soj 3254: Rain and Fgj 最小割

最新推荐文章于 2016-09-09 00:47:00 发布

原创最新推荐文章于 2016-09-09 00:47:00 发布 · 434 阅读

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#each #output #sap #input #go #struct

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本文探讨了一种利用最短路径与流量算法解决特定城市间旅行问题的方法。通过定义问题背景及输入输出要求，详细解释了如何使用增广路算法（SAP）来寻找最小破坏成本，使得从起始城市到目标城市无法到达。该问题涉及到图论中的网络流概念。

Description

There are N citys in RAIN's country.And there are M directed road between the N citys.Now she is in the city 0.And she want to go to city N-1.But the bad FGJ donot want RAIN go to city N-1.He can destroy some city to make it.RAIN cannot go to the city which be destroyed.Eeah city has a weight Wi to destroy.FGJ cannot destroy the city 0.Can you tell FGJ the minimal totle weight he must destroy?

Input

The first line of the input is the number of test cases.For each case there is M+1 lines.The first line contains two integers N M.The second line contains N-1 integers Wi ( 1 <= i < N ).The next M lines each contains two integers P and Q,represent there is a road from city P to city Q.( 2 <= N <= 1000 , 0 <= M <= 10^5 , 0 <= P,Q < N , 0 <= Wi <= 10^5 )There is a blank line before each test case.

Output

For each test case output the answer on a line:The minimal totle weight FGJ must destroy.

Sample Input

52 01002 11000 12 11001 02 51000 10 11 00 01 13 21 1000 11 2

Sample Output

010001001

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=55010;
const int M=950000;
const int inf=(1<<28);
int head[N];
struct Edge
{
    int v,next,w;
} edge[M];
int cnt,n,s,t;//n从0开始 0->n-1
void addedge(int u,int v,int w)
{
    edge[cnt].v=v;
    edge[cnt].w=w;
    edge[cnt].next=head[u];
    head[u]=cnt++;
    edge[cnt].v=u;
    edge[cnt].w=0;
    edge[cnt].next=head[v];
    head[v]=cnt++;
}
int sap()
{
    int pre[N],cur[N],dis[N],gap[N];
    int flow=0,aug=inf,u;
    bool flag;
    for(int i=0; i<n; i++)
    {
        cur[i]=head[i];
        gap[i]=dis[i]=0;
    }
    gap[s]=n;
    u=pre[s]=s;
    while(dis[s]<n)
    {
        flag=0;
        for(int &j=cur[u]; j!=-1; j=edge[j].next)
        {
            int v=edge[j].v;
            if(edge[j].w>0&&dis[u]==dis[v]+1)
            {
                flag=1;
                if(edge[j].w<aug) aug=edge[j].w;
                pre[v]=u;
                u=v;
                if(u==t)
                {
                    flow+=aug;
                    while(u!=s)
                    {
                        u=pre[u];
                        edge[cur[u]].w-=aug;
                        edge[cur[u]^1].w+=aug;
                    }
                    aug=inf;
                }
                break;
            }
        }
        if(flag) continue;
        int mindis=n;
        for(int j=head[u]; j!=-1; j=edge[j].next)
        {
            int v=edge[j].v;
            if(edge[j].w>0&&dis[v]<mindis)
            {
                mindis=dis[v];
                cur[u]=j;
            }
        }
        if((--gap[dis[u]])==0)
            break;
        gap[dis[u]=mindis+1]++;
        u=pre[u];
    }
    return flow;
}

//初始化 cnt=0;memset(head,-1,sizeof(head));

int main()
{
    int ci;scanf("%d",&ci);
    while(ci--)
    {
        int m,p;scanf("%d%d",&m,&p);
        cnt=0;
        memset(head,-1,sizeof(head));
        n=m*2+2;
        s=0,t=n-1;
        addedge(0,1,inf);
        addedge(1,1+m,inf);
        addedge(m*2,t,inf);
        for(int i=2;i<=m;i++)
        {
            int x;scanf("%d",&x);
            addedge(i,i+m,x);
        }
        while(p--)
        {
            int u,v;scanf("%d%d",&u,&v);u++,v++;
            addedge(u+m,v,inf);
        }
        int mc=sap();
        printf("%d\n",mc);
    }
    return 0;
}