Quick Sort as Divide and Conquer in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two elements in the array.

DSA C#

int temp = arr[[1]];
arr[[1]] = arr[j];
arr[j] = temp;

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

Ai

Bj

Clow

Dpivot

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with pivot index instead of i or j.

Using the wrong index variable for swapping.

We swap the element at index i with the element at index j to partition the array correctly.

2fill in blank

medium

Complete the code to choose the pivot element for partitioning.

DSA C#

int pivot = arr[[1]];

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

Alow

Bmiddle

Chigh

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing pivot as low index instead of high.

Using a fixed index like 0 regardless of segment.

The pivot is chosen as the element at the high index to partition the array.

3fill in blank

hard

Fix the error in the recursive quicksort call to sort the left partition.

DSA C#

QuickSort(arr, low, [1]);

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

Ahigh

BpivotIndex + 1

CpivotIndex

DpivotIndex - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Including pivot index in left partition.

Using pivotIndex + 1 instead of pivotIndex - 1.

We sort the left partition from low to pivotIndex - 1 to exclude the pivot element.

4fill in blank

hard

Fill both blanks to complete the partition method's loop and condition.

DSA C#

for (int j = [1]; j < high; j++) {
    if (arr[j] [2] pivot) {
        i++;
        Swap(arr, i, j);
    }
}

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

Alow

B<=

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Starting loop from 0 instead of low.

Using wrong comparison operator like > or <=

The loop starts from low and checks if arr[j] is less than pivot to partition correctly.

5fill in blank

hard

Fill all three blanks to complete the recursive quicksort calls and base case check.

DSA C#

if (low [1] high) {
    int pivotIndex = Partition(arr, low, high);
    QuickSort(arr, low, [2]);
    QuickSort(arr, [3], high);
}

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

A<

BpivotIndex - 1

CpivotIndex + 1

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in base case causing infinite recursion.

Including pivot index in recursive calls.

We recurse only if low < high, then sort left and right partitions excluding the pivot.

Practice

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

easy

A. Use extra memory to merge two sorted arrays

B. Sort the array by repeatedly swapping adjacent elements

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

D. Sort elements by counting their frequency

Solution

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

   Quick Sort divides the array into smaller parts using a pivot, then sorts each part separately.

2. Step 2: Compare with other sorting methods

   Unlike bubble sort or counting sort, Quick Sort uses division and conquering subproblems.

3. Final Answer:

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

4. Quick Check:

   Divide and conquer = splitting and sorting parts [OK]

Hint: Remember: Quick Sort splits and sorts parts separately [OK]

Common Mistakes:

• Confusing Quick Sort with bubble sort
• Thinking Quick Sort uses extra memory like merge sort
• Believing Quick Sort counts frequencies

2. Which of the following is the correct way to declare the partition method header in C# for Quick Sort?

easy

A. public static int Partition(int[] arr, int low, int high)

B. void Partition(int arr[], int low, int high)

C. int Partition(int[] arr, int low, int high, int pivot)

D. public int Partition(int arr, int low, int high)

Solution

1. Step 1: Check C# method declaration syntax

   In C#, arrays are declared as int[] arr, and method must specify return type and access modifier.

2. Step 2: Validate parameters and return type

   Partition returns an integer index, so return type is int. Parameters include array and two indices.

3. Final Answer:

   public static int Partition(int[] arr, int low, int high) -> Option A

4. Quick Check:

   C# method syntax with array and return int = public static int Partition(int[] arr, int low, int high) [OK]

Hint: Remember C# arrays use [] after type, method needs return type [OK]

Common Mistakes:

• Using C-style array syntax like int arr[]
• Missing return type or access modifier
• Passing pivot as parameter unnecessarily

3. What will be the output array after applying Quick Sort on int[] arr = {4, 2, 7, 1}?

medium

A. [1, 2, 4, 7]

B. [7, 4, 2, 1]

C. [2, 1, 4, 7]

D. [4, 7, 2, 1]

Solution

1. Step 1: Apply Quick Sort partition and recursive calls

   Pivot chosen (commonly last element 1), partition places 1 at start, then sort left and right parts recursively.

2. Step 2: Sort remaining parts

   After partitioning and recursive sorting, array becomes sorted ascending: 1, 2, 4, 7.

3. Final Answer:

   [1, 2, 4, 7] -> Option A

4. Quick Check:

   Sorted array ascending = [1, 2, 4, 7] [OK]

Hint: Quick Sort outputs sorted array ascending by default [OK]

Common Mistakes:

• Confusing pivot placement
• Not sorting both sides recursively
• Assuming output is reversed

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

int Partition(int[] arr, int low, int high) {
  int pivot = arr[high];
  int i = low;
  for (int j = low; j < high; j++) {
    if (arr[j] < pivot) {
      Swap(arr[i], arr[j]);
      i++;
    }
  }
  Swap(arr[i], arr[high]);
  return i;
}

medium

A. The initial value of i should be low - 1

B. Swap method is called with values, not indices

C. The loop should run until j <= high

D. Pivot should be arr[low], not arr[high]

Solution

1. Step 1: Analyze Swap usage in C#

   Swap is called with arr[i] and arr[j], which passes values, not array indices, so original array won't change.

2. Step 2: Correct Swap call

   Swap should be called with indices or use a method that swaps elements in the array by index.

3. Final Answer:

   Swap method is called with values, not indices -> Option B

4. Quick Check:

   Swap needs indices or ref to swap array elements [OK]

Hint: Swap array elements by indices, not by passing values [OK]

Common Mistakes:

• Using wrong loop range
• Incorrect pivot choice
• Initializing i incorrectly

5. Given an array int[] arr = {3, 6, 8, 10, 1, 2, 1}, how many recursive calls will Quick Sort make to fully sort this array using the last element as pivot each time?

hard

A. 7

B. 15

C. 13

D. 9

Solution

1. Step 1: Understand recursive calls in Quick Sort

   Each partition divides array into two parts; recursive calls happen on both sides unless base case reached.

2. Step 2: Trace recursive calls for given array

   Initial call on 7 elements, partitions and recurses on subarrays. Counting calls: initial + left + right calls totals 9.

3. Final Answer:

   9 -> Option D

4. Quick Check:

   Counting recursive calls carefully = 9 [OK]

Hint: Count initial call plus calls on subarrays after partition [OK]

Common Mistakes:

• Counting only partition steps, not recursive calls
• Assuming calls equal array length
• Ignoring base case stops