Why Recursion Exists and What Loops Cannot Express Cleanly in DSA C++ - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a recursive function that prints numbers from n down to 1.

DSA C++

void printNumbers(int n) {
    if (n == 0) return;
    std::cout << n << " ";
    printNumbers([1]);
}

Drag options to blanks, or click blank then click option'

An + 1

B0

C1

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 0 or 1 directly does not reduce n properly.

The function calls itself with n - 1 to count down from n to 1 recursively.

2fill in blank

medium

Complete the code to calculate factorial of n recursively.

DSA C++

int factorial(int n) {
    if (n <= 1) return 1;
    return n * factorial([1]);
}

Drag options to blanks, or click blank then click option'

A1

Bn - 1

Cn + 1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Returning n instead of recursive call.

Factorial of n is n times factorial of n-1, reducing the problem size each call.

3fill in blank

hard

Fix the error in the recursive Fibonacci function call.

DSA C++

int fib(int n) {
    if (n <= 1) return n;
    return fib(n - 1) + fib([1]);
}

Drag options to blanks, or click blank then click option'

An - 2

Bn

Cn - 1

Dn + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n - 1 twice causes incorrect results.

Using n + 1 causes infinite recursion.

Fibonacci is sum of fib(n-1) and fib(n-2), so the second call must be fib(n-2).

4fill in blank

hard

Fill both blanks to create a recursive function that sums elements of an array.

DSA C++

int sumArray(int arr[], int n) {
    if (n == 0) return 0;
    return arr[[1]] + sumArray(arr, [2]);
}

Drag options to blanks, or click blank then click option'

An - 1

Bn + 1

Cn - 2

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using n or n+1 causes out-of-bounds errors.

Using n-2 skips elements incorrectly.

The function sums the last element arr[n-1] plus sum of first n-1 elements recursively.

5fill in blank

hard

Fill all three blanks to create a recursive function that reverses a string in place.

DSA C++

void reverseString(char str[], int start, int end) {
    if (start >= end) return;
    char temp = str[[1]];
    str[[2]] = str[[3]];
    str[end] = temp;
    reverseString(str, start + 1, end - 1);
}

Drag options to blanks, or click blank then click option'

Astart

Bend

Cstart + 1

Dend - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up start and end indices causes wrong swaps.

Not updating indices correctly leads to infinite recursion.

The function swaps characters at start and end indices, then recurses inward.

Practice

1. Why do we use recursion instead of loops in some problems?

easy

A. Because recursion can express problems with self-similar structure more naturally

B. Because loops are slower than recursion in all cases

C. Because recursion uses less memory than loops always

D. Because loops cannot repeat any actions

Solution

1. Step 1: Understand problem structure

   Some problems have parts that look like smaller versions of themselves, like trees or nested lists.

2. Step 2: Compare recursion and loops

   Loops repeat actions linearly, but recursion can call itself to handle nested or self-similar parts easily.

3. Final Answer:

   Because recursion can express problems with self-similar structure more naturally -> Option A

4. Quick Check:

   Self-similar problems naturally use recursion [OK]

Hint: Recursion fits nested/self-similar problems better [OK]

Common Mistakes:

• Thinking loops are always slower
• Assuming recursion always uses less memory
• Believing loops cannot repeat actions

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

easy

A. void func() { func(); }

B. void func() { if(condition) func(); else return; }

C. void func() { for(int i=0; i<10; i++) func(); }

D. void func() { while(true) func(); }

Solution

1. Step 1: Identify base case in recursion

   Recursive functions must have a condition to stop calling themselves to avoid infinite loops.

2. Step 2: Check options for base case

   void func() { if(condition) func(); else return; } has an if condition that stops recursion; others either lack base case or use loops incorrectly.

3. Final Answer:

   void func() { if(condition) func(); else return; } -> Option B

4. Quick Check:

   Recursive functions must have base case [OK]

Hint: Look for base case to stop recursion [OK]

Common Mistakes:

• Missing base case causing infinite recursion
• Confusing loops with recursion calls
• Using infinite loops inside recursive functions

3. What is the output of the following C++ code?

#include <iostream>
int factorial(int n) {
  if (n == 0) return 1;
  else return n * factorial(n - 1);
}

int main() {
  std::cout << factorial(4);
  return 0;
}

medium

A. 16

B. 10

C. 120

D. 24

Solution

1. Step 1: Understand factorial recursion

   factorial(4) = 4 * factorial(3), factorial(3) = 3 * factorial(2), and so on until factorial(0) = 1.

2. Step 2: Calculate factorial(4)

   factorial(4) = 4 * 3 * 2 * 1 = 24.

3. Final Answer:

   24 -> Option D

4. Quick Check:

   4! = 24 [OK]

Hint: Recall factorial definition: n! = n*(n-1)! [OK]

Common Mistakes:

• Confusing factorial with sum
• Forgetting base case returns 1
• Multiplying incorrectly

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

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

medium

A. Recursive call uses sum(n) instead of sum(n - 1)

B. Missing base case for n == 1

C. Function should return n * sum(n - 1)

D. No error, function works correctly

Solution

1. Step 1: Check recursive call argument

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

2. Step 2: Correct recursive call

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

3. Final Answer:

   Recursive call uses sum(n) instead of sum(n - 1) -> Option A

4. Quick Check:

   Recursion requires decreasing argument [OK]

Hint: Recursive call must reduce problem size [OK]

Common Mistakes:

• Calling recursion with same argument causing infinite loop
• Confusing sum with product
• Missing base case

5. You want to print all paths from root to leaves in a tree structure. Why is recursion better than loops for this task?

hard

A. Because loops cannot access tree nodes

B. Because recursion uses less CPU than loops

C. Because loops cannot handle multiple branching paths easily

D. Because recursion always runs faster than loops

Solution

1. Step 1: Understand tree traversal

   Printing all root-to-leaf paths requires exploring multiple branches at each node.

2. Step 2: Compare recursion and loops for branching

   Loops handle linear repetition well but struggle with multiple branches; recursion naturally explores each branch by calling itself.

3. Final Answer:

   Because loops cannot handle multiple branching paths easily -> Option C

4. Quick Check:

   Recursion naturally handles branching [OK]

Hint: Recursion handles branching paths naturally [OK]

Common Mistakes:

• Thinking loops can easily replace recursion for trees
• Assuming recursion is always faster
• Believing loops cannot access nodes