<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>

typedef struct node{
    int index;
    int height;
};
class Solution {
public:
    int largestRectangleArea(vector<int>& heights) {
        stack<node> s;
        vector<int> maxs(heights.size(),0);
        s.push({0,heights[0]});
        maxs[0]=heights[0];
        
        for( int i=1;i<heights.size();i++){
            if( s.top().height<=heights[i] ){//no blocks bigger before heights[i]
                maxs[i]+=heights[i];
            }else{
                while( !s.empty()&&s.top().height>heights[i] ){
                    maxs[s.top().index]+=s.top().height*(i-s.top().index);
                    s.pop();
                }
                if( s.empty() ){//no blocks are bigger than the heights[i]
                    maxs[i]+=heights[i]*(i+1);   
                }else{
                    maxs[i]+=heights[i]*(i-s.top().index);
                }
            }
            s.push({i,heights[i]});
        }
        
        while( !s.empty() ){
            maxs[s.top().index]+=(heights.size()-s.top().index)*s.top().height;
            s.pop();
        }
        
        int res;
        for( int i=0;i<maxs.size();i++ ){
            maxs[i]-=heights[i];
            res=max(res,maxs[i]);
            cout << maxs[i] << " ";
        }
        cout << endl;
        
        return res;
    }
};
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