HDU 1505(动态规划-最大子矩阵)

墨蓝 2022-06-06 01:19 139阅读 0赞

问题描述:

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

Sample Output

45
    0

题目题意:题目让我们求出由F构成的最大子矩阵，其中R不能使用。

题目分析:我们先预处理dp\[i\]\[j\]数组，它表示这个点往下（包含它）最长连续的F的长度，我们然后枚举每一行。

例如如果是这几个数字的话： 0 2 2 5 5 5 那么很明显最大面积就是5\*3=15啦！这个和HDU 1506一样！  [HDU 1506][]

代码如下:

#include<iostream>
    #include<cstring>
    #include<cmath>
    #include<cstdio>
    using namespace std;
    
    const int maxn=1e3+10;
    char mmap[maxn][maxn];
    int dp[maxn][maxn],Left[maxn],Right[maxn];
    int main()
    {
        int t;
        scanf("%d",&t);
        while (t--) {
            int n,m;
            scanf("%d%d",&n,&m);
            for (int i=1;i<=n;i++)
                for (int j=1;j<=m;j++)
                  cin>>mmap[i][j];
             for (int i=n;i>=1;i--) {//预处理dp数组
                for (int j=1;j<=m;j++) {
                    if (mmap[i][j]=='F')
                        dp[i][j]=dp[i+1][j]+1;
                    else if (mmap[i][j]=='R')
                        dp[i][j]=0;
                }
             }
             int ans=0;
             for (int i=1;i<=n;i++) {//和1506一样!
                memset (Left,0,sizeof (Left));
                memset (Right,0,sizeof (Right));
                Left[1]=1;Right[m]=m;
                for (int j=2;j<=m;j++) {
                    int t=j;
                    while (t>1&&dp[i][j]<=dp[i][t-1])
                        t=Left[t-1];
                    Left[j]=t;
                }
                for (int j=m-1;j>=1;j--) {
                    int t=j;
                    while (t<m&&dp[i][j]<=dp[i][t+1])
                        t=Right[t+1];
                    Right[j]=t;
                }
                for (int j=1;j<=m;j++) {
                    ans=max(ans,(Right[j]-Left[j]+1)*dp[i][j]*3);
                }
             }
             printf("%d\n",ans);
        }
        return 0;
    }

[HDU 1506]: http://blog.csdn.net/wust_cyl/article/details/78351183