HDU-1505 City Game (线性dp)

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本文介绍了一款城市建造游戏中的算法挑战，玩家需在有限区域内建造最大可能的矩形建筑以获取租金收益。文章详细解析了算法实现过程，包括如何处理已有建筑障碍及计算最优解。

City Game

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7672 Accepted Submission(s): 3326

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

Sample Output

45
0

#include <bits/stdc++.h>
using namespace std;
int l[1001], r[1001], h[1001][1001];
int main(){
	int R, C, T;
	scanf("%d", &T);
	while(T--){
		scanf("%d %d", &R, &C);
		for(int i = 1; i <= C; ++i){
			h[0][i] = 0;
		}
		char s;
		for(int i = 1; i <= R; ++i){
			for(int j = 1; j <= C; ++j){
				s = getchar();
				while(s != 'F' && s != 'R'){
					s = getchar();
				}
				if(s == 'R'){
					h[i][j] = 0;
				}
				else{
					h[i][j] = h[i - 1][j] + 1;
				}
			}
		}
		int ans = 0;
		for(int i = 1; i <= R; ++i){
			for(int j = 1; j <= C; ++j){
				l[j] = r[j] = j;
			}
			h[i][0] = -1;
			for(int j = 2; j <= C; ++j){
				while(h[i][j] <= h[i][l[j] - 1]){
					l[j] = l[l[j] - 1];
				}
			}
			h[i][C + 1] = -1;
			for(int j = C - 1; j >= 1; --j){
				while(h[i][j] <= h[i][r[j] + 1]){
					r[j] = r[r[j] + 1];
				}
			}
			for(int j = 1; j <= C; ++j){
				ans = max(ans, (r[j] - l[j] + 1) * h[i][j]);
			}
		}
		printf("%d\n", ans * 3);
	}
}

/*
题意：
1000*1000个网格只包含R,F，求面积最大的只包含F的矩阵面积。

思路:
对于每一个F，记录其上面有多少个连续的F，然后对于每一行，看其中F的高度向左右可以
延伸多长，当其高度比周围F小时可以延伸。然后枚举所有F，根据延伸宽度和其高度，计算面积即可。
*/