2018-10-22 Ugly Number II [M]

4. Ugly Number II

LC: 264
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
If n=9, return 10.

Challenge
O(n log n) or O(n) time.

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

import heapq

class Solution:
    """
    @param n: An integer
    @return: the nth prime number as description.
    """
    def nthUglyNumber(self, n):
        heap = [1]
        visited = set([1])        

        for _ in range(n):
            curr = heapq.heappop(heap)
            for factor in [2, 3, 5]:
                new_num = curr * factor
                if new_num not in visited:
                    heapq.heappush(heap, new_num)
                    visited.add(new_num)
        
        return curr

Time: O(nlogn)
Space: O(n)

Notes:

1. key point here is use heap queue to keep all numbers in ascending order. Other than that, just think this as a BFS problem.
2. small thing to notice is that visited = set([1]) has bracket around.