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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Simple Recursive Sum Function

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

DSA Typescript

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

console.log(recursiveSum(4));

A 0

B 4

C 10

D Undefined (runtime error)

💡 Hint

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

The function adds n to the sum of numbers from n-1 down to 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 this recursive factorial function is called with 3?

DSA Typescript

function factorial(n: number): number {
  if (n === 0) return 1;
  return n * factorial(n - 1);
}

console.log(factorial(3));

A 9

B 6

C 0

D Error: Maximum call stack size exceeded

💡 Hint

Factorial multiplies n by factorial of n-1 until it reaches 0.

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

🔧 Debug

advanced

Identify the Error in Recursive Fibonacci Function

What is the output of this TypeScript code when calling fibonacci(5)?

DSA Typescript

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

console.log(fibonacci(5));

A 5

B 8

C Stack overflow error

D TypeError: fibonacci is not a function

💡 Hint

Trace fibonacci(5) calls and sum results.

fibonacci(5) = fibonacci(4) + fibonacci(3) = 3 + 2 = 5. The code runs correctly without errors.

❓ Predict Output

advanced

Output of Recursive Function with Multiple Calls

What is the output of this recursive function that prints numbers during the call and return phases?

DSA Typescript

function printNumbers(n: number): void {
  if (n <= 0) return;
  console.log('Call:', n);
  printNumbers(n - 1);
  console.log('Return:', n);
}

printNumbers(3);

A "Call: 3" "Call: 2" "Call: 1" "Return: 1" "Return: 2" "Return: 3"

B "Return: 1" "Return: 2" "Return: 3" "Call: 3" "Call: 2" "Call: 1"

C "Call: 1" "Call: 2" "Call: 3" "Return: 3" "Return: 2" "Return: 1"

D "Call: 3" "Return: 3" "Call: 2" "Return: 2" "Call: 1" "Return: 1"

💡 Hint

Notice the order of console.log before and after the recursive call.

The function prints 'Call:' before going deeper and 'Return:' after returning from recursion, so calls print down then returns print up.

🧠 Conceptual

expert

Maximum Call Stack Depth in Recursive Function

Consider this recursive function without a base case. What will happen when calling infiniteRecursion(1)?

DSA Typescript

function infiniteRecursion(n: number): number {
  return infiniteRecursion(n + 1) + 1;
}

infiniteRecursion(1);

A Returns Infinity

B Returns 1

C Runs forever without error

D Throws RangeError: Maximum call stack size exceeded

💡 Hint

Think about what happens when recursion never stops.

Without a base case, the function calls itself endlessly until the system runs out of stack space, causing a RangeError.

Practice

1. What happens when a recursive function calls itself without a stopping condition?

easy

A. It runs only once and stops

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

C. It immediately returns without doing anything

D. It throws a syntax error

Solution

1. Step 1: Understand recursion stopping condition

   A recursive function must have a base case to stop calling itself; otherwise, it keeps calling endlessly.

2. Step 2: Effect of missing stopping condition

   Without a stopping condition, the function calls stack up until memory runs out, causing a stack overflow error.

3. Final Answer:

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

4. Quick Check:

   Missing base case = infinite recursion [OK]

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

Common Mistakes:

• Assuming recursion stops automatically
• Confusing infinite loop with syntax error
• Thinking recursion runs only once without base case

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

easy

A. function recurse(n: number): number { if (n <= 0) return 0; return n + recurse(n - 1); }

B. function recurse(n: number) { while(n > 0) recurse(n - 1); }

C. function recurse(n: number): number { return n + recurse(n + 1); }

D. function recurse(n: number): number { return n * recurse(n); }

Solution

1. Step 1: Check for base case and recursive call

   function recurse(n: number): number { if (n <= 0) return 0; return n + recurse(n - 1); } has a base case (n <= 0) and calls itself with n - 1, which is correct for recursion.

2. Step 2: Analyze other options for errors

   The version with a while loop lacks a proper base case and return statement; another calls recurse with n + 1 causing infinite recursion; another calls recurse with the same n causing infinite recursion.

3. Final Answer:

   function recurse(n: number): number { if (n <= 0) return 0; return n + recurse(n - 1); } -> Option A

4. Quick Check:

   Base case + decreasing argument = correct recursion [OK]

Hint: Look for base case and argument reducing in recursion [OK]

Common Mistakes:

• Missing base case
• Increasing argument causing infinite recursion
• Using loops instead of recursion

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

function factorial(n: number): number {
  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

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

2. Step 2: Calculate return values

   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 factorial with sum
• Not tracing base case return
• Multiplying incorrectly

4. Identify the error in this recursive function and choose the fix:

function sumTo(n: number): number {
  return n + sumTo(n - 1);
}

medium

A. Change n - 1 to n + 1

B. Change return to console.log

C. Add a base case: if (n <= 0) return 0;

D. Remove the recursive call

Solution

1. Step 1: Identify missing base case

   The function lacks a stopping condition, so it will recurse infinitely causing stack overflow.

2. Step 2: Fix by adding base case

   Adding if (n <= 0) return 0; stops recursion when n reaches 0 or less.

3. Final Answer:

   Add a base case: if (n <= 0) return 0; -> Option C

4. Quick Check:

   Base case needed to stop recursion [OK]

Hint: Always add base case to recursive functions [OK]

Common Mistakes:

• Ignoring base case causes infinite recursion
• Changing recursive call incorrectly
• Removing recursion defeats purpose

5. Given the recursive function below, what will be the output when calling printNumbers(3)? Visualize the call stack.

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

hard

A. 1 2 3

B. 3 2 1

C. 3 3 3

D. 1 1 1

Solution

1. Step 1: Understand call stack order

   printNumbers(3) calls printNumbers(2), which calls printNumbers(1), which calls printNumbers(0) and returns immediately.

2. Step 2: Trace console.log calls after recursion

   After reaching base case, console.log prints 1, then 2, then 3 as the stack unwinds.

3. Final Answer:

   1 2 3 -> Option A

4. Quick Check:

   Post-recursion print = ascending order [OK]

Hint: Print after recursive call prints ascending order [OK]

Common Mistakes:

• Printing before recursion causes descending order
• Confusing call stack push/pop order
• Expecting repeated numbers