<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> nextSmallerElement(vector<int>height){
        stack<int> st;
        int n=height.size();
        vector<int> output(n,n);
        st.push(0);          
        for(int i=0;i<n;i++){
            while(!st.empty() and height[st.top()]>height[i]){
                output[st.top()]=i;
                st.pop();
            }
            st.push(i);                       
        }
        return output;
    }
    vector<int> prevSmallerElement(vector<int> height){
        int n=height.size();
        stack<int> st;
        st.push(n-1);
        vector<int> output(n,-1); 
        for(int i=n-1;i>=0;i--){
            while(!st.empty() and height[st.top()]>height[i]){
                output[st.top()]=i;
                st.pop();
            }
            st.push(i);
        }
        return output;
    }
    int largestRectangleArea(vector<int>& heights) {
        vector<int> nse=nextSmallerElement(heights);
        vector<int> pse=prevSmallerElement(heights);
        int area=0,n=heights.size(),width=0;
        for(int i=0;i<n;i++){
            width=abs(nse[i]-pse[i]-1);
            area=max(area,width*heights[i]);
        }          
        return area;
    }

};
93853