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


For example, given the following matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Return 6.
class Solution(object):
    def maximalRectangle(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        def histogram(height):
            if not height:
                return 0
            height.append(-1)
            stack = []
            ans = 0
            for i in xrange(0, len(height)):
                while stack and height[i] < height[stack[-1]]:
                    h = height[stack.pop()]
                    w = i - stack[-1] - 1 if stack else i
                    ans = max(ans, h * w)
                stack.append(i)
            return ans
        ans = 0
        dp = [[0] * len(matrix[0]) for _ in xrange(0, len(matrix))]
        for i in reversed(xrange(0, len(matrix))):
            if i == len(matrix) - 1:
                dp[i] = [int(h) for h in matrix[i]]
            else:
                for j in xrange(0, len(matrix[0])):
                    if matrix[i][j] != "0":
                        dp[i][j] = dp[i + 1][j] + 1
            ans = max(ans, histogram(dp[i]))
        return ans