Why Divide and Conquer and What It Gives You in DSA Javascript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to split the array into two halves.

DSA Javascript

const mid = Math.floor(arr.length [1] 2);

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

A/

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of division.

Using multiplication which makes the number bigger.

We divide the length by 2 to find the middle index.

2fill in blank

medium

Complete the code to recursively sort the left half of the array.

DSA Javascript

const left = divideAndConquer(arr.slice(0, [1]));

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

Amid

Barr.length

Carr.length - 1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using the full length which does not split the array.

Using 0 as the end index which results in an empty array.

We slice from 0 to mid to get the left half.

3fill in blank

hard

Fix the error in the base case condition to stop recursion.

DSA Javascript

if (arr.length [1] 2) return arr;

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

A!==

B>

C===

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using greater than which never stops recursion.

Using equality which misses empty arrays.

The recursion stops when the array length is less than 2 (0 or 1).

4fill in blank

hard

Fill both blanks to merge two sorted arrays correctly.

DSA Javascript

while (i < left.length && j [1] right.length) {
  if (left[i] [2] right[j]) {
    result.push(left[i]);
    i++;
  } else {
    result.push(right[j]);
    j++;
  }
}

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

A<

B>

C<=

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using >= or <= which can cause index errors.

Comparing with < instead of > which reverses order.

The loop runs while both indexes are within their arrays. We compare left[i] > right[j] to decide which to push.

5fill in blank

hard

Fill all three blanks to complete the merge function return statement.

DSA Javascript

return result.concat(left.slice([1])).concat(right.slice([2]));

// Variables used: i, j
// [3] is the variable for the right array index

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

Ai

Bj

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up i and j for slicing.

Using wrong variable name for right array index.

We slice the remaining elements from left starting at i and from right starting at j. The variable for right index is j.

Practice

1. What is the main advantage of using the Divide and Conquer approach in algorithms?

easy

A. It breaks a problem into smaller subproblems to solve them independently

B. It uses more memory to store all intermediate results

C. It always solves problems in a single step

D. It avoids recursion completely

Solution

1. Step 1: Understand the divide and conquer approach

   Divide and conquer splits a big problem into smaller parts that are easier to solve.

2. Step 2: Identify the main benefit

   Solving smaller subproblems independently helps reduce complexity and makes the problem manageable.

3. Final Answer:

   It breaks a problem into smaller subproblems to solve them independently -> Option A

4. Quick Check:

   Divide and conquer = break problem into smaller parts [OK]

Hint: Divide big problems into smaller parts to solve easily [OK]

Common Mistakes:

• Thinking divide and conquer avoids recursion
• Believing it solves problems in one step
• Confusing it with using more memory

2. Which of the following is the correct syntax to call a recursive divide and conquer function named divideConquer with argument n in JavaScript?

easy

A. function divideConquer(n);

B. divideConquer = n;

C. call divideConquer(n);

D. divideConquer(n);

Solution

1. Step 1: Identify correct function call syntax in JavaScript

   Functions are called by writing the function name followed by parentheses with arguments inside.

2. Step 2: Match the correct option

   divideConquer(n); uses the correct syntax: divideConquer(n);

3. Final Answer:

   divideConquer(n); -> Option D

4. Quick Check:

   Function call syntax = functionName(args) [OK]

Hint: Call functions with name and parentheses [OK]

Common Mistakes:

• Using assignment instead of call
• Adding 'call' keyword incorrectly
• Writing function declaration instead of call

3. Consider this JavaScript function using divide and conquer to sum an array:

function sumArray(arr) {
  if (arr.length === 1) return arr[0];
  const mid = Math.floor(arr.length / 2);
  const left = sumArray(arr.slice(0, mid));
  const right = sumArray(arr.slice(mid));
  return left + right;
}
console.log(sumArray([2, 4, 6, 8]));

What is the output?

medium

A. Error

B. 20

C. undefined

D. 10

Solution

1. Step 1: Understand the base case and recursion

   The function returns the single element if array length is 1, else splits array and sums left and right parts recursively.

2. Step 2: Trace the calls for [2,4,6,8]

   Split into [2,4] and [6,8]. Sum [2,4]: split into [2] and [4], sum = 2+4=6. Sum [6,8]: split into [6] and [8], sum = 6+8=14. Total sum = 6+14=20.

3. Final Answer:

   20 -> Option B

4. Quick Check:

   Sum of 2+4+6+8 = 20 [OK]

Hint: Sum halves recursively, then add results [OK]

Common Mistakes:

• Confusing slice ranges causing wrong sums
• Missing base case leading to errors
• Assuming output is half the sum

4. The following code tries to find the maximum number in an array using divide and conquer but has a bug:

function findMax(arr) {
  if (arr.length === 1) return arr[0];
  const mid = Math.floor(arr.length / 2);
  const leftMax = findMax(arr.slice(0, mid));
  const rightMax = findMax(arr.slice(mid));
  return leftMax - rightMax;
}
console.log(findMax([3, 7, 2, 9]));

What is the bug?

medium

A. It uses floor instead of ceil for mid

B. It does not handle empty arrays

C. It subtracts instead of comparing max values

D. It returns the wrong base case

Solution

1. Step 1: Analyze the return statement

   The function returns leftMax - rightMax, which subtracts values instead of comparing them.

2. Step 2: Identify correct operation for max

   To find maximum, it should return the greater of the two values, not their difference.

3. Final Answer:

   It subtracts instead of comparing max values -> Option C

4. Quick Check:

   Max requires comparison, not subtraction [OK]

Hint: Use max comparison, not subtraction, to find max [OK]

Common Mistakes:

• Using subtraction instead of Math.max
• Ignoring empty array edge case
• Misunderstanding mid calculation

5. You want to count how many times a number appears in a large sorted array using divide and conquer. Which approach best uses divide and conquer to solve this efficiently?

hard

A. Split array, count occurrences in left and right halves recursively, then add counts

B. Scan entire array linearly counting matches

C. Use a hash map to store counts of all numbers

D. Sort the array first, then count occurrences

Solution

1. Step 1: Understand the problem and array properties

   The array is sorted, so divide and conquer can split it to count occurrences efficiently.

2. Step 2: Choose the approach that uses divide and conquer

   Split array, count occurrences in left and right halves recursively, then add counts splits the array recursively, counts occurrences in each half, and sums them, which fits divide and conquer.

3. Final Answer:

   Split array, count occurrences in left and right halves recursively, then add counts -> Option A

4. Quick Check:

   Divide and conquer = split, solve parts, combine [OK]

Hint: Split and count in halves, then add counts [OK]

Common Mistakes:

• Using linear scan ignoring divide and conquer
• Using hash map which is not divide and conquer
• Sorting again unnecessarily