Quicksort Algorithm Overview

Quicksort Algorithm Steps

• The algorithm picks a pivot element from an array.
• It partitions the array around the pivot such that all numbers smaller than the pivot are placed to the left of the pivot.
• All numbers greater than the pivot are placed to the right of the pivot.
• Recursively apply steps 1 to 3 to the sub-arrays to the left and right of the pivot.

Partition Step

• The pivot element is fixed at the end of the array.
• Initialize left at the beginning of the array.
• Initialize right one position before the pivot.
• While left is less than right, the algorithm checks the following:
  • If data[left] is greater than data[pivot] and data[right] is greater than data[pivot], then decrement right.
  • If data[left] is greater than data[pivot] and data[right] is less than or equal to data[pivot], then swap data[left] and data[right], and increment left and decrement right.
  • If data[left] is less than or equal to data[pivot] and data[right] is less than or equal to data[pivot], then increment left.
  • If data[left] is less than or equal to data[pivot] and data[right] is greater than data[pivot], then decrement right.
• Swap data[right] with data[pivot] to place the pivot element in its correct position.

Quicksort Analysis

• The best-case running time of the quicksort algorithm is O(n log₂n).
• The worst-case running time of the quicksort algorithm is O(n²).
• In the best case, the pivot element always partitions the array into two sub-arrays of approximately equal size. This results in a balanced recursion tree with a depth of O(log₂n).
• In the worst case, the pivot element results in an unbalanced partition, where one sub-array is always empty. This leads to a linear depth recursion tree, resulting in O(n²) time complexity.
• Randomly selecting a pivot element is a strategy to avoid the worst-case scenario where the pivot element is always the smallest or the largest element in the array.

Insertion Sort

• Insertion sort is a simple sorting algorithm that works by iterating through the array, inserting each element into its correct position in the sorted subarray.
• The algorithm maintains two subarrays: a sorted subarray and an unsorted subarray.
• The sorted subarray is initially empty, and the unsorted subarray is the entire input array.
• In each iteration, the algorithm takes the first element from the unsorted subarray and inserts it into the sorted subarray at the correct position.
• The algorithm repeats this process until the unsorted subarray is empty.

Selection Sort

• Selection sort works by repeatedly finding the minimum element from the unsorted part of the array and swapping it with the element at the beginning of the unsorted part.
• The algorithm maintains two subarrays: a sorted subarray and an unsorted subarray.
• The sorted subarray is initially empty and the unsorted subarray is the entire input array.
• In each iteration, the algorithm finds the minimum element from the unsorted subarray and swaps it with the element at the beginning of the unsorted subarray.
• The algorithm repeats this process until the unsorted subarray is empty.

This quiz covers the essential steps of the Quicksort algorithm, including how to select a pivot and partition an array. Test your understanding of how the algorithm recursively organizes data into sorted order. Perfect for computer science students looking to master sorting algorithms.