Python program to print all Happy numbers between 1 and 100

A happy number is a number that eventually reaches 1 when replaced by the sum of the square of its digits repeatedly. For example, 7 is happy because 7² = 49, then 4² + 9² = 97, then 9² + 7² = 130, and so on until we reach 1.

Numbers that don't reach 1 will eventually cycle. The most common cycle includes 4, which is why we check for it as a stopping condition.

Algorithm

To find happy numbers between 1 and 100 ?

1. For each number, repeatedly calculate the sum of squares of its digits
2. If the result equals 1, it's a happy number
3. If the result equals 4, it will cycle and is not happy
4. Continue until we reach either 1 or 4

Example

def check_happy_num(my_num):
    remaining = sum_val = 0
    while(my_num > 0):
        remaining = my_num % 10
        sum_val = sum_val + (remaining * remaining)
        my_num = my_num // 10
    return sum_val

print("The list of happy numbers between 1 and 100 are:")
for i in range(1, 101):
    my_result = i
    while(my_result != 1 and my_result != 4):
        my_result = check_happy_num(my_result)
    if(my_result == 1):
        print(i)

Output

The list of happy numbers between 1 and 100 are:
1
7
10
13
19
23
28
31
32
44
49
68
70
79
82
86
91
94
97
100

How It Works

Let's trace through how 7 becomes a happy number ?

def trace_happy_number(num):
    print(f"Tracing {num}:")
    original = num
    while num != 1 and num != 4:
        digits = [int(d) for d in str(num)]
        squares = [d**2 for d in digits]
        num = sum(squares)
        print(f"  {' + '.join(map(str, squares))} = {num}")
    
    if num == 1:
        print(f"  {original} is a happy number!")
    else:
        print(f"  {original} is not happy (reached cycle)")

trace_happy_number(7)
print()
trace_happy_number(2)

Tracing 7:
  49 = 49
  97 = 97
  130 = 130
  10 = 10
  1 = 1
  7 is a happy number!

Tracing 2:
  4 = 4
  2 is not happy (reached cycle)

Alternative Implementation

Here's a more concise version using string manipulation ?

def is_happy(n):
    while n != 1 and n != 4:
        n = sum(int(digit)**2 for digit in str(n))
    return n == 1

happy_numbers = [i for i in range(1, 101) if is_happy(i)]
print("Happy numbers from 1 to 100:")
print(happy_numbers)

Happy numbers from 1 to 100:
[1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100]

Conclusion

Happy numbers are identified by repeatedly summing the squares of their digits until reaching 1 (happy) or 4 (unhappy cycle). There are 20 happy numbers between 1 and 100, with the algorithm efficiently detecting them using modular arithmetic or string manipulation.