<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> findSmall(const vector<int>& a) {
        vector<int> b(a.size(), -1);
        stack<int> s;

        for (int i = 0; i < a.size(); ++i) {
            while (!s.empty() && a[s.top()] > a[i]) {
                s.pop();
            }
            if (!s.empty()) {
                b[i] = a[s.top()];
            }
            s.push(i);
        }

        return b;
    }

    int largestRectangleArea(vector<int>& heights) {
        stack<int> s;
        int maxArea = 0;
        int n = heights.size();
        vector<int> nextSmaller = findSmall(heights);

        for (int i = 0; i < n; ++i) {
            while (!s.empty() && heights[s.top()] > heights[i]) {
                int height = heights[s.top()];
                s.pop();
                int width = s.empty() ? i : (i - s.top() - 1);
                maxArea = max(maxArea, height * width);
            }
            s.push(i);
        }

        while (!s.empty()) {
            int height = heights[s.top()];
            s.pop();
            int width = s.empty() ? n : (n - s.top() - 1);
            maxArea = max(maxArea, height * width);
        }

        return maxArea;
    }
};

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