Largest Rectangle in Histogram in Python

Suppose we have one integer array that is representing the height of a histogram. Each bar has unit width. We have to find the largest area rectangle as follows −

To solve this, we will follow these steps −

• Create stack, set i := 0, ans := 0

• while i < size of heights, then

  • if stack has 0 elements or height of stack top element <= height[i], then

    • insert i into stack, increase i by 1

  • otherwise −

    • x := stack top element, delete from stack.

    • height := heights[x]

    • temp := height * (i * stack[-1] – 1) when stack is not empty otherwise temp := height * i

    • ans := max of ans and temp

• while stack is not empty −

  • x := stack top element

  • height := height[x], delete from stack

  • temp := height * length of heights – stack top element – 1 when stack is not empty, otherwise temp := length of heights

  • ans := max of ans and temp

• return ans

Example

Let us see the following implementation to get a better understanding −

class Solution(object):
   def largestRectangleArea(self, heights):
      stack = []
      i = 0
      ans = 0
      while i < len(heights):
         if len(stack) == 0 or heights[stack[-1]]<=heights[i]:
            stack.append(i)
            i+=1
         else:
            x = stack[-1]
            stack.pop()
            height = heights[x]
            temp = height * (i-stack[-1]-1) if len(stack)!= 0 else height * i
            ans = max(ans,temp)
      while len(stack)>0:
         x = stack[-1]
         height = heights[x]
         stack.pop()
         temp = height * (len(heights)-stack[-1]-1) if len(stack)!= 0 else height* len(heights)
         ans = max(ans,temp)
      return ans
ob = Solution()
print(ob.largestRectangleArea([2,1,5,7,3,2]))

Input

[2,1,5,7,3,2]

Output

12