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264. Ugly Number II (Medium)

Write a program to find the n-th ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. 

Example:

Input: n = 10
Output: 12
Explanation: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.

Note:  

1. 1 is typically treated as an ugly number.
2. n does not exceed 1690.

Related Topics

[Heap] [Math] [Dynamic Programming]

Similar Questions

1. Merge k Sorted Lists (Hard)
2. Count Primes (Easy)
3. Ugly Number (Easy)
4. Perfect Squares (Medium)
5. Super Ugly Number (Medium)

Hints

Hint 1

The naive approach is to call isUgly for every number until you reach the n^th one. Most numbers are not ugly. Try to focus your effort on generating only the ugly ones.

Hint 2

An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.

Hint 3

The key is how to maintain the order of the ugly numbers. Try a similar approach of merging from three sorted lists: L₁, L₂, and L₃.

Hint 4

Assume you have U_k, the k^th ugly number. Then U_k+1 must be Min(L₁ * 2, L₂ * 3, L₃ * 5).