๐ Topic Summary
Quick Sort is a highly efficient sorting algorithm that uses a divide-and-conquer strategy. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted. Choosing a good pivot is crucial for Quick Sort's performance. A poor pivot choice can lead to worst-case $O(n^2)$ time complexity, while a good pivot results in average-case $O(n \log n)$ time complexity.
The process continues until the entire array is sorted. Quick Sort is known for its speed and efficiency, making it a popular choice for sorting large datasets. However, its performance can vary significantly depending on the pivot selection strategy.
๐ง Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Pivot |
A. Dividing a problem into smaller subproblems |
| 2. Partitioning |
B. An algorithm that calls itself to solve smaller instances of the same problem. |
| 3. Divide and Conquer |
C. Rearranging elements in an array so that elements smaller than the pivot are before it, and elements greater are after it. |
| 4. Recursion |
D. The average time complexity of Quick Sort with a good pivot selection. |
| 5. $O(n \log n)$ |
E. An element chosen from the array to divide it into two sub-arrays. |
(Answers: 1-E, 2-C, 3-A, 4-B, 5-D)
โ๏ธ Part B: Fill in the Blanks
Fill in the missing words in the paragraph below:
Quick Sort is a ________ algorithm that uses a ________-and-________ strategy. It selects a ________ element and ________ the array around it. The performance of Quick Sort depends heavily on choosing a good ________.
(Answers: sorting, divide, conquer, pivot, partitions, pivot)
๐ค Part C: Critical Thinking
Explain how the choice of pivot affects the performance of Quick Sort. What strategies can be used to select a good pivot, and why are they effective?