202. Happy Number

Problem Statement:

Write an algorithm to determine if a number n 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.
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:

Algorithm:

1. Initialize slow and fast by n.
2. Do following until slow and fast meet. a) Move slow by one iteration: compute square of digits of slow and add them. b) Move fast by two iteration: compute square of digits of fast and add them.
3. If slow becomes 1 then return true.

Code:

public class Solution {
    public boolean isHappy(int n){
        int slow = n;
        int fast = n;
        do {
            slow = squareSum(slow);
            fast = squareSum(squareSum(fast));
        } while (slow != fast);
        return slow == 1;


    }
    public int squareSum(int n){
        int sum = 0;
        while (n > 0) {
            int digit = n % 10;
            sum += digit * digit;
            n /= 10;
        }
        return sum;
    }

}

Time Complexity:

O(logN). We need to compute the square of digits of n at most O(logN) times.

Space Complexity:
O(1)