Thursday, January 7, 2016

Leetcode: 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.
Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.
Understand the problem:
The idea is very similar to the problem Super ugly number II



Code (Java):

public class Solution {
    public int nthSuperUglyNumber(int n, int[] primes) {
        if (n == 1 || primes == null || primes.length == 0) {
            return 1;
        }
        
        int k = primes.length;
        int[] index = new int[k];
        
        List<Integer> result = new ArrayList<>();
        result.add(1);
        
        for (int i = 1; i < n; i++) {
            int curr = Integer.MAX_VALUE;
            for (int j = 0; j < k; j++) {
                curr = Math.min(curr, primes[j] * result.get(index[j]));
            }
            
            result.add(curr);
            
            // update the index
            for (int j = 0; j < k; j++) {
                if (primes[j] * result.get(index[j]) == curr) {
                    index[j]++;
                }
            }
        }
        
        return result.get(result.size() - 1);
    }
}

Analysis:
Time complexity is O(k * n), space complexity is O(n)

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