Fibonacci Using Recursion in DSA Go - Build from Scratch

Fibonacci Using Recursion

📖 Scenario: You are helping a friend understand how to calculate Fibonacci numbers using a simple function that calls itself. Fibonacci numbers are a famous sequence where each number is the sum of the two before it, starting with 0 and 1.

🎯 Goal: Build a Go program that uses a recursive function to find the Fibonacci number at a given position.

📋 What You'll Learn

Create a variable called n with the value 7

Create a recursive function called fibonacci that takes an integer num and returns an integer

Use the base cases where num is 0 or 1 to return num

For other cases, return the sum of fibonacci(num-1) and fibonacci(num-2)

Print the Fibonacci number for n using the fibonacci function

💡 Why This Matters

🌍 Real World

Fibonacci numbers appear in nature, computer algorithms, and financial models. Understanding recursion helps solve problems that break down into smaller similar problems.

💼 Career

Recursion is a fundamental concept in programming interviews and algorithm design. Knowing how to implement recursive functions is useful for software development and problem-solving.

1

Create the input variable

Create a variable called n and set it to 7.

DSA Go

package main

import "fmt"

func main() {
    // Create variable n with value 7
    // Your code here
}

Hint

Use n := 7 inside the main function to create the variable.

2

Define the recursive Fibonacci function

Define a function called fibonacci that takes an integer num and returns an integer. Use base cases to return num if it is 0 or 1.

DSA Go

package main

import "fmt"

func fibonacci(num int) int {
    // Add base cases for num == 0 or num == 1
    // Your code here
}

func main() {
    n := 7
}

Hint

Use if num == 0 || num == 1 { return num } inside the fibonacci function.

3

Add the recursive call

In the fibonacci function, return the sum of fibonacci(num-1) and fibonacci(num-2) for other cases.

DSA Go

package main

import "fmt"

func fibonacci(num int) int {
    if num == 0 || num == 1 {
        return num
    }
    // Return fibonacci(num-1) + fibonacci(num-2)
    // Your code here
}

func main() {
    n := 7
}

Hint

Use return fibonacci(num-1) + fibonacci(num-2) to call the function recursively.

4

Print the Fibonacci number

Print the Fibonacci number for n using fmt.Println(fibonacci(n)) inside the main function.

DSA Go

package main

import "fmt"

func fibonacci(num int) int {
    if num == 0 || num == 1 {
        return num
    }
    return fibonacci(num-1) + fibonacci(num-2)
}

func main() {
    n := 7
    // Print the Fibonacci number for n
    // Your code here
}

Hint

Use fmt.Println(fibonacci(n)) to display the result.

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