Quick Sort as Divide and Conquer in DSA Javascript - Build from Scratch

Quick Sort as Divide and Conquer

📖 Scenario: You have a list of numbers that you want to sort from smallest to largest. Sorting helps you find things faster, like arranging books by height on a shelf.

🎯 Goal: You will build a program that uses the Quick Sort method to sort a list of numbers. Quick Sort works by picking a number, splitting the list into smaller parts, and sorting those parts step by step.

📋 What You'll Learn

Create an array called numbers with the exact values: [8, 3, 7, 6, 2, 5, 4, 1]

Write a function called partition that takes arr, low, high, uses pivot at arr[low], rearranges subarray [low..high], returns new pivot index

Write a recursive function called quickSort that takes arr, low, high and sorts the subarray using partition

Call quickSort(numbers, 0, numbers.length - 1) and print using console.log(numbers)

💡 Why This Matters

🌍 Real World

Sorting is used everywhere, like organizing files, searching data quickly, or arranging products by price in online stores.

💼 Career

Understanding Quick Sort helps in software development roles where efficient data handling and algorithm knowledge are important.

1

Create the initial array

Create an array called numbers with these exact values: [8, 3, 7, 6, 2, 5, 4, 1]

DSA Javascript

# Your code here

Hint

Use const to create the array named numbers with the given values.

2

Write the partition function

Write a function called partition that takes an array arr, low, high. Use arr[low] as pivot value. Rearrange the subarray so all smaller than pivot are left of pivot's final position, larger on right. Return the new index of the pivot.

DSA Javascript

const numbers = [8, 3, 7, 6, 2, 5, 4, 1];
# Your code here

Hint

Pivot at low. Loop from low + 1 to high inclusive. Swap smaller elements towards swapIndex. Place pivot at swapIndex at end.

3

Write the quickSort function

Write a recursive function called quickSort that takes arr, low, high. If low >= high, return. Partition the subarray, then recursively sort left (low to pi-1) and right (pi+1 to high).

DSA Javascript

const numbers = [8, 3, 7, 6, 2, 5, 4, 1];

function partition(arr, low, high) {
    const pivotValue = arr[low];
    let swapIndex = low;
    for (let i = low + 1; i <= high; i++) {
        if (arr[i] < pivotValue) {
            swapIndex++;
            [arr[i], arr[swapIndex]] = [arr[swapIndex], arr[i]];
        }
    }
    [arr[low], arr[swapIndex]] = [arr[swapIndex], arr[low]];
    return swapIndex;
}

# Your code here

Hint

Base case if (low >= high) return;. let pi = partition(arr, low, high); Recurse: quickSort(arr, low, pi - 1); quickSort(arr, pi + 1, high);

4

Call quickSort and print

Call quickSort(numbers, 0, numbers.length - 1). Then print the sorted array using console.log(numbers).

DSA Javascript

const numbers = [8, 3, 7, 6, 2, 5, 4, 1];

function partition(arr, low, high) {
    const pivotValue = arr[low];
    let swapIndex = low;
    for (let i = low + 1; i = high) {
        return;
    }
    let pi = partition(arr, low, high);
    quickSort(arr, low, pi - 1);
    quickSort(arr, pi + 1, high);
}

# Your code here

Hint

Add quickSort(numbers, 0, numbers.length - 1); console.log(numbers); at the end.

Practice

1. What is the main idea behind the Quick Sort algorithm in the divide and conquer approach?

easy

A. Divide the array into smaller parts, sort them, and combine the results

B. Sort the array by repeatedly swapping adjacent elements

C. Use extra space to merge two sorted arrays

D. Sort the array by selecting the smallest element each time

Solution

1. Step 1: Understand divide and conquer in Quick Sort

   Quick Sort divides the array into parts based on a pivot, sorts each part recursively.

2. Step 2: Compare with other sorting methods

   Unlike bubble or selection sort, Quick Sort uses division and recursion, not just swapping or selecting smallest.

3. Final Answer:

   Divide the array into smaller parts, sort them, and combine the results -> Option A

4. Quick Check:

   Quick Sort = Divide and conquer [OK]

Hint: Remember: divide, sort parts, then combine [OK]

Common Mistakes:

• Confusing Quick Sort with bubble or selection sort
• Thinking Quick Sort merges arrays like merge sort
• Ignoring the pivot selection step

2. Which of the following is the correct syntax to choose a pivot element in a Quick Sort function in JavaScript?

easy

A. const pivot = arr.push();

B. const pivot = arr.length;

C. const pivot = arr.sort();

D. const pivot = arr[0];

Solution

1. Step 1: Identify how to select pivot in Quick Sort

   The pivot is usually an element from the array, often the first or last element.

2. Step 2: Check each option's correctness

   const pivot = arr[0]; selects the first element as pivot correctly. Others use wrong methods or properties.

3. Final Answer:

   const pivot = arr[0]; -> Option D

4. Quick Check:

   Pivot selection = arr[0] [OK]

Hint: Pivot is an element, not array length or method result [OK]

Common Mistakes:

• Using array length as pivot
• Calling array methods instead of accessing element
• Confusing pivot with sorted array

3. What will be the output of the following JavaScript Quick Sort partition step?

const arr = [4, 2, 7, 1];
const pivot = arr[0]; // 4
let left = [];
let right = [];
for(let i = 1; i < arr.length; i++) {
  if(arr[i] <= pivot) left.push(arr[i]);
  else right.push(arr[i]);
}
console.log(left);
console.log(right);

medium

A. [4, 2] and [7, 1]

B. [7] and [2, 1]

C. [2, 1] and [7]

D. [1, 2, 4] and []

Solution

1. Step 1: Identify pivot and partition logic

   Pivot is 4. Elements less or equal to 4 go to left, others to right.

2. Step 2: Partition the array

   Elements: 2 <= 4 -> left, 7 > 4 -> right, 1 <= 4 -> left. So left = [2,1], right = [7].

3. Final Answer:

   [2, 1] and [7] -> Option C

4. Quick Check:

   Partition by pivot 4 = [2,1] left, [7] right [OK]

Hint: Compare each element to pivot, separate into left/right [OK]

Common Mistakes:

• Including pivot in left or right arrays
• Mixing up less than and greater than conditions
• Forgetting to start loop from index 1

4. Identify the error in this Quick Sort partition code snippet:

function partition(arr) {
  const pivot = arr[0];
  let left = [];
  let right = [];
  for(let i = 0; i < arr.length; i++) {
    if(arr[i] < pivot) left.push(arr[i]);
    else right.push(arr[i]);
  }
  return [...left, pivot, ...right];
}

medium

A. Use arr[i] <= pivot in condition instead of <

B. Loop should start from 1 to avoid including pivot twice

C. Pivot should be last element, not first

D. Return statement should not use spread operator

Solution

1. Step 1: Analyze loop range and pivot usage

   The loop starts at 0, so pivot element arr[0] is included in left or right arrays again.

2. Step 2: Correct loop start index

   Loop should start at 1 to skip pivot element and avoid duplication.

3. Final Answer:

   Loop should start from 1 to avoid including pivot twice -> Option B

4. Quick Check:

   Loop index = 1 to exclude pivot [OK]

Hint: Start loop after pivot index to avoid duplicates [OK]

Common Mistakes:

• Starting loop at 0 causing pivot duplication
• Changing pivot position unnecessarily
• Misunderstanding spread operator usage

5. Given the array [3, 6, 8, 10, 1, 2, 1], what is the correct sorted array after applying Quick Sort fully?

hard

A. [1, 1, 2, 3, 6, 8, 10]

B. [1, 2, 3, 6, 8, 10]

C. [3, 6, 8, 10, 1, 2, 1]

D. [10, 8, 6, 3, 2, 1, 1]

Solution

1. Step 1: Understand Quick Sort fully sorts the array

   Quick Sort recursively partitions and sorts all parts until fully sorted.

2. Step 2: Sort the array manually

   Sorted array is [1, 1, 2, 3, 6, 8, 10], including duplicates in order.

3. Final Answer:

   [1, 1, 2, 3, 6, 8, 10] -> Option A

4. Quick Check:

   Quick Sort output = sorted array ascending [OK]

Hint: Quick Sort returns fully sorted array ascending [OK]

Common Mistakes:

• Ignoring duplicate elements
• Confusing sorted with original array
• Thinking Quick Sort reverses array