Leetcode 313: Super Ugly Number

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

 

public class Solution {
    public int NthSuperUglyNumber(int n, int[] primes) {
        var dp = new int[n];
        dp[0] = 1;
             
        for (int i = 1; i < n; i++)
        {
            dp[i] = Int32.MaxValue;
            var shouldCut = false;
            
            for (int j = i - 1; j >= 0; j--)
            {
                for (int k = primes.Length - 1; k >= 0; k--)
                {
                    if (primes[k] * dp[j] <= dp[i - 1])
                    {
                        if (k == primes.Length - 1)
                        {
                            shouldCut = true;
                        }
                        
                        break;
                    }
                    
                    dp[i] = Math.Min(dp[i], primes[k] * dp[j]);
                    
                    if (shouldCut) break;
                }
            }
        }
        
        return dp[n - 1];
    }
}