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Jan 2026 - Python - Week 9 - WEEK9-GrPA 3

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Jan 2026 - Python - Week 9 - WEEK9-GrPA 3

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Graded Assignment

Course: Jan 2026 - Python

WEEK9-GrPA 3

Submission deadline has passed for this assignment

Due Apr 17, 2026 at 11:59 PM IST

Instructions

Use "Test Run" to verify your code with public test cases.

Press "Submit" to have your assignment evaluated.

You can submit your assignment multiple times up until the deadline.

Make sure to submit your final code by the deadline to receive your score.

Summary

100 out of100

Score

Public Tests

3/3 Passed

Submitted on Apr 17, 2026 at 5:36 AM IST

Private Tests

5/5 Passed

Submitted on Apr 17, 2026 at 5:36 AM IST

The Collatz function is defined for a positive integer

n

as follows.

f(n) = \begin{cases} 3n + 1 &\text{if } n \text{ is odd} \\ \cfrac{n}{2} &\text{if } n \text{ is even} \end{cases}

We consider the repeated application of the Collatz function starting with a given integer

n

, which results in the following sequence:

f(n), f(f(n)), f(f(f(n))),\dots

It is conjectured that no matter which positive integer

n

you start from, the sequence will always reach

1

. For example, if

n=10

, the sequence is:

.tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-0lax{text-align:left;vertical-align:top}

Thus, if you start from

n=10

, you need to apply the function

f

six times in order to first reach 1.

Write a recursive function named collatz that accepts a positive integer

n

as argument, where

1 < n \leq 32,000

, and returns the number of times

f

has to be applied repeatedly in order to first reach 1.

You do not have to accept input from the user or print output to the console. You just have to write the function definition.

Public Tests ( 3/3 )

Case 1

Input:


text
public
7

Expected Output:


text
16

Actual Output:


text
16

Case 2

Input:


text
public
10

Expected Output:


text
6

Actual Output:


text
6

Case 3

Input:


text
public
101

Expected Output:


text
25

Actual Output:


text
25

Private Tests ( 5/5 )

Case 1

Input:


text
private
30000

Expected Output:


text
178

Good, your function is recursive

Actual Output:


text
178

Good, your function is recursive

Case 2

Input:


text
private
31999

Expected Output:


text
98

Good, your function is recursive

Actual Output:


text
98

Good, your function is recursive

Case 3

Input:


text
private
2463

Expected Output:


text
208

Good, your function is recursive

Actual Output:


text
208

Good, your function is recursive

Case 4

Input:


text
private
999

Expected Output:


text
49

Good, your function is recursive

Actual Output:


text
49

Good, your function is recursive

Case 5

Input:


text
private
125

Expected Output:


text
108

Good, your function is recursive

Actual Output:


text
108

Good, your function is recursive

💻 IITM Official Solution


python
def collatz(n):
    # base case of the recursion
    # if n = 1, you don't need to call the function at all
    if n == 1:
        return 0
    # simple application of the piecewise defn of the
    # Collatz function
    if n % 2 == 0:
        return 1 + collatz(n // 2)
    else:
        return 1 + collatz(3 * n + 1)

💻 My Submitted Code


python
def collatz(n):
    """
    A recursive function to compute the number of calls to the Collatz function of n

    Argument:
        n: integer
        Assume that 1 < n <= 32,000
    Returns:
        result: integer
    """
    # Base case
    if n == 1:
        return 0

    # Recursive case
    if n % 2 == 0:
        return 1 + collatz(n // 2)
    else:
        return 1 + collatz(3 * n + 1)