Recursion Concept and Call Stack Visualization in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to make the factorial function call itself recursively.

DSA C#

int Factorial(int n) {
    if (n == 0) return 1;
    return n * Factorial([1]);
}

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

A1

Bn + 1

C0

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 1 or 0 directly ignores the recursive step.

The factorial function calls itself with n - 1 to reduce the problem size until it reaches 0.

2fill in blank

medium

Complete the code to correctly calculate the sum of numbers from 1 to n using recursion.

DSA C#

int Sum(int n) {
    if (n == 1) return 1;
    return n + Sum([1]);
}

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

An - 1

Bn + 1

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 0 as argument skips numbers.

The function sums numbers by adding n to the sum of numbers from 1 to n-1.

3fill in blank

hard

Fix the error in the recursive Fibonacci function call.

DSA C#

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

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

A1

Bn + 1

Cn - 1

Dn - 2

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 1 or n - 2 twice misses one recursive call.

The Fibonacci function calls itself with n - 1 and n - 2 to get the two previous numbers.

4fill in blank

hard

Fill both blanks to complete the recursive function that prints numbers from n down to 1.

DSA C#

void PrintDescending(int n) {
    if (n == 0) return;
    Console.WriteLine([1]);
    PrintDescending([2]);
}

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

An

Bn - 1

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Printing 1 always instead of n.

Calling with n + 1 causes infinite recursion.

The function prints n, then calls itself with n-1 to print the next smaller number.

5fill in blank

hard

Fill all three blanks to complete the recursive function that calculates the power of a number.

DSA C#

int Power(int baseNum, int exponent) {
    if (exponent == 0) return [1];
    return baseNum * Power(baseNum, [2]);
}

// Example call: Power(2, 3) returns [3]

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

A1

Bexponent - 1

C8

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 0 in base case causes wrong result.

Not reducing exponent causes infinite recursion.

Wrong expected output for Power(2, 3).

Power of any number to 0 is 1. The recursive call reduces exponent by 1. 2 to the power 3 is 8.

Practice

1. What happens when a recursive function calls itself without a stopping condition?

easy

A. It runs only once and stops

B. It immediately returns without doing anything

C. It causes an infinite loop leading to a stack overflow error

D. It converts into a normal loop automatically

Solution

1. Step 1: Understand recursion stopping condition

   A recursive function must have a base case to stop calling itself; otherwise, it keeps calling endlessly.

2. Step 2: Effect of missing base case

   Without a base case, the function calls stack up until memory runs out, causing a stack overflow error.

3. Final Answer:

   It causes an infinite loop leading to a stack overflow error -> Option C

4. Quick Check:

   Missing base case = infinite recursion [OK]

Hint: Always check for a base case to stop recursion [OK]

Common Mistakes:

• Assuming recursion stops automatically
• Confusing recursion with loops
• Thinking recursion runs only once without base case

2. Which of the following is the correct syntax to define a recursive method in C# that calculates factorial?

easy

A. int Factorial(int n) { if (n == 0) return 1; else return n * Factorial(n - 1); }

B. int Factorial(int n) { while (n > 0) return n * Factorial(n - 1); return 1; }

C. int Factorial(int n) { if (n == 1) return 0; else return n + Factorial(n - 1); }

D. int Factorial(int n) { if (n == 0) return 0; else return n * Factorial(n + 1); }

Solution

1. Step 1: Check base case correctness

   Factorial base case is when n == 0, return 1; this matches int Factorial(int n) { if (n == 0) return 1; else return n * Factorial(n - 1); } only.

2. Step 2: Check recursive call correctness

   Recursive call must reduce n by 1 and multiply; int Factorial(int n) { if (n == 0) return 1; else return n * Factorial(n - 1); } does this correctly.

3. Final Answer:

   int Factorial(int n) { if (n == 0) return 1; else return n * Factorial(n - 1); } -> Option A

4. Quick Check:

   Base case n==0 and n*Factorial(n-1) [OK]

Hint: Base case returns 1; recursive call multiplies by n-1 factorial [OK]

Common Mistakes:

• Using wrong base case value
• Increasing n instead of decreasing
• Returning 0 instead of 1 in base case

3. What is the output of the following C# code?

static void PrintNumbers(int n) {
  if (n == 0) return;
  Console.Write(n + " ");
  PrintNumbers(n - 1);
}

PrintNumbers(3);

medium

A. 1 2 3

B. 0 1 2 3

C. 3 2 1 0

D. 3 2 1

Solution

1. Step 1: Trace the recursive calls

   PrintNumbers(3) prints 3, then calls PrintNumbers(2), prints 2, calls PrintNumbers(1), prints 1, then calls PrintNumbers(0) which returns.

2. Step 2: Collect printed output

   Printed numbers are 3, 2, 1 in that order, each followed by a space.

3. Final Answer:

   3 2 1 -> Option D

4. Quick Check:

   Print then recurse = descending order [OK]

Hint: Print before recursive call prints descending sequence [OK]

Common Mistakes:

• Assuming print happens after recursion
• Including 0 in output
• Confusing order of prints

4. The following recursive method is intended to print numbers from 1 to n. What is the error?

void PrintUp(int n) {
  if (n == 0) return;
  PrintUp(n - 1);
  Console.Write(n + " ");
}

PrintUp(-1);

medium

A. Infinite recursion because negative n never reaches 0

B. No error; it prints numbers correctly

C. Syntax error due to missing return type

D. Runtime error because Console.Write is invalid

Solution

1. Step 1: Analyze base case condition

   Base case stops recursion when n == 0, but if n starts negative, it never reaches 0.

2. Step 2: Effect of negative input

   Calling PrintUp(-1) causes infinite recursion because n keeps decreasing and never hits 0.

3. Final Answer:

   Infinite recursion because negative n never reaches 0 -> Option A

4. Quick Check:

   Base case unreachable with negative input [OK]

Hint: Check base case covers all input ranges [OK]

Common Mistakes:

• Assuming negative input is handled
• Thinking syntax or Console.Write causes error
• Ignoring infinite recursion possibility

5. Consider this recursive method that sums numbers from 1 to n:

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

What is the output of Sum(4) and how many times is the method called?

hard

A. Output: 10, Method calls: 4

B. Output: 10, Method calls: 5

C. Output: 15, Method calls: 5

D. Output: 15, Method calls: 4

Solution

1. Step 1: Calculate Sum(4) step-by-step

   Sum(4) = 4 + Sum(3), Sum(3) = 3 + Sum(2), Sum(2) = 2 + Sum(1), Sum(1) = 1 + Sum(0), Sum(0) = 0. So total = 4+3+2+1+0 = 10.

2. Step 2: Count method calls

   Calls happen for n=4,3,2,1,0 totaling 5 calls.

3. Final Answer:

   Output: 10, Method calls: 5 -> Option B

4. Quick Check:

   Sum 1 to 4 = 10; calls = n+1 [OK]

Hint: Sum calls = n+1; sum formula n(n+1)/2 for output [OK]

Common Mistakes:

• Counting calls as n instead of n+1
• Calculating sum incorrectly
• Ignoring base case call