Python Collatz sequence generator using generators

Last update on December 21 2024 07:30:16 (UTC/GMT +8 hours)

Write a Python program to implement a generator that generates the Collatz sequence for a given number.

The Collatz sequence, also known as the Collatz conjecture or 3n+1 problem, is a sequence of numbers defined by the following rules:

• Start with any positive integer n.
• If n is even, divide it by 2 to get n/2.
• If n is odd, multiply it by 3 and add 1 to get 3n+1.
• Repeat the process, using the resulting number, until you reach the number 1.

For instance, starting with n = 12 and applying the function f without "shortcut", one gets the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.

The number n = 19 takes longer to reach 1: 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

Sample Solution:

Python Code:

def collatz_sequence(n):
    while n != 1:
        yield n
        if n % 2 == 0:
            n = n // 2
        else:
            n = 3 * n + 1
    yield 1

# Accept input from the user
n = int(input("Input a positive integer (n): "))

# Generate and print the Collatz sequence
print("Collatz sequence:")
for num in collatz_sequence(n):
    print(num, end=", ")

Sample Output:

Input a positive integer (n): 12
Collatz sequence:
12, 6, 3, 10, 5, 16, 8, 4, 2, 1,

Input a positive integer (n): 19
Collatz sequence:
19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1,

Explanation:

In the above exercise,

The "collatz_sequence()" function is a generator that generates the Collatz sequence for a given number n. It starts with n and repeatedly applies the Collatz rules until it reaches 1. Each number in the sequence is yielded using the yield keyword.

The program accepts a positive integer from the user and calls the collatz_sequence generator with that number. It iterates over the generated sequence and prints each number.

Flowchart:

Python Code Editor:

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