Recursion Concept and Call Stack Visualization in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Simple Recursive Sum Function

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

DSA Javascript

function recursiveSum(n) {
  if (n <= 1) return n;
  return n + recursiveSum(n - 1);
}
console.log(recursiveSum(4));

A 4

B 24

C 10

D Error: Maximum call stack size exceeded

💡 Hint

Think about how the function adds n to the sum of all numbers before it.

The function adds n to the sum of numbers from 1 to n-1 recursively. For n=4, it calculates 4 + 3 + 2 + 1 = 10.

❓ Predict Output

intermediate

Output of Recursive Factorial Function

What will be printed when the following recursive factorial function is called with 5?

DSA Javascript

function factorial(n) {
  if (n === 0) return 1;
  return n * factorial(n - 1);
}
console.log(factorial(5));

A 120

B 25

C 0

D Error: Maximum call stack size exceeded

💡 Hint

Factorial multiplies all numbers from n down to 1.

factorial(5) = 5 * 4 * 3 * 2 * 1 = 120.

🔧 Debug

advanced

Identify the Error in Recursive Fibonacci Function

What error will this code produce when calling fibonacci(5)?

DSA Javascript

function fibonacci(n) {
  if (n <= 1) return n;
  return fibonacci(n - 1) + fibonacci(n - 2);
}
console.log(fibonacci(5));

A Error: Maximum call stack size exceeded

B Undefined

C 10

D 5

💡 Hint

Trace the calls for fibonacci(5) carefully.

The function correctly computes fibonacci(5) = 5 by summing fibonacci(4) and fibonacci(3).

❓ Predict Output

advanced

Output of Recursive Function with Multiple Calls

What is the output of this code that prints numbers during recursion?

DSA Javascript

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

A

3
2
1
1
2
3

B

1
2
3
3
2
1

C

1
2
3
1
2
3

D

3
2
1
3
2
1

💡 Hint

Notice the two console.log calls: one before and one after the recursive call.

The function prints n before going deeper and after returning, so output is 3 2 1 1 2 3.

🧠 Conceptual

expert

Maximum Call Stack Size Exceeded Error Cause

Which of the following causes a 'Maximum call stack size exceeded' error in recursive functions?

A Iterative function using loops instead of recursion

B Recursive function without a proper base case causing infinite calls

C Function that returns immediately without recursion

D Recursive function with a correct base case and finite calls

💡 Hint

Think about what happens if recursion never stops.

Without a base case, recursion never ends, causing the call stack to overflow.

Practice

1. What happens when a recursive function calls itself without a base case?

easy

A. It returns immediately without doing anything

B. It causes an infinite loop leading to a stack overflow error

C. It executes only once and stops

D. It throws a syntax error

Solution

1. Step 1: Understand the role of base case in recursion

   The base case stops the recursion by providing a condition to end calls.

2. Step 2: Analyze what happens without a base case

   Without a base case, the function keeps calling itself endlessly, filling the call stack.

3. Final Answer:

   It causes an infinite loop leading to a stack overflow error -> Option B

4. Quick Check:

   No base case = infinite recursion = stack overflow [OK]

Hint: Always check for a base case to stop recursion [OK]

Common Mistakes:

• Thinking recursion stops automatically
• Confusing base case with recursive case
• Assuming syntax error occurs without base case

2. Which of the following is the correct syntax to define a recursive function countDown in JavaScript?

easy

A. function countDown(n) { if(n <= 0) return; countDown(n - 1); }

B. function countDown(n) { while(n > 0) countDown(n - 1); }

C. function countDown(n) { for(let i=0; i

D. function countDown(n) { if(n < 0) countDown(n + 1); }

Solution

1. Step 1: Identify correct base case and recursive call

   function countDown(n) { if(n <= 0) return; countDown(n - 1); } has a base case (if n <= 0 return) and calls itself with n-1.

2. Step 2: Check other options for syntax or logic errors

   function countDown(n) { while(n > 0) countDown(n - 1); } uses while loop causing infinite recursion; C uses for loop incorrectly; D lacks proper base case.

3. Final Answer:

   function countDown(n) { if(n <= 0) return; countDown(n - 1); } -> Option A

4. Quick Check:

   Base case + recursive call = correct syntax [OK]

Hint: Look for base case and self-call in function [OK]

Common Mistakes:

• Using loops instead of recursion
• Missing base case
• Wrong recursive call argument

3. What is the output of the following code?

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

medium

A. 9

B. 1

C. 3

D. 6

Solution

1. Step 1: Trace factorial calls for n=3

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

2. Step 2: Calculate return values step-by-step

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

3. Final Answer:

   6 -> Option D

4. Quick Check:

   3! = 6 [OK]

Hint: Factorial n! = n * (n-1)! [OK]

Common Mistakes:

• Confusing multiplication order
• Forgetting base case returns 1
• Calculating factorial(0) incorrectly

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

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

medium

A. The base case is missing

B. The function should return n - sum(n - 1)

C. The recursive call uses the same argument causing infinite recursion

D. The function should use a loop instead

Solution

1. Step 1: Check the recursive call argument

   The function calls sum(n) again without reducing n, causing infinite recursion.

2. Step 2: Identify correct recursive call

   It should call sum(n - 1) to reduce n and reach base case.

3. Final Answer:

   The recursive call uses the same argument causing infinite recursion -> Option C

4. Quick Check:

   Recursive call argument must change to reach base case [OK]

Hint: Recursive call argument must move toward base case [OK]

Common Mistakes:

• Calling function with same argument
• Missing base case
• Using wrong operator in return

5. Consider this recursive function that reverses a string:

function reverseStr(str) {
  if (str === "") return "";
  return reverseStr(str.substring(1)) + str[0];
}
console.log(reverseStr("code"));

What is the output and why?

hard

A. "edoc" because the function moves first character to the end recursively

B. "code" because substring does not change the string

C. "" because base case returns empty string immediately

D. SyntaxError because substring is used incorrectly

Solution

1. Step 1: Understand recursion on string substring

   The function calls itself with the string minus the first character each time.

2. Step 2: Trace the concatenation on return

   Each call adds the first character of the current string to the end of the reversed substring, reversing the string.

3. Final Answer:

   "edoc" because the function moves first character to the end recursively -> Option A

4. Quick Check:

   Recursive substring + concat reverses string [OK]

Hint: Recursion with substring(1) + first char reverses string [OK]

Common Mistakes:

• Thinking substring does not change string
• Confusing base case effect
• Assuming syntax error with substring