LeetCode OJ 202. Happy Number

Write an algorithm to determine if a number is "happy".

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

Example: 19 is a happy number

• 1² + 9² = 82
• 8² + 2² = 68
• 6² + 8² = 100
• 1² + 0² + 0² = 1

happy number是把一个数的各个位置的数字的平方相加，直到值为1为止。如果一个数是happy number，那么最终的结果一定会是1，如果不是，这个过程将一直持续下去，并且会重复出现以前曾经出现过的数。例如2。

2² = 4

4² = 16

1² + 6² = 37

3² + 7² = 58

5² + 8² = 89

8² + 9² = 145

1² + 4² + 5² = 42

4² + 2² = 20

2² + 0² = 4

···

所以2不是一个happy number。我们的思路就是记录这个过程中出现过的每一个数，如果某些数字在过程中重复出现，则该数肯定不是happy number。如果最后结果是1，则该数是happy number。代码如下：

 1 public class Solution {
 2     public boolean isHappy(int n) {
 3         List<Integer> list = new ArrayList<>();
 4         while (n != 1) {
 5             if (list.contains(n)) {
 6                 return false;
 7             }
 8             list.add(n);
 9             n = toArrayAndSum(n);
10         }
11         return true;
12     }
13
14     public static int toArrayAndSum(int n) {
15         int sum = 0;
16         while (n > 0) {
17             int x = n % 10;
18             n = n / 10;
19             sum = sum + x * x;
20         }
21             return sum;
22     }
23 }