263. Ugly Number 丑数

作者： 负雪明烛 id： fuxuemingzhu 个人博客： http://fuxuemingzhu.cn/

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[LeetCode]

题目地址：https://leetcode.com/problems/ugly-number/

Total Accepted: 22335 Total Submissions: 67449 Difficulty: Easy

题目描述

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.

Example 1:

Input: 6
Output: true
Explanation: 6 = 2 × 3

Example 2:

Input: 8
Output: true
Explanation: 8 = 2 × 2 × 2

Example 3:

Input: 14
Output: false 
Explanation: 14 is not ugly since it includes another prime factor 7.

Note:

1. 1 is typically treated as an ugly number.
2. Input is within the 32-bit signed integer range: [−231, 231 − 1].

题目大意

如果一个数的因子只有2,3,5，那么这个数是丑数。判断一个数是不是丑数。

解题方法

除去2,3,5因子

把这个数中的所有的2,3,5的因子全部除去，剩余的数为1，则说明全部为这几个因子构成。

python解法。

class Solution(object):
    def isUgly(self, num):
        """
        :type num: int
        :rtype: bool
        """
        if num <= 0: return False
        while num % 2 == 0:
            num /= 2
        while num % 3 == 0:
            num /= 3
        while num % 5 == 0:
            num /= 5
        return num == 1

Java解法：

public static boolean isUgly(int num) {
	if (num == 1) {
		return true;
	}

	while (num >= 2 && num % 2 == 0) {
		num = num / 2;
	}
	while (num >= 3 && num % 3 == 0) {
		num = num / 3;
	}
	while (num >= 5 && num % 5 == 0) {
		num = num / 5;
	}
	return num == 1;
}

另外有精简的答案如下。

public class Solution {
    public boolean isUgly(int num) {
        int[] divides ={2,3,5};
        for(int i = 0; i < divides.length && num > 0; i++){
            while(num % divides[i] == 0){
                num /= divides[i];
            }
        }
		return num == 1;
    }
}

日期

2015/10/16 21:20:23 2018 年 11 月 21 日 —— 又是一个美好的开始