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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two elements in the array.

DSA Java

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

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Aj

Bi

Cpivot

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with the pivot index instead of the smaller element index.

Using the same index for both swap positions.

We swap the element at index i with the element at index j to move smaller elements before the pivot.

2fill in blank

medium

Complete the code to choose the pivot element in the partition method.

DSA Java

int pivot = arr[[1]];

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Ahigh

B0

Cmid

Dlow

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing the pivot as the first element instead of the last.

Using a fixed index like 0 regardless of sub-array.

The pivot is chosen as the last element in the current array segment, which is at index high.

3fill in blank

hard

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

DSA Java

quickSort(arr, low, [1]);

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ApivotIndex

BpivotIndex + 1

CpivotIndex - 1

Dhigh

Attempts:

3 left

💡 Hint

Common Mistakes

Using pivotIndex instead of pivotIndex - 1 causes infinite recursion.

Using pivotIndex + 1 sorts the right partition instead.

The left partition ends just before the pivot index, so we use pivotIndex - 1.

4fill in blank

hard

Fill both blanks to complete the partition loop condition and increment.

DSA Java

for (int j = low; j [1] high; j[2]) {
    if (arr[j] <= pivot) {
        i++;
        // swap code here
    }
}

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A<

B<=

C++

D--

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= causes the pivot to be included in the loop.

Using j-- causes an infinite loop.

The loop runs while j is less than high, and j increments by 1 each time.

5fill in blank

hard

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

DSA Java

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<

B<=

CpivotIndex - 1

DpivotIndex + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in base case causes unnecessary recursion.

Swapping pivotIndex - 1 and pivotIndex + 1 in recursive calls.

The base case is when low is less than high. Then sort left partition low to pivotIndex - 1 and right partition pivotIndex + 1 to high.

Practice

1. What is the main idea behind the Quick Sort algorithm as a divide and conquer method?

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. Find the maximum element and place it at the end repeatedly

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 separately.

2. Step 2: Recognize the combining step

   After sorting parts, the array is combined naturally as parts are sorted in place.

3. Final Answer:

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

4. Quick Check:

   Divide and conquer = split, sort, combine [OK]

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

Common Mistakes:

• Confusing Quick Sort with Bubble Sort
• Thinking Quick Sort uses extra space like Merge Sort
• Believing Quick Sort only swaps adjacent elements

2. Which of the following is the correct way to choose a pivot in Quick Sort in Java?

easy

A. int pivot = arr[length / 2];

B. int pivot = arr[arr.length / 2];

C. int pivot = arr[arr.length];

D. int pivot = arr[-1];

Solution

1. Step 1: Identify valid pivot index

   Array indices go from 0 to length-1, so middle index is length/2.

2. Step 2: Check each option

   A uses length (undefined, invalid), B uses arr.length (out of bounds), C uses middle element (valid), D uses negative index (invalid in Java).

3. Final Answer:

   int pivot = arr[arr.length / 2]; -> Option B

4. Quick Check:

   Pivot index must be within 0 to length-1 [OK]

Hint: Pivot index must be valid array index [OK]

Common Mistakes:

• Using arr.length as index (out of bounds)
• Using negative indices (not allowed in Java)
• Always choosing first element without reason

3. What will be the output array after the first partition step of Quick Sort on int[] arr = {4, 7, 2, 9, 1} if pivot is chosen as the first element?

medium

A. [2, 1, 4, 7, 9]

B. [1, 2, 4, 9, 7]

C. [4, 7, 2, 9, 1]

D. [9, 7, 4, 2, 1]

Solution

1. Step 1: Choose pivot and partition

   Pivot = 4. Elements less than 4 go left, greater go right.

2. Step 2: Rearrange array after partition

   Left side: 2,1; pivot:4; right side:7,9. So array becomes [2, 1, 4, 7, 9].

3. Final Answer:

   [2, 1, 4, 7, 9] -> Option A

4. Quick Check:

   Partition arr around pivot 4 = [2,1,4,7,9] [OK]

Hint: Partition places pivot between smaller and larger elements [OK]

Common Mistakes:

• Not moving elements smaller than pivot to left
• Leaving array unchanged after partition
• Placing pivot at wrong position

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

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

medium

A. Variable i should start at low, not low - 1

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

C. Loop should run until j < high, not j <= high

D. Swap logic is incorrect

Solution

1. Step 1: Analyze loop boundary

   The loop runs j from low to high inclusive, but arr[high] is pivot and should not be compared inside loop.

2. Step 2: Correct loop condition

   Loop should run j from low to high-1 to avoid swapping pivot with itself.

3. Final Answer:

   Loop should run until j < high, not j <= high -> Option C

4. Quick Check:

   Partition loop excludes pivot index [OK]

Hint: Loop excludes pivot index during partition [OK]

Common Mistakes:

• Including pivot in partition loop
• Starting i at wrong index
• Changing pivot selection unnecessarily

5. Given the array {10, 80, 30, 90, 40, 50, 70}, if Quick Sort always chooses the last element as pivot, what is the sequence of pivot values chosen during the entire sorting process?

hard

A. [70, 50, 40, 30, 10, 90, 80]

B. [70, 90, 80, 50, 40, 10, 30]

C. [70, 90, 80, 50, 40, 30, 10]

D. [70, 50, 40, 30, 10, 80, 90]

Solution

1. Step 1: Identify pivots chosen at each recursive call

   First pivot: last element 70. After partition, left subarray ends at 50, right subarray ends at 80.

2. Step 2: Continue choosing last element as pivot in subarrays

   Next pivots: 50 (left), then 40, then 30, then 10; right subarray pivots: 80, then 90.

3. Final Answer:

   [70, 50, 40, 30, 10, 80, 90] -> Option D

4. Quick Check:

   Last element pivot sequence matches [OK]

Hint: Pivot is always last element in current subarray [OK]

Common Mistakes:

• Mixing pivot order with sorted array order
• Choosing first element as pivot instead
• Ignoring recursive calls on subarrays