Python Program to Print all Happy Numbers Between 1 and 100

A Happy Number n is defined by the following process. Starting with n, replace it with the sum of the squares of its digits, and repeat the process until n equals 1, or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are Happy Numbers, while those that do not end in 1 are unhappy numbers.

Example :

Input: n = 19
Output: True

Explanation
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.

Python Program to Print all Happy Numbers Between 1 and 100

Below, are the code examples of Python programs to Print all Happy Numbers Between 1 and 100.

• Using Set() Method
• Using Floyd’s Algorithm
• Using Recursion

Print all Happy Numbers Between 1 and 100 Using Set() Method

In this example, below Python code defines two functions: ‘numSquareSum()’ function computes the sum of squares of digits. ‘isHappyNumber()‘ uses ‘numSquareSum()‘ to determine happiness, tracking visited numbers with a set. The loop prints Happy Numbers between 1 and 100 using ‘isHappyNumber()’.

Python3

# Method returns true if n is a Happy Number
def numSquareSum(n):
    num = 0
    while(n):
        digit = n % 10
        num = num + digit*digit
        n = n // 10
    return num

def isHappyNumber(n):
    st = set()
    while (1):
        n = numSquareSum(n)
        if (n == 1):
            return True
        if n in st:
            return False
        st.add(n)

# Print all Happy Numbers between 1 and 100
for i in range(1, 101):
    if isHappyNumber(i):
        print(i, end=" ")

Output

1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100 

Print all Happy Numbers Between 1 and 100 Using Floyd’s Cycle Detection Algorithm

In this example, in below Python code loop checks numbers from 1 to 100 using ‘isHappyNumber()‘, which applies Floyd’s Cycle Detection Algorithm with ‘numSquareSum()‘ to find happy numbers. ‘numSquareSum()‘ calculates the sum of squares of digits.

Python3

# Utility method to return 
# sum of square of digits of n
def numSquareSum(n):
    squareSum = 0
    while n:
        squareSum += (n % 10) * (n % 10)
        n = n // 10
    return squareSum

# Method returns true if n is a Happy number
def isHappyNumber(n):
    slow = n
    fast = n
    while True:
        slow = numSquareSum(slow)
        fast = numSquareSum(numSquareSum(fast))
        if slow != fast:
            continue
        else:
            break
    return slow == 1

# Print all Happy Numbers between 1 and 100
for i in range(1, 101):
    if isHappyNumber(i):
        print(i, end=" ")

Output

1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100 

Print all Happy Numbers Between 1 and 100 Using Recursion

In this example, Python code defines two functions: ‘numSquareSum()‘ calculates the sum of squares of digits of a number, and ‘isHappyNumber()‘ determines if a number is happy by recursively applying ‘numSquareSum()’ until either 1 is reached (indicating happiness) or a cycle is detected, using a set to keep track of visited numbers.

Python3

# Utility method to return sum of square of digits of n
def numSquareSum(n):
    squareSum = 0
    while n:
        squareSum += (n % 10) * (n % 10)
        n = n // 10
    return squareSum

# Method returns true if n is a Happy number
def isHappyNumber(n, visited):
    if n == 1:
        return True
    elif n in visited:
        return False
    else:
        visited.add(n)
        return isHappyNumber(numSquareSum(n), visited)

# Print all Happy Numbers between 1 and 100
for i in range(1, 101):
    visited = set()
    if isHappyNumber(i, visited):
        print(i, end=" ")

Output

1 7 10 13 19 23 28 31 32 44 49 68 70 79 82 86 91 94 97 100