<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>& nums) {
        int n = nums.size();
        vector<int> nse(n);
        stack<int> st;
        for (int i = n - 1; i >= 0; i--) {
            while (!st.empty() && nums[st.top()] >= nums[i])
                st.pop();
            nse[i] = st.empty() ? n : st.top();
            st.push(i);
        }
        return nse;
    }

    vector<int> findPSEE(vector<int>& nums) {
        int n = nums.size();
        vector<int> psee(n);
        stack<int> st;
        for (int i = 0; i < n; i++) {
            while (!st.empty() && nums[st.top()] > nums[i])
                st.pop();
            psee[i] = st.empty() ? -1 : st.top();
            st.push(i);
        }
        return psee;
    }

    int largestRectangleArea(vector<int>& heights) {
        vector<int> nse = findNSE(heights);
        vector<int> psee = findPSEE(heights);
        int maxi = 0;
        
        for (int i = 0; i < heights.size(); i++) {
            int width = nse[i] - psee[i] - 1;
            int area = heights[i] * width;
            maxi = max(maxi, area);
        }
        
        return maxi;
    }
};

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