<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:
    void nsr(vector<int>&heights,vector<int>&nsr_v){
        stack<pair<int,int>>stk;
        for(int i=heights.size()-1;i>=0;i--){
                while(!stk.empty() && stk.top().first >= heights[i]){
                    stk.pop();
                }
                if(stk.empty()){
                     nsr_v.push_back(heights.size());
                }
                else{
                     nsr_v.push_back(stk.top().second);
                }
                stk.push({heights[i],i});
            
        }
        reverse(nsr_v.begin(),nsr_v.end());
    }
     void nsl(vector<int>&heights,vector<int>&nsl_v){
        stack<pair<int,int>>stk;
        for(int i=0;i<heights.size();i++){
            while(!stk.empty() && stk.top().first >= heights[i]){
                stk.pop();
            }
            if(stk.empty()){
                nsl_v.push_back(-1);
            }
            else{
                nsl_v.push_back(stk.top().second);
            }
            stk.push({heights[i],i});
        }
        
    }
    int largestRectangleArea(vector<int>& heights) {
        vector<int>nsl_v;
        vector<int>nsr_v;
        nsr(heights,nsr_v);
        nsl(heights,nsl_v);
        int ans=INT_MIN;
        for(int i=0;i<heights.size();i++){
            ans=max(ans,(heights[i]*((nsr_v[i]-i)+(i-nsl_v[i])-1)));
        }
        return ans;
    }
};
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