Shell Sort Algorithm in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the gap for Shell Sort.

DSA C++

int n = arr.size();
int gap = [1];

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

An * 2

Bn / 2

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using gap equal to the full array size causes no sorting.

Using gap larger than array size causes errors.

The initial gap in Shell Sort is usually set to half the array size to start sorting elements far apart.

2fill in blank

medium

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

DSA C++

while (gap > 0) {
    // sorting logic here
    gap = [1];
}

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

Agap - 1

Bgap + 1

Cgap / 2

Dgap * 2

Attempts:

3 left

💡 Hint

Common Mistakes

Subtracting 1 reduces gap too slowly.

Multiplying gap increases it, causing infinite loop.

Shell Sort reduces the gap by dividing it by 2 each iteration to gradually sort closer elements.

3fill in blank

hard

Fix the error in the inner loop condition to correctly compare elements during insertion sort step.

DSA C++

for (int i = gap; i < n; i++) {
    int temp = arr[i];
    int j = i;
    while (j >= gap && arr[j - gap] [1] temp) {
        arr[j] = arr[j - gap];
        j -= gap;
    }
    arr[j] = temp;
}

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

A>

B>=

C<

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' causes incorrect sorting order.

Using '>=' causes unnecessary shifts.

We move elements that are greater than temp to the right to insert temp in the correct position.

4fill in blank

hard

Fill both blanks to complete the insertion step inside the gap-based sorting.

DSA C++

int temp = arr[[1]];
int j = [2];
while (j >= gap && arr[j - gap] > temp) {
    arr[j] = arr[j - gap];
    j -= gap;
}

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

Ai

Bgap

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Using gap as index causes out-of-bound errors.

Using j before initialization causes errors.

We store the current element at index i in temp and start shifting from index j = i.

5fill in blank

hard

Fill all three blanks to complete the Shell Sort function.

DSA C++

void shellSort(std::vector<int>& arr) {
    int n = arr.size();
    for (int gap = [1]; gap > 0; gap = [2]) {
        for (int i = gap; i < n; i++) {
            int temp = arr[[3]];
            int j = i;
            while (j >= gap && arr[j - gap] > temp) {
                arr[j] = arr[j - gap];
                j -= gap;
            }
            arr[j] = temp;
        }
    }
}

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

An / 2

Bgap / 2

Ci

Dgap

Attempts:

3 left

💡 Hint

Common Mistakes

Using gap as index instead of i.

Increasing gap instead of decreasing causes infinite loop.

The Shell Sort starts with gap = n/2, reduces gap by half each iteration, and uses i as the current index for insertion.

Practice

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

easy

A. It sorts elements by building a binary heap.

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

C. It uses a divide and conquer approach like merge sort.

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

Solution

1. Step 1: Understand Shell Sort's approach

   Shell Sort starts by comparing elements far apart using a gap, not just neighbors.

2. Step 2: Gap reduction and sorting

   The gap reduces gradually until it becomes 1, performing insertion sort at each stage.

3. Final Answer:

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

4. Quick Check:

   Shell Sort = gap-based sorting [OK]

Hint: Remember: Shell Sort uses gaps that shrink over time [OK]

Common Mistakes:

• Thinking Shell Sort only swaps adjacent elements
• Confusing Shell Sort with merge or heap sort
• Ignoring the gap reduction step

2. Which of the following is the correct way to initialize the gap in Shell Sort for an array of size n in C++?

easy

A. int gap = n / 2;

B. int gap = n * 2;

C. int gap = n + 1;

D. int gap = 1;

Solution

1. Step 1: Identify the common gap initialization

   Shell Sort commonly starts with gap as half the array size, i.e., n/2.

2. Step 2: Check other options

   Multiplying or adding to n is incorrect; starting at 1 skips the gap sorting steps.

3. Final Answer:

   int gap = n / 2; -> Option A

4. Quick Check:

   Gap starts at half array size [OK]

Hint: Gap usually starts at half the array length [OK]

Common Mistakes:

• Starting gap at 1 instead of n/2
• Using gap larger than array size
• Confusing gap initialization with loop counters

3. What will be the output array after applying Shell Sort on arr = {9, 8, 3, 7, 5, 6, 4, 1}?

medium

A. [1, 3, 4, 5, 6, 7, 8, 9]

B. [9, 8, 7, 6, 5, 4, 3, 1]

C. [1, 4, 3, 5, 6, 7, 8, 9]

D. [3, 1, 4, 5, 6, 7, 8, 9]

Solution

1. Step 1: Apply Shell Sort steps on the array

   Start with gap = 4 (8/2), sort elements 4 apart, then gap = 2, then gap = 1.

2. Step 2: Final sorted array

   After all gap reductions and sorting, the array becomes fully sorted: [1, 3, 4, 5, 6, 7, 8, 9].

3. Final Answer:

   [1, 3, 4, 5, 6, 7, 8, 9] -> Option A

4. Quick Check:

   Shell Sort fully sorts array ascending [OK]

Hint: Shell Sort outputs a fully sorted array ascending [OK]

Common Mistakes:

• Confusing partial sorted arrays as final output
• Reversing the array order
• Ignoring gap-based sorting steps

4. Identify the error in the following Shell Sort code snippet:

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

medium

A. The inner while loop condition should be j > gap, not j >= gap.

B. No error; the code correctly implements Shell Sort.

C. The gap should start from n, not n/2.

D. The gap update should be gap = gap - 1 instead of gap /= 2.

Solution

1. Step 1: Review gap initialization and update

   Gap starts at n/2 and halves each iteration, which is correct for Shell Sort.

2. Step 2: Check inner loop and conditions

   The while loop uses j >= gap to avoid out-of-bound and correctly shifts elements.

3. Final Answer:

   No error; the code correctly implements Shell Sort. -> Option B

4. Quick Check:

   Code matches Shell Sort logic [OK]

Hint: Check gap halving and while loop conditions carefully [OK]

Common Mistakes:

• Changing gap update to subtract 1 breaks algorithm
• Using incorrect while loop boundary causes errors
• Starting gap at n causes out-of-bound issues

5. Given an array arr = {23, 12, 1, 8, 34, 54, 2, 3}, how many times will the inner while loop execute during the first gap iteration (gap = 4) in Shell Sort?

hard

A. 5 times

B. 4 times

C. 3 times

D. 6 times

Solution

1. Step 1: Identify elements compared with gap = 4

   Pairs compared: (23, 34), (12, 54), (1, 2), (8, 3).

2. Step 2: Count while loop executions

   Only pairs where left element > right element cause shifts. Here, (23 > 34) no, (12 > 54) no, (1 > 2) no, (8 > 3) yes. For (8,3), shifting occurs once. Also, elements at indices 4 to 7 are checked, total 4 iterations of the outer loop, but only 1 inner while loop execution occurs.

3. Final Answer:

   3 times -> Option C

4. Quick Check:

   Count actual inner while loop executions, not just comparisons [OK]

Hint: Count pairs separated by gap and check conditions [OK]

Common Mistakes:

• Counting only swaps, not all while loop checks
• Ignoring elements beyond first gap iteration
• Misunderstanding gap-based comparisons