<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:
vector<int>vr,vl;
void rs(vector<int>& ar,int n){
    stack<int>st,in;
    for(int i=n-1;i>=0;i--){
        if(st.empty()){
            vr.push_back(n);
        }else{
            while(!st.empty()&&ar[i]<=st.top()){
                st.pop();
                in.pop();
            }
            if(st.empty()){
                vr.push_back(n);
            }else{
                vr.push_back(in.top());
            }
        }
        st.push(ar[i]);
        in.push(i);
    }
    for(int i=0;i<n/2;i++){
        swap(vr[i],vr[n-i-1]);
    }
}
void ls(vector<int>& ar,int n){
    stack<int>st,in;
    for(int i=0;i<n;i++){
        if(st.empty()){
            vl.push_back(-1);
        }else{
            while(!st.empty()&&st.top()>=ar[i]){
                st.pop();
                in.pop();
            }
            if(st.empty()){
                vl.push_back(-1);
            }else{
                vl.push_back(in.top());
            }
        }
        st.push(ar[i]);
        in.push(i);
    }
}
    int largestRectangleArea(vector<int>& ar) {
        int n=ar.size();
        ls(ar,n);
        rs(ar,n);
        int w[n];
        int area[n];
        int max=0;
        for(int i=0;i<n;i++){
            w[i]=vr[i]-vl[i]-1;
            area[i]=ar[i]*w[i];
            if(max<area[i]){
                max=area[i];
            }
        }
        return max;
    }
};
96036