<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:

    void nextSmallerElement(vector<int>& arr, vector<int>& nextAns) {
        stack<int> st;
        st.push(-1);
        int n = arr.size();

        for(int i=n-1; i>=0; i--) {

            int element = arr[i];

            
            while(st.top() != -1 && arr[st.top()] >= element) {
                st.pop();
            } 
            //agar yaha tk pohocha hu, iska mtlb
            //k ya toh koi choota number stack top pr h 
            //ya fer -1 stack top pr h 
            nextAns.push_back(st.top());
            //current number ko toh stack me push krna hi h 
            st.push(i);
        }
    }

    void prevSmallerElement(vector<int>& arr, vector<int>& prevAns) {
        stack<int> st;
        st.push(-1);
        int n = arr.size();

        for(int i=0; i<n; i++) {
            int element = arr[i];
            
            
            
            while( st.top()!= -1 && arr[ st.top()] >= element) {
                st.pop();
            } 
         
            prevAns.push_back(st.top());
           
            st.push(i);
        }
    }

    int largestRectangleArea(vector<int>& heights) {
        vector<int> nextAns;
        vector<int> prevAns;
        nextSmallerElement(heights,nextAns);
        reverse(nextAns.begin(), nextAns.end());
       
        for(int i=0 ;i<nextAns.size(); i++) {
            if(nextAns[i] == -1) {
                nextAns[i] = nextAns.size(); 
            }
        }
      

        prevSmallerElement(heights, prevAns);

        int maxArea = INT_MIN;
        for(int i=0; i<nextAns.size(); i++) {
            int width = nextAns[i]-prevAns[i]-1;
            int height = heights[i];
            int currArea = width * height;
            maxArea = max(maxArea, currArea);
        }
        
        return maxArea;
    }
};
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