(i << 1);
            printf("
");
        }
    }
    printf("%d", cnt);
    return 0;
}