Maximal Rectangle

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

Analyse: For each row, we can determine the all 1's height of each element. 

Runtime: 28ms.

class Solution {
public:
    int maximalRectangle(vector<vector<char> >& matrix) {
        if(matrix.empty() || matrix[0].empty()) return 0;
        
        int row = matrix.size();
        int col = matrix[0].size();
        vector<vector<int> > bar(row, vector<int> (col, 0));
        for(int i = 0; i < row; i++){
            for(int j = 0; j < col; j++){
                if(matrix[i][j] == '0') bar[i][j] = 0;
                else bar[i][j] = (i == 0 ? 1 : bar[i - 1][j] + 1);
            }
        }
        
        int result = 0;
        for(int i = 0; i < row ; i++){
            result = max(result, largestRectangleArea(bar[i]));
        }
        return result;
    }
    int largestRectangleArea(vector<int>& height) {
        height.push_back(-1);
        stack<int> index;
        int i = 0, result = 0;
        while(i < height.size()){
            if(index.empty() || height[i] > height[index.top()])
                index.push(i++);
            else{
                int temp = index.top();
                index.pop();
                result = max(result, height[temp] * (index.empty() ? i :(i-index.top()-1)));
            }
        }
        return result;
    }
};