codeforces 573A （數論）

題意描述

Limak is an old brown bear. He often plays poker with his friends. Today they went to a casino. There are n players (including Limak himself) and right now all of them have bids on the table. i-th of them has bid with size a i dollars.

Each player can double his bid any number of times and triple his bid any number of times. The casino has a great jackpot for making all bids equal. Is it possible that Limak and his friends will win a jackpot?

給你幾個數字，你可以對這些數字進行無限次的乘2和乘3操作，詢問你最後是否能將它們變爲相同

思路

假設最後相同的數字爲k，則得到式子：2^x3^xz=k，我們只需要將每個數所有的2和3去除，最後判斷數字是否相同即可

AC代碼

#include<bits/stdc++.h>
#define x first
#define y second
#define pb push_back
#define IOS ios::sync_with_stdio(false);cin.tie(0);
using namespace std;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long,long> PLL;
typedef pair<char,char> PCC;
typedef long long LL;
const int N=2*1e5+10;
const int M=150;
const int INF=0x3f3f3f3f;
const int MOD=998244353;
int a[N];
int ff[4],ft[4]={1,2,3,6};
int main(){
    IOS;
    int n;cin>>n;
    for(int i=1;i<=n;i++) cin>>a[i];
    for(int i=1;i<=n;i++){
        while(a[i]%2==0) a[i]/=2;
        while(a[i]%3==0) a[i]/=3;
    }
    string ans="Yes";
    for(int i=1;i<n;i++) if(a[i]!=a[i+1]) ans="No";
    cout<<ans<<endl;
    return 0;
}