Python program to check if the given number is Happy Number

Last Updated : 15 Apr, 2024

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")