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.

Solution:

The idea is exactly the same as ugly number.

Time complxity: O(n*k) k is the length of prime array.

 public int nthSuperUglyNumber(int n, int[] primes) {  
     if(n==1) return 1;  
     int[] ugly=new int[n];  
     ugly[0]=1;  
     int[] index=new int[primes.length];  
     for(int i=1;i<n;i++){  
       ugly[i]=Integer.MAX_VALUE;  
       for(int j=0;j<primes.length;j++){  
         ugly[i]=Math.min(ugly[i],primes[j]*ugly[index[j]]);  
       }  
       if(i==n-1) break;  
       for(int j=0;j<primes.length;j++){  
         if(ugly[i]%primes[j]==0) index[j]++;  
       }  
     }  
     return ugly[n-1];  
   }