Quick Sort Partition Lomuto and Hoare in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Lomuto Partition on given array

What is the output array after applying Lomuto partition on the array [8, 3, 7, 6, 2, 5, 4] with pivot as last element?

DSA C++

int lomutoPartition(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++;
            std::swap(arr[i], arr[j]);
        }
    }
    std::swap(arr[i + 1], arr[high]);
    return i + 1;
}

int main() {
    int arr[] = {8, 3, 7, 6, 2, 5, 4};
    int n = 7;
    int p = lomutoPartition(arr, 0, n - 1);
    for (int i = 0; i < n; i++) {
        std::cout << arr[i] << " ";
    }
    return 0;
}

A [3, 7, 6, 2, 5, 4, 8]

B [3, 2, 4, 5, 6, 7, 8]

C [3, 2, 4, 5, 6, 8, 7]

D [2, 3, 4, 5, 6, 7, 8]

💡 Hint

Remember Lomuto partition places pivot at correct position and all smaller elements to left.

Lomuto partition uses last element as pivot. It moves all elements <= pivot to left and finally swaps pivot to position i+1. Here pivot=4, after partition array becomes [3, 2, 4, 6, 7, 5, 8] but 6,7,5 are not <=4 so they stay right. Only 3 and 2 move left.

❓ Predict Output

intermediate

Output of Hoare Partition on given array

What is the output array after applying Hoare partition on the array [9, 4, 8, 3, 1, 2, 5] with pivot as first element?

DSA C++

int hoarePartition(int arr[], int low, int high) {
    int pivot = arr[low];
    int i = low - 1;
    int j = high + 1;
    while (true) {
        do {
            i++;
        } while (arr[i] < pivot);
        do {
            j--;
        } while (arr[j] > pivot);
        if (i >= j) return j;
        std::swap(arr[i], arr[j]);
    }
}

int main() {
    int arr[] = {9, 4, 8, 3, 1, 2, 5};
    int n = 7;
    int p = hoarePartition(arr, 0, n - 1);
    for (int i = 0; i < n; i++) {
        std::cout << arr[i] << " ";
    }
    return 0;
}

A [5, 4, 8, 3, 1, 2, 9]

B [2, 4, 3, 1, 5, 8, 9]

C [1, 2, 3, 4, 5, 8, 9]

D [4, 2, 3, 1, 5, 8, 9]

💡 Hint

Hoare partition uses first element as pivot and swaps elements crossing from left and right.

Pivot is 9. Hoare partition moves i right until element >= pivot and j left until element <= pivot, then swaps. Since pivot is largest, only last swap happens putting 9 at end. Result is [5,4,8,3,1,2,9].

🧠 Conceptual

advanced

Difference between Lomuto and Hoare partition schemes

Which statement correctly describes a key difference between Lomuto and Hoare partition schemes?

A Lomuto partition always uses the first element as pivot, Hoare uses the last element.

B Hoare partition returns the final pivot index, Lomuto returns an index that may not be the pivot position.

C Hoare partition requires extra space, Lomuto partition works in-place.

D Lomuto partition places the pivot in its final sorted position, Hoare partition may not.

💡 Hint

Think about where the pivot ends after partitioning.

Lomuto partition places pivot at its correct sorted position after partitioning. Hoare partition returns an index but pivot may not be at final position.

🔧 Debug

advanced

Identify error in Lomuto partition code snippet

What error will this Lomuto partition code produce when run on array [5, 3, 8, 4, 2]? int lomutoPartition(int arr[], int low, int high) { int pivot = arr[high]; int i = low; for (int j = low; j < high; j++) { if (arr[j] <= pivot) { std::swap(arr[i], arr[j]); i++; } } std::swap(arr[i], arr[high]); return i; }

A Off-by-one error causing incorrect pivot placement

B Runtime error due to invalid array index

C No error, code runs correctly

D Infinite loop due to wrong loop condition

💡 Hint

Check initial value of i and how it moves.

Variable i should start at low-1, not low. Starting at low causes pivot to be placed incorrectly, leading to wrong partitioning.

🚀 Application

expert

Number of swaps in Hoare partition

Given array [10, 7, 8, 9, 1, 5] and pivot as first element, how many swaps does Hoare partition perform?

DSA C++

int hoarePartition(int arr[], int low, int high) {
    int pivot = arr[low];
    int i = low - 1;
    int j = high + 1;
    int swapCount = 0;
    while (true) {
        do {
            i++;
        } while (arr[i] < pivot);
        do {
            j--;
        } while (arr[j] > pivot);
        if (i >= j) return swapCount;
        std::swap(arr[i], arr[j]);
        swapCount++;
    }
}

int main() {
    int arr[] = {10, 7, 8, 9, 1, 5};
    int n = 6;
    int swaps = hoarePartition(arr, 0, n - 1);
    std::cout << swaps;
    return 0;
}

A 2

B 3

C 4

D 5

💡 Hint

Trace i and j pointers and count swaps carefully.

Hoare partition swaps pairs crossing pivot boundary. For this array, swaps happen between (10,5), (9,1), and (8,7) totaling 3 swaps.

Practice

1. What is the main difference between Lomuto and Hoare partition schemes in Quick Sort?

easy

A. Lomuto uses a single pointer, Hoare uses two pointers moving inward

B. Lomuto sorts in descending order, Hoare sorts in ascending order

C. Lomuto uses recursion, Hoare uses iteration

D. Lomuto chooses the last element as pivot, Hoare chooses the first element always

Solution

1. Step 1: Understand Lomuto partition

   Lomuto partition uses one pointer to track the boundary of smaller elements and swaps elements accordingly.

2. Step 2: Understand Hoare partition

   Hoare partition uses two pointers starting from both ends moving inward to swap elements around the pivot.

3. Final Answer:

   Lomuto uses a single pointer, Hoare uses two pointers moving inward -> Option A

4. Quick Check:

   Lomuto single pointer, Hoare two pointers inward [OK]

Hint: Remember: Lomuto single pointer, Hoare two pointers inward [OK]

Common Mistakes:

• Confusing pivot selection with partition method
• Thinking both use same pointer approach
• Assuming Hoare always picks first element as pivot

2. Which of the following is the correct Lomuto partition function header in C++?

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 start, int end, int pivot)

D. bool partition(int arr[], int low, int high)

Solution

1. Step 1: Check return type

   Lomuto partition returns the pivot index as int after partitioning.

2. Step 2: Check parameters

   It takes array, low index, and high index as parameters to partition the subarray.

3. Final Answer:

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

4. Quick Check:

   Returns int pivot index, low high params [OK]

Hint: Partition returns pivot index as int with low and high params [OK]

Common Mistakes:

• Using void return type instead of int
• Adding extra pivot parameter unnecessarily
• Returning bool instead of pivot index

3. What is the output array after applying Lomuto partition on arr = [8, 3, 7, 6, 2] with low=0 and high=4?

medium

A. [2, 3, 6, 7, 8]

B. [3, 2, 7, 6, 8]

C. [8, 3, 7, 6, 2]

D. [2, 3, 7, 6, 8]

Solution

1. Step 1: Choose pivot and initialize pointers

   Pivot = arr[4] = 2, i = -1 initially.

2. Step 2: Iterate and swap smaller elements

   Check elements from index 0 to 3:
   - arr[0]=8 > 2 no swap
   - arr[1]=3 > 2 no swap
   - arr[2]=7 > 2 no swap
   - arr[3]=6 > 2 no swap
   After loop, swap arr[i+1]=arr[0] and pivot arr[4].

3. Final Answer:

   [2, 3, 7, 6, 8] -> Option D

4. Quick Check:

   Pivot swapped to front since no smaller elements [OK]

Hint: Pivot last element, swap smaller left, pivot final swap [OK]

Common Mistakes:

• Swapping elements incorrectly during iteration
• Confusing pivot position after partition
• Assuming pivot is first element

4. Identify the bug in this Hoare partition code snippet:

int hoarePartition(int arr[], int low, int high) {
  int pivot = arr[low];
  int i = low - 1, j = high + 1;
  while (true) {
    do { i++; } while (arr[i] < pivot);
    do { j--; } while (arr[j] > pivot);
    if (i >= j) return j;
    std::swap(arr[i], arr[j]);
  }
}

medium

A. Initialization of i and j is incorrect

B. No bug, code is correct

C. The loop condition should be i > j instead of i >= j

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

Solution

1. Step 1: Verify pointer initialization

   In standard Hoare partition, i starts at low-1 and j at high+1 to work with the do-while loops correctly.

2. Step 2: Check other parts

   Pivot selection arr[low], movement conditions arr[i] < pivot and arr[j] > pivot, i >= j return, and swap are all correct.

3. Final Answer:

   No bug, code is correct -> Option B

4. Quick Check:

   Standard Hoare uses i=low-1, j=high+1 [OK]

Hint: i starts at low, j at high in Hoare partition [OK]

Common Mistakes:

• Setting i and j outside array bounds
• Confusing pivot position with pointer initialization
• Misusing loop exit condition

5. Given the array [10, 80, 30, 90, 40, 50, 70], after applying Hoare partition with low=0 and high=6, what is the resulting array?

hard

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

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

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

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

Solution

1. Step 1: Set pivot and pointers

   Pivot = arr[0] = 10, i = low - 1 = -1, j = high + 1 = 7.

2. Step 2: Move pointers and check swaps

   do {i++;} while (arr[i] < 10): i=0, arr[0]=10 not <10, stop i=0.
   do {j--;} while (arr[j] > 10): j=6(70>10),5(50>10),4(40>10),3(90>10),2(30>10),1(80>10),0(10 not >10), stop j=0.
   i=0 < j=0 is false, so i >= j, return j=0, no swap.
   But since i == j, partition ends with pivot index 0.
   However, this means no swaps, so array remains same.

3. Step 3: Re-examine pointer movement

   Actually, the do-while loops stop at i=0 and j=0, so no swaps occur.
   Therefore, the array remains unchanged.

4. Final Answer:

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

5. Quick Check:

   All elements ≥ pivot, array unchanged [OK]

Hint: Track i and j moving inward, swap when i < j [OK]

Common Mistakes:

• Swapping after pointers cross
• Misplacing pivot after partition
• Confusing Hoare with Lomuto output