<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:
    vector<int> nextSmall(vector<int> &arr){
        vector<int> sol(arr.size());
        stack<int> st;
        st.push(-1);
        for(int i = arr.size()-1; i>=0; i--){
            while(st.top()!=-1 && arr[st.top()]>=arr[i]){
                st.pop();
            }
            sol[i] = st.top();
            st.push(i);
        }
        return sol;
    }

    vector<int> prevSmall(vector<int> &arr){
        vector<int> sol(arr.size());
        stack<int> st;
        st.push(-1);
        for(int i = 0; i<arr.size(); i++){
            while(st.top()!= -1 && arr[st.top()]>=arr[i]){
                st.pop();
            }
            sol[i] = st.top();
            st.push(i);
        }
        return sol;
    }

    int largestRectangleArea(vector<int>& heights) {
        vector<int> next = nextSmall(heights);
        for(int i = 0; i<heights.size(); i++){
            if(next[i] == - 1){
                next[i] = heights.size();
            }
        }
        vector<int> prev = prevSmall(heights);
        vector<int> areaVec(next.size());
        for(int i = 0; i<next.size();i++){
            int height = heights[i];
            int width = next[i] - prev[i] - 1;
            int area = height * width;
            areaVec[i] = area;
        }
        int maxi = INT_MIN;
        for(int i = 0; i<areaVec.size(); i++){
            maxi = max(maxi, areaVec[i]);
        }
        return maxi;

    }
};
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