<p>You are given an array of people, <code>people</code>, which are the attributes of some people in a queue (not necessarily in order). Each <code>people[i] = [h<sub>i</sub>, k<sub>i</sub>]</code> represents the <code>i<sup>th</sup></code> person of height <code>h<sub>i</sub></code> with <strong>exactly</strong> <code>k<sub>i</sub></code> other people in front who have a height greater than or equal to <code>h<sub>i</sub></code>.</p>

<p>Reconstruct and return <em>the queue that is represented by the input array </em><code>people</code>. The returned queue should be formatted as an array <code>queue</code>, where <code>queue[j] = [h<sub>j</sub>, k<sub>j</sub>]</code> is the attributes of the <code>j<sup>th</sup></code> person in the queue (<code>queue[0]</code> is the person at the front of the queue).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> people = [[7,0],[4,4],[7,1],[5,0],[6,1],[5,2]]
<strong>Output:</strong> [[5,0],[7,0],[5,2],[6,1],[4,4],[7,1]]
<strong>Explanation:</strong>
Person 0 has height 5 with no other people taller or the same height in front.
Person 1 has height 7 with no other people taller or the same height in front.
Person 2 has height 5 with two persons taller or the same height in front, which is person 0 and 1.
Person 3 has height 6 with one person taller or the same height in front, which is person 1.
Person 4 has height 4 with four people taller or the same height in front, which are people 0, 1, 2, and 3.
Person 5 has height 7 with one person taller or the same height in front, which is person 1.
Hence [[5,0],[7,0],[5,2],[6,1],[4,4],[7,1]] is the reconstructed queue.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> people = [[6,0],[5,0],[4,0],[3,2],[2,2],[1,4]]
<strong>Output:</strong> [[4,0],[5,0],[2,2],[3,2],[1,4],[6,0]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= people.length &lt;= 2000</code></li>
	<li><code>0 &lt;= h<sub>i</sub> &lt;= 10<sup>6</sup></code></li>
	<li><code>0 &lt;= k<sub>i</sub> &lt; people.length</code></li>
	<li>It is guaranteed that the queue can be reconstructed.</li>
</ul>

class Solution {
    int n;
    int getNext(int val){
        return val + (val&-val);
    }

    int getParent(int val){
        return val - (val&-val);
    }

    void update(vector<int>& tree, int index, int val){
        if(index>=tree.size()){
            return;
        }
        tree[index]+=val;
        update(tree, getNext(index), val);
    }

    void buildFenwickTree( vector <int> &t)
    {
        for(int i=1;i<n;i++)
        {
            int p= i + (i&-i);
            if(p<=n)
                t[p]+=t[i]; 
        }
    }

    void buildTree(vector<int>& tree){
        for(int i=1;i<=n;i++){
            update(tree, i, 1);
        }
    }

    int emptyTillPos(vector<int>& tree, int index){
        int sum=0;
        while(index>0){
            sum+=tree[index];
            index=getParent(index);
        }
        return sum;
    }
public:
    vector<vector<int>> reconstructQueue(vector<vector<int>>& people) {
        n=people.size();
        vector<int> tree(n+1, 0);
        buildTree(tree);
        vector<int> tree2(n+1, 1);
        buildFenwickTree(tree2);
        for(auto i: tree){
            cout<<i<<" ";
        }
        cout<<endl;
        for(auto i: tree2){
            cout<<i<<" ";
        }
        cout<<endl;
        auto compareFunction = [](vector<int>& p1, vector<int>& p2){
            if(p1[0]!=p2[0]){
                return p1[0]<p2[0];
            }
            return p1[1]>p2[1];
        };
        sort(people.begin(), people.end(), compareFunction);
        vector<vector<int>> ans(n);
        for(int i=0;i<n;i++){
            int l=1, r=n, mid;
            while(l<r){
                mid = (l+r)/2; 
                if(emptyTillPos(tree, mid)<=people[i][1]){
                    l=mid+1;
                }else{
                    r=mid;
                }
            }
            update(tree, l, -1);
            ans[l-1]=people[i];
        }
        return ans;
    }
};
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