Climbing Stairs Problem in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the base cases for climbing stairs.

DSA Python

def climb_stairs(n):
    if n == 1:
        return [1]
    if n == 2:
        return 2

Drag options to blanks, or click blank then click option'

An

B1

C0

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 2 for n == 1

Returning 0 for n == 1

When there is only 1 stair, there is exactly 1 way to climb it.

2fill in blank

medium

Complete the code to create a list to store the number of ways to climb each stair.

DSA Python

def climb_stairs(n):
    ways = [0] * (n + [1])
    ways[1] = 1
    ways[2] = 2

Drag options to blanks, or click blank then click option'

A2

B0

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of n + 1

Using n + 2 unnecessarily

We add 1 to n to create a list that includes index n.

3fill in blank

hard

Fix the error in the loop to correctly calculate ways to climb stairs.

DSA Python

for i in range(3, n + 1):
    ways[i] = ways[i - [1]] + ways[i - 2]

Drag options to blanks, or click blank then click option'

A2

B3

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2 instead of 1

Using 0 which causes index error

We add ways from one step before and two steps before the current stair.

4fill in blank

hard

Fill both blanks to complete the function that returns the total ways to climb n stairs.

DSA Python

def climb_stairs(n):
    if n <= 2:
        return n
    ways = [0] * (n + 1)
    ways[1] = 1
    ways[2] = 2
    for i in range(3, n + 1):
        ways[i] = ways[i - [1]] + ways[i - [2]]
    return ways[n]

Drag options to blanks, or click blank then click option'

A1

B2

C3

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the order of 1 and 2

Using 3 or 0 causing errors

The ways to reach stair i come from stair i-1 and stair i-2.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps stairs to ways if ways are more than 2.

DSA Python

def climb_stairs(n):
    if n <= 2:
        return {}
    ways = [0] * (n + 1)
    ways[1], ways[2] = 1, 2
    for i in range(3, n + 1):
        ways[i] = ways[i - 1] + ways[i - 2]
    result = [1]: [2] for [3] in range(1, n + 1) if ways[i] > 2}}
    return result

Drag options to blanks, or click blank then click option'

Ai

Bways[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong variable names

Swapping keys and values

The dictionary maps stair number i to ways[i] for i in the range.

Practice

1. What does the Climbing Stairs problem ask you to find?
Given n steps, how many distinct ways can you climb to the top if you can take 1 or 2 steps at a time?

easy

A. The total number of steps climbed

B. The maximum number of steps you can climb at once

C. The minimum number of steps to reach the top

D. The number of distinct ways to reach the top

Solution

1. Step 1: Understand the problem statement

   The problem asks for the count of different ways to climb to the top using 1 or 2 steps at a time.

2. Step 2: Identify what is being asked

   We want the total number of distinct sequences of 1-step and 2-step moves that sum to n.

3. Final Answer:

   The number of distinct ways to reach the top -> Option D

4. Quick Check:

   Count ways to climb = number of sequences [OK]

Hint: Count sequences of 1 or 2 steps to reach n [OK]

Common Mistakes:

• Confusing number of ways with minimum steps
• Thinking about maximum steps instead of ways
• Counting total steps instead of sequences

2. Which of the following Python function signatures correctly represents a function to solve the Climbing Stairs problem?

easy

A. def climb_stairs(n: int) -> int:

B. def climb_stairs(n): return str

C. def climb_stairs(n: str) -> int:

D. def climb_stairs() -> int:

Solution

1. Step 1: Check parameter and return types

   The input n is an integer representing steps, and output is an integer count of ways.

2. Step 2: Match function signature

   def climb_stairs(n: int) -> int: correctly uses int input and int output with type hints.

3. Final Answer:

   def climb_stairs(n: int) -> int: -> Option A

4. Quick Check:

   Input int, output int function signature [OK]

Hint: Input is int steps, output is int ways [OK]

Common Mistakes:

• Using string type for input
• Returning string instead of int
• Missing input parameter

3. What is the output of this code?

def climb_stairs(n: int) -> int:
    if n <= 2:
        return n
    a, b = 1, 2
    for _ in range(3, n + 1):
        a, b = b, a + b
    return b

print(climb_stairs(5))

medium

A. 5

B. 8

C. 13

D. 10

Solution

1. Step 1: Trace initial values and base cases

   For n=5, start with a=1, b=2. Loop runs for i=3 to 5.

2. Step 2: Calculate loop iterations

   Iteration 3: a=2, b=3; Iteration 4: a=3, b=5; Iteration 5: a=5, b=8.

3. Final Answer:

   8 -> Option B

4. Quick Check:

   Ways to climb 5 steps = 8 [OK]

Hint: Use Fibonacci-like addition for steps count [OK]

Common Mistakes:

• Returning n for all inputs
• Off-by-one errors in loop
• Mixing a and b values

4. Find the error in this code snippet for climbing stairs:

def climb_stairs(n: int) -> int:
    if n == 1:
        return 1
    a, b = 1, 2
    for i in range(2, n):
        a = b
        b = a + b
    return b

print(climb_stairs(4))

medium

A. Variables a and b are updated incorrectly

B. Loop range should start from 3

C. Base case for n == 2 is missing

D. Return statement should be 'return a'

Solution

1. Step 1: Analyze variable updates inside loop

   Inside loop, a is set to b, then b = a + b uses updated a, causing wrong sum.

2. Step 2: Correct update order

   We must update both simultaneously like a, b = b, a + b to avoid using updated a prematurely.

3. Final Answer:

   Variables a and b are updated incorrectly -> Option A

4. Quick Check:

   Simultaneous update needed for correct Fibonacci logic [OK]

Hint: Update a,b together to avoid wrong sums [OK]

Common Mistakes:

• Updating variables sequentially causing wrong values
• Wrong loop range causing missed steps
• Missing base cases

5. You want to find the number of ways to climb 10 steps but can take 1, 2, or 3 steps at a time. Which modification to the standard climbing stairs solution is correct?

hard

A. Use dp[i] = dp[i-1] * dp[i-2] * dp[i-3] with base dp[0]=1, dp[1]=1, dp[2]=2

B. Use dp[i] = dp[i-1] + dp[i-2] with base dp[0]=1, dp[1]=1

C. Use dp[i] = dp[i-1] + dp[i-2] + dp[i-3] with base dp[0]=1, dp[1]=1, dp[2]=2

D. Use dp[i] = dp[i-1] + dp[i-3] with base dp[0]=1, dp[1]=1, dp[2]=2

Solution

1. Step 1: Understand step options and recurrence

   With steps 1, 2, or 3 allowed, ways to reach i = sum of ways to reach i-1, i-2, and i-3.

2. Step 2: Set correct base cases

   dp[0]=1 (one way to stand still), dp[1]=1, dp[2]=2 (1+1 or 2 steps).

3. Final Answer:

   Use dp[i] = dp[i-1] + dp[i-2] + dp[i-3] with base dp[0]=1, dp[1]=1, dp[2]=2 -> Option C

4. Quick Check:

   Sum previous three dp values for 3-step climb [OK]

Hint: Sum ways from last 3 steps for 1-2-3 step climb [OK]

Common Mistakes:

• Multiplying dp values instead of adding
• Using only two previous dp values
• Incorrect base cases