问题描述
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
思路1：直接计算出该数的所有因数，保存在一个数组里，然后比较该数和数组里的数的总和是否相等
/**
* @param {number} num
* @return {boolean}
*/
var checkPerfectNumber = function(num) {
if(num === 0){
return false;
}else{
var j = 0;
var arr = [];
var sum = 0;
for(var i = 1; i <= num/2; i++){
if(num%i === 0){
arr[j] = i;
sum+=arr[j];
j++;
}
}
if(sum === num){
return true;
}
else{
return false;
}
}
};
思路2：利用一个数的平方根和其因数之间的大小关系，这样做可以减少一半的循环中止条件
var checkPerfectNumber = function(num) {
if(num === 0){
return false;
}
var sum=0;
for(var i = 1; i < Math.sqrt(num); i++){
if(num%i === 0){
sum+=(i+num/i);
}
}
if(num == sum-num){
return true;
}
else{
return false;
}
};```