Ugly Number

Question

Write a program to check whether a given number is an ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 6, 8 are ugly while 14 is not ugly since it includes another prime factor 7.

Notice

Note that 1 is typically treated as an ugly number.

Example

Given num = 8 return true
Given num = 14 return false

Analysis

基本思路就是,对于num,如果取余数(2,3,5中其一)为0,说明对应的prime number能够被整除,所以一直除下去。最终如果是Ugly Number,该结果应当是1。时间复杂度是O(logn)。

Solution

public class Solution {
    /**
     * @param num an integer
     * @return true if num is an ugly number or false
     */
    public boolean isUgly(int num) {
        if (num == 0) {
            return false;
        }
        if (num == 1) {
            return true;
        }
        int[] primes = new int[]{2, 3, 5};
        for (int i = 0; i < primes.length; i++) {
            while (num % primes[i] == 0) {
                num = num / primes[i];
            }
        }
        return num == 1;
    }
}

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