"""
84. Largest Rectangle in Histogram
Difficulty: Hard
https://leetcode.com/problems/largest-rectangle-in-histogram/

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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.



Example 1:

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.

Example 2:

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



Constraints:

        • 1 <= heights.length <= 10^5

        • 0 <= heights[i] <= 10^4
"""


class Solution:
    def largestRectangleArea(self, heights: list[int]) -> int:
        maxArea = 0
        stack = []

        for i, h in enumerate(heights):
            start = i
            while stack and stack[-1][1] > h:
                index, height = stack.pop()
                width = i - index
                maxArea = max(maxArea, height * width)
                start = index
            stack.append((start, h))

        for i, h in stack:
            maxArea = max(maxArea, h * (len(heights) - i))

        return maxArea