Merge Two Sorted Arrays Without Extra Space in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to merge two sorted arrays without extra space?

It means combining two sorted arrays into one sorted sequence without using any extra array or storage space. The elements are rearranged within the original arrays.

beginner

Why can't we just concatenate and sort the two arrays when merging without extra space?

Concatenating requires extra space to hold the combined array. Sorting after concatenation also needs extra space or changes the original arrays. The goal is to avoid extra space and keep arrays sorted by rearranging elements in place.

intermediate

What is the main idea behind the 'gap method' for merging two sorted arrays without extra space?

The gap method compares elements at a certain gap distance and swaps them if out of order. The gap reduces gradually until it becomes 1. This helps move larger elements to the right and smaller to the left, merging arrays in place.

intermediate

In the gap method, how do you calculate the next gap?

Next gap is calculated as Math.ceil(current_gap / 2). This reduces the gap gradually until it reaches 1, ensuring all elements are compared and sorted properly.

intermediate

What is the time complexity of merging two sorted arrays without extra space using the gap method?

The time complexity is approximately O((n + m) log(n + m)), where n and m are the sizes of the two arrays. This is because the gap reduces logarithmically and each pass compares elements linearly.

What is the main goal when merging two sorted arrays without extra space?

A Use extra space to store merged elements

B Create a new sorted array

C Combine arrays without using extra storage

D Sort each array separately

The goal is to merge arrays by rearranging elements within the original arrays without extra storage.

Which method is commonly used to merge two sorted arrays without extra space?

A Merge sort with extra array

B Bubble sort

C Quick sort

D Gap method

The gap method efficiently merges arrays in place by comparing elements at a gap distance.

How is the gap updated in the gap method?

A gap = Math.ceil(gap / 2)

B gap = gap * 2

C gap = gap - 1

D gap = gap + 1

The gap is reduced by half (rounded up) each iteration to compare closer elements gradually.

What happens when elements compared at the gap are out of order?

A They are ignored

B They are swapped

C The gap is increased

D The arrays are merged separately

Swapping out-of-order elements moves larger elements right and smaller left, sorting arrays in place.

What is the approximate time complexity of the gap method for merging?

A O((n + m) log(n + m))

B O(n * m)

C O(n + m)

D O(log(n + m))

The gap method runs in about O((n + m) log(n + m)) due to repeated passes with reducing gap.

Explain how the gap method works to merge two sorted arrays without extra space.

Think about comparing elements far apart and bringing them closer step by step.

Describe why merging two sorted arrays without extra space is useful and what challenges it solves.

Consider situations with limited memory or large data.

Practice

1. What is the main goal when merging two sorted arrays without extra space?

easy

A. Sort each array separately without merging

B. Create a new array to hold all elements from both arrays

C. Copy elements from one array to another without sorting

D. Combine both arrays into one sorted array without using extra memory

Solution

1. Step 1: Understand the problem requirement

   The problem asks to merge two sorted arrays into a single sorted sequence without using extra space, meaning no additional arrays or large memory allocations.

2. Step 2: Identify the approach

   We must rearrange elements within the given arrays themselves to maintain sorted order combined.

3. Final Answer:

   Combine both arrays into one sorted array without using extra memory -> Option D

4. Quick Check:

   Merge without extra space = Combine in-place [OK]

Hint: Think in-place rearrangement, not new arrays [OK]

Common Mistakes:

• Assuming extra arrays are allowed
• Sorting arrays separately without merging
• Copying elements without sorting

2. Which of the following JavaScript syntax snippets correctly swaps two elements a[i] and b[j] without using a temporary variable?

easy

A. [a[i], b[j]] = [b[j], a[i]];

B. temp = a[i]; a[i] = b[j]; b[j] = temp;

C. a[i] = b[j]; b[j] = a[i];

D. a[i], b[j] = b[j], a[i];

Solution

1. Step 1: Identify correct swap syntax in JavaScript

   Using destructuring assignment, [a[i], b[j]] = [b[j], a[i]]; swaps values without a temporary variable.

2. Step 2: Check other options

   temp = a[i]; a[i] = b[j]; b[j] = temp; uses a temporary variable, C incorrectly assigns twice, D is invalid syntax.

3. Final Answer:

   [a[i], b[j]] = [b[j], a[i]]; -> Option A

4. Quick Check:

   Destructuring swap = [a[i], b[j]] = [b[j], a[i]]; [OK]

Hint: Use destructuring assignment for swap without temp [OK]

Common Mistakes:

• Using invalid syntax like option D
• Forgetting to use a temporary variable if not destructuring
• Assigning values incorrectly causing data loss

3. What will be the content of arrays a and b after running this code?

let a = [1, 5, 9, 10];
let b = [2, 3, 8, 13];

for (let i = 0; i < a.length; i++) {
  if (a[i] > b[0]) {
    [a[i], b[0]] = [b[0], a[i]];
    b.sort((x, y) => x - y);
  }
}

medium

A. a = [1, 2, 3, 5], b = [8, 9, 10, 13]

B. a = [1, 3, 5, 8], b = [2, 9, 10, 13]

C. a = [1, 2, 5, 8], b = [3, 9, 10, 13]

D. a = [1, 2, 3, 8], b = [5, 9, 10, 13]

Solution

1. Step 1: Trace the loop and swaps

   i=0: a[0]=1 <= b[0]=2 no swap
   i=1: a[1]=5 > b[0]=2 swap -> a[1]=2, b[0]=5; b sorted: [3,5,8,13]
   i=2: a[2]=9 > b[0]=3 swap -> a[2]=3, b[0]=9; b sorted: [5,8,9,13]
   i=3: a[3]=10 > b[0]=5 swap -> a[3]=5, b[0]=10; b sorted: [8,9,10,13]

2. Step 2: Final arrays after loop

   a = [1, 2, 3, 5]
   b = [8, 9, 10, 13]

3. Final Answer:

   a = [1, 2, 3, 5], b = [8, 9, 10, 13] -> Option A

4. Quick Check:

   Swapped and sorted b each time = a = [1, 2, 3, 5], b = [8, 9, 10, 13] [OK]

Hint: Swap if a[i] > b[0], then sort b [OK]

Common Mistakes:

• Not sorting array b after swap
• Swapping incorrectly causing wrong order
• Assuming arrays merge into one

4. Identify the error in this code snippet intended to merge two sorted arrays without extra space:

let a = [1, 4, 7];
let b = [2, 5, 6];

for (let i = 0; i < a.length; i++) {
  if (a[i] > b[0]) {
    let temp = a[i];
    a[i] = b[0];
    b[0] = temp;
  }
  b.sort();
}

medium

A. The if condition should be a[i] < b[0] instead of a[i] > b[0]

B. The sort() method is called without a compare function, causing incorrect sorting

C. Loop should run over array b length instead of a length

D. Swapping elements uses a temporary variable incorrectly

Solution

1. Step 1: Check the sorting method used

   The code uses b.sort() without a compare function, which sorts elements as strings, not numbers, causing wrong order.

2. Step 2: Correct sorting approach

   Use b.sort((x, y) => x - y) to sort numbers correctly.

3. Final Answer:

   The sort() method is called without a compare function, causing incorrect sorting -> Option B

4. Quick Check:

   sort() without compare = wrong numeric order [OK]

Hint: Always provide compare function for numeric sort [OK]

Common Mistakes:

• Using default sort() for numbers
• Swapping incorrectly without temp variable
• Wrong loop range

5. Given two sorted arrays a = [1, 3, 5, 7] and b = [0, 2, 6, 8, 9], how can you merge them without extra space so that after merging, a contains the first 4 smallest elements and b contains the remaining elements sorted? Which approach is best?

hard

A. Swap elements only if a[i] > b[j] without sorting b after swaps

B. Concatenate arrays and sort the combined array

C. Use a gap method to compare and swap elements between arrays until fully sorted

D. Copy all elements to a new array and then split back

Solution

1. Step 1: Understand the gap method

   The gap method compares elements at a certain gap distance in both arrays and swaps if needed, reducing the gap until 1, ensuring sorted order without extra space.

2. Step 2: Why other options fail

   Concatenate arrays and sort the combined array and D use extra space, violating constraints. Swap elements only if a[i] > b[j] without sorting b after swaps misses sorting after swaps, causing incorrect order.

3. Final Answer:

   Use a gap method to compare and swap elements between arrays until fully sorted -> Option C

4. Quick Check:

   Gap method = in-place merge without extra space [OK]

Hint: Use gap method to merge in-place efficiently [OK]

Common Mistakes:

• Using extra arrays violating constraints
• Not sorting after swaps causing disorder
• Assuming simple swaps suffice without gap reduction