Recursion Base Case and Recursive Case in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the base case for the factorial function.

DSA C#

if (n == [1]) return 1;

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

A1

B-1

Cn

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 as base case which is incorrect for this factorial implementation.

Using n instead of a constant value.

The base case for factorial is when n equals 1, returning 1 stops the recursion.

2fill in blank

medium

Complete the code to write the recursive call for factorial.

DSA C#

return n * factorial([1]);

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

An - 1

Bn

Cn + 1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of n - 1 causing infinite recursion.

Using n + 1 which increases the problem size.

The recursive call reduces n by 1 each time to approach the base case.

3fill in blank

hard

Fix the error in the base case condition to prevent infinite recursion.

DSA C#

if (n [1] 1) return 1;

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

A<

B==

C>

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '!=' causes the function to return 1 for all n except 1.

Using '<' or '>' does not correctly identify the base case.

The base case must check if n equals 1 to stop recursion correctly.

4fill in blank

hard

Fill both blanks to complete the recursive factorial function.

DSA C#

public int Factorial(int n) {
    if (n [1] 1) return 1;
    return n [2] Factorial(n - 1);
}

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

A==

B*

C+

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '*' in recursive case.

Using '!=' instead of '==' in base case.

The base case uses '==' to check if n is 1, and the recursive case multiplies n by factorial of n-1.

5fill in blank

hard

Fill all three blanks to complete the recursive Fibonacci function.

DSA C#

public int Fibonacci(int n) {
    if (n [1] 0) return 0;
    if (n [2] 1) return 1;
    return Fibonacci(n [3] 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 '+' instead of '-' in recursive call.

Using '!=' instead of '==' in base cases.

The base cases check if n equals 0 or 1. The recursive call uses n - 1 and n - 2 to sum previous Fibonacci numbers.

Practice

1. What is the purpose of the base case in a recursive function?

easy

A. To print the result of the recursion

B. To call the function again with a smaller input

C. To stop the recursion and prevent infinite calls

D. To increase the input size for the next call

Solution

1. Step 1: Understand the role of base case

   The base case is the condition where the recursion stops to avoid infinite calls.

2. Step 2: Differentiate base case from recursive case

   The recursive case calls the function again, but the base case returns a value without further calls.

3. Final Answer:

   To stop the recursion and prevent infinite calls -> Option C

4. Quick Check:

   Base case = stop recursion [OK]

Hint: Base case stops recursion to avoid endless loops [OK]

Common Mistakes:

• Confusing base case with recursive case
• Thinking base case calls function again
• Ignoring base case leads to infinite recursion

2. Which of the following is the correct syntax for a base case in this C# recursive function to calculate factorial?

int Factorial(int n) {
    if (___) return 1;
    return n * Factorial(n - 1);
}

easy

A. n == 0

B. n > 0

C. n < 0

D. n == 1

Solution

1. Step 1: Identify the base case for factorial

   Factorial of 0 is defined as 1, so base case is when n == 0.

2. Step 2: Check options for correct base case condition

   Only 'n == 0' correctly stops recursion and returns 1.

3. Final Answer:

   n == 0 -> Option A

4. Quick Check:

   Factorial base case = n == 0 [OK]

Hint: Factorial base case is n equals zero [OK]

Common Mistakes:

• Using n > 0 as base case causes infinite recursion
• Using n == 1 misses factorial(0) definition
• Using n < 0 causes wrong behavior

3. What will be the output of this C# code?

int Sum(int n) {
    if (n == 0) return 0;
    return n + Sum(n - 1);
}

Console.WriteLine(Sum(3));

medium

A. 6

B. 3

C. 0

D. Error

Solution

1. Step 1: Trace recursive calls for Sum(3)

   Sum(3) = 3 + Sum(2), Sum(2) = 2 + Sum(1), Sum(1) = 1 + Sum(0), Sum(0) = 0.

2. Step 2: Calculate return values step-by-step

   Sum(0) = 0, Sum(1) = 1 + 0 = 1, Sum(2) = 2 + 1 = 3, Sum(3) = 3 + 3 = 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Sum 1+2+3 = 6 [OK]

Hint: Sum from n to 0 adds all numbers [OK]

Common Mistakes:

• Confusing base case return value
• Adding n instead of subtracting in recursive call
• Expecting output as input value

4. Identify the error in this recursive function to find factorial:

int Factorial(int n) {
    if (n == 1) return 1;
    else return n * Factorial(n + 1);
}

medium

A. Missing else block causes syntax error

B. Base case should be n == 0, not n == 1

C. Function should return void, not int

D. Recursive call should use n - 1, not n + 1

Solution

1. Step 1: Analyze recursive call parameter

   The function calls Factorial(n + 1), which increases n, causing infinite recursion.

2. Step 2: Correct recursive call for factorial

   Factorial should call Factorial(n - 1) to reduce n and reach base case.

3. Final Answer:

   Recursive call should use n - 1, not n + 1 -> Option D

4. Quick Check:

   Factorial recursion decreases n [OK]

Hint: Recursive call must reduce input to reach base case [OK]

Common Mistakes:

• Increasing n causes infinite recursion
• Confusing base case condition
• Thinking else block is mandatory

5. You want to write a recursive function in C# to reverse a string. Which base case and recursive case are correct?

string Reverse(string s) {
    if (___) return ___;
    return Reverse(___) + s[0];
}

hard

A. s.Length == 1; ""; s.Substring(1)

B. s.Length == 0; s; s.Substring(1)

C. s.Length == 1; s; s.Substring(0, s.Length - 1)

D. s == null; null; s.Substring(1)

Solution

1. Step 1: Identify base case for empty string

   When string length is 0, return the string itself (empty string).

2. Step 2: Understand recursive case for reversing

   Call Reverse on substring from index 1 to end, then add first character at the end.

3. Final Answer:

   s.Length == 0; s; s.Substring(1) -> Option B

4. Quick Check:

   Empty string base case, substring recursive call [OK]

Hint: Base case empty string; recursive call on substring from index 1 [OK]

Common Mistakes:

• Using s == null instead of empty string
• Wrong substring indices causing errors
• Returning s instead of empty string in base case