Largest Rectangle in Histogram

Question

Given n non-negative integers representing the histogram’s bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.

Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

The largest rectangle is shown in the shaded area, which has area = 10 unit.

For example,
Given height = [2,1,5,6,2,3],
return 10.

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My first try

class Solution(object):    def largestRectangleArea(self, height):        """        :type height: List[int]        :rtype: int        """        if height==[]:            return 0        stack = []        cur, maxnum = 0, 0        for ind, elem in enumerate(height):            while stack!=[] and elem<=height[stack[-1]]:                index = stack.pop()                cur = ind*height[index] if stack==[] else (ind - index)*height[index]                maxnum = max(cur, maxnum)            stack.append(ind)        while stack!=[]:            index = stack.pop()            cur = len(height)*height[index] if stack==[] else (len(height)-index)*height[index]            maxnum = max(cur, maxnum)        return maxnum

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Solution

Analysis

Get idea from here1, here2

Code

class Solution(object):    def largestRectangleArea(self, height):        """        :type height: List[int]        :rtype: int        """        if height==[]:            return 0        stack = []      # stack contains elements in increasing order        cur, maxnum = 0, 0        for ind, elem in enumerate(height):            while stack!=[] and elem<=height[stack[-1]]:                index = stack.pop()                # if stack==[], it means all elems with index less than ind are higher than elem, so area = ind*height[index]                 cur = ind*height[index] if stack==[] else (ind - stack[-1] -1)*height[index]                  maxnum = max(cur, maxnum)            stack.append(ind)        while stack!=[]:            index = stack.pop()            cur = len(height)*height[index] if stack==[] else (len(height)-stack[-1]-1)*height[index]            maxnum = max(cur, maxnum)        return maxnum