Shell Sort Algorithm in DSA Javascript - 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 array [23, 12, 1, 8, 34, 54, 2, 3] using the gap sequence [4, 2, 1]?

DSA Javascript

function shellSort(arr) {
  let gaps = [4, 2, 1];
  for (let gap of gaps) {
    for (let i = gap; i < arr.length; i++) {
      let temp = arr[i];
      let j = i;
      while (j >= gap && arr[j - gap] > temp) {
        arr[j] = arr[j - gap];
        j -= gap;
      }
      arr[j] = temp;
    }
  }
  return arr;
}

console.log(shellSort([23, 12, 1, 8, 34, 54, 2, 3]));

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

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

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

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

💡 Hint

Shell Sort sorts elements by comparing elements at a certain gap and reducing the gap gradually.

Shell Sort starts with a large gap and sorts elements that are far apart. Then it reduces the gap and sorts again until the gap is 1, which is a normal insertion sort. This process results in a sorted array.

🧠 Conceptual

intermediate

Understanding the gap sequence effect in Shell Sort

Which statement best describes the effect of the gap sequence on the Shell Sort algorithm's performance?

A A larger initial gap helps move elements farther apart closer to their final position early, improving efficiency.

B The gap sequence does not affect the sorting performance; it only changes the order of comparisons.

C A smaller initial gap leads to faster sorting because fewer elements are compared.

D Using a gap sequence of only 1 is the most efficient way to perform Shell Sort.

💡 Hint

Think about how moving elements far apart early can reduce the total number of moves later.

Starting with a larger gap allows the algorithm to move elements that are far apart closer to their correct positions early, which reduces the total number of comparisons and shifts needed in later passes.

🔧 Debug

advanced

Identify the error in this Shell Sort implementation

What error does the following Shell Sort code produce when run?

DSA Javascript

function shellSort(arr) {
  let n = arr.length;
  let gap = Math.floor(n / 2);
  while (gap > 0) {
    for (let i = gap; i < n; i++) {
      let temp = arr[i];
      let j = i;
      while (j >= gap && arr[j - gap] < temp) {
        arr[j] = arr[j - gap];
        j -= gap;
      }
      arr[j] = temp;
    }
    gap = Math.floor(gap / 2);
  }
  return arr;
}

console.log(shellSort([5, 3, 8, 4, 2]));

A The code runs but outputs an incorrectly sorted array [8, 5, 4, 3, 2]

B The code runs and outputs [5, 3, 8, 4, 2]

C The code runs and outputs [2, 3, 4, 5, 8]

D The code runs and outputs [8, 5, 4, 3, 2]

💡 Hint

Check the comparison operator in the inner while loop.

The comparison operator in the inner while loop is '<' which causes the array to be sorted in descending order incorrectly. Shell Sort should use '>' to sort in ascending order.

📝 Syntax

advanced

Identify the syntax error in this Shell Sort snippet

Which option correctly fixes the syntax error in the following code snippet?

DSA Javascript

for (let gap = Math.floor(arr.length / 2); gap > 0; gap = Math.floor(gap / 2)) {
  for (let i = gap; i < arr.length; i++) {
    let temp = arr[i]
    let j = i
    while (j >= gap && arr[j - gap] > temp) {
      arr[j] = arr[j - gap]
      j -= gap
    }
    arr[j] = temp
  }
}

A Replace 'let' with 'var' for all variable declarations.

B Remove the Math.floor calls from the gap calculation.

C Change 'while' to 'if' in the inner loop condition.

D Add semicolons at the end of lines missing them inside the loops.

💡 Hint

JavaScript requires semicolons to separate statements, especially inside loops.

The code is missing semicolons at the end of some statements, which can cause syntax errors or unexpected behavior. Adding semicolons fixes the syntax.

🚀 Application

expert

Shell Sort on a large nearly sorted array

Given a nearly sorted array of 1000 elements where only 10 elements are out of place, which gap sequence would likely give the best performance for Shell Sort?

A A gap sequence with random gaps unrelated to array size

B A gap sequence of only 1 (normal insertion sort)

C A gap sequence with small gaps only (e.g., 5, 3, 1)

D A gap sequence that starts large and reduces by half each time (e.g., 500, 250, 125, ... 1)

💡 Hint

Nearly sorted arrays benefit from small gaps to quickly fix minor disorder.

For nearly sorted arrays, small gap sequences like (5, 3, 1) help quickly fix the few misplaced elements with minimal overhead, making the sort efficient.