Reference: LeetCode

Difficulty: 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:**

1 | Input: 19 |

**Follow up:** Use $O(1)$ space.

## Analysis

### Hash Set

Since you will get repeat numbers again and again, we can put all visited numbers in a hash set to know whether we can stop trying.

I list two ways of writing `squareSum()`

.

1 | public boolean isHappy(int n) { |

**Time:** N/A**Space:** N/A It depends on the input.

### Cycle Detection

We can solve it without extra space.

1 | public boolean isHappy(int n) { |

**Time:** N/A**Space:** $O(1)$