6.29 - hard - 19

84. Largest Rectangle in Histogram

这道题用stack记录递增序列，计算以某个点为高度的矩形，就要用这个点的高度乘以最右和最左的边界, 因为是递增序列，那么它的最左0或者stack[-1]，最右就是当它被pop出去时候的index-1

这题稍微tricky的地方在于在heights的右边界都加上一个值，这样保证最后一个值可以被访问到，然后stack永远不为空

class Solution(object):
   def largestRectangleArea(self, heights):
       """
       :type heights: List[int]
       :rtype: int
       """
       if not heights:
           return 0
       if len(heights) == 1:
           return heights[0]
       stack = [-1]
       heights = heights + [0]
       max_area = 0
       for i in range(len(heights)):
           while heights[i] < heights[stack[-1]]:
               cur = heights[stack.pop()]
               max_area = max(max_area, cur*(i - stack[-1] - 1))
           stack.append(i)
       
       return max_area