How to Determine if a Number is Happy

Have you ever wondered if a number can be considered “happy”? In this tutorial, we will explore what a happy number is and how to determine if a given number is happy using a simple algorithm. This guide is designed for beginners, so don’t worry if you’re new to programming or algorithms!

What is a Happy Number?

A happy number is defined as a number which eventually reaches 1 when replaced by the sum of the square of each digit. If it does not reach 1, it will enter a cycle that does not include 1. For example:

• The number 19 is happy because:
  • 1² + 9² = 1 + 81 = 82
  • 8² + 2² = 64 + 4 = 68
  • 6² + 8² = 36 + 64 = 100
  • 1² + 0² + 0² = 1
• The number 2 is not happy because:
  • 2² = 4
  • 4² = 16
  • 1² + 6² = 1 + 36 = 37
  • 3² + 7² = 9 + 49 = 58
  • 5² + 8² = 25 + 64 = 89
  • 8² + 9² = 64 + 81 = 145
  • 1² + 4² + 5² = 1 + 16 + 25 = 42
  • 4² + 2² = 16 + 4 = 20
  • 2² + 0² = 4

As you can see, the number 2 enters a cycle and never reaches 1, making it an unhappy number.

Prerequisites

Before we dive into the algorithm, make sure you have a basic understanding of:

• Basic programming concepts
• Functions and loops
• Conditional statements

Step-by-Step Guide to Determine if a Number is Happy

Now that we understand what a happy number is, let’s write an algorithm to determine if a number is happy.

Step 1: Create a Function

First, we need to create a function that will take a number as input and return whether it is happy or not.

def is_happy(n):
    seen = set()
    while n != 1 and n not in seen:
        seen.add(n)
        n = sum(int(digit) ** 2 for digit in str(n))
    return n == 1

Step 2: Explanation of the Function

Let’s break down the function:

• seen = set(): We create a set to keep track of numbers we have already encountered. This helps us detect cycles.
• while n != 1 and n not in seen:: We continue the loop until we either reach 1 or encounter a number we’ve seen before.
• seen.add(n): We add the current number to our set of seen numbers.
• n = sum(int(digit) ** 2 for digit in str(n)): We calculate the sum of the squares of the digits of the current number.
• return n == 1: Finally, we return True if we reached 1, indicating the number is happy; otherwise, we return False.

Step 3: Testing the Function

Now that we have our function, let’s test it with some numbers:

print(is_happy(19))  # Output: True
print(is_happy(2))   # Output: False

Conclusion

In this tutorial, we learned what a happy number is and how to determine if a number is happy using a simple algorithm. By following the steps outlined above, you can easily implement this in your preferred programming language. Happy coding!

For more information, check out the following resources:

• Continue reading on deluxify »”>Understanding Happy Numbers