<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 {
public:
    int largestRectangleArea(vector<int>& heights) {
        int n=heights.size();
        vector<int>nextSmaller(n,n-1);
        stack<int>st;
        for(int i=0;i<n;i++){
            int curr=heights[i];
            while(!st.empty()&&curr<heights[st.top()]){
                  nextSmaller[st.top()]=i-1;
                st.pop();
            }
            st.push(i);
            
        }
        
        while(!st.empty())st.pop();
        
        
         vector<int>prevSmaller(n,0);
        for(int i=n-1;i>=0;i--){
            int curr=heights[i];
            while(!st.empty()&&curr<heights[st.top()]){
                  prevSmaller[st.top()]=i+1;
                st.pop();
            }
            st.push(i);
            
        }
        
        int ans=0;
     for(int i=0;i<n;i++){
         int temp=heights[i]*(nextSmaller[i]-prevSmaller[i]+1);
         ans=max(ans,temp);
     }        
        
        
        return ans;
        
        
        
    }
};
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