Quick Sort Algorithm in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Quick Sort algorithm?

Quick Sort works by picking a 'pivot' element and rearranging the array so that elements smaller than the pivot come before it, and elements larger come after. Then it sorts the smaller and larger parts separately.

beginner

What role does the 'pivot' play in Quick Sort?

The pivot is the element used to split the array into two parts: elements less than the pivot and elements greater than the pivot. It helps organize the array for sorting.

intermediate

Explain the partition step in Quick Sort.

Partitioning rearranges the array so that all elements smaller than the pivot come before it, and all larger elements come after it. The pivot ends up in its correct sorted position.

intermediate

What is the average time complexity of Quick Sort?

The average time complexity of Quick Sort is O(n log n), where n is the number of elements to sort.

beginner

Why can Quick Sort be faster than other sorting algorithms like Bubble Sort?

Quick Sort uses a divide and conquer approach, sorting parts of the array independently and efficiently, which usually leads to faster sorting than simple methods like Bubble Sort that compare elements one by one.

What does Quick Sort use to divide the array?

A A temporary array

B A pivot element

C A sorted list

D A linked list

Quick Sort uses a pivot element to divide the array into smaller and larger parts.

After partitioning, where is the pivot element placed?

A At its correct sorted position

B At the end of the array

C At the beginning of the array

D In a temporary variable

The pivot is placed at its correct sorted position after partitioning.

What is the worst-case time complexity of Quick Sort?

A O(n^2)

B O(n log n)

C O(log n)

D O(n)

The worst-case time complexity of Quick Sort is O(n^2), which happens when the pivot divides the array very unevenly.

Which sorting method does Quick Sort use?

A Brute force

B Dynamic programming

C Greedy algorithm

D Divide and conquer

Quick Sort uses the divide and conquer method to sort the array.

Which of these is NOT a step in Quick Sort?

A Choosing a pivot

B Partitioning the array

C Merging sorted arrays

D Recursively sorting subarrays

Quick Sort does not merge sorted arrays; merging is used in Merge Sort.

Describe how Quick Sort sorts an array step-by-step.

Think about how the array is split and sorted in parts.

Explain why Quick Sort is generally faster than simple sorting methods like Bubble Sort.

Focus on how Quick Sort handles the array compared to comparing elements one by one.

Practice

1. What is the main idea behind the Quick Sort algorithm?

easy

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

B. Compare every element with every other element and swap if needed

C. Insert elements one by one into a sorted list

D. Merge two sorted arrays into one sorted array

Solution

1. Step 1: Understand Quick Sort's approach

   Quick Sort picks a pivot element 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 them to get the sorted array.

3. Final Answer:

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

4. Quick Check:

   Quick Sort = Divide and conquer [OK]

Hint: Remember: Quick Sort uses a pivot to split and sort recursively [OK]

Common Mistakes:

• Confusing Quick Sort with Bubble Sort
• Thinking Quick Sort merges arrays like Merge Sort
• 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. int partition(int arr[], int low, int high);

C. void partition(int arr[], int low, int high);

D. int partition(int arr[], int start, int end, int pivot);

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: Confirm return type

   It returns an integer index of the pivot after partitioning.

3. Final Answer:

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

4. Quick Check:

   Partition returns pivot index [OK]

Hint: Partition returns pivot index; use array and low, high indices [OK]

Common Mistakes:

• Using void return type for partition
• Passing array as int instead of int[]
• Adding extra parameters like pivot

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

medium

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

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

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

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

Solution

1. Step 1: Apply Quick Sort logic on the array

   Quick Sort rearranges elements around pivots recursively, sorting the array in ascending order.

2. Step 2: Sort the given array

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

3. Final Answer:

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

4. Quick Check:

   Sorted array ascending = [1,1,2,3,6,8,10] [OK]

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

Common Mistakes:

• Assuming Quick Sort keeps original order
• Confusing ascending with descending order
• Not sorting duplicates correctly

4. Identify the error in this Quick Sort partition function 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. Variable i should start at low - 1, not low

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

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

D. Swap function is called with wrong arguments

Solution

1. Step 1: Check initialization of i

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

2. Step 2: Analyze loop and swaps

   Starting i at low causes skipping the first element comparison and wrong swaps.

3. Final Answer:

   Variable i should start at low - 1, not low -> Option A

4. Quick Check:

   i = low - 1 fixes partition indexing [OK]

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

Common Mistakes:

• Starting i at low causes incorrect partitioning
• Changing pivot position unnecessarily
• Extending loop beyond high index

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

hard

A. Use Bubble Sort instead for duplicates

B. Always choose the first element as pivot

C. Skip sorting duplicates by checking equality before partition

D. Use 3-way partitioning to separate less than, equal to, and greater than pivot

Solution

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

   Standard Quick Sort can degrade with many duplicates due to repeated swaps and partitions.

2. Step 2: Apply 3-way partitioning

   3-way partitioning divides array into three parts: less than, equal to, and greater than pivot, reducing unnecessary work.

3. Final Answer:

   Use 3-way partitioning to separate less than, equal to, and greater than pivot -> Option D

4. Quick Check:

   3-way partitioning optimizes duplicates [OK]

Hint: 3-way partitioning handles duplicates efficiently [OK]

Common Mistakes:

• Choosing fixed pivot without randomization
• Skipping duplicates without partitioning
• Switching to slower sorts unnecessarily