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

Recursion Base Case and Recursive Case

📖 Scenario: Imagine you want to find the factorial of a number. Factorial means multiplying the number by all smaller numbers down to 1. For example, 4 factorial is 4 x 3 x 2 x 1 = 24.

🎯 Goal: You will write a recursive function in C that calculates the factorial of a number using a base case and a recursive case.

📋 What You'll Learn

Create a function called factorial that takes an integer n as input.

Use a base case where if n is 1, the function returns 1.

Use a recursive case where the function returns n multiplied by factorial(n - 1).

Call the factorial function with the value 5 and print the result.

💡 Why This Matters

🌍 Real World

Recursion is used in many places like calculating factorials, navigating file systems, and solving puzzles.

💼 Career

Understanding recursion helps in solving problems that require breaking down tasks into smaller similar tasks, common in software development and algorithm design.

1

Create the factorial function with base case

Write a function called factorial that takes an integer n and returns 1 if n is 1.

DSA C

# Write the factorial function with base case
int factorial(int n) {
    // Your code here
}

Hint

The base case stops the recursion. If n is 1, return 1.

2

Add the recursive case to factorial function

Inside the factorial function, add a recursive case that returns n * factorial(n - 1) when n is not 1.

DSA C

int factorial(int n) {
    if (n == 1) {
        return 1;
    }
    // Your code here
}

Hint

The recursive case calls factorial again with n - 1 and multiplies the result by n.

3

Call factorial function with 5

In the main function, call factorial with the value 5 and store the result in an integer variable called result.

DSA C

int factorial(int n) {
    if (n == 1) {
        return 1;
    }
    return n * factorial(n - 1);
}

int main() {
    // Call factorial with 5 and store in result
    // Your code here
    return 0;
}

Hint

Use int result = factorial(5); to call the function and save the answer.

4

Print the factorial result

Add a printf statement in main to print the value of result with the message: "Factorial of 5 is: %d\n".

DSA C

int factorial(int n) {
    if (n == 1) {
        return 1;
    }
    return n * factorial(n - 1);
}

int main() {
    int result = factorial(5);
    // Print the result
    // Your code here
    return 0;
}

Hint

Use printf("Factorial of 5 is: %d\n", result); to show the answer.

Practice

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

easy

A. To call the function again with a smaller input

B. To stop the recursion and prevent infinite calls

C. To increase the input size for the next call

D. To print the result of the recursion

Solution

1. Step 1: Understand what recursion does

   Recursion calls the same function repeatedly with smaller inputs.

2. Step 2: Identify the role of the base case

   The base case stops the recursion by providing a condition where no further calls happen.

3. Final Answer:

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

4. Quick Check:

   Base case = stop recursion [OK]

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

Common Mistakes:

• Confusing base case with recursive case
• Thinking base case calls function again
• Ignoring the need for a stopping condition

2. Which of the following is the correct syntax for a base case in a recursive function in C?

easy

A. if (n == 0) return 1;

B. while (n > 0) callFunction(n-1);

C. for (int i=0; i

D. return callFunction(n+1);

Solution

1. Step 1: Identify base case syntax

   The base case uses an if condition to check when to stop recursion.

2. Step 2: Check each option

   if (n == 0) return 1; uses if (n == 0) return 1; which correctly stops recursion. Others use loops or increase n, which are incorrect.

3. Final Answer:

   if (n == 0) return 1; -> Option A

4. Quick Check:

   Base case uses if condition [OK]

Hint: Base case uses if condition to stop recursion [OK]

Common Mistakes:

• Using loops instead of base case
• Increasing input instead of decreasing
• Missing return statement in base case

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

int factorial(int n) {
  if (n == 0) return 1;
  else return n * factorial(n - 1);
}

int main() {
  printf("%d", factorial(3));
  return 0;
}

medium

A. 6

B. 9

C. 3

D. 0

Solution

1. Step 1: Trace factorial(3) calls

   factorial(3) calls factorial(2), factorial(2) calls factorial(1), factorial(1) calls factorial(0).

2. Step 2: Calculate return values

   factorial(0) = 1; factorial(1) = 1*1=1; factorial(2) = 2*1=2; factorial(3) = 3*2=6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   3! = 6 [OK]

Hint: Factorial n! = n*(n-1)! with base case 0! = 1 [OK]

Common Mistakes:

• Not returning 1 for factorial(0)
• Multiplying incorrectly
• Confusing output with input

4. Identify the error in this recursive function that calculates the sum of numbers from 1 to n:

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

medium

A. Base case condition is incorrect

B. Missing return statement

C. Function should not be recursive

D. Recursive call does not reduce input

Solution

1. Step 1: Check base case

   Base case is if (n == 1) return 1; which is correct.

2. Step 2: Analyze recursive call

   Recursive call is sum(n) which does not reduce n, causing infinite recursion.

3. Final Answer:

   Recursive call does not reduce input -> Option D

4. Quick Check:

   Recursive input must decrease [OK]

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

Common Mistakes:

• Calling sum(n) instead of sum(n-1)
• Wrong base case value
• Forgetting to return recursive call

5. You want to write a recursive function to reverse a string in C. Which of the following correctly shows the base case and recursive case?

hard

A. Base case: always call reverse with length-1; Recursive case: print string

B. Base case: if string length > 1, call reverse again; Recursive case: return string as is

C. Base case: if string is empty or length 1, return string; Recursive case: return last char + reverse(rest of string)

D. Base case: if string is empty, print string; Recursive case: add first char to end

Solution

1. Step 1: Understand base case for string reversal

   Base case stops recursion when string is empty or length 1, returning string as is.

2. Step 2: Understand recursive case

   Recursive case returns last character plus reversed substring excluding last character.

3. Final Answer:

   Base case: if string is empty or length 1, return string; Recursive case: return last char + reverse(rest of string) -> Option C

4. Quick Check:

   Base case stops; recursive case reduces string [OK]

Hint: Base case returns small string; recursive case reduces string size [OK]

Common Mistakes:

• Wrong base case condition
• Recursive case not reducing string length
• Confusing base and recursive cases