[LintCode] Amicable Pair

Problem

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other.

Given an integer k, find all amicable pairs between 1 and k.

Notice

For each pair, the first number should be smaller than the second one.

Example

Given 300, return [[220, 284]].

Tags

Enumeration

Solution

public class Solution {
    /*
     * @param k: An integer
     * @return: all amicable pairs
     */
    public List<List<Integer>> amicablePair(int k) {
        // loop through 1 to k, do calculation, save amicable pairs
        List<List<Integer>> res = new ArrayList<>();
        for (int i = 1; i <= k; i++) {
            int second = calculateSum(i);
            if (second > k) {
                continue;
            } else {
                int first = calculateSum(second);
                if (first == i && first < second) {
                    List<Integer> pair = new ArrayList<>();
                    pair.add(first);
                    pair.add(second);
                    res.add(pair);
                }
            }
        }
        
        return res;
    }
    
    public int calculateSum(int n) {
        int sum = 0;
        for (int i = 1; i * i < n; i++) {
            if (n % i == 0) {
                sum += (i+n/i);
            }
            if ((i+1)*(i+1) == n) {
                sum += (i+1);
            }
        }
        return sum-n;
    }
}