Fibonacci Using Recursion in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Fibonacci Recursive Call

What is the output of the following C# code that prints Fibonacci numbers using recursion?

DSA C#

using System;
class Program {
  static int Fib(int n) {
    if (n <= 1) return n;
    return Fib(n - 1) + Fib(n - 2);
  }
  static void Main() {
    for (int i = 0; i < 6; i++) {
      Console.Write(Fib(i) + " ");
    }
  }
}

A 1 2 3 5 8 13

B 1 1 2 3 5 8

C 0 1 2 3 5 8

D 0 1 1 2 3 5

💡 Hint

Remember Fibonacci starts with 0 and 1, then sums previous two numbers.

The Fibonacci sequence starts with 0 and 1. The function returns n if n is 0 or 1. For other n, it returns sum of Fib(n-1) and Fib(n-2). So for i from 0 to 5, the outputs are 0,1,1,2,3,5.

❓ Predict Output

intermediate

Value of Fibonacci at n=7

What is the value returned by Fib(7) in the following recursive Fibonacci function?

DSA C#

int Fib(int n) {
  if (n <= 1) return n;
  return Fib(n - 1) + Fib(n - 2);
}

A 13

B 8

C 21

D 34

💡 Hint

Calculate Fibonacci numbers step by step or recall the sequence: 0,1,1,2,3,5,8,13,21...

The function defines the standard Fibonacci sequence where Fib(0)=0, Fib(1)=1, and Fib(n)=Fib(n-1)+Fib(n-2) for n>1. Thus: Fib(2)=1, Fib(3)=2, Fib(4)=3, Fib(5)=5, Fib(6)=8, Fib(7)=13.

🔧 Debug

advanced

Identify the error in Fibonacci recursion

What error will the following C# code produce when calling Fib(5)?

DSA C#

int Fib(int n) {
  if (n == 0) return 0;
  if (n == 1) return 1;
  return Fib(n - 1) - Fib(n - 2);
}

A Returns correct Fibonacci value

B Returns incorrect Fibonacci value

C StackOverflowException

D Compile-time error

💡 Hint

Check the operator used in the recursive return statement.

The function subtracts Fib(n-2) from Fib(n-1) instead of adding. This causes incorrect Fibonacci values but no runtime or compile errors.

❓ Predict Output

advanced

Output of Fibonacci with memoization

What is the output of this C# program that uses recursion with memoization to print Fibonacci numbers up to n=5?

DSA C#

using System;
using System.Collections.Generic;
class Program {
  static Dictionary<int,int> memo = new Dictionary<int,int>();
  static int Fib(int n) {
    if (memo.ContainsKey(n)) return memo[n];
    if (n <= 1) return n;
    int result = Fib(n - 1) + Fib(n - 2);
    memo[n] = result;
    return result;
  }
  static void Main() {
    for (int i = 0; i <= 5; i++) {
      Console.Write(Fib(i) + " ");
    }
  }
}

A 0 1 2 3 5 8

B 1 1 2 3 5 8

C 0 1 1 2 3 5

D 1 2 3 5 8 13

💡 Hint

Memoization stores results to avoid repeated calculations.

Memoization does not change the Fibonacci sequence output. It only optimizes the recursion. The output remains 0 1 1 2 3 5.

🧠 Conceptual

expert

Time complexity of naive recursive Fibonacci

What is the time complexity of the naive recursive Fibonacci function without memoization?

A O(2^n)

B O(n^2)

C O(n)

D O(log n)

💡 Hint

Consider how many calls are made for each Fib(n).

Naive recursive Fibonacci 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 sum of the two preceding numbers

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

D. Each number is the division of the two preceding numbers

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: Apply to recursion context

   Recursion calculates this by calling the function for the two previous numbers and adding their results.

3. Final Answer:

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

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 subtraction or division with addition
• Assuming Fibonacci uses only one previous number

2. Which of the following is the correct C# syntax to define a recursive Fibonacci function header?

easy

A. void Fibonacci(int n)

B. int Fibonacci()

C. int Fibonacci(int n)

D. int Fibonacci(int)

Solution

1. Step 1: Identify function return type and parameters

   The Fibonacci function returns an integer and takes an integer parameter for the position.

2. Step 2: Match correct C# syntax

   Correct syntax includes return type, function name, and parameter with type: int Fibonacci(int n)

3. Final Answer:

   int Fibonacci(int n) -> Option C

4. Quick Check:

   Function returns int and takes int parameter [OK]

Hint: Function must return int and take int parameter [OK]

Common Mistakes:

• Using void return type instead of int
• Missing parameter type or name
• Incorrect parameter list syntax

3. What is the output of this C# code snippet?

static int Fibonacci(int n) {
  if (n <= 1) return n;
  return Fibonacci(n - 1) + Fibonacci(n - 2);
}

Console.WriteLine(Fibonacci(4));

medium

A. 3

B. 5

C. 4

D. 7

Solution

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

   Fibonacci(4) = Fibonacci(3) + Fibonacci(2). Fibonacci(3) = Fibonacci(2) + Fibonacci(1) = 1 + 1 = 2. Fibonacci(2) = Fibonacci(1) + Fibonacci(0) = 1 + 0 = 1. So Fibonacci(4) = 2 + 1 = 3.

2. Step 2: Confirm output

   The printed output is 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Fibonacci(4) = 3 [OK]

Hint: Trace calls down to base cases to sum results [OK]

Common Mistakes:

• Confusing Fibonacci(4) with Fibonacci(5)
• Miscounting base cases
• Adding wrong recursive results

4. Identify the error in this recursive Fibonacci function:

int Fibonacci(int n) {
  if (n == 0) return 0;
  if (n == 1) return 1;
  return Fibonacci(n - 1) - Fibonacci(n - 2);
}

medium

A. The recursive call uses subtraction instead of addition

B. Parameter type is missing

C. Function lacks return type

D. Base cases are incorrect

Solution

1. Step 1: Check base cases

   Base cases for n=0 and n=1 are correct and return 0 and 1 respectively.

2. Step 2: Analyze recursive return statement

   The function uses subtraction (Fibonacci(n - 1) - Fibonacci(n - 2)) instead of addition, which is incorrect for Fibonacci sequence.

3. Final Answer:

   The recursive call uses subtraction instead of addition -> Option A

4. Quick Check:

   Fibonacci sums previous two, not subtracts [OK]

Hint: Fibonacci adds two previous calls, not subtracts [OK]

Common Mistakes:

• Using subtraction instead of addition in recursion
• Forgetting to return in base cases
• Missing parameter or return type in function

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

hard

A. Increase the recursion depth limit

B. Replace recursion with a while loop only

C. Use subtraction instead of addition in recursion

D. Use memoization to store and reuse computed values

Solution

1. Step 1: Understand problem with naive recursion

   Naive recursion recalculates Fibonacci values many times, causing inefficiency.

2. Step 2: Apply memoization technique

   Memoization stores results of Fibonacci calls in a cache to reuse, avoiding repeated work.

3. Final Answer:

   Use memoization to store and reuse computed values -> Option D

4. Quick Check:

   Memoization optimizes recursion by caching results [OK]

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

Common Mistakes:

• Thinking only loops can optimize recursion
• Increasing recursion depth does not improve efficiency
• Using subtraction breaks Fibonacci logic