<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) {
        int n = heights.size();
        vector<pair<int, int>> vec;
        //<tall, idx>
        //only check when it pop
        // and the last vec
        int res = 0;

        for(int i = 0; i < n; i++){
            int h = heights[i];
            //binary search vec
            int left = 0, right = vec.size();
            while(left < right){
                int mid = (left + right) / 2;
                if(vec[mid].first < h){
                    left = mid + 1; 
                }
                else{
                    right = mid;
                }
            }
            //put new h into newvec
            if(left < vec.size()){
                vec.insert(vec.begin() + left, {h, vec[left].second});
                
                //others check max
                left++;
                int len = left;
                for( ; left < vec.size(); left++){
                    res = max(res, vec[left].first * (i - vec[left].second ));
                }
                vec.resize(len);
            }
            else vec.push_back({h, i});
            
        }
        for(int left = 0, i = n ; left < vec.size(); left++){
            res = max(res, vec[left].first * (i - vec[left].second));
        }

        return res;
    }
    // void printp(vector<pair<int, int>>& v){
    //     for(auto p: v) {
    //         cout << p.first << " " <<  p.second << ", ";
    //     }
    //     cout << endl;
    // }
};
/*      
        
        unordered_map<int , int> mp;
        //<tall, maxlen>

        queue<pair<int, int>> que;
        for(int& h: heights){
            que.push({h, 0});
            queue<pair<int, int>> newque;
            while(!que.empty()){
                if(h == 0) break;
                // can be binary search by using vector
                auto [tall, curlen] = que.front();
                curlen += 1;
                que.pop();
                if(h <= tall){
                    tall = h;
                }
                newque.push({tall, curlen });
                if(mp[tall] < curlen ){
                    mp[tall] = curlen ;
                    res = max(res, tall * curlen);
                }
                if(tall == h) break;
            }
            que = move(newque);
        }
*/
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