SuperUglyNumber.java

/**
 * Write a program to find the nth super ugly number.
 * <p>
 * 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.
 * <p>
 * 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.
 * <p>
 * Tags: Math, Heap
 * Similar Problems: (M) Ugly Number II
 */

public class SuperUglyNumber {

    /**
     * Refer to ugly number 2
     * Use an array to keep all indices for primes
     */
    public int nthSuperUglyNumber(int n, int[] primes) {
        int len = primes.length;
        int[] index = new int[len];
        int[] res = new int[n];
        res[0] = 1;
        for (int i = 1; i < n; i++) {
            int min = Integer.MAX_VALUE;
            for (int j = 0; j < len; j++) {
                min = Math.min(res[index[j]] * primes[j], min);
            }
            res[i] = min;
            for (int j = 0; j < len; j++) {
                if (res[i] % primes[j] == 0) index[j]++;
            }
        }
        return res[n - 1];
    }
}