[LeetCode] Maximal Rectangle

This link shares a nice solution with explanation using DP. You will be clear of the algorithm after running it on its suggested example:

matrix = [
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0]];

The code is rewritten as follows.

class Solution {
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        if (matrix.empty()) return 0;
        const int m = matrix.size(), n = matrix[0].size();
        int *left = new int[n](), *right = new int[n](), *height = new int[n]();
        fill_n(right, n, n);
        int area = 0;
        for (int i = 0; i < m; i++) {
            int l = 0, r = n;
            for (int j = 0; j < n; j++)
                height[j] += matrix[i][j] == '1' ? 1 : -height[j];
            for (int j = 0; j < n; j++) {
                if (matrix[i][j] == '1') left[j] = max(left[j], l);
                else left[j] = 0, l = j + 1;
            }
            for (int j = n - 1; j >= 0; j--) {
                if (matrix[i][j] == '1') right[j] = min(right[j], r);
                else right[j] = n, r = j;
            }
            for (int j = 0; j < n; j++)
                area = max(area, (right[j] - left[j]) * height[j]);
        }
        return area;
    }
};