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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two integers using pointers.

DSA C

void swap(int *a, int *b) {
    int temp = *a;
    *a = [1];
    *b = temp;
}

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

A*b

B*a

Ctemp

Da

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning *a = temp instead of *a = *b

Using a or b instead of *a or *b

To swap values, assign *a = *b and *b = temp.

2fill in blank

medium

Complete the code to choose the last element as pivot in partition function.

DSA C

int partition(int arr[], int low, int high) {
    int pivot = arr[[1]];
    int i = low - 1;
    for (int j = low; j < high; j++) {
        if (arr[j] < pivot) {
            i++;
            swap(&arr[i], &arr[j]);
        }
    }
    swap(&arr[i + 1], &arr[high]);
    return i + 1;
}

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Ahigh

Blow

C0

Dlow + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing pivot as arr[low] instead of arr[high]

Using an index outside the array bounds

The pivot is chosen as the last element, which is at index high.

3fill in blank

hard

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

DSA C

void quickSort(int arr[], int low, int high) {
    if (low < high) {
        int pi = partition(arr, low, high);
        quickSort(arr, low, [1]);
        quickSort(arr, pi + 1, high);
    }
}

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Api + 1

Blow

Chigh

Dpi - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using pi + 1 for left partition causing overlap

Using high instead of pi - 1

The left partition ends at pi - 1, so quickSort should be called with that.

4fill in blank

hard

Fill both blanks to complete the partition function's for loop condition and swap call.

DSA C

int partition(int arr[], int low, int high) {
    int pivot = arr[high];
    int i = low - 1;
    for (int j = low; j [1] high; j++) {
        if (arr[j] < pivot) {
            i++;
            swap(&arr[i], &arr[[2]]);
        }
    }
    swap(&arr[i + 1], &arr[high]);
    return i + 1;
}

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

A<

B<=

Cj

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in loop causing pivot to be included

Swapping with arr[i] instead of arr[j]

The loop runs while j < high, and swap uses arr[j] to swap with arr[i].

5fill in blank

hard

Fill all three blanks to complete the quickSort function with correct recursive calls and base condition.

DSA C

void quickSort(int arr[], int low, int high) {
    if (low [1] high) {
        int pi = partition(arr, low, high);
        quickSort(arr, low, [2]);
        quickSort(arr, [3], high);
    }
}

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

A<

Bpi - 1

Cpi + 1

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in base condition causing infinite recursion

Swapping recursive call bounds

The base condition is low < high; recursive calls are on low to pi-1 and pi+1 to high.

Practice

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

easy

A. Compare each element with every other element to sort

B. Divide the array into smaller parts using a pivot and sort them recursively

C. Merge two sorted arrays into one sorted array

D. Insert elements one by one into the correct position

Solution

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

   Quick Sort picks a pivot and divides the array into parts smaller and larger than the pivot.

2. Step 2: Recursive sorting of parts

   It then sorts these parts recursively, combining results to get a sorted array.

3. Final Answer:

   Divide the array into smaller parts using a pivot and sort them recursively -> Option B

4. Quick Check:

   Quick Sort = Divide and conquer with pivot [OK]

Hint: Remember pivot splits array for recursive sorting [OK]

Common Mistakes:

• Confusing Quick Sort with Merge Sort
• Thinking Quick Sort compares all pairs
• Believing Quick Sort inserts elements one by one

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

easy

A. 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);

D. int partition(int arr[], int low);

Solution

1. Step 1: Check parameter types for partition

   The partition function takes an array and two indices low and high to work on a subarray.

2. Step 2: Check return type

   It returns an integer index where the pivot ends after partitioning.

3. Final Answer:

   int partition(int arr[], int low, int high); -> Option A

4. Quick Check:

   Partition returns pivot index with array and bounds [OK]

Hint: Partition returns pivot index, needs array and bounds [OK]

Common Mistakes:

• Using void return type instead of int
• Passing array as int instead of int[]
• Missing one of the index parameters

3. What will be the output array after calling Quick Sort on arr = {3, 6, 8, 10, 1, 2, 1}?

medium

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

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

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

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

Solution

1. Step 1: Apply Quick Sort to the array

   Quick Sort rearranges elements so smaller come before pivot and larger after, recursively sorting subarrays.

2. Step 2: Sort the given array

   Sorting {3,6,8,10,1,2,1} results in {1,1,2,3,6,8,10} in ascending order.

3. Final Answer:

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

4. Quick Check:

   Sorted array = ascending order [OK]

Hint: Quick Sort outputs sorted array ascending [OK]

Common Mistakes:

• Assuming original array stays same
• Confusing ascending with descending order
• Misplacing duplicate elements

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) {
      i++;
      swap(&arr[i], &arr[j]);
    }
  }
  swap(&arr[i + 1], &arr[high]);
  return i + 1;
}

medium

A. For loop should run until j <= high

B. Pivot should be arr[low] instead of arr[high]

C. Swap should be called outside the loop only

D. Variable i should start at low - 1

Solution

1. Step 1: Check initialization of i

   In partition, i should start at low - 1 to correctly track smaller elements before j.

2. Step 2: Analyze loop and swaps

   Starting i at low causes incorrect swaps and wrong pivot placement.

3. Final Answer:

   Variable i should start at low - 1 -> Option D

4. Quick Check:

   i = low - 1 fixes partition indexing [OK]

Hint: Initialize i to low - 1 before loop [OK]

Common Mistakes:

• Starting i at low causes off-by-one errors
• Changing pivot position incorrectly
• Loop running beyond high index

5. Given an array with many duplicate elements, which modification to Quick Sort helps improve performance?

hard

A. Avoid recursion and use iterative sorting only

B. Always pick the first element as pivot

C. Use a three-way partitioning to separate less, equal, and greater elements

D. Skip sorting duplicates to save time

Solution

1. Step 1: Understand problem with duplicates in Quick Sort

   Duplicates cause many equal elements to be repeatedly partitioned, slowing sorting.

2. Step 2: Apply three-way partitioning

   Three-way partitioning divides array into less than, equal to, and greater than pivot, reducing redundant work.

3. Final Answer:

   Use a three-way partitioning to separate less, equal, and greater elements -> Option C

4. Quick Check:

   Three-way partitioning optimizes duplicates [OK]

Hint: Three-way partition handles duplicates efficiently [OK]

Common Mistakes:

• Picking fixed pivot causes worst-case time
• Skipping duplicates breaks sorting correctness
• Avoiding recursion does not fix duplicate issue