POJ 1730 Perfect Pth Powers (枚举||分解质因子)

Perfect Pth Powers

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 16638		Accepted: 3771

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 = b^p. 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

Sample Output

1
30
2

Source

Waterloo local 2004.01.31

从31往前枚举(因为数据最大不会超过32-bit (int))，用pow将要求的数字求出来，再进行验证，这里要注意精度问题。

这道题比较坑的是会有负数，对于负数的话，只能开奇数次方。

 1 #include<cmath>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<stdlib.h>
 5 #include<algorithm>
 6 #define LL __int64
 7 using namespace std;
 8 int main()
 9 {
10     //freopen("in.txt","r",stdin);
11     int n,x,y;
12     while(scanf("%d",&n)&&n)
13     {
14         if(n>0)
15         {
16             for(int i=31;i>=1;i--)
17             {
18                 x=(int)(pow(n*1.0,1.0/i)+0.5);
19                 y=(int)(pow(x*1.0,1.0*i)+0.5);
20                 if(n==y)
21                 {
22                     printf("%d
",i);
23                     break;
24                 }
25             }
26         }
27         else
28         {
29             n=-n;
30             for(int i=31;i>=1;i-=2)
31             {
32                 x=(int)(pow(n*1.0,1.0/i)+0.5);
33                 y=(int)(pow(x*1.0,1.0*i)+0.5);
34                 if(n==y)
35                 {
36                     printf("%d
",i);
37                     break;
38                 }
39             }
40         }
41     }
42     return 0;
43 }

View Code

还可以用分解质因子的方法来做

所求的答案就是所给的数的所有质因子的指数的最大公约数

大牛是这么做的

http://www.cnblogs.com/Lyush/archive/2012/07/14/2591872.html