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Matrix Again(最大费用最大流)

Matrix Again

Time Limit: 5000/2000 MS (Java/Others) Memory Limit: 102400/102400 K (Java/Others)
Total Submission(s): 16 Accepted Submission(s): 7
 
Problem Description
Starvae very like play a number game in the n*n Matrix. A positive integer number is put in each area of the Matrix.
Every time starvae should to do is that choose a detour which from the top left point to the bottom right point and than back to the top left point with the maximal values of sum integers that area of Matrix starvae choose. But from the top to the bottom can only choose right and down, from the bottom to the top can only choose left and up. And starvae can not pass the same area of the Matrix except the start and end..
Do you know why call this problem as “Matrix Again”? AS it is like the problem 2686 of HDU.
 
Input
The input contains multiple test cases.
Each case first line given the integer n (2<=n<=600) 
Then n lines, each line include n positive integers. (<100)
 
Output
For each test case output the maximal values starvae can get.
 
Sample Input
210 35 10310 3 32 5 36 7 1051 2 3 4 52 3 4 5 63 4 5 6 74 5 6 7 85 6 7 8 9
 
Sample Output
284680
 
Author
Starvae
 
Source
HDOJ Monthly Contest – 2010.04.04
 
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lcy
 
/*题意:给你一个n*n的矩阵每个点都有相应的权值,然后让你求出从左上角走到右下角,再返回能讲过的最大权值是多少,但是两次的路    线不能经过同一个点。#初步思路:最大费用最大流由于每个数只能取一次,所以对当前每一个数要进行拆点,将i拆为i和i‘‘,然后从i连接一条边到i‘‘    ,容量为1,费用为第i个点的费用,然后将i和取完i点后能取的数连一条边,容量为1,费用为0。因为是从(1,1)->(n,n)->(1,    1),所以我们建立超级源点S,连接S和第一个节点,容量为2(因为要走两条路径),费用为0,建立超级汇点T,连接点(n*n)‘‘ 到    T,容量为1,费用为0,然后求一次最大费用最大流,因为1和n*n这两个点算了两次,故需要减去一次他们的费用之和,发现网络流的题    目数组的大小很重要,之前因为数组问题出现了各种错误,望今后引起高度重视#补充:超内存......用数组来模拟栈就过了*/#include<bits/stdc++.h>using namespace std;int n;int mapn[610][610];int tol=0;/**************************************************数组模拟************************************************************/const int MAXN = 720010;const int MAXM = 3501000;const int INF = 1<<30;struct EDG{    int to,next,cap,flow;    int cost;  //单价}edg[MAXM];int head[MAXN],eid;int pre[MAXN], cost[MAXN] ; //点0~(n-1)void init(){    eid=0;    memset(head,-1,sizeof(head));}void addEdg(int u,int v,int cap,int cst){    edg[eid].to=v; edg[eid].next=head[u]; edg[eid].cost = cst;    edg[eid].cap=cap; edg[eid].flow=0; head[u]=eid++;    edg[eid].to=u; edg[eid].next=head[v]; edg[eid].cost = -cst;    edg[eid].cap=0; edg[eid].flow=0; head[v]=eid++;}bool inq[MAXN];int q[MAXN];bool spfa(int sNode,int eNode , int n){    int l=0,r=0;    for(int i=0; i<n; i++){        inq[i]=false; cost[i]= -1;    }    cost[sNode]=0; inq[sNode]=1; pre[sNode]=-1;    q[r++]=sNode;    while(l!=r){        int u=q[l++]; //数组模拟        if(l==MAXN)l=0;        inq[u]=0;        for(int i=head[u]; i!=-1; i=edg[i].next){            int v=edg[i].to;            if(edg[i].cap-edg[i].flow>0 && cost[v]<cost[u]+edg[i].cost){ //在满足可增流的情况下,最小花费                cost[v] = cost[u]+edg[i].cost;                pre[v]=i;   //记录路径上的边                if(!inq[v]){                    if(r==MAXN)r=0;                    q[r++]=v; inq[v]=1;                }            }        }    }    return cost[eNode]!=-1;    //判断有没有增广路}//反回的是最大流,最小花费为minCostint minCost_maxFlow(int sNode,int eNode ,int& minCost , int n){    int ans=0;    while(spfa(sNode,eNode , n)){        for(int i=pre[eNode]; i!=-1; i=pre[edg[i^1].to]){            edg[i].flow+=1; edg[i^1].flow-=1;            minCost+=edg[i].cost;        }        ans++;        if(ans==2)break;    }    return ans;}/**************************************************数组模拟************************************************************/int main(){    // freopen("in.txt","r",stdin);    while(scanf("%d",&n)!=EOF){        //cout<<n<<endl;        tol=n*n;//总的点数        init();        //  首先是初始化,总共可能n*n个点 0到n*n-1        //  但是这个题还需要回来,所以可能走的点就是         //  2*n*n        for(int i=0;i<n;i++){            for(int j=0;j<n;j++){                scanf("%d",&mapn[i][j]);            }        }        for(int i=0;i<n;i++){            for(int j=0;j<n;j++){                if(i||j){ //如果这个点不是起点                                        addEdg(i*n+j, i*n+j+n*n , 1 , mapn[i][j]);                      //如果这个点还没有到达右边的边界                    if(j+1<n)//向右边走一步                        addEdg(i*n+j+n*n, i*n+j+1 , 1 , 0 );                    //如果这个点还没有到达下面的边界                    if(i+1<n)//想下边走一步                        addEdg(i*n+j+n*n, (i+1)*n+j , 1 , 0);                  }                  else{//如果这个点是原点的话                    addEdg(0 , 1 , 1,0) , addEdg(0 , n , 1 , 0);                  }              }        }        int ans=0;        minCost_maxFlow(0,tol-1,ans,tol*2);        ans+=mapn[0][0];        if(n>1) ans+=(mapn[n-1][n-1]);        printf("%d\n",ans);    }    return 0;}

 

Matrix Again(最大费用最大流)