Fibonacci Using Recursion in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Fibonacci Recursive Call

What is the output of the following Go code that prints Fibonacci numbers recursively for n=5?

DSA Go

package main
import "fmt"

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

func main() {
    for i := 0; i < 5; i++ {
        fmt.Print(fib(i), " ")
    }
}

A 1 1 2 3 5

B 0 1 2 3 5

C 0 1 1 2 3

D 1 2 3 5 8

💡 Hint

Remember Fibonacci sequence starts with 0 and 1.

The Fibonacci sequence starts with 0 and 1. The function returns n if n is 0 or 1. For n=5, the printed sequence is 0 1 1 2 3.

❓ Predict Output

intermediate

Value of fib(6) Using Recursion

What is the value returned by fib(6) in the following Go recursive Fibonacci function?

DSA Go

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

A 5

B 13

C 21

D 8

💡 Hint

Calculate fib(6) by adding fib(5) and fib(4).

fib(6) = fib(5) + fib(4) = 5 + 3 = 8.

🔧 Debug

advanced

Identify the Runtime Error in Fibonacci Code

What error will the following Go code produce when calling fib(-1)?

DSA Go

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

func main() {
    fmt.Println(fib(-1))
}

A Returns -1 without error

B Runtime panic: index out of range

C Stack overflow due to infinite recursion

D Compilation error: missing return statement

💡 Hint

Check the base case condition for negative input.

For n = -1, the base case n <= 1 returns n (-1), so no infinite recursion occurs. But since fib(-1) returns -1, no error occurs. However, the function is not designed for negative inputs, so it returns -1 safely.

❓ Predict Output

advanced

Output of Fibonacci Sequence with Memoization

What is the output of this Go program that uses memoization to print Fibonacci numbers up to n=7?

DSA Go

package main
import "fmt"

var memo = map[int]int{}

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

func main() {
    for i := 0; i <= 7; i++ {
        fmt.Print(fib(i), " ")
    }
}

A 1 1 2 3 5 8 13 21

B 0 1 1 2 3 5 8 13

C 0 1 2 3 5 8 13 21

D 1 2 3 5 8 13 21 34

💡 Hint

Memoization stores previously calculated results to avoid repeated work.

The memoization technique caches results, so fib(n) returns the correct Fibonacci number. The sequence printed is 0 1 1 2 3 5 8 13.

🧠 Conceptual

expert

Time Complexity of Recursive Fibonacci

What is the time complexity of the naive recursive Fibonacci function fib(n) without memoization?

A O(2^n)

B O(n)

C O(n^2)

D O(log n)

💡 Hint

Consider how many calls fib(n) makes to fib(n-1) and fib(n-2).

The naive recursive Fibonacci function calls itself twice for each n > 1, leading to exponential growth in calls, so time complexity is O(2^n).

Practice

1. What does the Fibonacci sequence represent when calculated using recursion?

easy

A. Each number is the product of the two preceding numbers

B. Each number is the difference of the two preceding numbers

C. Each number is the sum of the two preceding numbers

D. Each number is the square of the previous number

Solution

1. Step 1: Understand Fibonacci sequence definition

   The Fibonacci sequence is defined such that each number is the sum of the two numbers before it.

2. Step 2: Relate to recursion

   Recursion calls the function for the two previous numbers and adds their results.

3. Final Answer:

   Each number is the sum of the two preceding numbers -> Option C

4. Quick Check:

   Fibonacci = sum of two previous numbers [OK]

Hint: Remember Fibonacci adds two previous numbers [OK]

Common Mistakes:

• Thinking Fibonacci multiplies previous numbers
• Confusing difference with sum
• Assuming Fibonacci squares previous number

2. Which of the following is the correct Go function signature for a recursive Fibonacci function?

easy

A. func fibonacci(n int) int

B. func fibonacci(n string) string

C. func fibonacci(n float64) float64

D. func fibonacci() int

Solution

1. Step 1: Identify parameter and return types

   The Fibonacci function takes an integer input and returns an integer output.

2. Step 2: Match correct Go syntax

   func fibonacci(n int) int matches the correct signature: func fibonacci(n int) int.

3. Final Answer:

   func fibonacci(n int) int -> Option A

4. Quick Check:

   Input and output are integers [OK]

Hint: Fibonacci uses int input and int output [OK]

Common Mistakes:

• Using string or float types incorrectly
• Omitting function parameters
• Wrong return type

3. What is the output of the following Go code?

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

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

medium

A. 5

B. 8

C. 3

D. 13

Solution

1. Step 1: Trace fibonacci(5) calls

   fibonacci(5) = fibonacci(4) + fibonacci(3), fibonacci(4) = 3, fibonacci(3) = 2, so total = 5.

2. Step 2: Calculate final value

   Sum of fibonacci(4) and fibonacci(3) is 3 + 2 = 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Fibonacci(5) = 5 [OK]

Hint: Recall Fibonacci(5) = 5 from sequence 0,1,1,2,3,5 [OK]

Common Mistakes:

• Confusing index starting at 0 or 1
• Adding wrong recursive results
• Miscounting base cases

4. Identify the error in this recursive Fibonacci function and select the fix:

func fibonacci(n int) int {
    if n == 0 {
        return 0
    } else if n == 1 {
        return 1
    }
    return fibonacci(n-1) - fibonacci(n-2)
}

medium

A. Add a loop instead of recursion

B. Change base case n == 0 to n == 2

C. Remove else if condition

D. Change '-' to '+' in the return statement

Solution

1. Step 1: Check recursive return operation

   The Fibonacci sequence sums previous two numbers, but code subtracts them.

2. Step 2: Correct the operation

   Replace '-' with '+' to correctly add fibonacci(n-1) and fibonacci(n-2).

3. Final Answer:

   Change '-' to '+' in the return statement -> Option D

4. Quick Check:

   Fibonacci sums previous two numbers [OK]

Hint: Fibonacci adds, never subtracts previous two numbers [OK]

Common Mistakes:

• Using subtraction instead of addition
• Changing base cases incorrectly
• Removing necessary conditions

5. How can you optimize the recursive Fibonacci function to avoid repeated calculations?

hard

A. Increase the recursion depth limit

B. Use memoization to store and reuse results

C. Use a global variable to count calls

D. Replace recursion with a random number generator

Solution

1. Step 1: Understand repeated calculations problem

   Recursive Fibonacci recalculates same values many times, causing inefficiency.

2. Step 2: Apply memoization technique

   Memoization stores results of previous calls to reuse them, reducing repeated work.

3. Final Answer:

   Use memoization to store and reuse results -> Option B

4. Quick Check:

   Memoization optimizes recursion by caching [OK]

Hint: Cache results to avoid repeated recursion calls [OK]

Common Mistakes:

• Increasing recursion depth does not fix inefficiency
• Counting calls doesn't optimize calculation
• Random numbers unrelated to Fibonacci