Climbing Stairs Problem in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Climbing Stairs Recursive Function

What is the output of the following Go code that calculates the number of ways to climb 4 stairs?

DSA Go

package main
import "fmt"

func climbStairs(n int) int {
    if n <= 2 {
        return n
    }
    return climbStairs(n-1) + climbStairs(n-2)
}

func main() {
    fmt.Println(climbStairs(4))
}

A 7

B 5

C 6

D 4

💡 Hint

Think about how many ways to climb 3 stairs and 2 stairs add up for 4 stairs.

The function uses recursion where climbStairs(4) = climbStairs(3) + climbStairs(2). climbStairs(3) = 3 and climbStairs(2) = 2, so total is 5.

🧠 Conceptual

intermediate

Understanding Base Cases in Climbing Stairs

Why is it important to have the base cases 'if n <= 2 return n' in the climbing stairs recursive function?

A To handle negative inputs correctly

B To make the function run faster by skipping calculations

C To stop infinite recursion and provide known answers for small inputs

D To initialize the result variable before recursion

💡 Hint

Base cases prevent the function from calling itself forever.

Base cases provide the simplest answers and stop the recursion from continuing infinitely.

❓ Predict Output

advanced

Output of Climbing Stairs with Memoization

What is the output of this Go code that uses memoization to calculate ways to climb 5 stairs?

DSA Go

package main
import "fmt"

func climbStairsMemo(n int, memo map[int]int) int {
    if n <= 2 {
        return n
    }
    if val, ok := memo[n]; ok {
        return val
    }
    memo[n] = climbStairsMemo(n-1, memo) + climbStairsMemo(n-2, memo)
    return memo[n]
}

func main() {
    memo := make(map[int]int)
    fmt.Println(climbStairsMemo(5, memo))
}

A 10

B 7

C 5

D 8

💡 Hint

Memoization stores results to avoid repeated calculations.

The function calculates climbStairs(5) = climbStairs(4) + climbStairs(3) = 5 + 3 = 8.

🔧 Debug

advanced

Identify the Error in Climbing Stairs Iterative Code

What error will this Go code produce when trying to calculate ways to climb 3 stairs?

DSA Go

package main
import "fmt"

func climbStairsIter(n int) int {
    if n <= 2 {
        return n
    }
    dp := make([]int, n)
    dp[0], dp[1] = 1, 2
    for i := 2; i < n; i++ {
        dp[i] = dp[i-1] + dp[i-2]
    }
    return dp[n-1]
}

func main() {
    fmt.Println(climbStairsIter(3))
}

A runtime error: index out of range

B prints 5

C prints 3

D compilation error

💡 Hint

Check the loop boundary and array size carefully.

The loop tries to access dp[3] when dp slice length is 3 (indices 0 to 2), causing index out of range error.

🚀 Application

expert

Number of Ways to Climb Stairs with Steps 1, 3, or 5

Given you can climb stairs by 1, 3, or 5 steps at a time, how many ways are there to climb 5 stairs? Choose the correct output of this Go code.

DSA Go

package main
import "fmt"

func climbStairsVariant(n int) int {
    dp := make([]int, n+1)
    dp[0] = 1
    for i := 1; i <= n; i++ {
        if i-1 >= 0 {
            dp[i] += dp[i-1]
        }
        if i-3 >= 0 {
            dp[i] += dp[i-3]
        }
        if i-5 >= 0 {
            dp[i] += dp[i-5]
        }
    }
    return dp[n]
}

func main() {
    fmt.Println(climbStairsVariant(5))
}

A 5

B 8

C 6

D 9

💡 Hint

Count all combinations using steps 1, 3, and 5 to reach 5.

The dp array counts ways to reach each step by summing ways from steps 1, 3, and 5 behind. For 5 stairs, total ways are 5.

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 distinct ways to reach the top

B. The minimum number of steps to reach the top

C. The maximum number of steps you can take at once

D. The number of steps you skip

Solution

1. Step 1: Understand the problem statement

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

2. Step 2: Identify what is being counted

   We count all possible sequences of 1-step and 2-step moves that sum to n steps.

3. Final Answer:

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

4. Quick Check:

   Counting sequences of 1 or 2 steps = total ways [OK]

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

Common Mistakes:

• Confusing number of ways with minimum steps
• Thinking about maximum steps allowed
• Counting skipped steps instead of ways

2. Which Go function signature correctly represents a function to solve the Climbing Stairs problem for n steps?

easy

A. func climbStairs(n int) bool

B. func climbStairs(n string) string

C. func climbStairs() int

D. func climbStairs(n int) int

Solution

1. Step 1: Identify input and output types

   The input is the number of steps (integer), output is the count of ways (integer).

2. Step 2: Match function signature

   Only func climbStairs(n int) int matches input int and output int.

3. Final Answer:

   func climbStairs(n int) int -> Option D

4. Quick Check:

   Input int, output int = correct signature [OK]

Hint: Input and output both must be int for steps and ways [OK]

Common Mistakes:

• Using string instead of int for steps
• Missing input parameter
• Returning bool instead of int

3. What is the output of this Go code for n = 4?

func climbStairs(n int) int {
    if n <= 2 {
        return n
    }
    a, b := 1, 2
    for i := 3; i <= n; i++ {
        a, b = b, a+b
    }
    return b
}

fmt.Println(climbStairs(4))

medium

A. 7

B. 6

C. 5

D. 4

Solution

1. Step 1: Trace initial values and loop

   Start with a=1, b=2. Loop i=3 to 4:
   i=3: a=2, b=3
   i=4: a=3, b=5

2. Step 2: Return final value

   Return b=5 after loop ends.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Ways for 4 steps = 5 [OK]

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

Common Mistakes:

• Returning a instead of b
• Off-by-one error in loop range
• Incorrect initial values

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

func climbStairs(n int) int {
    if n == 1 {
        return 1
    }
    a, b := 1, 2
    for i := 2; i <= n; i++ {
        a, b = b, a+b
    }
    return b
}

medium

A. Return statement should return a instead of b

B. Loop starts at wrong index causing extra iteration

C. Initial values of a and b are incorrect

D. Missing base case for n == 2

Solution

1. Step 1: Analyze loop start and iterations

   Loop starts at i=2 but initial values already cover steps 1 and 2, causing one extra iteration.

2. Step 2: Correct loop start

   Loop should start at i=3 to avoid counting extra ways.

3. Final Answer:

   Loop starts at wrong index causing extra iteration -> Option B

4. Quick Check:

   Loop index off by one causes wrong count [OK]

Hint: Start loop at 3 when initial values cover steps 1 and 2 [OK]

Common Mistakes:

• Starting loop at 2 instead of 3
• Changing initial values incorrectly
• Returning wrong variable

5. You want to find the number of ways to climb 10 steps but can take 1, 2, or 3 steps at a time. How would you modify the climbing stairs approach?

hard

A. Use dynamic programming with dp[i] = dp[i-1] + dp[i-2] + dp[i-3]

B. Use the same formula dp[i] = dp[i-1] + dp[i-2]

C. Only count ways taking 3 steps at a time

D. Multiply the number of ways for 1 and 2 steps

Solution

1. Step 1: Understand the new step options

   Now you can take 1, 2, or 3 steps at a time, so ways to reach step i depend on previous 3 steps.

2. Step 2: Formulate recurrence relation

   Number of ways dp[i] = dp[i-1] + dp[i-2] + dp[i-3] to include all possibilities.

3. Final Answer:

   Use dynamic programming with dp[i] = dp[i-1] + dp[i-2] + dp[i-3] -> Option A

4. Quick Check:

   Include all step sizes in sum for dp [OK]

Hint: Sum ways from last 3 steps for 1,2,3 step moves [OK]

Common Mistakes:

• Using old formula for only 1 or 2 steps
• Ignoring 3-step moves
• Multiplying counts instead of adding