<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) {
        stack<pair<int, int>> higher;
        vector<pair<int, int>> border;
        // higher stack: l -> r
        for (int i = 0; i < heights.size(); ++i) {
            int leftBorder;
            while (!higher.empty() && higher.top().first >= heights[i]) {
                higher.pop();
            }
            if (higher.empty()) {
                leftBorder = 0;
            } else {
                leftBorder = higher.top().second + 1;
            }
            higher.push(make_pair(heights[i], i));
            border.push_back(make_pair(leftBorder, i));
        }
        while (!higher.empty()) {
            higher.pop();
        }
        // higher stack: r -> l
        for (int i = heights.size() - 1; i >= 0; --i) {
            int rightBorder;
            while (!higher.empty() && higher.top().first >= heights[i]) {
                higher.pop();
            }
            if (higher.empty()) {
                rightBorder = heights.size() - 1;
            } else {
                rightBorder = higher.top().second - 1;
            }
            higher.push(make_pair(heights[i], i));
            border[i].second = rightBorder;
        }
        int result = 0;
        for (int i = 0; i < heights.size(); ++i) {
            result = max(result, heights[i] * (border[i].second - border[i].first + 1));
        }
        return result;
    }
};
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