<p>Given an array of integers <code>heights</code> representing the histogram&#39;s bar height where the width of each bar is <code>1</code>, return <em>the area of the largest rectangle in the histogram</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram.jpg" style="width: 522px; height: 242px;" />
<pre>
<strong>Input:</strong> heights = [2,1,5,6,2,3]
<strong>Output:</strong> 10
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram-1.jpg" style="width: 202px; height: 362px;" />
<pre>
<strong>Input:</strong> heights = [2,4]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= heights.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= heights[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def largestRectangleArea(self, heights: List[int]) -> int:

        
        # prev small val index
        def pse(arr):

            stack = []
            res = [-1] * len(arr)

            for i in range(len(arr)):
                
                # prev eq is impl, we dont want to calc double 
                while stack and arr[stack[-1]] >= arr[i]:
                    stack.pop()
                
                if stack:
                    res[i] = stack[-1]

                stack.append(i)
            return res

        # next small val index
        def nse(arr):
            stack = []
            res = [len(arr)] * len(arr)

            for i in range(len(arr)-1,-1,-1):

                while stack and arr[stack[-1]] > arr[i]:
                    stack.pop()

                if stack:
                    res[i] = stack[-1]

                stack.append(i)
            return res

        pseArr = pse(heights)
        nseArr = nse(heights)
        maxArea = 0
        for i in range(len(heights)):
            
            # dist between two smaller ele
            width = nseArr[i] - pseArr[i]-1
            maxArea = max(maxArea, width * heights[i])
        
        return maxArea
30800