Happy Number

This question is part of NeetCode150 series.

Problem Description

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.

leetcode

Solution

The important thing in this problem is to realize that the numbers will not be in ever increasing (non-decreasing sequence). It would have been tricky to solve this problem, if they sum of squares of N kept increasing.

For a number with 3 digits, it’s impossible for it to ever go larger than 243. This means it will have to either get stuck in a cycle below 243 or go down to 1. Numbers with 4 or more digits will always lose a digit at each step until they are down to 3 digits. So we know that at worst, the algorithm might cycle around all the numbers under 243 and then go back to one it’s already been to (a cycle) or go to 1.

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class Solution {

    public boolean isHappy(int n) {
        
        Set<Integer> set = new HashSet<>();

        //while the number has not already been seen before, keep adding it to the set
        while(!set.contains(n)){
            set.add(n);
            n = sumOfSquaresOfDigits(n);
        }

        return n==1;

    }

    //calculate sum of squares of each digits in N
    public int sumOfSquaresOfDigits(int n){
        int total = 0;

        while(n!=0){
            total = total + (int)Math.pow(n%10, 2);
            n = n/10;
        }

        return total;
    }
    
}