Largest Rectangle in Histogram Python Solution

Tested Python solution for LeetCode 84 with 16 pytest cases. Generate a practice environment with lcpy.

LeetCode 84, Hard. Topics: Array, Stack, Monotonic Stack. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 16 parametrized pytest cases, and a playground notebook:

lcpy gen -n 84   # by problem number
lcpy gen -s largest_rectangle_in_histogram   # by problem name

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Problem

Given an array of integers heights representing the histogram’s bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

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Examples

Input: heights = [2,1,5,6,2,3]
Output: 10

Explanation: The above is a histogram where width of each bar is 1. The largest rectangle is shown in the red area, which has an area = 10 units.

Input: heights = [2,4]
Output: 4

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Constraints

• 1 <= heights.length <= 10^5
• 0 <= heights[i] <= 10^4

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(n)
    # Space: O(n)
    # Monotonic stack approach
    # Stack stores indices of bars in increasing height order
    # When we find a shorter bar, we calculate area using previous bars
    def largest_rectangle_area(self, heights: list[int]) -> int:
        stack: list[int] = []  # Stack of indices
        max_area = 0

        for i, height in enumerate(heights):
            # While current height is less than stack top height
            # Pop from stack and calculate area with popped height as smallest
            while stack and heights[stack[-1]] > height:
                max_area = max(max_area, self.calculate_area(heights, stack, i))

            stack.append(i)

        while stack:
            max_area = max(max_area, self.calculate_area(heights, stack, len(heights)))

        return max_area

    @staticmethod
    def calculate_area(heights: list[int], stack: list[int], right_bound: int) -> int:
        h = heights[stack.pop()]
        w = right_bound if not stack else right_bound - stack[-1] - 1
        return h * w

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Complexity

Time	Space
O(n)	O(n)

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Tags

Grind 75, Grind, NeetCode 150, NeetCode 250, NeetCode All, AlgoMaster 75.