Quick Sort Partition Lomuto and Hoare in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to select the pivot as the last element in Lomuto partition.

DSA Javascript

function lomutoPartition(arr, low, high) {
  let pivot = arr[1];
  let i = low - 1;
  for (let j = low; j < high; j++) {
    if (arr[j] <= pivot) {
      i++;
      [arr[i], arr[j]] = [arr[j], arr[i]];
    }
  }
  [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]];
  return i + 1;
}

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

A[low]

B[high]

C[low + 1]

D[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing the first element as pivot instead of the last.

Using an index outside the current subarray.

In Lomuto partition, the pivot is chosen as the last element, which is at index 'high'.

2fill in blank

medium

Complete the code to swap elements in Lomuto partition when arr[j] is less than or equal to pivot.

DSA Javascript

if (arr[j] [1] pivot) {
  i++;
  [arr[i], arr[j]] = [arr[j], arr[i]];
}

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

A<=

B>

C<

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using only '<' and missing equal elements.

Using '>' which reverses the logic.

We swap when arr[j] is less than or equal to pivot to group smaller or equal elements to the left.

3fill in blank

hard

Fix the error in the Hoare partition loop condition to correctly partition the array.

DSA Javascript

while (arr[i] [1] pivot) i++;
while (arr[j] [2] pivot) 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 infinite loops.

Swapping the comparison directions.

In Hoare partition, we move i forward while arr[i] is less than pivot, and j backward while arr[j] is greater than pivot.

4fill in blank

hard

Fill both blanks to complete the Hoare partition swap condition and return statement.

DSA Javascript

if (i >= j) return [1];
[arr[i], arr[j]] = [arr[j], arr[i]];

// Return index to split array
return [2];

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

Aj

Bi

Clow

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Returning i instead of j.

Returning low or high which are boundaries, not partition index.

When i >= j, we return j as the partition index in Hoare partition.

5fill in blank

hard

Fill all three blanks to complete the Lomuto partition function with correct pivot selection, swap, and return.

DSA Javascript

function lomutoPartition(arr, low, high) {
  let pivot = arr[1];
  let i = low - 1;
  for (let j = low; j < high; j++) {
    if (arr[j] [2] pivot) {
      i++;
      [arr[i], arr[j]] = [arr[j], arr[i]];
    }
  }
  [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]];
  return [3];
}

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

A[high]

B<=

Ci + 1

D[low]

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong pivot index.

Using wrong comparison operator.

Returning wrong partition index.

Pivot is last element arr[high], swap when arr[j] <= pivot, and return i+1 as partition index.

Practice

1. What is the main difference between Lomuto and Hoare partition schemes in Quick Sort?

easy

A. Lomuto uses one pointer, Hoare uses two pointers moving inward

B. Lomuto sorts in descending order, Hoare sorts in ascending order

C. Lomuto is used only for arrays of even length, Hoare for odd length

D. Lomuto swaps elements only once, Hoare swaps multiple times

Solution

1. Step 1: Understand Lomuto partition

   Lomuto partition uses a single pointer to track the boundary of smaller elements and swaps with the pivot at the end.

2. Step 2: Understand Hoare partition

   Hoare partition uses two pointers starting from both ends moving inward to swap elements out of place.

3. Final Answer:

   Lomuto uses one pointer, Hoare uses two pointers moving inward -> Option A

4. Quick Check:

   Pointer count difference = Lomuto(1), Hoare(2) [OK]

Hint: Remember: Lomuto one pointer, Hoare two pointers inward [OK]

Common Mistakes:

• Confusing the number of pointers used
• Thinking Lomuto sorts differently by order
• Assuming partition depends on array length

2. Which of the following is the correct syntax to swap two elements arr[i] and arr[j] in JavaScript during partition?

easy

A. temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;

B. arr[i], arr[j] = arr[j], arr[i];

C. swap(arr[i], arr[j]);

D. arr[i] = arr[j]; arr[j] = arr[i];

Solution

1. Step 1: Identify correct swap syntax in JavaScript

   JavaScript does not support tuple unpacking; swapping requires a temporary variable.

2. Step 2: Check each option

   temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; uses a temp variable correctly; B is Python syntax; C is undefined function; D overwrites values incorrectly.

3. Final Answer:

   temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; -> Option A

4. Quick Check:

   Use temp variable for swap in JS [OK]

Hint: Use temp variable to swap in JS, no tuple unpacking [OK]

Common Mistakes:

• Using Python-style tuple swap in JavaScript
• Calling undefined swap function
• Overwriting values without temp variable

3. What is the output array after applying Lomuto partition on arr = [8, 3, 7, 6, 2] with pivot as last element?

medium

A. [8, 3, 7, 6, 2]

B. [3, 2, 7, 6, 8]

C. [2, 3, 7, 6, 8]

D. [2, 3, 6, 7, 8]

Solution

1. Step 1: Identify pivot and initialize pointers

   Pivot = 2 (last element). i starts at -1.

2. Step 2: Iterate and swap elements smaller than pivot

   Check elements: 8 > 2 no swap; 3 > 2 no swap; 7 > 2 no swap; 6 > 2 no swap. Finally swap pivot with arr[i+1] = arr[0].

3. Step 3: Final array after swap

   Swap arr[0] and arr[4]: [2, 3, 7, 6, 8]

4. Final Answer:

   [2, 3, 7, 6, 8] -> Option C

5. Quick Check:

   Lomuto partition places pivot correctly [OK]

Hint: Pivot is last element; swap smaller elements left [OK]

Common Mistakes:

• Not swapping pivot at the end
• Swapping elements incorrectly
• Confusing pivot position

4. Given this Hoare partition code snippet, what is the bug?

function hoarePartition(arr, low, high) {
  let pivot = arr[low];
  let i = low - 1;
  let j = high + 1;
  while (true) {
    do { i++; } while (arr[i] < pivot);
    do { j--; } while (arr[j] > pivot);
    if (i >= j) return j;
    [arr[i], arr[j]] = [arr[j], arr[i]];
  }
}

medium

A. Pivot should be arr[high], not arr[low]

B. The loop condition should be while(i < j), not while(true)

C. Swap syntax is invalid in JavaScript

D. Initialization of i and j is incorrect; should be i=low, j=high

Solution

1. Step 1: Check initialization of pointers

   Hoare partition requires i = low and j = high to start inside the array.

2. Step 2: Analyze effect of incorrect initialization

   Standard Hoare partition initializes i = low, j = high, starting the pointers at the array bounds and moving inward.

3. Final Answer:

   Initialization of i and j is incorrect; should be i=low, j=high -> Option D

4. Quick Check:

   Correct pointer start = i=low, j=high [OK]

Hint: Start pointers inside array for Hoare partition [OK]

Common Mistakes:

• Setting i and j outside array bounds
• Confusing pivot position
• Misusing swap syntax

5. You want to sort an array using Quick Sort with Hoare partition. Which of these is the correct recursive call pattern after partitioning at index p?

hard

A. quickSort(arr, low, p - 1); quickSort(arr, p, high);

B. quickSort(arr, low, p); quickSort(arr, p + 1, high);

C. quickSort(arr, low, p + 1); quickSort(arr, p, high);

D. quickSort(arr, low, p - 1); quickSort(arr, p + 1, high);

Solution

1. Step 1: Understand Hoare partition return value

   Hoare partition returns an index p such that elements arr[low..p] ≤ pivot and arr[p+1..high] ≥ pivot. The pivot is not guaranteed to be at position p.

2. Step 2: Determine correct recursive calls

   Recurse on the left subarray from low to p (inclusive) and right subarray from p+1 to high: quickSort(arr, low, p); quickSort(arr, p + 1, high).

3. Final Answer:

   quickSort(arr, low, p); quickSort(arr, p + 1, high); -> Option B

4. Quick Check:

   Hoare recursion: low to p, p+1 to high [OK]

Hint: Hoare: quickSort(low, p); quickSort(p+1, high) [OK]

Common Mistakes:

• Using p+1 in left recursive call
• Ignoring infinite recursion risk
• Confusing Lomuto and Hoare recursion