4. Ugly Number II / 264. Ugly Number II

• 本題難度: Medium

• Topic: Data Structure

  Description

  Ugly number is a number that only have factors 2, 3 and 5.

Design an algorithm to find the nth ugly number. The first 10 ugly numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12...

Example
Example 1:

Input: 9
Output: 10
Example 2:

Input: 1
Output: 1
Challenge
O(n log n) or O(n) time.

Notice
Note that 1 is typically treated as an ugly number.

我的代碼 超時。因為每個數都要判斷一次

    def nthUglyNumber(self, n: ‘int‘) -> ‘int‘:
        cur = 1
        while(n-1):
            cur += 1
            if self.isUgly(cur):
                n -= 1       
        return cur
    def isUgly(self, n):
        ugly = [2,3,5]
        for i in ugly:
            while(n % i == 0):
                n //= i
        return n == 1 
 

別人的代碼

class Solution:
    def nthUglyNumber(self, n: ‘int‘) -> ‘int‘:
        res = [1]
        i2 = i3 = i5 = 0
        while(n>1):
            u2, u3, u5 = 2*res[i2], 3*res[i3], 5*res[i5]
            uCurr = min(u2,u3,u5)
            if uCurr == u2:
                i2 += 1
            if uCurr == u3:
                i3 += 1
            if uCurr == u5:
                i5 += 1
            res.append(uCurr)
            n -= 1
        return res[-1]
 

思路
非常巧妙的思路。
所有ugly number都是由2，3，5組成的，所以他們肯定都是由2，3，5乘以之前的數得到，i2,i3,i5記錄的分別是當前還未被乘2，3，5過的數字，接下來的ugly number肯定在其中，因為比它們更小的都已經在res中了

• 時間復雜度 O(n)

[Lintcode]4. Ugly Number II/[Leetcode]264. Ugly Number II