Python program to check if the given number is Happy Number

A number is called happy if it leads to 1 after a sequence of steps wherein each step number is replaced by the sum of squares of its digit that is if we start with a Happy Number and keep replacing it with digits square sum, we reach 1. In this article, we will check if the given number is a Happy Number

Examples

Input: n = 19
Output: True
19 is Happy Number,

1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1
As we reached to 1, 19 is a Happy Number.

Input: n = 20
Output: False

Python Program to Check if Given Number is Happy Number

Below are the example of Python program to check if the given number is Happy Number.

• Using Set() Method
• Using No Extra Space
• Using Extra Space.

Check if Given Number is Happy Number Using Set Method

In this example, below code defines two functions: numSquareSum calculates the sum of squares of digits of a number, and isHappyNumber checks if a number is a Happy Number, using a set to detect cycles. The example usage demonstrates checking if the number 20 is a Happy Number, which returns False.

Python3

# Function to return the sum of squares of digits of n
def numSquareSum(n):
    squareSum = 0
    while (n != 0):
        squareSum += (n % 10) * (n % 10)
        n = n // 10
    return squareSum

# Function to return true if n is a Happy Number
def isHappyNumber(n):
    st = set()
    while (1):
        n = numSquareSum(n)
        if (n == 1):
            return True
        if n in st:
            return False
        st.add(n)

# Example usage:
print(isHappyNumber(20))  

Output

False

Time Complexity: O(n*log(n)).
Auxiliary Space: O(n) since we are using set.

Check if Given Number is Happy Number Using No Extra Space

In this example, we have a method named numSquareSum which calculates the sum of the squares of the digits of a given number. The isHappynumber method determines whether a number is a “happy number” or not. It employs two pointers, slow and fast, to iterate through the sum of squares until they either meet or reach 1, indicating a happy number.

Python3

# Utility method to return 
# sum of square of digit of n
def numSquareSum(n):
    squareSum = 0;
    while(n):
        squareSum += (n % 10) * (n % 10);
        n = int(n / 10);
    return squareSum;
 
# method return true if
# n is Happy number
def isHappynumber(n):
 
    # initialize slow 
    # and fast by n
    slow = n;
    fast = n;
    while(True):
         
        # move slow number
        # by one iteration
        slow = numSquareSum(slow);
 
        # move fast number
        # by two iteration
        fast = numSquareSum(numSquareSum(fast));
        if(slow != fast):
            continue;
        else:
            break;
 
    # if both number meet at 1, 
    # then return true
    return (slow == 1);
 
# Driver Code
n = 13;
if (isHappynumber(n)):
    print(n , "is a Happy number");
else:
    print(n , "is not a Happy number");
 

Output

13 is a Happy number

Time Complexity: O(n*log(n)).
Auxiliary Space: O(1). 

Check if Given Number is Happy Number Using Extra Space.

In this example, below code defines a method isHappynumber to check if a given number is a “happy number”. It first checks if the number is 1 or 7, which are happy numbers, and returns True. Otherwise, it iterates through the sum of squares of digits until it either reaches 1 or 7, or enters a cycle. If it reaches 1 or 7, it returns True; otherwise, it returns False.

Python3

# Method - returns true if the input is
# a happy number else returns false
def isHappynumber(n):
    if n == 1 or n == 7:
        return True
          
    Sum, x = n, n
  
    # This loop executes till the sum
    # of square of digits obtained is
    # not a single digit number
    while Sum > 9:
        Sum = 0
          
        # This loop finds the sum of
        # square of digits
        while x > 0:
            d = x % 10
            Sum += d * d
            x = int(x / 10)
         
        if Sum == 1:
            return True
              
        x = Sum
     
    if Sum == 7:
        return True
          
    return False
 
n = 13
      
if isHappynumber(n):
    print(n, "is a Happy number")
else:
    print(n, "is not a Happy number")

Output

13 is a Happy number

Time Complexity: O(n*log(n)).
Auxiliary Space: O(1).