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.

Solution: 1. dp. (72 milli secs for the large).
a) dp[i][j] records the number of consecutive '1' on the left and up of the element matrix[i][j].
b) For each element(i,j), calculate the area of rectangle including the element itself.
2. calculate 'Largest Rectangle in Histogram' for each row.
Note... understanding

class Solution {
public:
    int maximalRectangle(vector<vector<char> > &matrix) {
        if (matrix.empty() || matrix[0].empty()) return 0;
        int N = matrix.size(), M = matrix[0].size();
        pair<int, int> dp[N][M];
        memset(dp, 0, sizeof(dp));
        int res = 0;
        for (int i = 0; i < N; ++i)
        {
            for (int j = 0; j < M; ++j)
            {
                if (matrix[i][j] == '0')
                    continue;
                
                int x = (j == 0) ? 1 : dp[i][j-1].first + 1;
                int y = (i == 0) ? 1 : dp[i-1][j].second + 1;
                dp[i][j] = make_pair(x, y);
                
                int minHeight = y;
                for (int k = j; k > j - x; --k)
                {
                    minHeight = min(minHeight, dp[i][k].second);
                    res = max(res, minHeight * (j - k + 1));
                }
            }
        }
        return res;
    }
};