Recursion Base Case and Recursive Case in DSA C# - Build from Scratch

Recursion Base Case and Recursive Case

📖 Scenario: Imagine you have a stack of boxes, and you want to count how many boxes are in the stack by taking one box off at a time until none are left.

🎯 Goal: You will write a recursive function in C# that counts down from a number to zero using a base case and a recursive case.

📋 What You'll Learn

Create an integer variable called number with the value 5

Create a recursive method called CountDown that takes an integer parameter n

In CountDown, write a base case that stops recursion when n is 0

In CountDown, write a recursive case that calls CountDown with n - 1

Print each number from n down to 1 during the recursive calls

Call CountDown with the variable number

Print Done! after the recursion finishes

💡 Why This Matters

🌍 Real World

Recursion is used in many real-world problems like searching files in folders, solving puzzles, and processing tree structures.

💼 Career

Understanding recursion helps in software development roles that involve algorithms, data processing, and problem solving.

1

Create the starting number

Create an integer variable called number and set it to 5.

DSA C#

# Your code here

Hint

Use int number = 5; to create the variable.

2

Define the recursive method

Define a recursive method called CountDown that takes an integer parameter n.

DSA C#

int number = 5;
// Define the CountDown method here
# Your code here

Hint

Use void CountDown(int n) to define the method.

3

Add base case and recursive case

Inside CountDown, add a base case that returns when n is 0. Otherwise, print n and call CountDown with n - 1.

DSA C#

int number = 5;

void CountDown(int n)
{
    // Add base case and recursive call here
    # Your code here
}

Hint

The base case stops recursion when n is 0. The recursive case prints n and calls CountDown(n - 1).

4

Call the method and print done

Call CountDown with the variable number and then print Done!.

DSA C#

int number = 5;

void CountDown(int n)
{
    if (n == 0)
    {
        return;
    }
    Console.WriteLine(n);
    CountDown(n - 1);
}

// Call CountDown and print Done!
# Your code here

Hint

Call CountDown(number); and then Console.WriteLine("Done!");.

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