<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:
    int largestRectangleArea(vector<int>& heights) {
        int maxA = 0; 
        int H = heights.size(); 

        vector<int> leftArr (H, 0); 
        vector<int> rightArr (H, 0); 

        int idx; 
        for (int i = 1; i < H; i++) {
            idx = i - 1; 
            while(idx >= 0 && heights[idx] >= heights[i]) {
                idx = idx - leftArr[idx] - 1;
            } idx++; 

            leftArr[i] = i - idx; 
        }

        for (int i = H - 2; i >= 0; i--) {
            idx = i + 1; 
            while(idx < H && heights[idx] >= heights[i]) {
                idx = idx + rightArr[idx] + 1;
            } idx--;

            rightArr[i] = idx - i; 
        }

        // for (auto& l : leftArr) {
        //     cout << l << " "; 
        // } cout << endl;

        // for (auto& r : rightArr) {
        //     cout << r << " "; 
        // } cout << endl; 

        for (int i = 0; i < H; i++) {
            maxA = max(maxA, (rightArr[i] + leftArr[i] + 1) * heights[i]); 
        }

        return maxA;
        
    }
};
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