Write a program to find the nth super ugly number.
Super ugly numbers are positive numbers whose all prime factors are in the given prime list
primes
of size k
. For example, [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32]
is the sequence of the first 12 super ugly numbers given primes
= [2, 7, 13, 19]
of size 4.
Note:
(1)
(2) The given numbers in
(3) 0 <
Understand the problem:(1)
1
is a super ugly number for any given primes
.(2) The given numbers in
primes
are in ascending order.(3) 0 <
k
≤ 100, 0 < n
≤ 106, 0 < primes[i]
< 1000.The idea is very similar to the problem Super ugly number II
Code (Java):
public class Solution { public int nthSuperUglyNumber(int n, int[] primes) { if (n == 1 || primes == null || primes.length == 0) { return 1; } int k = primes.length; int[] index = new int[k]; List<Integer> result = new ArrayList<>(); result.add(1); for (int i = 1; i < n; i++) { int curr = Integer.MAX_VALUE; for (int j = 0; j < k; j++) { curr = Math.min(curr, primes[j] * result.get(index[j])); } result.add(curr); // update the index for (int j = 0; j < k; j++) { if (primes[j] * result.get(index[j]) == curr) { index[j]++; } } } return result.get(result.size() - 1); } }
Analysis:
Time complexity is O(k * n), space complexity is O(n)
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