<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 n = heights.size(), maximum = 0;
    stack<int> sta;
    vector<pair<int, int>> vc(n, make_pair(-1, n));

    for (int i = 0; i < n; i++) {
      while (!sta.empty() && heights[i] <= heights[sta.top()]) {
        vc[sta.top()].second = i;
        sta.pop();
      }
      vc[i].first = (sta.empty()) ? -1 : sta.top();
      sta.push(i);
    }

    for (int i = 0; i < n; i++) {
      maximum = max(maximum, (vc[i].second - vc[i].first - 1) * heights[i]);
    }

    return maximum;
  }
};
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