<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> nextsmaller(vector<int>& arr){
        int n = arr.size();
        stack<pair<int, int>> st;
        vector<int>ns;
        for(int i = n-1; i >= 0; i--){
            int curr = arr[i];
            while(!st.empty() && st.top().first >= curr){
                st.pop();
            }
            if(st.empty()){
                ns.push_back(n);
            }
            else{
                ns.push_back(st.top().second);
            }
            st.push({curr, i});
        }
        reverse(ns.begin(), ns.end());
        return ns;
    }

    vector<int> prevsmaller(vector<int>& arr1){
        int m = arr1.size();
        stack<pair<int, int>> st1;
        vector<int>ps;
        for(int j = 0; j < m; j++){
            int curr1 = arr1[j];
            while(!st1.empty() && st1.top().first >= curr1){
                st1.pop();
            }
            if(st1.empty()){
                ps.push_back(-1);
            }
            else{
                ps.push_back(st1.top().second);
            }
            st1.push({curr1, j});
        }
        return ps;
    }


    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        vector<int>ns = nextsmaller(heights);
        vector<int>ps = prevsmaller(heights);

        int max_area = INT_MIN;
        for(int i = 0; i < heights.size(); i++){
            int width = ns[i] - ps[i] - 1;
            int area = heights[i] * width;

            max_area = max(max_area, area);
        }
        return max_area;
    }
};
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