Recursion Base Case and Recursive Case in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the base case in recursion?

The base case is the condition that stops the recursion. It prevents infinite calls by providing a simple answer without further recursion.

beginner

What is the recursive case in recursion?

The recursive case is where the function calls itself with a smaller or simpler input, moving towards the base case.

beginner

Why do we need both base case and recursive case in a recursive function?

The base case stops the recursion to avoid infinite loops, and the recursive case breaks the problem into smaller parts to solve it step by step.

beginner

Consider this C function snippet:

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

Identify the base case and recursive case.

Base case: if (n == 0) return 1;
Recursive case: return n * factorial(n - 1);

beginner

What happens if a recursive function has no base case?

The function will keep calling itself forever, causing a stack overflow error and crashing the program.

In recursion, what is the purpose of the base case?

A To increase the input size

B To call the function again

C To stop the recursion

D To print the result

The base case stops the recursion by providing a simple answer without further calls.

Which part of a recursive function calls itself with a smaller input?

A Base case

B Return statement

C Main function

D Recursive case

The recursive case calls the function itself with a smaller or simpler input.

What will happen if a recursive function lacks a base case?

A It will run forever causing a crash

B It will print an error message

C It will return zero

D It will stop immediately

Without a base case, recursion never stops, causing a stack overflow and crash.

In the factorial function, what is the base case?

A n == 0

B n > 0

C n == 1

D n < 0

The base case is when n equals 0, returning 1 to stop recursion.

Why is the recursive case important?

A It stops the recursion

B It breaks the problem into smaller parts

C It prints the output

D It initializes variables

The recursive case breaks the problem into smaller parts to solve it step by step.

Explain in your own words what the base case and recursive case are in recursion.

Think about how recursion stops and how it keeps going.

Describe what would happen if a recursive function does not have a base case.

Imagine calling a function again and again without stopping.

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