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

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.
• 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.

Return true if n is a happy number, and false if not.

Example 1:

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


Example 2:

Input: n = 2
Output: false


Constraints:

• 1 <= n <= 231 - 1

## Solution: Simulation

We can use a hasthable to store all the number we generated so far.

Time complexity: O(L)
Space complexity: O(L)

## Optimization: Space reduction

Since the number sequence always has a cycle, we can use slow / fast pointers to detect the cycle without using a hastable.

Time complexity: O(L)
Space complexity: O(1)

## C++

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