# 202 Happy Number

## 202. [Happy Number](https://leetcode.com/problems/happy-number/description/)

## 1. Question

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

* 1 ^ 2 + 9^2 = 82
* 8 ^ 2 + 2 ^ 2 = 68
* 6 ^ 2 + 8 ^ 2 = 100
* 1 ^ 2 + 0 ^ 2 + 0 ^ 2 = 1

## 2. Implementation

**(1)** **Two Pointers (Cycle Detection)**

```java
class Solution {
    public boolean isHappy(int n) {
        int fast = n, slow = n;

        do {
            slow = getNextNumber(slow);
            fast = getNextNumber(getNextNumber(fast));

            if (fast == 1) {
                return true;
            }

        } while (slow != fast);
        return false;
    }

    public int getNextNumber(int num) {
        int sum = 0;
        while (num > 0) {
            sum += (num % 10) * (num % 10);
            num /= 10;
        }
        return sum;
    }
}
```

## 3. Time & Space Complexity

**Two Pointers:** 时间复杂度不详，空间复杂度O(1)
