<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>& nums) {
        stack<pair<int,int>> s1,s2;
        int n=nums.size();
        vector<int> v1(n),v2(n);
        int i=n-1;
        while(i>=0){
            if(s1.empty() || s1.top().first<=nums[i]){
                s1.push({nums[i],i});
            }
            else{
                while(!s1.empty() && nums[i]<s1.top().first){
                    v1[s1.top().second]=i;
                    s1.pop();
                }
                s1.push({nums[i],i});
            }
            i--;
        }
        while(!s1.empty()){
            v1[s1.top().second]=-1;
            s1.pop();
        }
        i=0;
        while(i<n){
            if(s1.empty() || s1.top().first<=nums[i]){
                s1.push({nums[i],i});
            }
            else{
                while(!s1.empty() && nums[i]<s1.top().first){
                    v2[s1.top().second]=i;
                    s1.pop();
                }
                s1.push({nums[i],i});
            }
            i++;
        }
        while(!s1.empty()){
            v2[s1.top().second]=n;
            s1.pop();
        }
        int ans=0;
        // for(auto i: v2){
        //     cout<<i<<" ";
        // }
        // cout<<endl;
        // for(auto i: v1){
        //     cout<<i<<" ";
        // }
        for(int i=0;i<n;i++){ 
            ans=max(ans,nums[i]*(v2[i]-v1[i]-1));
        }
        return ans;
    }
};
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