Perfect Pth Powers解题报告

Description


We say that x is a perfect square if, for some integer b, x = b2. Similarly, x is a perfect cube if, for some integer b, x
= b3. More generally, x is a perfect pth power if, for some integer b, x = bp. Given an integer x you are to determine the largest p such that x is a perfect pth power.

Input

Each test case is given by a line of input containing x. The value of x will have magnitude at least 2 and be within the range of a (32-bit) int in C, C++, and Java. A line containing 0 follows the
last test case.

Output

For each test case, output a line giving the largest integer p such that x is a perfect pth power.

Sample Input

17
1073741824
25
0

Sample Output

1
30
2
#include<stdio.h>
#include<math.h>
int main()
{
double n,b;
long x,y;
int i;
while(scanf("%lf",&n)!=EOF)
{
if(n==0)
break;
if(n>0)
{
for(i=32;i>=0;i--)
{
b=pow(n,1.0/i);
x=b;    //类型转换为long
y=x+1;  //
if(b-x<=1e-12||y-b<=1e-12)
{
printf("%d\n",i);
break;
}
}
}
if(n<0)
{
n=-n;  //if n《0，先转化为正数先，然后i 只能为奇数，查找i。
for(i=31;i>=1;i-=2)
{
b=pow(n,1.0/i);
x=b;      //类型转换为long。
y=x+1;    //
if(b-x<=1e-12||y-b<=1e-12)
{
printf("%d\n",i);
break;
}
}
}
}
return 0;
}