<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:
    int largestRectangleArea(vector<int>& heights) {
        vector<int> lefts;
        stack<int> next_sm;

        for(int i =0; i<heights.size(); i++){
            if(next_sm.empty()){
                lefts.push_back(i);
                next_sm.push(i);
            }else{
                int curr = next_sm.top();
                while(!next_sm.empty() && heights[curr] >= heights[i]){
                    next_sm.pop();
                    if(next_sm.empty())
                        curr = -1;
                    else
                        curr = next_sm.top();
                }
                lefts.push_back(curr+1);
                next_sm.push(i);
            }
        }
        
        vector<int> rights(heights.size());
        stack<int> prev_sm;

        for(int i = heights.size()-1; i >= 0; i--){
            if(prev_sm.empty()){
                prev_sm.push(i);
                rights[i] = i;
            }else{
                int curr = prev_sm.top();
                while(!prev_sm.empty() && heights[curr] >= heights[i]){
                    prev_sm.pop();
                    if(prev_sm.empty())
                        curr = heights.size();
                    else
                        curr = prev_sm.top();
                }
                rights[i] = curr - 1;
                prev_sm.push(i);
            }
        }

        int ar_max = 0;
        for(int i =0; i<heights.size(); i++){
            // cout << lefts[i] << " " << rights[i] <<endl;
            ar_max = max(ar_max, heights[i]*(rights[i] - lefts[i] + 1));
        }
        return ar_max;
    }
};
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