class Solution(object):
def largestRectangleArea(self, heights):
"""
:type heights: List[int]
:rtype: int
"""
#O(n) solution
#for each rectangle, calculate the max area formed with its height h(with h being the smallest rectangle)
#then get the max of all the results
#get the index of the first smaller rectangle to its left: left_index
#and the index of the first smaller rectangle to its right: right_index
#use mono increasing stack
if not heights: return 0
l=len(heights)
if l==1: return heights[0]
#store the index of the rectangles
#stack is mono increasing, therefore we can easily locate the most adjacent index
stack=[-1,0]
res=0
for i in range(1,l):
while len(stack)>1 and heights[i]<heights[stack[-1]]:
res=max(res,heights[stack.pop()]*(i-stack[-1]-1))
stack.append(i)
while len(stack)>1:
res=max(res,heights[stack.pop()]*(l-stack[-1]-1))
return res
84. Largest Rectangle in Histogram
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