<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> findNse(vector<int>& heights) {
        int n = heights.size();
        vector<int> ns(n, n);
        stack<pair<int,int>> st;

        for (int i = n - 1; i >= 0; i--) {
            while (!st.empty() && st.top().first > heights[i]) {
                st.pop();
            }
            ns[i] = st.empty() ? n : st.top().second;
            st.push({heights[i],i});
        }
        return ns;
    }
    vector<int> findPse(vector<int>& heights) {
        int n = heights.size();
        vector<int> ps(n, -1);
        stack<pair<int,int>> st;

        for (int i = 0; i < n; i++) {
            while (!st.empty() && st.top().first >= heights[i]) {
                st.pop();
            }
            ps[i] = st.empty() ? -1 : st.top().second;
            st.push({heights[i],i});
        }
        return ps;
    }
    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        vector<int> pse(n);
        vector<int> nse(n);

        pse = findPse(heights);
        nse = findNse(heights);

        int maxi = 0;

        for (int i = 0; i < n; i++) {
            int area = heights[i] * (nse[i] - pse[i] - 1);
            maxi = max(maxi, area);
        }
        return maxi;
    }
};
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