507. Perfect Number

题目：

We define the Perfect Number is a positive integer that is equal to the sum of all its positive divisors except itself.

Now, given an integer n, write a function that returns true when it is a perfect number and false when it is not.
Example:
Input: 28
Output: True
Explanation: 28 = 1 + 2 + 4 + 7 + 14
Note: The input number n will not exceed 100,000,000. (1e8)

链接：https://leetcode.com/problems/perfect-number/#/description

3/31/2017

注意1要返回false

public class Solution {
    public boolean checkPerfectNumber(int num) {
        if (num <= 1) return false;
        Set<Integer> s = new HashSet<Integer>();
        s.add(1);

        for (int i = 2; i <= Math.sqrt(num); i++) {
            if (num % i == 0) {
                s.add(i);
                s.add(num / i);
            }
            if (i == num / i) break;
        }
        if (s.size() == 0) return false;
        int sum = 0;
        for (Integer v : s) sum += v;
        return sum == num;
    }
}

别人的算法，更加节省空间复杂度，第11行是加上1

https://discuss.leetcode.com/topic/84259/simple-java-solution

public class Solution {
    public boolean checkPerfectNumber(int num) {
        if (num == 1) return false;
        
        int sum = 0;
        for (int i = 2; i <= Math.sqrt(num); i++) {
            if (num % i == 0) {
                sum += i + num / i;
            }
        }
        sum++;
        
        return sum == num;
    }
}

有人提醒test case缺失，不要加相同元素两遍。

https://discuss.leetcode.com/topic/84337/missing-test-cases

更多讨论：

https://leetcode.com/problems/perfect-number/#/solutions