hdu 1719

Friend

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2073    Accepted Submission(s): 1046

Problem Description

Friend number are defined recursively as follows. (1) numbers 1 and 2 are friend number; (2) if a and b are friend numbers, so is ab+a+b; (3) only the numbers defined in (1) and (2) are friend number. Now your task is to judge whether an integer is a friend number.

 

Input

There are several lines in input, each line has a nunnegative integer a, 0<=a<=2^30.

 

Output

For the number a on each line of the input, if a is a friend number, output “YES!”, otherwise output “NO!”.

 

Sample Input

3 13121 12131

 

Sample Output

YES! YES! NO!

 

Source

2007省赛集训队练习赛（2）

 

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心塞的一题。。。。。。。

friend 数为ab+a+b，那么可以变成(a+1)(b+1)-1,只要给一个数加上1，然后判断他是否是由一系列2和一系列3组成的，

因为所有的数都是有(a+1)(b+1) ,2,3递推而来的。

#include <iostream>
#include <cstdio>
#define LL int
using namespace std;

void solve(LL x)
{
    while((x%2)==0)
    {
        x/=2;
        if(x==1)
            break;
    }
    while((x%3)==0)
    {
        x/=3;
        if(x==1)
            break;
    }
    if(x==1)
       printf("YES!
");
    else
        printf("NO!
");
}
int main()
{
    LL x,T;
    while(~scanf("%d",&x))
    {
        if(x==1 || x==2)
            printf("YES!
");
        if(x==0)
             printf("NO!
");
        if(x!=1 && x!=2 && x!=0)
        solve(x+1);
    }
    return 0;
}