C. Amr and Chemistry（Codeforces Round #312 (Div. 2) 二进制+暴力）

C. Amr and Chemistry

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Amr loves Chemistry, and specially doing experiments. He is preparing for a new interesting experiment.

Amr has n different types of chemicals. Each chemical i has an initial volume of ai liters. For this experiment, Amr has to mix all the chemicals together, but all the chemicals volumes must be equal first. So his task is to make all the chemicals volumes equal.

To do this, Amr can do two different kind of operations.

• Choose some chemical i and double its current volume so the new volume will be 2ai
• Choose some chemical i and divide its volume by two (integer division) so the new volume will be 

Suppose that each chemical is contained in a vessel of infinite volume. Now Amr wonders what is the minimum number of operations required to make all the chemicals volumes equal?

Input

The first line contains one number n (1 ≤ n ≤ 105), the number of chemicals.

The second line contains n space separated integers ai (1 ≤ ai ≤ 105), representing the initial volume of the i-th chemical in liters.

Output

Output one integer the minimum number of operations required to make all the chemicals volumes equal.

Sample test(s)

input

3
4 8 2

output

2

input

3
3 5 6

output

5

Note

In the first sample test, the optimal solution is to divide the second chemical volume by two, and multiply the third chemical volume by two to make all the volumes equal 4.

In the second sample test, the optimal solution is to divide the first chemical volume by two, and divide the second and the third chemical volumes by two twice to make all the volumes equal 1.

题意：给定n长的序列，每次能够选一个数 让其 乘以2 或者 除以2。问至少操作多少次使得全部数相等。

点击打开链接

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

using namespace std;

int a[1000050];
int num[1000010];
int v[10000060];
int maxx;
int n;

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        memset(num,0,sizeof(num));
        memset(v,0,sizeof(v));
        maxx = -1;
        for(int i=0; i<n; i++)
        {
            scanf("%d",&a[i]);
            v[a[i]]++;
            if(maxx<a[i])
            {
                maxx = a[i];
            }
        }
        for(int i=0; i<n; i++)
        {
            int t = a[i];
            int cnt = 0;
            while(t<maxx)
            {
                t = t<<1;
                cnt++;
                v[t]++;
                num[t] += cnt;
            }
            cnt = 0;
            int pp;
            t = a[i];
            while(t>0)
            {
                int flag = 0;
                if(t%2 == 1 && t!=1)
                {
                    flag = 1;
                }
                t = t>>1;
                cnt++;
                v[t]++;
                num[t] += cnt;
                if(flag == 1)
                {
                    pp = t;
                    int pcnt = cnt;
                    while(pp<maxx)
                    {
                        pp = pp<<1;
                        pcnt++;
                        v[pp]++;
                        num[pp] += pcnt;
                    }

                }
            }
        }
        int minn = 9999999;
        for(int i=0; i<=maxx; i++)
        {

            if(v[i] == n && minn > num[i])
            {
                minn = num[i];
            }
        }
        printf("%d
",minn);
    }
    return 0;
}