Fibonacci Using Recursion in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the base case value for n equals 0.

DSA Typescript

function fibonacci(n: number): number {
  if (n === 0) {
    return [1];
  }
  return -1; // placeholder
}

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

A-1

B1

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 1 instead of 0 for n=0

Returning n directly without checking the base case

The Fibonacci sequence starts with 0 at position 0, so the function should return 0 when n is 0.

2fill in blank

medium

Complete the code to return the base case value for n equals 1.

DSA Typescript

function fibonacci(n: number): number {
  if (n === 0) {
    return 0;
  }
  if (n === 1) {
    return [1];
  }
  return -1; // placeholder
}

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

A1

B0

Cn

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 0 instead of 1 for n=1

Not handling the base case for n=1

The Fibonacci sequence has 1 at position 1, so the function should return 1 when n is 1.

3fill in blank

hard

Fix the error in the recursive call to compute Fibonacci numbers.

DSA Typescript

function fibonacci(n: number): number {
  if (n === 0) return 0;
  if (n === 1) return 1;
  return fibonacci(n [1] 1) + fibonacci(n - 2);
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of subtraction in the recursive call

Using multiplication or division which are incorrect here

To get the previous Fibonacci number, subtract 1 from n in the recursive call.

4fill in blank

hard

Fill both blanks to complete the recursive Fibonacci function correctly.

DSA Typescript

function fibonacci(n: number): number {
  if (n === 0) return 0;
  if (n === 1) return 1;
  return fibonacci(n [1] 1) [2] fibonacci(n - 2);
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong operators like multiplication or division

Mixing up the order of operations

The Fibonacci number is the sum of the two previous Fibonacci numbers at n-1 and n-2.

5fill in blank

hard

Fill all three blanks to create a recursive Fibonacci function with a base case and recursive calls.

DSA Typescript

function fibonacci(n: number): number {
  if (n === [1]) return 0;
  if (n === [2]) return 1;
  return fibonacci(n [3] 1) + fibonacci(n - 2);
}

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

A0

B1

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping base case values

Using addition instead of subtraction in recursive call

The base cases are for n=0 returning 0 and n=1 returning 1. The recursive call subtracts 1 from n.

Practice

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

easy

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

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

C. Each number is the difference 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: Recognize recursion use

   Recursion calls the function itself to calculate previous two numbers and sums them.

3. Final Answer:

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

4. Quick Check:

   Fibonacci = sum of two previous numbers [OK]

Hint: Fibonacci adds last two numbers, not multiply or subtract [OK]

Common Mistakes:

• Thinking Fibonacci multiplies previous numbers
• Confusing subtraction or squares with addition
• Assuming Fibonacci is a product sequence

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

easy

A. function fib(n: string): string

B. function fib(n: boolean): boolean

C. function fib(n: number): number

D. function fib(): void

Solution

1. Step 1: Identify input and output types

   The Fibonacci function takes a number input and returns a number output.

2. Step 2: Match correct function signature

   Only the signature with number input and number output matches the Fibonacci function requirements.

3. Final Answer:

   function fib(n: number): number -> Option C

4. Quick Check:

   Input and output types must be number [OK]

Hint: Fibonacci input/output are numbers, not strings or booleans [OK]

Common Mistakes:

• Using wrong parameter types like string or boolean
• Missing return type or using void
• Confusing function signature syntax

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

function fib(n: number): number {
  if (n <= 1) return n;
  return fib(n - 1) + fib(n - 2);
}
console.log(fib(4));

medium

A. 5

B. 7

C. 4

D. 3

Solution

1. Step 1: Calculate fib(4) using recursion

   fib(4) = fib(3) + fib(2) - fib(3) = fib(2) + fib(1) = (fib(1) + fib(0)) + 1 = (1 + 0) + 1 = 2 - fib(2) = fib(1) + fib(0) = 1 + 0 = 1 So fib(4) = 2 + 1 = 3

2. Step 2: Confirm output

   The console.log prints 5 as the result of fib(4).

3. Final Answer:

   5 -> Option A

4. Quick Check:

   fib(4) = 5 [OK]

Hint: Trace fib calls step-by-step to sum previous two results [OK]

Common Mistakes:

• Confusing fib(4) with fib(5)
• Miscounting base cases fib(0) and fib(1)
• Adding wrong recursive results

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

function fib(n: number): number {
  if (n == 0) return 0;
  if (n == 1) return 1;
  return fib(n - 1) - fib(n - 2);
}

medium

A. Change base case n == 0 to n <= 0

B. Change subtraction to addition in return statement

C. Remove base cases completely

D. Change function to return string instead of number

Solution

1. Step 1: Analyze return statement

   The function uses subtraction (fib(n - 1) - fib(n - 2)) which is incorrect for Fibonacci.

2. Step 2: Correct the operation

   Fibonacci requires addition of previous two numbers, so change '-' to '+'.

3. Final Answer:

   Change subtraction to addition in return statement -> Option B

4. Quick Check:

   Fibonacci sums previous two numbers [OK]

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

Common Mistakes:

• Using subtraction instead of addition
• Removing base cases causing infinite recursion
• Changing return type unnecessarily

5. Given the recursive Fibonacci function below, what is the output of fib(0) and fib(1)? Why are these base cases important?

function fib(n: number): number {
  if (n <= 1) return n;
  return fib(n - 1) + fib(n - 2);
}

hard

A. fib(0) = 0, fib(1) = 1; base cases are optional

B. fib(0) = 1, fib(1) = 0; base cases speed up recursion

C. fib(0) = 1, fib(1) = 1; base cases prevent wrong output

D. fib(0) = 0, fib(1) = 1; base cases stop infinite recursion

Solution

1. Step 1: Evaluate base cases fib(0) and fib(1)

   fib(0) returns 0 and fib(1) returns 1 as per the condition n <= 1 returns n.

2. Step 2: Understand importance of base cases

   Base cases stop the recursion from continuing infinitely by providing direct answers for smallest inputs.

3. Final Answer:

   fib(0) = 0, fib(1) = 1; base cases stop infinite recursion -> Option D

4. Quick Check:

   Base cases return 0 and 1 to end recursion [OK]

Hint: Base cases return n for n ≤ 1 to stop recursion [OK]

Common Mistakes:

• Mixing up fib(0) and fib(1) values
• Thinking base cases are optional
• Ignoring recursion stopping condition