What is the average time complexity of the Quick Sort algorithm?
Practice Questions
Q1
What is the average time complexity of the Quick Sort algorithm?
O(n)
O(n log n)
O(n^2)
O(log n)
Questions & Step-by-Step Solutions
What is the average time complexity of the Quick Sort algorithm?
Step 1: Understand what time complexity means. It measures how the time to complete an algorithm grows as the size of the input (n) increases.
Step 2: Learn about Quick Sort. It is a sorting algorithm that works by dividing the array into smaller parts (sub-arrays) and sorting them.
Step 3: Recognize that Quick Sort uses a method called 'divide-and-conquer'. This means it breaks the problem into smaller problems, solves them, and combines the results.
Step 4: In Quick Sort, the average case occurs when the pivot (the element used to divide the array) splits the array into two roughly equal parts.
Step 5: When the array is divided into two parts, the algorithm needs to sort both parts. This leads to a logarithmic number of divisions (log n).
Step 6: Each division requires going through all n elements to place them in the correct part, which takes linear time (n).
Step 7: Combine the two parts: The average time complexity is calculated as n (for the elements) multiplied by log n (for the divisions), resulting in O(n log n).
