# [231. Power of Two](https://leetcode.com/problems/power-of-two/)

## 题目

Given an integer, write a function to determine if it is a power of two.

**Example 1**:

    Input: 1
    Output: true 
    Explanation: 2^0 = 1

**Example 2**:

    Input: 16
    Output: true
    Explanation: 2^4 = 16

**Example 3**:

    Input: 218
    Output: false

## 题目大意

给定一个整数，编写一个函数来判断它是否是 2 的幂次方。


## 解题思路

- 判断一个数是不是 2 的 n 次方。
- 这一题最简单的思路是循环，可以通过。但是题目要求不循环就要判断，这就需要用到数论的知识了。这一题和第 326 题是一样的思路。


## 代码

```go

package leetcode

// 解法一 二进制位操作法
func isPowerOfTwo(num int) bool {
	return (num > 0 && ((num & (num - 1)) == 0))
}

// 解法二 数论
func isPowerOfTwo1(num int) bool {
	return num > 0 && (1073741824%num == 0)
}

// 解法三 打表法
func isPowerOfTwo2(num int) bool {
	allPowerOfTwoMap := map[int]int{1: 1, 2: 2, 4: 4, 8: 8, 16: 16, 32: 32, 64: 64, 128: 128, 256: 256, 512: 512, 1024: 1024, 2048: 2048, 4096: 4096, 8192: 8192, 16384: 16384, 32768: 32768, 65536: 65536, 131072: 131072, 262144: 262144, 524288: 524288, 1048576: 1048576, 2097152: 2097152, 4194304: 4194304, 8388608: 8388608, 16777216: 16777216, 33554432: 33554432, 67108864: 67108864, 134217728: 134217728, 268435456: 268435456, 536870912: 536870912, 1073741824: 1073741824}
	_, ok := allPowerOfTwoMap[num]
	return ok
}

// 解法四 循环
func isPowerOfTwo3(num int) bool {
	for num >= 2 {
		if num%2 == 0 {
			num = num / 2
		} else {
			return false
		}
	}
	return num == 1
}

```