LintCode_510 Maximal Rectangle

Given a 2D boolean matrix filled with False and True, find the largest rectangle containing all True and return its area.

Have you met this question in a real interview? 

Yes

Example

Given a matrix:

[
  [1, 1, 0, 0, 1],
  [0, 1, 0, 0, 1],
  [0, 0, 1, 1, 1],
  [0, 0, 1, 1, 1],
  [0, 0, 0, 0, 1]
]

return 6.

参考 http://blog.csdn.net/qq_31552435/article/details/51839175

class Solution {
public:
    /**
     * @param matrix a boolean 2D matrix
     * @return an integer
     */
    int maximalRectangle(vector > &matrix) {
        // Write your code here
        int res = 0;
        if (matrix.empty()) {
            return res;
        }
        const int m = matrix.size();
        const int n = matrix[0].size();
        
        vector temp (n, 0);
        vector> dp(m, temp);
        
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && matrix[i][j]) {
                    dp[i][j] = 1;
                    continue;
                }
                if (matrix[i][j]) {
                    dp[i][j] = dp[i - 1][j] + 1;
                }
            }
        }
        for (int i = 0; i < m; i++) {
            res = max(res, largestRectangleArea(dp[i]));
        }
        return res;
    }
    
    int largestRectangleArea(vector &height) {
        // write your code here
        // write your code here
        stack S;  
        height.push_back(0);  
        int sum = 0;  
        for (int i = 0; i < height.size(); i++) {  
            if (S.empty() || height[i] > height[S.top()]) S.push(i);  
            else {  
                 int tmp = S.top();  
                 S.pop();  
                 sum = max(sum, height[tmp]*(S.empty()? i : i-S.top()-1));  
                 i--;  //拿着右边界， 寻找左边界；！！！！！
            }  
       }  
       return sum; 
    }
};