<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:
    int d1[100004];
    int d2[100004];
    int largestRectangleArea(vector<int>& heights) {
        memset(d2,-1,sizeof(d2));
        stack<pair<int,int>> st;
        int n = heights.size();
        st.push({heights[0],0});
        for(int i = 1; i < n; i++)
        {
            if(heights[i] < st.top().first)
            {
                while(!st.empty() and st.top().first > heights[i])
                {
                    d1[st.top().second] = i;
                    st.pop();

                }
                st.push({heights[i],i});
            }
            else
            {
                st.push({heights[i],i});
            }
        }
        int ans = 0;
        for(int i = 0; i < n;i++)
        {
            if(d1[i] == 0)
                d1[i] = n;
            // cout << d1[i] << " ";
            // ans = max(ans,(d1[i]-i) * heights[i]);
        }
        // cout << ans << endl;
        while(!st.empty()){
            st.pop();
        }
        st.push({heights[n-1],n-1});
        for(int i = n-2; i >= 0; i--)
        {
            if(heights[i] < st.top().first )
            {
                while(!st.empty() and  st.top().first > heights[i])
                {
                    d2[st.top().second] = i;
                    st.pop();
                }
                st.push({heights[i],i});
            }
            else
            {
                st.push({heights[i],i});
            }
        }
        // for(int i = 0; i < n; i++)
        // {
        //     cout << d2[i] << " ";
        //     ans = max(ans,(i-d2[i]) * heights[i]);
        // }
        // cout << endl;
        for(int i = 0; i < n; i++)
        {
            // cout<< i << " " << d2[i] << " " << d1[i] << " " << (i-d2[i] + d1[i]-i-1) * heights[i] << endl;
            ans = max(ans,(i-d2[i] + d1[i]-i-1) * heights[i]);
        }
        return ans;
    }
};
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