leetcode85. Maximal Rectangle

问题描述：

Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.

Example:

Input:
[
  ["1","0","1","0","0"],
  ["1","0","1","1","1"],
  ["1","1","1","1","1"],
  ["1","0","0","1","0"]
]
Output: 6

解题思路：

这给我们一个二维矩阵要我们求出其中可以构成的最大矩形。

可以把它降维度到一维：即可变成求histgram可以构成的最大矩形。

每一行和上面的行形成一个histogram。

如图所示（以所给例子的最后一行为例）：

一定要为连续的不为0的才能累成柱状图！

代码：

class Solution {
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        if(matrix.empty())
            return 0;
        vector<int> height(matrix[0].size(), 0);
        height.push_back(0);
        int m = 0;
        for(int i = 0; i < matrix.size(); i++){
            stack<int> stk;
            for(int j = 0; j < matrix[0].size(); j++){
                int num = matrix[i][j] - '0';
                if(num != 0){
                    height[j] += num;
                }else{
                    height[j] = 0;
                }
            }
            
            for(int j = 0; j <= matrix[0].size(); j++){
                while(!stk.empty() && height[j] <= height[stk.top()]){
                    int cur = stk.top();
                    stk.pop();
                    m = max(m, height[cur] * (stk.empty() ? j : (j - stk.top() - 1)));
                }
                stk.push(j);
            }
        }
        return m;
    }
};