Ugly Number

263 Ugly Number I

Check if a number is ugly number. Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. 1 is usually consider as an ugly number.

public boolean isUgly(int num) {
    int[] ugly = {2, 3, 5};
    for (int prime : ugly){
        while(num % prime == 0 && num > 0){
            num /= prime;
        }
    }
    return num == 1;
}

264 Ugly number II

Write a program to find the n-th ugly number.

• All the ugly numbers are in format 2^a x 3^b x 5^c, ugly numbers are subsequence factor of ugly numbers.

  1. Time O(n^2), Space O(1). Loop increasing number, check if it is a ugly number.

  2. Time O(n), Space O(n). Dynamic programming, Record the subsequence of prime factors and find the smallest.

public int nthUglyNumber(int n) {
    int index_2 = 0, index_3 = 0, index_5 = 0; // the index on array
    int factor_2 = 1, factor_3 = 1, factor_5 = 1; // start with 1
    int[] arr = new int[n];
    int min = 1;

    for( int i = 0; i < n; i++){
        arr[i] = min;
        if (factor_2 == min) factor_2 = arr[index_2++] * 2;
        if (factor_3 == min) factor_3 = arr[index_3++] * 3;
        if (factor_5 == min) factor_5 = arr[index_5++] * 5;

        min = Math.min(factor_2, Math.min(factor_3, factor_5));
    }
    return arr[n-1];
}

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.

public int nthSuperUglyNumber(int n, int[] primes) {
    int[] primes_idx = new int[primes.length];
    int[] primes_val = new int[primes.length];
    Arrays.fill(primes_val, 1);
    int[] ugly = new int[n];
    int min = 1;

    for (int i = 0; i < n; i++){
        ugly[i] = min;

        min = Integer.MAX_VALUE;
        for (int j = 0; j < primes.length; j++){

            if (primes_val[j] == ugly[i]) primes_val[j] = primes[j] * ugly[primes_idx[j]++];
            min = Math.min(min, primes_val[j]);
        }
    }
    return ugly[n-1];
}