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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Recursive Sum Function

What is the output of the following JavaScript code that uses recursion to sum numbers from n down to 1?

DSA Javascript

function recursiveSum(n) {
  if (n <= 0) {
    return 0;
  }
  return n + recursiveSum(n - 1);
}

console.log(recursiveSum(4));

A 0

B 24

C 10

D Undefined

💡 Hint

Think about what happens when n reaches 0 and how the function adds up the numbers.

The function adds n to the sum of all numbers below it until it reaches 0, where it stops. So, 4 + 3 + 2 + 1 = 10.

❓ Predict Output

intermediate

Output of Recursive Factorial Function

What will be printed when this recursive factorial function is called with 3?

DSA Javascript

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

console.log(factorial(3));

A 1

B 6

C 9

D 3

💡 Hint

Factorial means multiplying all numbers from n down to 1.

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

🔧 Debug

advanced

Identify the Error in Recursive Fibonacci Function

What error will this recursive Fibonacci function cause when called with 5?

DSA Javascript

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

console.log(fibonacci(5));

A No error, output is 5

B Stack overflow error

C TypeError

D ReferenceError

💡 Hint

Check if the base cases cover all needed conditions to stop recursion.

The function correctly defines base cases for 0 and 1, so it stops recursion properly and returns 5 for fibonacci(5).

❓ Predict Output

advanced

Output of Recursive String Reversal

What is the output of this recursive function that reverses a string?

DSA Javascript

function reverseString(str) {
  if (str === "") {
    return "";
  }
  return reverseString(str.substr(1)) + str[0];
}

console.log(reverseString("code"));

A "edoc"

B "code"

C "odec"

D ""

💡 Hint

The function takes the first character off and adds it to the end after reversing the rest.

The function reverses the string by moving the first character to the end recursively. So "code" becomes "edoc".

🧠 Conceptual

expert

Understanding Base Case Importance in Recursion

Why is the base case essential in a recursive function?

A It allows the function to call itself more times

B It makes the function run faster

C It helps the function use more memory

D It stops the recursion to prevent infinite calls

💡 Hint

Think about what happens if the function never stops calling itself.

The base case stops the recursion by providing a condition where the function no longer calls itself, preventing infinite loops and stack overflow.

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 increase the input size for the next call

C. To stop the recursion and prevent infinite calls

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 C

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 recursion again
• Ignoring base case leads to infinite recursion

2. Which of the following is the correct syntax for a base case in this recursive function to calculate factorial?

function factorial(n) {
  if (___) {
    return 1;
  }
  return n * factorial(n - 1);
}

easy

A. n > 0

B. n === 0

C. n === 1

D. n < 0

Solution

1. Step 1: Recall factorial base case

   Factorial of 0 is 1, so base case is when n equals 0.

2. Step 2: Match condition to code

   The condition n === 0 correctly stops recursion and returns 1.

3. Final Answer:

   n === 0 -> Option B

4. Quick Check:

   Base case for factorial = 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 < 0 which is invalid for factorial
• Using n === 1 misses factorial(0) base case

3. What will be the output of this recursive function call?

function sumTo(n) {
  if (n === 0) {
    return 0;
  }
  return n + sumTo(n - 1);
}
console.log(sumTo(3));

medium

A. 6

B. 3

C. 0

D. Error

Solution

1. Step 1: Trace recursive calls

   sumTo(3) calls 3 + sumTo(2), sumTo(2) calls 2 + sumTo(1), sumTo(1) calls 1 + sumTo(0), sumTo(0) returns 0.

2. Step 2: Calculate total sum

   sumTo(3) = 3 + 2 + 1 + 0 = 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   3+2+1+0 = 6 [OK]

Hint: Sum from n down to 0 adds all numbers [OK]

Common Mistakes:

• Forgetting to add current n before recursive call
• Confusing base case return value
• Assuming output is just n instead of sum

4. Find the error in this recursive function to compute the nth Fibonacci number:

function fib(n) {
  if (n === 0) return 0;
  if (n === 1) return 1;
  return fib(n - 1) + fib(n - 2);
}
console.log(fib(-1));

medium

A. Missing base case for negative n causing infinite recursion

B. Incorrect base case values for fib(0) and fib(1)

C. Wrong recursive calls should be fib(n + 1) and fib(n + 2)

D. No error, output is correct

Solution

1. Step 1: Analyze base cases and input

   Base cases cover n=0 and n=1, but input is n=-1 which is not handled.

2. Step 2: Understand recursion with negative input

   Calling fib(-1) leads to fib(-2) and fib(-3) calls infinitely, no stop condition.

3. Final Answer:

   Missing base case for negative n causing infinite recursion -> Option A

4. Quick Check:

   Negative input needs base case [OK]

Hint: Check base cases cover all input ranges [OK]

Common Mistakes:

• Ignoring negative inputs in recursion
• Assuming fib(-1) is valid without base case
• Changing recursive calls incorrectly

5. You want to write a recursive function to reverse a string. Which base case and recursive case correctly achieve this?

function reverse(str) {
  if (___) {
    return ___;
  }
  return reverse(___) + str[0];
}

hard

A. str.length === 0 / str / str.slice(1)

B. str.length === 1 / str / str.slice(0, -1)

C. str === null / null / str.slice(1)

D. str === '' / str[0] / str.slice(1)

Solution

1. Step 1: Identify base case for empty string

   When string is empty (''), return the empty string to stop recursion.

2. Step 2: Define recursive call correctly

   Call reverse on substring from index 1 to end, then add first character at the end.

3. Final Answer:

   str === '' / str / str.slice(1) -> Option D

4. Quick Check:

   Empty string base case and slice(1) recursive call [OK]

Hint: Base case empty string, recursive call slice(1) [OK]

Common Mistakes:

• Using null instead of empty string as base case
• Returning wrong substring in recursive call
• Incorrect base case condition