C# Program to Check If a Number is a Happy Number

We are given a number as input, and we need to check whether it is a happy number or not. In this article, we will learn how to check if a number is a happy number using C#.

What is a Happy Number?

A happy number is a number that eventually becomes equal to 1 when we repeatedly replace it with the sum of the squares of its digits. If the number gets stuck in a cycle and never reaches 1, then it is not a happy number.

Example 1

• Input: 19
• Output: True

Explanation: 19 is a happy number because repeatedly calculating the sum of squares of its digits eventually leads to 1

Step 1: 1² + 9² = 1 + 81 = 82
Step 2: 8² + 2² = 64 + 4 = 68
Step 3: 6² + 8² = 36 + 64 = 100
Step 4: 1² + 0² + 0² = 1 + 0 + 0 = 1

Example 2

• Input: 20
• Output: False

Explanation: 20 is not a happy number because it gets trapped in a cycle and never reaches 1

Step 1: 2² + 0² = 4 + 0 = 4
Step 2: 4² = 16
Step 3: 1² + 6² = 1 + 36 = 37
Step 4: 3² + 7² = 9 + 49 = 58
Step 5: 5² + 8² = 25 + 64 = 89
Step 6: 8² + 9² = 64 + 81 = 145
Step 7: 1² + 4² + 5² = 1 + 16 + 25 = 42
Step 8: 4² + 2² = 16 + 4 = 20

We get back to 20, forming a cycle. Since we never reach 1, the number 20 is not happy.

Algorithm

We use a HashSet to track sums we have encountered to detect cycles. The algorithm calculates the sum of squares of digits repeatedly until either reaching 1 (happy number) or detecting a cycle (not happy).

Steps for Implementation

1. Create a function that calculates the sum of squares of digits for a given number.
2. Use a HashSet to store previously seen sums to detect cycles.
3. If the sum equals 1, the number is happy.
4. If the sum is already in the HashSet, the number is not happy (cycle detected).
5. Repeat the process until we reach 1 or detect a cycle.

C# Program to Check if a Number is a Happy Number

using System;
using System.Collections.Generic;

class HappyNumberChecker {
   // Calculates the sum of the squares of digits of the given number
   static int GetSumOfSquares(int number) {
      int sum = 0;
      while (number > 0) {
         int digit = number % 10;
         sum += digit * digit;
         number /= 10;
      }
      return sum;
   }

   // Checks if the given number is a Happy Number
   public static bool IsHappyNumber(int number) {
      HashSet<int> seenSums = new HashSet<int>();

      while (number != 1 && !seenSums.Contains(number)) {
         seenSums.Add(number);
         number = GetSumOfSquares(number);
      }
      return number == 1;
   }

   static void Main() {
      int[] testNumbers = {19, 20, 7, 10};

      foreach (int num in testNumbers) {
         if (IsHappyNumber(num)) {
            Console.WriteLine($"{num} is a Happy Number.");
         } else {
            Console.WriteLine($"{num} is not a Happy Number.");
         }
      }
   }
}

The output of the above code is

19 is a Happy Number.
20 is not a Happy Number.
7 is a Happy Number.
10 is not a Happy Number.

Time and Space Complexity

• Time Complexity: O(log n × m), where calculating sum of squares takes O(log n) time and m is the number of iterations before detecting 1 or a cycle.
• Space Complexity: O(m), where m is the maximum number of unique sums stored in the HashSet before reaching 1 or detecting a cycle.

Conclusion

A happy number is determined by repeatedly replacing it with the sum of squares of its digits until either reaching 1 (happy) or detecting a cycle (not happy). Using a HashSet to track previously seen sums efficiently detects cycles and determines if a number is happy.