标签：while tip integer oop signed nbsp bsp XA mat
Given an integer (signed 32 bits), write a function to check whether it is a power of 4.
Example:
Given num = 16, return true.
Given num = 5, return false.
Follow up: Could you solve it without loops/recursion?
解法1，经典的数学解法：
class Solution(object):
def isPowerOfFour(self, num):
"""
:type num: int
:rtype: bool
"""
if num <= 0: return False
n = int(round(math.log(num, 4)))
return 4**n == num
解法2，迭代：
class Solution(object):
def isPowerOfFour(self, num):
"""
:type num: int
:rtype: bool
"""
if num <= 0: return False
while num >= 4:
if num % 4 != 0:
return False
num = num / 4
return num == 1
解法3，最牛叉，
class Solution(object):
def isPowerOfFour(self, num):
"""
:type num: int
:rtype: bool
"""
return num > 0 and (num & (num - 1)) == 0 and (num - 1) % 3 == 0
因为，4^n - 1 = C(n,1)*3 + C(n,2)*3^2 + C(n,3)*3^3 +.........+ C(n,n)*3^n
i.e (4^n - 1) = 3 * [ C(n,1) + C(n,2)*3 + C(n,3)*3^2 +.........+ C(n,n)*3^(n-1) ]
This implies that (4^n - 1) is multiple of 3.
类似解法：
return n & (n-1) == 0 and n & 0xAAAAAAAA == 0
或者是：
class Solution(object):
def isPowerOfFour(self, n):
"""
:type num: int
:rtype: bool
"""
#1, 100, 10000, 1000000, 100000000, ....
#1, 100 | 10000 | 1000000 | 100000000, ... = 0101 0101 0101 0101 0101 0101 0101 0101
return n > 0 and n & (n-1) == 0 and (n & 0x55555555 != 0)
因为n & n-1 == 0 就可以确定只有1个1， so 只要保证1的位置在1，3，5，7，。。。。这些位置上就行。
标签：while tip integer oop signed nbsp bsp XA mat
原文地址：https://www.cnblogs.com/bonelee/p/9206525.html
