Super Ugly Number

Problem

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.

Notice

  • 1 is a super ugly number for any given primes.
  • The given numbers in primes are in ascending order.
  • 0 < k ≤ 100, 0 < n ≤ 10^6, 0 < primes[i] < 1000

Example

Given n = 6, primes = [2, 7, 13, 19] return 13

Code - Java

public class Solution {
    /**
     * @param n      a positive integer
     * @param primes the given prime list
     * @return the nth super ugly number
     */
    public int nthSuperUglyNumber(int n, int[] primes) {
        int[] a = new int[n + 1];
        a[0] = 1;
        int[] p = new int[primes.length];

        for (int i = 1; i < n; i++) {
            int min = Integer.MAX_VALUE;
            for (int j = 0; j < p.length; j++) {
                min = Math.min(a[p[j]] * primes[j], min);
            }
            //a[i] = Collections.min(Arrays.asList(a[i2] * 2, a[i7] * 7, a[i13] * 13, a[i19] * 19));
            a[i] = min;

            for (int j = 0; j < p.length; j++) {
                if (a[i] % primes[j] == 0) {
                    p[j]++;
                }
            }
        }
        return a[n - 1];
    }
}

Online Judge

LintCode 518: http://www.lintcode.com/en/problem/super-ugly-number/