<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:
        def prev_smallest(height):
            n=len(height)
            stack=[]
            prev_small=[0]*n

            for i in range(n):
                while stack and height[stack[-1]]>=height[i]:
                    stack.pop()
                
                if not stack:
                    prev_small[i]=-1
                else:
                    prev_small[i]=stack[-1]
                
                stack.append(i)
            
            return prev_small

        def next_smallest(height):
            n=len(height)
            stack=[]
            next_small=[0]*n

            for i in range(n-1,-1,-1):
                while stack and height[stack[-1]]>=height[i]:
                    stack.pop()
                
                if not stack:
                    next_small[i]=n
                else:
                    next_small[i]=stack[-1]
                
                stack.append(i)
            
            return next_small

        prev_small=prev_smallest(heights)
        next_small=next_smallest(heights)
        # next_small.reverse()
        print(prev_small,next_small)

        max_area=0
        for i in range(len(heights)):

            max_area=max(max_area,(next_small[i]-prev_small[i]-1)*heights[i])

        return max_area


31000