Leetcode: Largest Rectangle in Histogram

## https://code.dennyzhang.com/largest-rectangle-in-histogram
## Basic Ideas: Monotone stack
##              For each element, find the next non-greater value
##     Key Questions: How to get the left?
##                    What if right is not found, any special logic?
##
## Complexity:
class Solution(object):
    def largestRectangleArea(self, heights):
        """
        :type heights: List[int]
        :rtype: int
        """
        length = len(heights)
        next_smallers = [-1] * length
        stack = []
        max_width = 0
        # pad with fake items for the end
        for i in xrange(length+1):
            current = heights[i] if i != length else -1
            # When heights[i] is not greater than the stack top, it's the target of stack top
            while len(stack) != 0 and  current <= heights[stack[-1]]:
                k = stack.pop()
                h = heights[k]
                left = -1 if len(stack) == 0 else stack[-1]
                left = left + 1
                right = i
                max_width = max(max_width, h*(right-left))
            stack.append(i)
        return max_width

# s = Solution()
# print s.largestRectangleArea([2, 1, 2]) # 3