<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 {
void print(vector<int> arr, int n){
    for(int i = 0; i<n; i++) cout<<arr[i]<<' ';
    cout<<endl;
}
vector<int> findNse(vector<int> heights, int n){
    vector<int> nse(n, -1);
    stack<int> st; // Monotonic stack stores elements in ascending order
    for(int i = n-1; i>=0; i--){
        while(!st.empty() && heights[st.top()] >= heights[i]) st.pop();
        int nse_elei;
        if(!st.empty()) nse_elei = st.top();
        else nse_elei = n;
        st.push(i);
        nse[i] = nse_elei;

    }
    return nse;
}
vector<int> findPse(vector<int> heights, int n){
    vector<int> pse(n, -1);
    stack<int> st;
    for(int i = 0; i<n; i++){
        while(!st.empty() && heights[st.top()] >= heights[i]) st.pop();
        int p;
        if(!st.empty()) p = st.top();
        else p = -1;
        st.push(i);
        pse[i] = p;
    }
    return pse;
}
public:
    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        vector<int> pse = findPse(heights, n);
        vector<int> nse = findNse(heights, n);
        print(pse, n);
        print(nse, n);
        int maxi_area = 0;
        for(int i = 0; i < n; i++){
            int a = heights[i] * (nse[i] - pse[i] - 1);
            maxi_area = max(a, maxi_area);
        }
        return maxi_area;
    }
};
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