[LeetCode] 507. Perfect Number 完美数字

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)

定义Perfect Number是一个正整数，它等于除了它自己之外的所有正除数的总和。现在，给定一个整数n，编写一个函数，当它是一个完美数字时返回true，否则返回false。

解法：直接解就可以。注意处理num是1的时候。还有技巧是，只计算num/2就可以，如果能整除就把除数和结果都累加。

Java:

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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;     } }

Python:

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class Solution(object):     def checkPerfectNumber(self, num):         """         :type num: int         :rtype: bool         """         if num <= 0: return False         ans, SQRT = 0, int(num ** 0.5)         ans = sum(i + num//i for i in range(1, SQRT+1) if not num % i)         if num == SQRT ** 2: ans -= SQRT         return ans - num == num

Python:

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class Solution(object):     def checkPerfectNumber(self, num):         """         :type num: int         :rtype: bool         """         if num == 1:             return False         i = 2         s = 1         while i * i < num:             if num % i == 0:                 s += i                 s += num / i             i += 1              return True if s == num else False

C++:

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class Solution { public:     bool checkPerfectNumber(int num) {         if (num == 1) return false;         int sum = 1;         for (int i = 2; i * i <= num; ++i) {             if (num % i == 0) sum += (i + num / i);             if (i * i == num) sum -= i;             if (sum > num) return false;         }         return sum == num;     } };

C++:

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class Solution { public:     bool checkPerfectNumber(int num) {         return num==6 || num==28 || num==496 || num==8128 || num==33550336;     } };

　　

 

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