Comparison Based vs Non Comparison Based Sorting in DSA Javascript - Compare & Choose

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Comparison Based Sorting Algorithm

What is the output of the following JavaScript code that uses a comparison based sorting method?

DSA Javascript

const arr = [5, 3, 8, 1, 2];
arr.sort((a, b) => a - b);
console.log(arr.join(' -> ') + ' -> null');

A 1 -> 3 -> 2 -> 5 -> 8 -> null

B 5 -> 3 -> 8 -> 1 -> 2 -> null

C 8 -> 5 -> 3 -> 2 -> 1 -> null

D 1 -> 2 -> 3 -> 5 -> 8 -> null

💡 Hint

Remember that the sort method with (a, b) => a - b sorts numbers in ascending order.

The sort method compares elements and arranges them from smallest to largest, so the output is sorted ascending.

❓ Predict Output

intermediate

Output of Non Comparison Based Sorting Algorithm

What is the output of the following JavaScript code that uses a non comparison based sorting method (counting sort) on a small array?

DSA Javascript

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max + 1).fill(0);
  for (const num of arr) count[num]++;
  const sorted = [];
  for (let i = 0; i <= max; i++) {
    while (count[i] > 0) {
      sorted.push(i);
      count[i]--;
    }
  }
  return sorted;
}
const arr = [4, 2, 2, 8, 3, 3, 1];
const sortedArr = countingSort(arr);
console.log(sortedArr.join(' -> ') + ' -> null');

A 1 -> 2 -> 2 -> 3 -> 3 -> 4 -> 8 -> null

B 8 -> 4 -> 3 -> 3 -> 2 -> 2 -> 1 -> null

C 1 -> 3 -> 2 -> 4 -> 8 -> 2 -> 3 -> null

D 2 -> 2 -> 3 -> 3 -> 4 -> 8 -> 1 -> null

💡 Hint

Counting sort counts occurrences and outputs sorted values in order.

Counting sort outputs elements in ascending order by counting their frequency.

🧠 Conceptual

advanced

Time Complexity Difference

Which statement correctly describes the time complexity difference between comparison based and non comparison based sorting algorithms?

A Non comparison based sorting algorithms can achieve linear time O(n) under certain conditions, while comparison based sorting algorithms cannot do better than O(n log n).

B Both comparison based and non comparison based sorting algorithms always run in O(n log n) time regardless of input.

C Comparison based sorting algorithms have a best time complexity of O(n), while non comparison based sorting algorithms always run in O(n log n).

D Comparison based sorting algorithms are always faster than non comparison based sorting algorithms.

💡 Hint

Think about the theoretical lower bound for comparison based sorting.

Comparison based sorting algorithms have a lower bound of O(n log n). Non comparison based algorithms like counting sort can run in O(n) if input range is limited.

❓ Predict Output

advanced

Output of Non Comparison Based Sorting Algorithm (Radix Sort)

What is the output of the following JavaScript code that uses a non comparison based sorting method (radix sort)?

DSA Javascript

function radixSort(arr) {
  const max = Math.max(...arr);
  let exp = 1;
  while (Math.floor(max / exp) > 0) {
    const output = new Array(arr.length).fill(0);
    const count = new Array(10).fill(0);
    for (let i = 0; i < arr.length; i++) {
      const index = Math.floor(arr[i] / exp) % 10;
      count[index]++;
    }
    for (let i = 1; i < 10; i++) {
      count[i] += count[i - 1];
    }
    for (let i = arr.length - 1; i >= 0; i--) {
      const index = Math.floor(arr[i] / exp) % 10;
      output[count[index] - 1] = arr[i];
      count[index]--;
    }
    arr = output;
    exp *= 10;
  }
  return arr;
}
const arr = [170, 45, 75, 90, 802, 24, 2, 66];
console.log(radixSort(arr).join(' -> ') + ' -> null');

A TypeError: Assignment to constant variable.

B Outputs sorted array correctly: 2 -> 24 -> 45 -> 66 -> 75 -> 90 -> 170 -> 802 -> null

C ReferenceError: arr is not defined.

D RangeError: Maximum call stack size exceeded.

💡 Hint

This is a correct implementation of LSD radix sort using counting sort per digit.

The code correctly implements radix sort (non-comparison based) and outputs the sorted array.

🚀 Application

expert

Choosing Sorting Algorithm for Large Dataset with Small Range

You have a large dataset of 10 million integers, but all values are between 0 and 1000. Which sorting algorithm is the best choice for fastest sorting?

A MergeSort (comparison based) because it guarantees O(n log n) time and is stable.

B QuickSort (comparison based) because it has average O(n log n) time and works well on large datasets.

C Counting Sort (non comparison based) because it can sort in O(n) time when the range is small.

D Bubble Sort (comparison based) because it is simple and easy to implement.

💡 Hint

Consider the input range and how it affects non comparison based sorting.

Counting sort is ideal for large datasets with small value ranges because it sorts in linear time O(n + k), where k is the range size.

Practice

1. Which of the following sorting algorithms is non-comparison based?

easy

A. Heap Sort

B. Merge Sort

C. Quick Sort

D. Counting Sort

Solution

1. Step 1: Understand comparison based sorting

   Comparison based sorting algorithms decide order by comparing elements, like Merge Sort, Quick Sort, and Heap Sort.

2. Step 2: Identify non-comparison based sorting

   Counting Sort uses counting of element frequencies instead of comparisons, so it is non-comparison based.

3. Final Answer:

   Counting Sort -> Option D

4. Quick Check:

   Non-comparison based = Counting Sort [OK]

Hint: Counting Sort uses counts, no element comparisons [OK]

Common Mistakes:

• Confusing Quick Sort as non-comparison
• Thinking Merge Sort is non-comparison
• Assuming Heap Sort is non-comparison

2. Which of the following is the correct syntax to call a non-comparison based sorting function countingSort(arr) in JavaScript?

easy

A. countingSort(arr);

B. countingSort arr;

C. countingSort{arr};

D. countingSort[arr];

Solution

1. Step 1: Recall JavaScript function call syntax

   Functions are called with parentheses enclosing arguments, like func(args).

2. Step 2: Match syntax with options

   Only countingSort(arr); uses correct parentheses syntax for function call.

3. Final Answer:

   countingSort(arr); -> Option A

4. Quick Check:

   Function call syntax = countingSort(arr); [OK]

Hint: Use parentheses () to call functions in JavaScript [OK]

Common Mistakes:

• Using square brackets [] instead of parentheses
• Missing parentheses around arguments
• Using curly braces {} incorrectly

3. What will be the output of the following JavaScript code?

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max + 1).fill(0);
  arr.forEach(num => count[num]++);
  let sorted = [];
  count.forEach((c, num) => {
    for (let i = 0; i < c; i++) sorted.push(num);
  });
  return sorted;
}

const arr = [3, 1, 4, 1, 5];
console.log(countingSort(arr));

medium

A. [1, 1, 3, 4, 5]

B. [3, 1, 4, 1, 5]

C. [5, 4, 3, 1, 1]

D. [1, 3, 4, 5]

Solution

1. Step 1: Count frequencies of each number

   Input array is [3,1,4,1,5]. Counting frequencies: 1 appears 2 times, 3 once, 4 once, 5 once.

2. Step 2: Build sorted array from counts

   Using counts, output array is [1,1,3,4,5] in ascending order.

3. Final Answer:

   [1, 1, 3, 4, 5] -> Option A

4. Quick Check:

   Counting Sort output = sorted ascending array [OK]

Hint: Counting Sort outputs sorted array by frequency counts [OK]

Common Mistakes:

• Confusing input and output arrays
• Assuming original order is preserved
• Thinking output is reversed

4. The following code attempts to implement Counting Sort but has a bug. What is the bug?

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max).fill(0);
  arr.forEach(num => count[num]++);
  let sorted = [];
  count.forEach((c, num) => {
    for (let i = 0; i < c; i++) sorted.push(num);
  });
  return sorted;
}

medium

A. Should use Math.min instead of Math.max

B. Array count size should be max + 1

C. Should initialize count with zeros

D. Should not use forEach on count array

Solution

1. Step 1: Check count array size

   Count array size is max, but indices go from 0 to max, so size must be max + 1.

2. Step 2: Identify impact of wrong size

   Without max + 1 size, count[max] index is undefined, causing errors or missing counts.

3. Final Answer:

   Array count size should be max + 1 -> Option B

4. Quick Check:

   Count array size = max + 1 [OK]

Hint: Count array size must cover max index + 1 [OK]

Common Mistakes:

• Using max instead of max + 1 for array size
• Confusing max with min
• Ignoring array initialization

5. You have an array of integers ranging from 0 to 1000. Which sorting algorithm is best to sort this array efficiently and why?

hard

A. Quick Sort, because it has average O(n log n) time

B. Merge Sort, because it is stable and uses divide and conquer

C. Counting Sort, because it sorts in O(n + k) where k is range size

D. Heap Sort, because it uses a binary heap structure

Solution

1. Step 1: Analyze input constraints

   Array elements range from 0 to 1000, so range size k = 1001, which is small and fixed.

2. Step 2: Choose sorting algorithm based on range

   Counting Sort runs in O(n + k), which is efficient for small k, better than O(n log n) comparison sorts.

3. Step 3: Confirm Counting Sort suitability

   Counting Sort is non-comparison based and ideal for small integer ranges.

4. Final Answer:

   Counting Sort, because it sorts in O(n + k) where k is range size -> Option C

5. Quick Check:

   Small range + Counting Sort = efficient sorting [OK]

Hint: Use Counting Sort for small integer ranges [OK]

Common Mistakes:

• Choosing Quick Sort ignoring range size
• Assuming Merge Sort is always best
• Not considering non-comparison sorts