<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 nxtsmall(vector<int>&height,vector<int>&left,vector<int>&right){
        stack<int>st;
        st.push(-1);
        int n=height.size();
        for(int i=0;i<n;i++){
            while(st.top()!=-1&&height[st.top()]>height[i]){
                st.pop();
            }
            left.push_back(st.top());
            st.push(i);
        }
        stack<int>st1;
        st1.push(n);
        for(int i=0;i<n;i++){
            while(st1.top()!=n&&height[st1.top()]>=height[n-1-i]){
                st1.pop();
            }
            right[n-1-i]=(st1.top());
            st1.push(n-1-i);
        }
    }
    int largestRectangleArea(vector<int>& heights) {
        int n=heights.size();
        vector<int>left,right(n);
        nxtsmall(heights,left,right);
        int ans=0;
        for(int i=0;i<n;i++){
            int area=(right[i]-left[i]-1)*heights[i];
            ans=max(area,ans);
        }
     return ans;   
    }
};
91186