Merge Sort Algorithm in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Merge Sort algorithm?

Merge Sort works by dividing the list into smaller parts, sorting each part, and then merging them back together in order.

intermediate

What is the time complexity of Merge Sort in the average and worst cases?

The time complexity of Merge Sort is O(n log n) for both average and worst cases, where n is the number of elements to sort.

intermediate

Why is Merge Sort considered a stable sorting algorithm?

Merge Sort is stable because it keeps the original order of equal elements when merging the sorted parts.

beginner

Show the basic steps of Merge Sort on the array [4, 1, 3, 2].

Step 1: Divide into [4,1] and [3,2]
Step 2: Divide further to [4], [1], [3], [2]
Step 3: Merge [4] and [1] to get [1,4]
Step 4: Merge [3] and [2] to get [2,3]
Step 5: Merge [1,4] and [2,3] to get [1,2,3,4]

intermediate

What is the space complexity of Merge Sort and why?

Merge Sort has a space complexity of O(n) because it requires extra space to hold the temporary arrays during the merge process.

What technique does Merge Sort use to sort an array?

A Brute force

B Divide and conquer

C Dynamic programming

D Greedy approach

Merge Sort divides the array into smaller parts, sorts them, and merges them back, which is the divide and conquer technique.

Which of the following is true about Merge Sort?

A It is a stable sorting algorithm

B It has a worst-case time complexity of O(n^2)

C It sorts in place without extra space

D It only works on sorted arrays

Merge Sort is stable because it preserves the order of equal elements during merging.

What is the first step in the Merge Sort algorithm?

A Divide the array into halves

B Merge two sorted arrays

C Compare all elements

D Swap elements

Merge Sort starts by dividing the array into two halves recursively.

How does Merge Sort combine the divided parts?

A By reversing the arrays

B By swapping elements randomly

C By sorting each part separately without merging

D By merging sorted subarrays

Merge Sort merges the sorted subarrays to form a fully sorted array.

What is the space complexity of Merge Sort?

A O(1)

B O(log n)

C O(n)

D O(n^2)

Merge Sort requires extra space proportional to the size of the array for merging, so space complexity is O(n).

Explain how Merge Sort sorts an array step-by-step.

Think about breaking the problem into smaller pieces and then combining them.

Describe the advantages and disadvantages of using Merge Sort.

Consider speed, memory use, and stability.

Practice

1. What is the main idea behind the Merge Sort algorithm?

easy

A. Insert elements one by one into a sorted sublist

B. Sort the array by repeatedly swapping adjacent elements

C. Pick a pivot and partition the array around it

D. Divide the array into halves, sort each half, then merge them

Solution

1. Step 1: Understand the divide and conquer approach

   Merge Sort splits the array into two halves recursively until single elements remain.

2. Step 2: Merge sorted halves

   It then merges these sorted halves back together to form a sorted array.

3. Final Answer:

   Divide the array into halves, sort each half, then merge them -> Option D

4. Quick Check:

   Merge Sort = Divide, sort halves, merge [OK]

Hint: Remember: split, sort halves, then merge [OK]

Common Mistakes:

• Confusing Merge Sort with Bubble Sort
• Thinking Merge Sort uses a pivot like Quick Sort
• Believing Merge Sort sorts in place without extra space

2. Which of the following is the correct way to split an array arr into two halves in JavaScript for Merge Sort?

easy

A. const mid = Math.floor(arr.length / 2); const left = arr.slice(0, mid); const right = arr.slice(mid);

B. const mid = arr.length / 2; const left = arr.splice(0, mid); const right = arr.splice(mid);

C. const mid = arr.length / 2; const left = arr.slice(mid); const right = arr.slice(0, mid);

D. const mid = Math.ceil(arr.length / 2); const left = arr.slice(mid); const right = arr.slice(0, mid);

Solution

1. Step 1: Calculate middle index correctly

   Use Math.floor to get the middle index for even or odd lengths.

2. Step 2: Use slice to split without modifying original array

   Slice(0, mid) gets left half; slice(mid) gets right half correctly.

3. Final Answer:

   const mid = Math.floor(arr.length / 2); const left = arr.slice(0, mid); const right = arr.slice(mid); -> Option A

4. Quick Check:

   Use Math.floor and slice for splitting [OK]

Hint: Use Math.floor and slice to split arrays safely [OK]

Common Mistakes:

• Using splice which modifies the original array
• Not flooring the middle index causing float errors
• Swapping left and right halves incorrectly

3. What will be the output of the following JavaScript code using Merge Sort?

function mergeSort(arr) {
  if (arr.length <= 1) return arr;
  const mid = Math.floor(arr.length / 2);
  const left = mergeSort(arr.slice(0, mid));
  const right = mergeSort(arr.slice(mid));
  return merge(left, right);
}

function merge(left, right) {
  let result = [];
  while (left.length && right.length) {
    if (left[0] < right[0]) result.push(left.shift());
    else result.push(right.shift());
  }
  return result.concat(left, right);
}

console.log(mergeSort([4, 1, 3, 2]));

medium

A. [1, 3, 2, 4]

B. [4, 3, 2, 1]

C. [1, 2, 3, 4]

D. [2, 1, 3, 4]

Solution

1. Step 1: Recursively split and sort the array

   The array [4,1,3,2] is split into [4,1] and [3,2], then further until single elements.

2. Step 2: Merge sorted halves step-by-step

   Merge [4] and [1] to [1,4], merge [3] and [2] to [2,3], then merge [1,4] and [2,3] to [1,2,3,4].

3. Final Answer:

   [1, 2, 3, 4] -> Option C

4. Quick Check:

   Sorted array = [1, 2, 3, 4] [OK]

Hint: Trace splits and merges carefully to find sorted output [OK]

Common Mistakes:

• Confusing merge order causing wrong output
• Not handling empty arrays in merge
• Using shift inefficiently causing performance issues

4. Identify the bug in this Merge Sort implementation:

function mergeSort(arr) {
  if (arr.length === 1) return arr;
  const mid = Math.floor(arr.length / 2);
  const left = mergeSort(arr.slice(0, mid));
  const right = mergeSort(arr.slice(mid));
  return merge(left, right);
}

function merge(left, right) {
  let result = [];
  while (left.length && right.length) {
    if (left[0] < right[0]) result.push(left.shift());
    else result.push(right.shift());
  }
  return result.concat(left, right);
}

medium

A. Base case should be arr.length <= 1, not arr.length === 1

B. Using shift() inside merge causes infinite loop

C. Math.floor should be Math.ceil for mid calculation

D. merge function should return result.reverse()

Solution

1. Step 1: Check base case condition

   Base case returns when array length is 1, but it should also handle empty arrays (length 0) to avoid errors.

2. Step 2: Correct base case to include empty arrays

   Change condition to arr.length <= 1 to safely return arrays of length 0 or 1.

3. Final Answer:

   Base case should be arr.length <= 1, not arr.length === 1 -> Option A

4. Quick Check:

   Base case = arr.length <= 1 [OK]

Hint: Base case must handle empty arrays too [OK]

Common Mistakes:

• Ignoring empty array base case causing stack overflow
• Incorrect mid calculation causing wrong splits
• Misunderstanding shift() usage as a bug

5. You want to sort a large array of objects by a numeric property score using Merge Sort. Which modification is needed in the merge function to correctly sort by score?

hard

A. Use JSON.stringify to compare objects

B. Compare left[0].score and right[0].score instead of elements directly

C. Convert objects to strings before comparing

D. Sort only keys, then map back to objects

Solution

1. Step 1: Understand sorting objects by property

   Objects cannot be compared directly; comparison must use the numeric property score.

2. Step 2: Modify merge comparison to use score

   Change condition to compare left[0].score and right[0].score to merge correctly.

3. Final Answer:

   Compare left[0].score and right[0].score instead of elements directly -> Option B

4. Quick Check:

   Compare object properties for sorting [OK]

Hint: Compare object properties, not whole objects [OK]

Common Mistakes:

• Trying to compare objects directly causing NaN or errors
• Using string conversion which breaks numeric order
• Sorting keys separately losing object structure