Recursion Base Case and Recursive Case in DSA C - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Recursive Factorial Function

What is the output of the following C code when calling factorial(4)?

DSA C

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

int main() {
    int result = factorial(4);
    printf("%d\n", result);
    return 0;
}

A 120

B 10

C 0

D 24

💡 Hint

Remember factorial of 4 is 4 * 3 * 2 * 1.

The function calls itself reducing n by 1 until it reaches 0, then multiplies all values: 4 * 3 * 2 * 1 = 24.

❓ Predict Output

intermediate

Output of Recursive Sum Function

What is printed when the following C code runs sum(3)?

DSA C

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

int main() {
    int result = sum(3);
    printf("%d\n", result);
    return 0;
}

A 0

B 6

C 3

D 9

💡 Hint

Sum of numbers from 1 to 3 is 6.

The function adds n to the sum of numbers below it until it reaches 0: 3 + 2 + 1 + 0 = 6.

🔧 Debug

advanced

Identify the Error in Recursive Fibonacci Function

What error will occur when running this C code?

DSA C

int fibonacci(int n) {
    if (n == 0) {
        return 0;
    } else if (n == 1) {
        return 1;
    } else {
        return fibonacci(n - 1) + fibonacci(n - 2);
    }
}

int main() {
    int result = fibonacci(-1);
    printf("%d\n", result);
    return 0;
}

A Returns -1 as output

B Returns 0 without error

C Compilation error due to missing return

D Stack overflow due to infinite recursion

💡 Hint

Check what happens when n is negative.

The function does not handle negative inputs, so it keeps calling itself with decreasing n, never reaching base cases, causing infinite recursion and stack overflow.

🧠 Conceptual

advanced

Base Case Importance in Recursion

Why is the base case essential in a recursive function?

A It initializes variables for recursion

B It makes the function run faster

C It stops the recursion to prevent infinite calls

D It allows the function to call other functions

💡 Hint

Think about what happens if recursion never stops.

The base case tells the function when to stop calling itself, preventing infinite loops and stack overflow.

❓ Predict Output

expert

Output of Recursive String Length Function

What is the output of this C code when calling strlen_recursive("abc")?

DSA C

#include <stdio.h>

int strlen_recursive(const char *str) {
    if (*str == '\0') {
        return 0;
    } else {
        return 1 + strlen_recursive(str + 1);
    }
}

int main() {
    int length = strlen_recursive("abc");
    printf("%d\n", length);
    return 0;
}

A 3

B 4

C 0

D Segmentation fault

💡 Hint

Count characters until the null character '\0'.

The function counts each character until it finds the end '\0', so for "abc" it returns 3.

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