<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>


#include <iostream>
#include <utility>
#include <vector>

class Solution {
private:
    struct Record { int height_; std::size_t index_; };
public:
    int largestRectangleArea(std::vector<int>& heights) {
        if (heights.empty()) {
            return 0;
        }
        std::vector<Record> trail{};
        trail.reserve(heights.size());
        std::size_t largestArea = 0;
        for (std::size_t i = 0; i < heights.size(); i++) {
            int currHeight = heights[i];
            std::size_t start = i;
            Record prev = trail.back();
            while (!trail.empty() && currHeight <= trail.back().height_) {
                Record prev = trail.back();
                largestArea = std::max(largestArea, (i - prev.index_) * prev.height_);
                start = prev.index_;
                trail.pop_back();
                if (trail.empty()) {
                    break;
                }
                prev = trail.back();
            }
            trail.emplace_back(currHeight, start);
        }
        for (const auto& record : trail) {
            largestArea = std::max(largestArea, (heights.size() - record.index_) * record.height_);
        }
        return largestArea;
    }

};
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