HDU 3452 Bonsai

题意：给出一颗树和树根，每条树边都有边权，要你砍断一些边，使得所有的叶子节点都与根节点分离，且要求砍断的边权之和最小。

以树根root为源点S，添加一个汇点T，对所有的非跟叶子节点i，加边(i,T,inf)，求最小割即可。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define INF 1<<30
#define maxn 1010
#define maxm 10000
using namespace std;

int u[maxm],v[maxm],next[maxm],w[maxm];
int first[maxn],d[maxn],work[maxn],q[maxn],vis[maxn];
int e,S,T;
int degree[maxn];

void init(){
    e = 0;
    memset(first,-1,sizeof(first));
}

void add_edge(int a,int b,int c){
    u[e] = a;v[e] = b;next[e] = first[a];w[e] = c;first[a] = e++;
    u[e] = b;v[e] = a;next[e] = first[b];w[e] = 0;first[b] = e++;
}

int bfs(){
    int rear = 0;
    memset(d,-1,sizeof(d));
    d[S] = 0;q[rear++] = S;
    for(int i = 0;i < rear;i++){
        for(int j = first[q[i]];j != -1;j = next[j])
            if(w[j] && d[v[j]] == -1){
                d[v[j]] = d[q[i]] + 1;
                q[rear++] = v[j];
                if(v[j] == T)   return 1;
            }
    }
    return 0;
}

int dfs(int cur,int a){
    if(cur == T)    return a;
    for(int &i = work[cur];i != -1;i = next[i]){
        if(w[i] && d[v[i]] == d[cur] + 1)
            if(int t = dfs(v[i],min(a,w[i]))){
                w[i] -= t;w[i^1] += t;
                return t;
            }
    }
    return 0;
}

int dinic(){
    int ans = 0;
    while(bfs()){
        memcpy(work,first,sizeof(first));
        while(int t = dfs(S,INF))   ans += t;
    }
    return ans;
}

int main()
{
    int n,root;
    while(scanf("%d%d",&n,&root) == 2){
        if(!n && !root) break;
        memset(degree,0,sizeof(degree));
        S = root,T = n+1;
        init();
        for(int i = 0;i < n-1;i++){
            int a,b,c;
            scanf("%d%d%d",&a,&b,&c);
            add_edge(a,b,c);
            add_edge(b,a,c);
            degree[a]++;degree[b]++;
        }
        for(int i = 1;i <= n;i++){
            if(degree[i] == 1 && i != root)
                add_edge(i,T,INF);
        }
        printf("%d
",dinic());
    }
    return 0;
}