hdu 1506 City Game 二维的多重背包

City Game

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2580    Accepted Submission(s): 1032

Problem Description

Bob is a strategy game programming specialist. In his new city building game the gaming environment is as follows: a city is built up by areas, in which there are streets, trees,factories and buildings. There is still some space in the area that is unoccupied. The strategic task of his game is to win as much rent money from these free spaces. To win rent money you must erect buildings, that can only be rectangular, as long and wide as you can. Bob is trying to find a way to build the biggest possible building in each area. But he comes across some problems – he is not allowed to destroy already existing buildings, trees, factories and streets in the area he is building in.

Each area has its width and length. The area is divided into a grid of equal square units.The rent paid for each unit on which you're building stands is 3$.

Your task is to help Bob solve this problem. The whole city is divided into K areas. Each one of the areas is rectangular and has a different grid size with its own length M and width N.The existing occupied units are marked with the symbol R. The unoccupied units are marked with the symbol F.

 

Input

The first line of the input contains an integer K – determining the number of datasets. Next lines contain the area descriptions. One description is defined in the following way: The first line contains two integers-area length M<=1000 and width N<=1000, separated by a blank space. The next M lines contain N symbols that mark the reserved or free grid units,separated by a blank space. The symbols used are:

R – reserved unit

F – free unit

In the end of each area description there is a separating line.

 

Output

For each data set in the input print on a separate line, on the standard output, the integer that represents the profit obtained by erecting the largest building in the area encoded by the data set.

 

Sample Input

2

5 6

R F F F F F

F F F F F F

R R R F F F

F F F F F F

F F F F F F

 

5 5

R R R R R

R R R R R

R R R R R

R R R R R

R R R R R

 

 参考代码：

#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <string.h>
using namespace std;

__int64 map[1010][1010];        //map[i][j]储存的对于是第i行j列这个字母其上有多少个F
__int64 l[1010],r[1010];
__int64 ans;

void dp(int cur,int n)
{    
    int i;
    for(i=1;i<=n;i++)
        l[i]=r[i]=i;
    for(i=1;i<=n;i++)
    {
        if(map[cur][l[i]]<=map[cur][l[i]-1])
            l[i]=l[l[i]-1];
    }
    for(i=n;i>=1;i--)
    {
        if(map[cur][r[i]]<=map[cur][r[i]+1])
            r[i]=r[r[i]+1];
    }

    for(i=1;i<=n;i++)
        ans= max(ans,map[cur][i]*(r[i]-l[i]+1));    

}

int main()
{
    int i,j,n,m,t;
    scanf("%d",&t);
    while(t--)
    {
        char c;
        scanf("%d%d",&n,&m);
        for(i=1;i<=n;i++) map[i][0]=-1;
        map[n+1][0]=-2;                            //边界
        for(i=1;i<=n;i++)
        {
            for(j=1;j<=m;j++)
            {
                cin>>c;
                if(c=='R')
                {
                    map[i][j]=0;
                    map[i][0]=-2;                //-2记录这一行有R
                }
                else map[i][j]=map[i-1][j]+1;        //这里很重要，就是计算该F是其上的连续第几个F的；
            }
            map[i][j]=-1;
        }
        ans=0;
        for(j=1;j<=n;j++)
        {
            if(map[j+1][0]==-2)                    //每次搜索只要从存在R的上面一行的开始
                dp(j,m);
        }
        printf("%I64d\n",ans*3);
    }
    return 0;
}

Sample Output

45

0

 

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二维的多重背包，而上一个博客题目相似。想了半天不知道怎么写，上网看了人家的代码想了很久才懂了。