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Jan 2026 - Python - Week 9 - WEEK9-GrPA 4

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Jan 2026 - Python - Week 9 - WEEK9-GrPA 4

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WEEK9-GrPA 4

Course: Jan 2026 - Python

WEEK9-GrPA 4

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 5:37 AM IST

Private Tests

5/5 Passed

Submitted on Apr 17, 2026 at 5:37 AM IST

Fibonacci

Fibonacci is a young resident of the Italian city of Pisa. He spends a lot of time visiting the Leaning Tower of Pisa, one of the iconic buildings in the city, that is situated close to his home. During all his visits to the tower, he plays a strange game while climbing the marble steps of the tower.

The Game

Fibonacci likes to climb the steps either one at a time, two at a time or three at a time. This adds variety to the otherwise monotonous task of climbing. He wants to find the total number of ways in which he can climb

n

steps, assuming that the order of his individual steps matters. Your task is to help Fibonacci compute this number.

For example, if he wishes to climb three steps, the case of

n = 3

, he could do it in four different ways:

$(1, 1, 1)$ : do it in three moves, one step at a time
$(1, 2)$ : do it in two moves, first take a single step, then a double step
$(2, 1)$ : do it in two moves, first take a double step, then a single step
$(3)$ : do it in just one move, directly leaping to the third step

To take another example, if

n = 5

, then some of the sequences could be:

(1, 3, 1), (1, 1, 3), (3, 1, 1), (2, 1, 1, 1), (1, 2, 1, 1), (2, 1, 2)

Each sequence is one of the ways of climbing five steps. The point to note here is that each element of a sequence can only be

1

2

3

Write a recursive function named steps that accepts a positive integer

n

as argument. It should return the total number of ways in which Fibonacci can ascend

n

steps. Note that the order of his steps is important.

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
1

Expected Output:


text
1

Actual Output:


text
1

Case 2

Input:


text
public
2

Expected Output:


text
2

Actual Output:


text
2

Case 3

Input:


text
public
5

Expected Output:


text
13

Actual Output:


text
13

Private Tests ( 5/5 )

Case 1

Input:


text
private
10

Expected Output:


text
274

Good, your function is recursive

Actual Output:


text
274

Good, your function is recursive

Case 2

Input:


text
private
20

Expected Output:


text
121415

Good, your function is recursive

Actual Output:


text
121415

Good, your function is recursive

Case 3

Input:


text
private
15

Expected Output:


text
5768

Good, your function is recursive

Actual Output:


text
5768

Good, your function is recursive

Case 4

Input:


text
private
8

Expected Output:


text
81

Good, your function is recursive

Actual Output:


text
81

Good, your function is recursive

Case 5

Input:


text
private
12

Expected Output:


text
927

Good, your function is recursive

Actual Output:


text
927

Good, your function is recursive

💻 IITM Official Solution


python
# Basic idea behind the solution:
# The sum of all steps in a sequence should add up to n
# The last term in any sequence could be either 1, 2 or 3
# The number of sequences with last step as 1 is given by steps(n - 1)
# The number of sequences with last step as 2 is given by steps(n - 2)
# The number of sequences with last step as 3 is given by steps(n - 3)
# So, total number of sequences is steps(n - 1) + steps(n - 2) + steps(n - 3)
def steps(n):
    if n == 1:
        return 1
    if n == 2:
        return 2
    if n == 3:
        return steps(1) + steps(2) + 1
    return steps(n - 1) + steps(n - 2) + steps(n - 3)

💻 My Submitted Code


python
def steps(n):
    """
    A recursive function to compute the number of ways to ascend steps

    Argument:
        n: integer
    Return:
        result: integer
    """
    # Base cases
    if n == 1:
        return 1
    if n == 2:
        return 2
    if n == 3:
        return 4

    # Recursive case
    return steps(n - 1) + steps(n - 2) + steps(n - 3)