/* 很经典的最大流最小割的题目 题意:求最小割,但因为最小割是不唯一的,题目要求得到最小割的条件下使得割边最少 搜到usaco类似的一个题目才出的,构造很巧妙 建边的时候每条边权 w=w*(E+1)+1; 这样得到最大流maxflow/(E+1) 就是答案了 道理很简单,如果原先两类割边都是最小割,那么求出的最大流相等 但边权变换后只有边数小的才是最小割了,至于为什么乘的是(E+1)是为了保证边数叠加后依然是余数,不至于影响求最小割的结果 */ #include <cstdio> #include <iostream> #include <memory.h> #include<queue> using namespace std; const int maxn=1009; const __int64 inf=(1LL)<<60; typedef __int64 LL; //************************************************** //为dinic求最大流模版 struct edge { int v, next; LL val; } net[ 500010 ]; int n,m; int level[maxn], Qu[maxn], out[maxn],next[maxn]; class Dinic { public: int end; Dinic() { end = 0; memset( next, -1, sizeof(next) ); } inline void insert( int x, int y, LL c) { net[end].v = y, net[end].val = c, net[end].next = next[x], next[x] = end ++; net[end].v = x, net[end].val = 0, net[end].next = next[y], next[y] = end ++; } bool BFS( int S, int E ) { memset( level, -1, sizeof(level) ); int low = 0, high = 1; Qu[0] = S, level[S] = 0; for( ; low < high; ) { int x = Qu[low]; for( int i = next[x]; i != -1; i = net[i].next ) { if( net[i].val == 0 ) continue; int y = net[i].v; if( level[y] == -1 ) { level[y] = level[x] + 1; Qu[ high ++] = y; } } low ++; } return level[E] != -1; } LL MaxFlow( int S, int E ){ LL maxflow = 0; for( ; BFS(S, E) ; ) { memcpy( out, next, sizeof(out) ); int now = -1; for( ;; ) { if( now < 0 ) { int cur = out[S]; for(; cur != -1 ; cur = net[cur].next ) if( net[cur].val && out[net[cur].v] != -1 && level[net[cur].v] == 1 ) break; if( cur >= 0 ) Qu[ ++now ] = cur, out[S] = net[cur].next; else break; } int u = net[ Qu[now] ].v; if( u == E ) { LL flow = inf; int index = -1; for( int i = 0; i <= now; i ++ ) { if( flow > net[ Qu[i] ].val ) flow = net[ Qu[i] ].val, index = i; } maxflow += flow; for( int i = 0; i <= now; i ++ ) net[Qu[i]].val -= flow, net[Qu[i]^1].val += flow; for( int i = 0; i <= now; i ++ ) { if( net[ Qu[i] ].val == 0 ) { now = index - 1; break; } } } else{ int cur = out[u]; for(; cur != -1; cur = net[cur].next ) if (net[cur].val && out[net[cur].v] != -1 && level[u] + 1 == level[net[cur].v]) break; if( cur != -1 ) Qu[++ now] = cur, out[u] = net[cur].next; else out[u] = -1, now --; } } } return maxflow; } }; int main() { int ca,t,u,v; LL w; scanf("%d",&ca); for(int k=1;k<=ca;k++) { Dinic my; scanf("%d%d",&n,&m); while(m--) { scanf("%d%d%I64d%d",&u,&v,&w,&t); my.insert(u,v,w*100001+1); if(t==1) { my.insert(v,u,w*100001+1); } } LL ans=my.MaxFlow(0,n-1); //cout<<ans<<endl; printf("Case %d: %I64d\n",k,(ans%100001)); } return 0; }