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Intel code challenge elimination round (Div.1 + div.2, combined) d. generating sets greedy

2021-07-27 15:31:24 Sleepy

D. Generating Sets

Topic linking :

http://codeforces.com/contest/722/problem/D

Description

You are given a set Y of n distinct positive integers y1, y2, ..., yn.

Set X of n distinct positive integers x1, x2, ..., xn is said to generate set Y if one can transform X to Y by applying some number of the following two operation to integers in X:

Take any integer xi and multiply it by two, i.e. replace xi with 2·xi.
Take any integer xi, multiply it by two and add one, i.e. replace xi with 2·xi + 1. 

Note that integers in X are not required to be distinct after each operation.

Two sets of distinct integers X and Y are equal if they are equal as sets. In other words, if we write elements of the sets in the array in the increasing order, these arrays would be equal.

Note, that any set of integers (or its permutation) generates itself.

You are given a set Y and have to find a set X that generates Y and the maximum element of X is mininum possible.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 50 000) — the number of elements in Y.

The second line contains n integers y1, ..., yn (1 ≤ yi ≤ 109), that are guaranteed to be distinct.

Output

Print n integers — set of distinct integers that generate Y and the maximum element of which is minimum possible. If there are several such sets, print any of them.

Sample Input

5
1 2 3 4 5

Sample Output

4 5 2 3 1

Hint

The question

a number x, Can become 2x, Or become 2x+1, Can change several times

Now here you are n A different number Y, You need to find n Different x, Make this n Different x After changes , Can get Y Array , You have to minimize the initial maximum .

Ask what you should do .

Answer key :

greedy , Select the maximum number at a time , Then make the maximum number smaller , Change as you can , Use one set Just maintain it .

Code

#include<bits/stdc++.h>
using namespace std;

set<int> S;
int main()
{
    int n;scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        int x;scanf("%d",&x);
        S.insert(-x);
    }
    while(1)
    {
        int x=-*S.begin();
        int k = *S.begin();
        x/=2;
        while(x)
        {
            if(S.find(-x)==S.end())
            {
                S.insert(-x);
                break;
            }
            x/=2;
        }
        if(x==0)
        {
            for(auto it=S.begin();it!=S.end();it++)
                cout<<-*it<<" ";
            cout<<endl;
            return 0;
        }
        S.erase(k);
    }
    return 0;
}

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