Shell Sort Algorithm in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Shell Sort with a specific gap sequence

What is the output array after running the Shell Sort algorithm on the input array [23, 12, 1, 8, 34, 54, 2, 3] using the gap sequence [4, 2, 1]?

DSA C++

void shellSort(int arr[], int n) {
    int gaps[] = {4, 2, 1};
    for (int gap : gaps) {
        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;
        }
    }
}

int main() {
    int arr[] = {23, 12, 1, 8, 34, 54, 2, 3};
    int n = sizeof(arr)/sizeof(arr[0]);
    shellSort(arr, n);
    for (int i = 0; i < n; i++) {
        std::cout << arr[i] << " ";
    }
    return 0;
}

A [1, 2, 3, 8, 12, 23, 34, 54]

B [1, 3, 2, 8, 12, 23, 34, 54]

C [2, 3, 1, 8, 12, 23, 34, 54]

D [23, 12, 1, 8, 34, 54, 2, 3]

💡 Hint

Shell Sort sorts the array by comparing elements at a certain gap and reducing the gap gradually until it becomes 1.

Shell Sort starts with a large gap and sorts elements far apart from each other. Then it reduces the gap and sorts again. Finally, it does a normal insertion sort with gap 1. This results in a sorted array.

🧠 Conceptual

intermediate

Understanding the role of gap sequence in Shell Sort

Why does Shell Sort use a gap sequence instead of just sorting adjacent elements like Insertion Sort?

A Because it avoids sorting the array completely.

B Because sorting elements far apart first reduces the total number of swaps needed later.

C Because it only works on arrays with even length.

D Because it makes the algorithm run slower and more complex.

💡 Hint

Think about how sorting far apart elements can help bring the array closer to sorted faster.

Sorting elements far apart helps move elements closer to their final position quickly. This reduces the total work needed when the gap becomes 1, making the algorithm faster than simple insertion sort.

🔧 Debug

advanced

Identify the error in this Shell Sort implementation

What error will this Shell Sort code produce when run?

DSA C++

void shellSort(int arr[], int n) {
    int gap = n / 2;
    while (gap > 0) {
        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;
        }
        gap /= 2;
    }
}

A The code will not compile due to syntax errors.

B The code will cause a runtime error due to invalid array access.

C The array will be sorted in descending order, not ascending.

D The array will remain unsorted.

💡 Hint

Check the comparison operator inside the inner while loop.

The comparison uses '<' instead of '>'. This causes the algorithm to sort the array in descending order instead of ascending order.

📝 Syntax

advanced

Find the syntax error in this Shell Sort code snippet

Which option correctly fixes the syntax error in the following code? for (int gap : gaps) { 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; } }

DSA C++

int gaps[] = {5, 3, 1};
int n = 10;
int arr[10];

A Remove the semicolon after 'arr[j] = temp;'

B Change 'for (int gap : gaps)' to 'for int gap in gaps'

C Replace 'while' with 'if' in the inner loop

D Add a semicolon after 'int temp = arr[i]'

💡 Hint

Check for missing punctuation after variable declarations.

The line 'int temp = arr[i]' is missing a semicolon at the end, causing a syntax error.

🚀 Application

expert

Choosing the best gap sequence for Shell Sort

Which gap sequence is known to provide better average performance for Shell Sort compared to simple halving (n/2, n/4, ...)?

A Using the sequence of gaps as the Ciura sequence (e.g., 701, 301, 132, 57, 23, 10, 4, 1)

B Using the sequence of gaps as powers of two (e.g., 8, 4, 2, 1)

C Using the sequence of gaps as Fibonacci numbers (e.g., 13, 8, 5, 3, 2, 1)

D Using the sequence of gaps as prime numbers only (e.g., 17, 13, 7, 3, 1)

💡 Hint

Some gap sequences are experimentally proven to reduce the number of comparisons and swaps.

The Ciura sequence is a well-known gap sequence that improves Shell Sort's efficiency by reducing the number of comparisons and swaps compared to simple halving.