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

	Example:

	Input:
	[
	  ["1","0","1","0","0"],
	  ["1","0","1","1","1"],
	  ["1","1","1","1","1"],
	  ["1","0","0","1","0"]
	]
	Output: 6
'''

class Solution(object):
    def largestRectangleArea(self, heights):
        """
        :type heights: List[int]
        :rtype: int
        """
        if not heights:
        	return 0

        stack = []
        result, index = 0, 0

        while index < len(heights):
        	if not stack or heights[index] >= heights[stack[-1]]:
        		stack.append(index)
        		index += 1
        	else:
        		curr = stack.pop()
        		if not stack:
        			area = heights[curr]*index
        		else:
        			area = heights[curr] * (index-stack[-1]-1)
        		result = max(result, area)

        while stack:
        	curr = stack.pop()
        	if not stack:
        		area = heights[curr]*index
        	else:
        		area = heights[curr] * (index-stack[-1]-1)
        	result = max(result, area)
        return result

    def maximalRectangle(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        if not matrix:
            return 0
        m, n = len(matrix), len(matrix[0])
        heights = [0 for index in range(n)]
        result = 0
        
        for index_i in range(m):
            for index_j in range(n):
                if matrix[index_i][index_j] != '0':
                    heights[index_j] = heights[index_j] + 1
                else:
                    heights[index_j] = 0
                    
            result = max(result, self.largestRectangleArea(heights))
        return result