SPOJ 839 Optimal Marks（巧妙构造-最小割）
题意：http://www.spoj.com/problems/OPTM/
题意：给出一个图，每个点有一个权值p(i)，对于一条边(u,v)，权值为p(u)^p(v)。现在给出一些点的权值，确定另一些点的权值使得边权和最小？
思路：对于权值的每一位，则每个点的权值为0或者1，将S和权值为1的连边INF，权值为0的和T连边INF，每个边连双向边权值1，跑最大流，从S开始DFS，则在S集合中的点为1。
#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <map>
#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define abs(x) ((x)>=0?(x):-(x))
#define i64 long long
#define u32 unsigned int
#define u64 unsigned long long
#define clr(x,y) memset(x,y,sizeof(x))
#define CLR(x) x.clear()
#define ph(x) push(x)
#define pb(x) push_back(x)
#define Len(x) x.length()
#define SZ(x) x.size()
#define PI acos(-1.0)
#define sqr(x) ((x)*(x))
#define MP(x,y) make_pair(x,y)
#define EPS 1e-9
#define FOR0(i,x) for(i=0;i<x;i++)
#define FOR1(i,x) for(i=1;i<=x;i++)
#define FOR(i,a,b) for(i=a;i<=b;i++)
#define FORL0(i,a) for(i=a;i>=0;i--)
#define FORL1(i,a) for(i=a;i>=1;i--)
#define FORL(i,a,b)for(i=a;i>=b;i--)
using namespace std;
void RD(int &x){scanf("%d",&x);}
void RD(u32 &x){scanf("%u",&x);}
void RD(double &x){scanf("%lf",&x);}
void RD(int &x,int &y){scanf("%d%d",&x,&y);}
void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}
void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}
void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}
void RD(int &x,int &y,int &z,int &t){scanf("%d%d%d%d",&x,&y,&z,&t);}
void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}
void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}
void RD(char &x){x=getchar();}
void RD(char *s){scanf("%s",s);}
void RD(string &s){cin>>s;}
void PR(int x) {printf("%d\n",x);}
void PR(int x,int y) {printf("%d %d\n",x,y);}
void PR(i64 x) {printf("%lld\n",x);}
void PR(u32 x) {printf("%u\n",x);}
void PR(double x) {printf("%.5lf\n",x);}
void PR(char x) {printf("%c\n",x);}
void PR(char *x) {printf("%s\n",x);}
void PR(string x) {cout<<x<<endl;}
const int INF=1000000000;
const int N=100005;
struct Node
{
int v,cap,flow,next;
};
Node edges[N];
int n,m,s,t,head[N],e;
int num[N],h[N],curedge[N],pre[N];
void add(int u,int v,int cap)
{
edges[e].v=v;
edges[e].cap=cap;
edges[e].flow=0;
edges[e].next=head[u];
head[u]=e++;
}
void Add(int u,int v,int cap)
{
add(u,v,cap);
add(v,u,0);
}
int Maxflow(int s,int t,int n)
{
int ans=0,i,k,x,d,u;
memset(num,0,sizeof(num));
memset(h,0,sizeof(h));
for(i=0;i<=n;i++) curedge[i]=head[i];
num[n]=n;u=s;
while(h[u]<n)
{
if(u==t)
{
d=INF+1;
for(i=s;i!=t;i=edges[curedge[i]].v) if(d>edges[curedge[i]].cap)
k=i,d=edges[curedge[i]].cap;
for(i=s;i!=t;i=edges[curedge[i]].v)
{
x=curedge[i];
edges[x].cap-=d;
edges[x].flow+=d;
edges[x^1].cap+=d;
edges[x^1].flow-=d;
}
ans+=d;u=k;
}
for(i=curedge[u];i!=-1;i=edges[i].next) if(edges[i].cap>0&&h[u]==h[edges[i].v]+1)
break;
if(i!=-1)
{
curedge[u]=i;
pre[edges[i].v]=u;
u=edges[i].v;
}
else
{
if(--num[h[u]]==0) break;
curedge[u]=head[u];
for(x=n,i=head[u];i!=-1;i=edges[i].next) if(edges[i].cap>0&&h[edges[i].v]<x)
x=h[edges[i].v];
h[u]=x+1;num[h[u]]++;
if(u!=s) u=pre[u];
}
}
return ans;
}
struct node
{
int u,v;
void input() {RD(u,v);}
};
node a[3005];
int w[505],maxL,K,ans[505],visit[505];
void DFS(int u)
{
visit[u]=1;
int i;
for(i=head[u];i!=-1;i=edges[i].next)
{
if(!visit[edges[i].v]&&edges[i].cap>0)
{
DFS(edges[i].v);
}
}
}
void deal()
{
clr(ans,0);
int i,j;
FOR0(i,maxL)
{
s=0,t=n+1;
clr(head,-1); e=0;
FOR1(j,n) if(w[j]!=-1)
{
if(w[j]&(1<<i)) Add(s,j,INF);
else Add(j,t,INF);
}
FOR1(j,m) Add(a[j].u,a[j].v,1),Add(a[j].v,a[j].u,1);
Maxflow(s,t,t+1); clr(visit,0); DFS(s);
FOR1(j,n) if(visit[j]) ans[j]+=(1<<i);
}
FOR1(i,n) PR(ans[i]);
}
int main()
{
int C;
RD(C);
while(C--)
{
RD(n,m);
int i,u,t;
FOR1(i,m) a[i].input();
clr(w,-1);t=0; RD(K);
FOR1(i,K) RD(u),RD(w[u]),t=max(t,w[u]);
maxL=0;
while(t) maxL++,t>>=1;
if(maxL==0) maxL++;
deal();
}
return 0;
}