# Happy Number

Leetcode Easy

## Problem

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:**

```
Input: 19
Output: true
Explanation:
12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1
```

## Submission

```
class Solution {
public boolean isHappy(int n) {
HashSet<Integer> sums = new HashSet<>();
while (n != 1) {
n = sumSquareDigits(n);
// If we've seen this number before it's a cycle
if (sums.contains(n)) {
return false;
}
sums.add(n);
}
return true;
}
// Replace the number by the sum of the squared digits
public int sumSquareDigits(int n) {
int total = 0;
// Loop one digit at a time
while (n != 0) {
total += (int) Math.pow((n % 10), 2);
n /= 10;
}
return total;
}
}
```

## Why This Works

We detect if there is a cycle by storing all of the previous sums we see in a hashSet, and if we see it again, it will already be in the set.