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

Practice - 5 Tasks

1fill in blank

easy

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

DSA Javascript

function countdown(n) {
  if (n <= 0) return;
  console.log(n);
  countdown([1]);
}

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

An

Bn + 1

Cn - 1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using n does not change the argument, causing infinite recursion.

The function calls itself with n - 1 to count down until it reaches 0.

2fill in blank

medium

Complete the code to calculate factorial of n using recursion.

DSA Javascript

function factorial(n) {
  if (n === 0) return 1;
  return n * factorial([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.

Returning 0 in base case breaks factorial logic.

Factorial multiplies n by factorial of n - 1 until n is 0.

3fill in blank

hard

Fix the error in the recursive Fibonacci function to correctly compute fib(n).

DSA Javascript

function fib(n) {
  if (n <= 1) return n;
  return fib([1]) + fib(n - 2);
}

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

An - 2

Bn

C1

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using fib(n-2) twice causes wrong results.

Using fib(n) causes infinite recursion.

Fibonacci is sum of fib(n-1) and fib(n-2). The first recursive call must be fib(n-1).

4fill in blank

hard

Fill both blanks to create a recursive function that sums numbers from 1 to n.

DSA Javascript

function sumToN(n) {
  if (n === 0) return 0;
  return n [1] sumToN([2]);
}

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

A+

Bn - 1

C*

Dn + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of addition changes the logic.

Increasing n causes infinite recursion.

To sum numbers from 1 to n, add n to sumToN(n - 1).

5fill in blank

hard

Fill the blanks to create a recursive function that reverses a string.

DSA Javascript

function reverseStr(str) {
  if (str.length === 0) return '';
  return reverseStr(str.[1]) + str[2];
}

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

Aslice(1)

B[0]

CcharAt(0)

Dslice(0, 1)

Attempts:

3 left

💡 Hint

Common Mistakes

Using slice(0,1) instead of slice(1) causes infinite recursion.

Adding str[0] before recursive call reverses the logic.

The function calls reverseStr on the string without the first character (slice(1)) and adds the first character (str[0]) at the end.

Practice

1. Why do we use recursion instead of loops in some problems?
function factorial(n) { if (n === 0) return 1; return n * factorial(n - 1); }

easy

A. Loops are always slower than recursion.

B. Recursion can express problems with self-similar structure more naturally.

C. Recursion uses less memory than loops.

D. Loops cannot perform repeated actions.

Solution

1. Step 1: Understand recursion's purpose

   Recursion solves problems by breaking them into smaller similar problems, like factorial breaking n! into n * (n-1)!.

2. Step 2: Compare recursion and loops

   Loops repeat actions but do not naturally express self-similar or nested structures, which recursion handles clearly.

3. Final Answer:

   Recursion can express problems with self-similar structure more naturally. -> Option B

4. Quick Check:

   Recursion = natural for self-similar problems [OK]

Hint: Recursion fits problems breaking into smaller similar parts [OK]

Common Mistakes:

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

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

easy

A. function recurse(n) { for(let i=0; i

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

C. function recurse(n) { if (n > 0) return n; }

D. function recurse(n) { if (n <= 0) return; recurse(n - 1); }

Solution

1. Step 1: Identify recursive call structure

   function recurse(n) { if (n <= 0) return; recurse(n - 1); } calls itself with a smaller argument and has a base case to stop recursion.

2. Step 2: Check other options for recursion correctness

   The options using for or while loops include recursive calls but lack base cases, leading to infinite recursion. The option that returns n without a recursive call is not recursive.

3. Final Answer:

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

4. Quick Check:

   Correct recursion has base case and self-call [OK]

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

Common Mistakes:

• Missing base case causing infinite recursion
• Using loops instead of recursion
• No recursive call inside function

3. What is the output of this recursive function?

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 sumTo(2), sumTo(1), sumTo(0). sumTo(0) returns 0.

2. Step 2: Calculate return values

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

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Sum 1+2+3 = 6 [OK]

Hint: Add numbers down to zero recursively [OK]

Common Mistakes:

• Confusing base case return value
• Adding incorrectly during return
• Expecting loop output instead

4. Find the error in this recursive function that tries to calculate factorial:

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

medium

A. Recursive call uses same argument causing infinite recursion

B. Return statement is missing

C. Should use a loop instead of recursion

D. Missing base case for n < 0

Solution

1. Step 1: Check recursive call argument

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

2. Step 2: Identify fix

   The recursive call should be factorial(n - 1) to move toward base case.

3. Final Answer:

   Recursive call uses same argument causing infinite recursion -> Option A

4. Quick Check:

   Recursive call must reduce argument [OK]

Hint: Ensure recursive call moves toward base case [OK]

Common Mistakes:

• Not reducing argument in recursive call
• Ignoring base case
• Confusing recursion with loops

5. Which problem below is best solved using recursion rather than loops because it involves nested self-similar structure?

hard

A. Calculating the sum of numbers from 1 to n

B. Finding the maximum value in a flat array

C. Traversing a directory tree to list all files and folders

D. Repeating a task 10 times

Solution

1. Step 1: Analyze problem structures

   Sum and max in flat arrays are simple linear tasks suited for loops.

2. Step 2: Identify nested self-similar structure

   Directory trees have folders inside folders, a nested structure best handled by recursion.

3. Final Answer:

   Traversing a directory tree to list all files and folders -> Option C

4. Quick Check:

   Nested structures = recursion best [OK]

Hint: Use recursion for nested or tree-like data [OK]

Common Mistakes:

• Using recursion for simple linear tasks
• Ignoring nested structure complexity
• Confusing repetition with recursion need