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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two elements in the array.

DSA Go

func swap(arr []int, i, j int) {
    temp := arr[[1]]
    arr[i] = arr[j]
    arr[j] = temp
}

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

Aj

Bi

C0

Dlen(arr)-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr[j] instead of arr[i] for temp causes incorrect swapping.

Forgetting to store the value before overwriting.

We store the element at index i in temp to swap arr[i] and arr[j].

2fill in blank

medium

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

DSA Go

func lomutoPartition(arr []int, low, high int) int {
    pivot := arr[[1]]
    i := low - 1
    for j := low; j < high; j++ {
        if arr[j] <= pivot {
            i++
            swap(arr, i, j)
        }
    }
    swap(arr, i+1, high)
    return i + 1
}

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

Alow

Blen(arr)-1

C0

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing pivot as low or 0 index causes incorrect partitioning.

Using len(arr)-1 instead of high when partitioning subarrays.

In Lomuto partition, the pivot is the last element at index high.

3fill in blank

hard

Fix the error in the Hoare partition loop condition.

DSA Go

func hoarePartition(arr []int, low, high int) int {
    pivot := arr[low]
    i := low - 1
    j := high + 1
    for {
        for {
            i++
            if arr[i] [1] pivot {
                break
            }
        }
        for {
            j--
            if arr[j] [1] pivot {
                break
            }
        }
        if i >= j {
            return j
        }
        swap(arr, i, j)
    }
}

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

A>

B>=

C<

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= or >= causes infinite loops or wrong partition.

Mixing comparison directions for i and j.

In Hoare partition, increment i while arr[i] < pivot and decrement j while arr[j] > pivot.

4fill in blank

hard

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

DSA Go

func lomutoPartition(arr []int, low, high int) int {
    pivot := arr[high]
    i := low - 1
    for j := low; j < high; j++ {
        if arr[j] <= pivot {
            i++
            swap(arr, [1], j)
        }
    }
    swap(arr, [2], high)
    return i + 1
}

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

Ai

Bj

Clow

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping wrong indices causes incorrect partition.

Using j instead of i+1 in the final swap.

Swap arr[i] and arr[j] inside the loop, then swap arr[i+1] and arr[high] after the loop.

5fill in blank

hard

Fill all three blanks to complete the Hoare partition loop increments and swap.

DSA Go

func hoarePartition(arr []int, low, high int) int {
    pivot := arr[low]
    i := low - 1
    j := high + 1
    for {
        for {
            i++
            if arr[i] [1] pivot {
                break
            }
        }
        for {
            j--
            if arr[j] [2] pivot {
                break
            }
        }
        if i >= j {
            return j
        }
        swap(arr, [3], j)
    }
}

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

A<

B>

Ci

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping arr[j] and arr[j] instead of arr[i] and arr[j].

Using wrong comparison operators causing infinite loops.

i increments while arr[i] < pivot, j decrements while arr[j] > pivot, then swap arr[i] and arr[j].

Practice

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

easy

A. Lomuto uses a single pointer to partition, Hoare uses two pointers moving inward

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

C. Lomuto requires extra memory, Hoare works in-place

D. Lomuto always picks the last element as pivot, Hoare always picks the first

Solution

1. Step 1: Understand Lomuto partition

   Lomuto partition uses one pointer to track the boundary of smaller elements and swaps elements accordingly.

2. Step 2: Understand Hoare partition

   Hoare partition uses two pointers starting from both ends moving inward to swap elements around the pivot.

3. Final Answer:

   Lomuto uses a single pointer to partition, Hoare uses two pointers moving inward -> Option A

4. Quick Check:

   Partition pointers = single vs two [OK]

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

Common Mistakes:

• Confusing pivot selection with partition method
• Thinking Lomuto uses two pointers
• Assuming Hoare needs extra memory

2. Which of the following is the correct Lomuto partition function header in Go?

easy

A. func lomutoPartition(arr []int, low int, high int) int

B. func lomutoPartition(arr []int) int

C. func lomutoPartition(arr []int, pivot int) int

D. func lomutoPartition(arr []int, start int, end int) bool

Solution

1. Step 1: Check parameters needed for Lomuto

   Lomuto partition requires the array and indices low and high to define the subarray.

2. Step 2: Check return type

   It returns an integer index of the pivot after partitioning.

3. Final Answer:

   func lomutoPartition(arr []int, low int, high int) int -> Option A

4. Quick Check:

   Function signature = arr, low, high, returns int [OK]

Hint: Lomuto needs array and low, high indices, returns pivot index [OK]

Common Mistakes:

• Omitting low and high parameters
• Returning bool instead of int
• Passing pivot as parameter explicitly

3. What is the output array after applying Lomuto partition on [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 is last element 2. Initialize i = low - 1 = -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. i stays -1. Finally swap pivot with arr[i+1] = arr[0].

3. Final Answer:

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

4. Quick Check:

   Pivot 2 placed at start, smaller elements left [OK]

Hint: Pivot last element, swap smaller left, pivot next [OK]

Common Mistakes:

• Swapping elements incorrectly
• Not updating i pointer properly
• Confusing pivot position after partition

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

func hoarePartition(arr []int, low, high int) int {
    pivot := arr[low]
    i := low - 1
    j := high + 1
    for {
        for arr[i] < pivot {
            i++
        }
        for arr[j] > pivot {
            j--
        }
        if i >= j {
            return j
        }
        arr[i], arr[j] = arr[j], arr[i]
    }
}

medium

A. The inner loops should use <= and >= instead of < and >

B. Pivot should be arr[high] instead of arr[low]

C. i and j initialization should be i = low, j = high

D. The swap should happen after checking i > j

Solution

1. Step 1: Check pointer initialization

   In Hoare partition, i starts at low and j at high, not outside the array bounds.

2. Step 2: Understand loop conditions

   Starting i at low - 1 and j at high + 1 causes index out of range errors during arr[i] and arr[j] access.

3. Final Answer:

   i and j initialization should be i = low, j = high -> Option C

4. Quick Check:

   Pointer start = low, high [OK]

Hint: Hoare pointers start at low and high, not outside [OK]

Common Mistakes:

• Initializing pointers outside array bounds
• Using wrong pivot element
• Swapping before pointer check

5. You want to sort an array with many duplicate elements efficiently. Which partition scheme is better and why?

hard

A. Lomuto, because it handles duplicates by placing them all on one side

B. Hoare, because it partitions elements more evenly and reduces swaps with duplicates

C. Lomuto, because it uses two pointers to handle duplicates quickly

D. Hoare, because it always picks the last element as pivot

Solution

1. Step 1: Consider duplicate handling in Lomuto

   Lomuto tends to put duplicates on one side, causing unbalanced partitions and more recursive calls.

2. Step 2: Consider duplicate handling in Hoare

   Hoare's two-pointer approach partitions more evenly, reducing swaps and improving performance with duplicates.

3. Final Answer:

   Hoare, because it partitions elements more evenly and reduces swaps with duplicates -> Option B

4. Quick Check:

   Duplicates handled better by Hoare [OK]

Hint: Hoare partitions evenly, better for duplicates [OK]

Common Mistakes:

• Assuming Lomuto is better for duplicates
• Confusing pivot choice with partition efficiency
• Ignoring swap count impact