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power of number

admin 11月 11, 2020 0

Power of Two

Question

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

Analysis

  • 2^n的二进制数中只存在一个1，所以利用num&(num-1)==0 可以判断是否为2^n
  • Java中可以利用bitcount()

Code

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public class  {
    public boolean isPowerOfThree(int n) {
        return (n>0)&&Integer.bitcount(n)==1;
    }
}

Power of Three

Question

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

Analysis

Summary in LeetCode Discuss

利用log计算，

log3 12=2.26186
int(log3 12)=2
log3 12−int(log3 12)=0.26186

Log

Code

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public class  {
    public boolean isPowerOfThree(int n) {
        return (n>0)&&(Math.log10(n)/Math.log10(3))%1==0;
    }
}
 
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public class  {
    public boolean isPowerOfThree(int n) {
        if (n <= 0) {
            return false;
        } else {
            return Integer.toString(n, 3).matches("10*");
        }
    }
}

Power of Four

Question

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

Analysis

The basic idea is from power of 2, We can use “n&(n-1) == 0” to determine if n is power of 2. For power of 4, the additional restriction is that in binary form, the only “1” should always located at the odd position. For example, 4^0 = 1, 4^1 = 100, 4^2 = 10000. So we can use “num & 0x55555555==num” to check if “1” is located at the odd position.

Code

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public class  {
    public boolean isPowerOfThree(int n) {
        return (n>0)&&(num&(num-1)==0)&&(num&0x55555555)==num;
    }
}
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