Find Largest Rectangle Area Under Histogram in Python

Suppose we have a list of numbers representing heights of bars in a histogram. We have to find area of the largest rectangle that can be formed under the bars.

So, if the input is like nums = [3, 2, 5, 7]

then the output will be 10

To solve this, we will follow these steps −

• stk := a stack and initially insert -1 into it
• insert 0 at the end of heights
• ans := 0
• for i in range 0 to size of heights, do
  • while heights[i] < heights[top of stk], do
    • h := heights[top of stk] and pop from stk
    • w := i - top of stk - 1
    • ans := maximum of ans and (h * w)
  • push i into stk
• return ans

Let us see the following implementation to get better understanding −

Example 

Live Demo

class Solution:
   def solve(self, heights):
      stk = [-1]
      heights.append(0)
      ans = 0
      for i in range(len(heights)):
         while heights[i] < heights[stk[-1]]:
            h = heights[stk.pop()]
            w = i - stk[-1] - 1
            ans = max(ans, h * w)
         stk.append(i)
      return ans

ob = Solution()
nums = [3, 2, 5, 7]
print(ob.solve(nums))

Input

[3, 2, 5, 7]

Output

10