<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> ps(vector<int> &height) {
        vector<int> p(height.size());
        stack<int> s;
        for (int i=0;i<height.size();i++) {
            while (!s.empty()&&height[s.top()]>=height[i]) {
                s.pop();}
            if (s.empty()) {p[i] = -1;} 
            else {p[i]=s.top();} 
            s.push(i);}
        return p;}
    vector<int> ns(vector<int> &height) {
        vector<int> n(height.size());
        stack<int> s;
        for (int i=height.size()-1;i>= 0;i--) {
            while (!s.empty() && height[s.top()] >= height[i]) {
                s.pop();}
            if (s.empty()) {n[i] = height.size();} 
            else {n[i] = s.top();}
            s.push(i);}
        return n;}
    int largestRectangleArea(vector<int>& heights) {
        int maxi = 0;
        vector<int>son=ps(heights);
        vector<int>uph=ns(heights);
        for (int i=0;i<heights.size();i++) {
            int cur=(uph[i]-son[i]-1)*heights[i];
            maxi=max(cur,maxi);}
        return maxi;    
    }
};
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