Shell Sort Algorithm in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the gap for Shell Sort.

DSA Go

gap := len(arr) [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 multiplication instead of division for gap initialization.

The gap starts as half the length of the array, so dividing by 2 is correct.

2fill in blank

medium

Complete the code to reduce the gap in each iteration of Shell Sort.

DSA Go

gap = gap [1] 2

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

A-

B/

C+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of division to reduce the gap.

The gap is reduced by dividing it by 2 each time until it reaches zero.

3fill in blank

hard

Fix the error in the inner loop condition to correctly compare elements during Shell Sort.

DSA Go

for j := i; j >= gap && arr[j-gap] [1] arr[j]; j -= gap {

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

A>

B<

C==

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using less than or equal instead of greater than in the comparison.

We compare if the element at j-gap is greater than the element at j to decide if swapping is needed.

4fill in blank

hard

Fill both blanks to correctly insert the element in its sorted position during Shell Sort.

DSA Go

temp := arr[i]
for j := i; j >= [1] && arr[j-[2]] > temp; j -= [2] {
    arr[j] = arr[j-[2]]
}

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

Agap

Bi

Ctemp

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong variable like i or temp instead of gap.

The gap variable is used to compare and shift elements in the inner loop.

5fill in blank

hard

Fill all three blanks to complete the Shell Sort insertion step correctly.

DSA Go

arr[j] = [1]
}

for gap > 0 {
    for i := gap; i < len(arr); i++ {
        temp := arr[i]
        j := i
        for j >= gap && arr[j-gap] > temp {
            arr[j] = arr[j-gap]
            j -= [2]
        }
        arr[j] = [3]
    }
    gap /= 2

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

Atemp

Bgap

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong variables for decrement or insertion.

The element to insert is stored in temp, the gap is used to decrement j, and finally temp is placed at the correct position.

Practice

1. What is the main idea behind the Shell Sort Algorithm?

easy

A. It uses a divide and conquer approach to split and merge arrays.

B. It sorts elements by repeatedly swapping adjacent elements only.

C. It sorts elements by comparing distant elements and gradually reducing the gap.

D. It builds a sorted array by inserting elements one by one in order.

Solution

1. Step 1: Understand Shell Sort concept

   Shell Sort improves insertion sort by comparing elements far apart, reducing the gap over iterations.

2. Step 2: Compare with other sorting methods

   Unlike bubble or insertion sort, Shell Sort starts with distant comparisons, not just adjacent swaps.

3. Final Answer:

   It sorts elements by comparing distant elements and gradually reducing the gap. -> Option C

4. Quick Check:

   Shell Sort = distant comparisons + gap reduction [OK]

Hint: Shell Sort uses gaps to compare far elements first [OK]

Common Mistakes:

• Thinking Shell Sort only swaps adjacent elements
• Confusing Shell Sort with merge or quick sort
• Assuming it inserts elements one by one without gaps

2. Which of the following is the correct way to initialize the gap variable in Shell Sort in Go?

easy

A. gap = len(arr) * 2

B. gap := len(arr) / 2

C. gap := 0

D. gap = len(arr) + 1

Solution

1. Step 1: Identify gap initialization in Shell Sort

   The gap usually starts as half the array length to compare distant elements first.

2. Step 2: Check Go syntax for variable initialization

   Using gap := len(arr) / 2 correctly declares and initializes gap in Go.

3. Final Answer:

   gap := len(arr) / 2 -> Option B

4. Quick Check:

   gap = half array length [OK]

Hint: Start gap as half array length in Go [OK]

Common Mistakes:

• Using gap larger than array length
• Initializing gap to zero which stops sorting
• Incorrect Go syntax for variable declaration

3. What will be the output of the following Go code snippet using Shell Sort on array [9, 8, 3, 7, 5]?

func shellSort(arr []int) []int {
    n := len(arr)
    for gap := n / 2; gap > 0; gap /= 2 {
        for i := gap; i < n; i++ {
            temp := arr[i]
            j := i
            for j >= gap && arr[j-gap] > temp {
                arr[j] = arr[j-gap]
                j -= gap
            }
            arr[j] = temp
        }
    }
    return arr
}

fmt.Println(shellSort([]int{9, 8, 3, 7, 5}))

medium

A. [3 5 7 8 9]

B. [9 8 7 5 3]

C. [5 3 7 8 9]

D. [3 7 5 8 9]

Solution

1. Step 1: Trace first gap iteration (gap=2)

   Compare elements 2 apart and sort: array changes from [9,8,3,7,5] to [3,8,9,7,5] then [3,5,9,7,8].

2. Step 2: Trace second gap iteration (gap=1)

   Standard insertion sort on nearly sorted array results in [3,5,7,8,9].

3. Final Answer:

   [3 5 7 8 9] -> Option A

4. Quick Check:

   Shell Sort output = sorted array [OK]

Hint: Shell Sort outputs sorted array [OK]

Common Mistakes:

• Confusing gap steps and final output
• Assuming no change after first gap
• Mixing up array indices during swaps

4. Identify the error in this Go Shell Sort code snippet:

func shellSort(arr []int) {
    n := len(arr)
    gap := n / 2
    for gap > 0 {
        for i := gap; i < n; i++ {
            temp := arr[i]
            j := i
            for j >= gap && arr[j-gap] < temp {
                arr[j] = arr[j-gap]
                j -= gap
            }
            arr[j] = temp
        }
        gap /= 2
    }
}

medium

A. The gap should increase instead of decrease.

B. The outer loop should use for gap < n instead of gap > 0.

C. The variable temp is not initialized properly.

D. The comparison operator should be > instead of < in inner loop.

Solution

1. Step 1: Analyze inner loop comparison

   The inner loop compares arr[j-gap] and temp to decide swapping. It should move larger elements up, so condition must be arr[j-gap] > temp.

2. Step 2: Check current comparison operator

   Current code uses arr[j-gap] < temp which incorrectly moves smaller elements, breaking sort order.

3. Final Answer:

   The comparison operator should be > instead of < in inner loop. -> Option D

4. Quick Check:

   Correct comparison = > [OK]

Hint: Inner loop compares if previous element is greater [OK]

Common Mistakes:

• Using < instead of > in inner loop condition
• Increasing gap instead of decreasing
• Misplacing gap update outside loop

5. Given an array with many duplicate values, how can Shell Sort be adapted to maintain stable sorting (preserving original order of equal elements)?

hard

A. Use a stable gap sequence like Hibbard's sequence and avoid swapping equal elements.

B. Increase the gap size to skip duplicates during sorting.

C. Shell Sort cannot be made stable; use a different algorithm instead.

D. Modify the inner loop to use >= instead of > when comparing elements.

Solution

1. Step 1: Understand stability in sorting

   Stable sorting means equal elements keep their original order after sorting.

2. Step 2: Adapt Shell Sort for stability

   Using a stable gap sequence like Hibbard's and avoiding swaps when elements are equal helps maintain stability.

3. Step 3: Evaluate other options

   Using >= breaks stability, increasing gap skips elements, and claiming impossibility is incorrect.

4. Final Answer:

   Use a stable gap sequence like Hibbard's sequence and avoid swapping equal elements. -> Option A

5. Quick Check:

   Stable Shell Sort = stable gaps + no equal swaps [OK]

Hint: Use stable gap sequences and skip swapping equals [OK]

Common Mistakes:

• Using >= comparison breaking stability
• Assuming Shell Sort cannot be stable
• Increasing gap size to skip duplicates