<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 <bits/stdc++.h>
using namespace std;

class Solution {
public:
  // Here goes a function
  int largestRectangleArea(vector<int> &heights) {
    stack<int> next_lower;
    vector<pair<int, int>> limits(heights.size());
    for (int i = 0; i < heights.size(); ++i) {
      while (!next_lower.empty() && heights[next_lower.top()] > heights[i]) {
        limits[next_lower.top()].second = i - 1;
        next_lower.pop();
      }
      next_lower.push(i);
    }
    while (!next_lower.empty()) {
      limits[next_lower.top()].second = heights.size() - 1;
      next_lower.pop();
    }
    for (int i = heights.size() - 1; i >= 0; --i) {
      while (!next_lower.empty() && heights[next_lower.top()] > heights[i]) {
        limits[next_lower.top()].first = i + 1;
        next_lower.pop();
      }
      next_lower.push(i);
    }
    while (!next_lower.empty()) {
      limits[next_lower.top()].first = 0;
      next_lower.pop();
    }

    int max_rectangle = 0;
    for (int i = 0; i < limits.size(); i++) {
      max_rectangle = max(
          max_rectangle, heights[i] * (limits[i].second - limits[i].first + 1));
    }
    return max_rectangle;
  };
};


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