Uva10480_Sabotage(最小割)

题意：

给定n和m，n表示点的数量，m表示边的数量。
再给m条边（u，v，w）。w表示割该边的花费。注意是无向图，反向边的容量与正向边一致。将结点1看作源点，结点2看作汇点，求一组最小割边集。

思路：

跑最大流。跑完的残余网络中，将源点S能到达的点看作S集，其他点看作T集。如果边的一个点属于S集，另一个点属于T集，那么该边属于最小割边集。

#include 
#include 
#include 
typedef long long LL;
const int INF = 0x3f3f3f3f;
const int maxn = 50+5;
const int maxm = 500 + 50;
using namespace std;

int n,m;

// 图 
struct Edge{
    int v, cap, flow, next;
};
Edge edges[maxm*2];
int head[maxn], cnt;

int dis[maxn];    // 分层的编号 
int cur[maxn]; // 当前弧，重要优化！！！ 

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

void addEdge(int u, int v, int cap){
    edges[cnt].v = v; edges[cnt].cap = cap; edges[cnt].flow = 0;
	edges[cnt].next = head[u]; head[u] = cnt++;
	// 反向弧
	edges[cnt].v = u; edges[cnt].cap = cap; edges[cnt].flow = 0;
	edges[cnt].next = head[v]; head[v] = cnt++;
}

// 分层 
int Q[maxn];		// 模拟队列 
bool bfs(int s, int t){
	memset(dis, -1, sizeof(dis));
	dis[s] = 0;
	int front = 0, rear = 0;
	Q[rear++] = s;
	while(front < rear){
		int x = Q[front++];
		if(x == t) return true;
		for(int i = head[x]; i != -1; i = edges[i].next){
			Edge& e = edges[i];
			if(dis[e.v] == -1&&e.cap > e.flow){
				dis[e.v] = dis[x] + 1;
				Q[rear++] = e.v;
			}
		}
	}
	return dis[t] != -1;
}

int dfs(int s, int t, int cur_flow){
    if(s == t||cur_flow == 0) return cur_flow;
    int ans = 0;
    for(int& i = cur[s]; i != -1; i = edges[i].next){
        int c = i;
        Edge e = edges[c];
        if(dis[e.v] == dis[s] + 1&&e.cap > e.flow){
            int a2 = min(cur_flow, e.cap-e.flow);
            int w = dfs(e.v, t, a2);
            edges[c].flow += w;
            edges[c^1].flow -= w; 
            cur_flow -= w;
            ans += w;
            if(cur_flow <= 0) break;
        }
    }
    return ans;
}

// 最大流 
int Dinic(int s, int t){
    int ans = 0;
    while(bfs(s,t)){
        memcpy(cur, head, sizeof(head));
        ans += dfs(s,t,INF);
    }
    return ans;    
}

int vis[maxn];
void find_S(int u){
	vis[u] = 1;
	for(int i = head[u]; i != -1; i = edges[i].next){
		int v = edges[i].v;
		if(vis[v] || edges[i].cap == edges[i].flow) continue;
		find_S(v);
	}
}

int x[maxm], y[maxm];

int main()
{
    //freopen("in.txt","r",stdin);

	while(scanf("%d%d",&n,&m) == 2){
		if(n == 0&&m == 0) break;
		init();
		//for(int i = 1; i <= n; ++i) addEdge(i, i+n, 1);
		for(int i = 0; i < m; ++i){
			int c; scanf("%d%d%d",&x[i],&y[i],&c);
			addEdge(x[i], y[i],c);
		}
		LL c;
		int s = 1, t = 2;
		
		Dinic(s, t);
		
		memset(vis, 0, sizeof(vis));
		find_S(s);
		for(int i = 0; i < m; ++i){
			int u = x[i], v = y[i];
			if((!vis[u]&&vis[v]) || (vis[u]&&!vis[v])) printf("%d %d\n",u,v);
		}printf("\n");
	}
    fclose(stdin);
	return 0;
}