313. Super-Ugly-Number

difficulty: Medium

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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.

Example:

Input: n = 12, primes = [2,7,13,19]
Output: 32 
Explanation: [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 is a super ugly number for any given primes.

• The given numbers in primes are in ascending order.

• 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.

• The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

Method One

class Solution {
    public int nthSuperUglyNumber(int n, int[] primes) {
        if( n < 2 ){
            return n;
        } 
        int[] pointers = new int[primes.length];
        int[] uglyNumbers = new int[n];
        uglyNumbers[0] = 1;
        for(int i = 1; i < n; i++){
            int min = Integer.MAX_VALUE;
            for(int j = 0; j < primes.length; j++ ){
                min = Math.min( min, primes[j]*uglyNumbers[ pointers[j] ] );
            }
            uglyNumbers[i] = min;
            for(int j = 0; j < primes.length; j++ ){
                if( min == primes[j]*uglyNumbers[ pointers[j] ] ){
                    pointers[j]++;
                }
            }
        }
        return uglyNumbers[ n - 1];
    }
}
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