<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>

int lsp(vector<int>& heights) {

        int n = heights.size();
        stack<int> a;

        vector<int> pref(n), suff(n);
        for (int i = 0; i < n; i++) {
            while (!a.empty() && heights[a.top()] >= heights[i])
                a.pop();

            if (a.empty())
                pref[i] = -1;
            else
                pref[i] = a.top();
            a.push(i);
        }

        while (!a.empty())
            a.pop();

    

        for (int i = n - 1; i >= 0; i--) {
            while (!a.empty() && heights[a.top()] >= heights[i])
                a.pop();

            if (a.empty())
                suff[i] = n;
            else
                suff[i] = a.top();
            a.push(i);
        }
        

        int ans =0;

        for (int i = 0; i < n; i++) {
            int cnt = 1;
            while (i + 1 < n && heights[i] == heights[i + 1]) {
                i++;
                cnt++;
            }
            ans = max(ans, cnt * heights[i]);
        }

        for (int i = 0; i < n; i++) {
                
                if(pref[i]==-1&&suff[i]==n)ans=max(ans,heights[i]*n);
                else if(pref[i]==-1)
                {
                    int mp=suff[i]-1;
                    ans=max(ans,(mp+1)*heights[i]);
                }
                else if(suff[i]==n)
                {
                    int mp=pref[i]+1;
                    ans=max(ans,(n-mp)*heights[i]);
                }
                else
                {
                    int p=pref[i]+1;
                    int q=suff[i]-1;
                    ans=max(ans,(q-p+1)*heights[i]);
                }
            
            }
        

        return ans;
    }

class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        int ans=0;
      int n=heights.size();
        for(int i=0;i<n;i++)
        {
            vector<int>a;
            while(i<n&&heights[i]>0){a.push_back(heights[i]);i++;}
            if(a.size()>0)
            {
              ans=max(ans,lsp(a));
            }
        }
        return ans;
     
    }
};
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