Super Ugly Number 518

Question

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

Solution

用HashMap + PriorityQueue。取n-1次最小堆堆顶元素,最后堆顶元素为第n个prime。

代码如下:

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) {
        // Write your code here
        if(primes == null || primes.length == 0 || n <= 0){
            return 0;
        }

        Queue<Long> Q = new PriorityQueue<Long>();
        HashSet<Long> inQ = new HashSet<Long>();
        Q.add(Long.valueOf(1));
        inQ.add(Long.valueOf(1));

        for(int i = 1; i < n; i++){
            Long curt = Q.poll();
            for(int j = 0; j < primes.length; j++){
                Long next = curt * primes[j];
                if(!inQ.contains(next)){
                    Q.add(next);
                    inQ.add(next);
                }
            }
        }

        return Q.peek().intValue();
    }
}

Ugly Number II 4

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