What’s a Perfect Power anyway?
Codewars Kata 34√
Description
https://www.codewars.com/kata/54d4c8b08776e4ad92000835
-简述：本题给定一个整数n，试判断该数字是否为perfect power，如果是，则存在两个整数m,k，使得m^k==n
-思路：遍历m和k，进行判断
-难点：1 for循环的范围不能超时
A perfect power is a classification of positive integers:
In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that mk = n.
Your task is to check wheter a given integer is a perfect power. If it is a perfect power, return a pair m and k with mk = n as a proof. Otherwise return Nothing, Nil, null, NULL, None or your language’s equivalent.
Note: For a perfect power, there might be several pairs. For example 81 = 3^4 = 9^2, so (3,4) and (9,2) are valid solutions. However, the tests take care of this, so if a number is a perfect power, return any pair that proves it.
Examples
isPP(4) => [2,2]
isPP(9) => [3,2]
isPP(5) => None
My solution
from math import log, sqrt
def isPP(n):
for m in range(2, int(sqrt(n)) + 1):
k = int(round(log(n, m)))
if m ** k == n:
return [m, k]
return None
Points
1 round() 方法返回浮点数x的四舍五入值。
2 对m的范围设定很重要，否则会超时。
