Question

Draw a diagram that shows the contents of the array 87654 after each number is moved in a bubble sort, until the 8 arrives at the end of the array.

Short answer

Array after each move: [8, 7, 6, 5, 4]; [7, 8, 6, 5, 4]; [7, 6, 8, 5, 4]; [7, 6, 5, 8, 4]; [7, 6, 5, 4, 8]

Step-by-step solution

- Initial Array

Start with the initial array: [8, 7, 6, 5, 4]

- First Swap

Compare the first two elements (8 and 7). Since 8 is greater than 7, swap them. Array: [7, 8, 6, 5, 4]

- Second Swap

Compare the next pair (8 and 6). Since 8 is greater than 6, swap them. Array: [7, 6, 8, 5, 4]

- Third Swap

Compare the next pair (8 and 5). Since 8 is greater than 5, swap them. Array: [7, 6, 5, 8, 4]

- Fourth Swap

Compare the next pair (8 and 4). Since 8 is greater than 4, swap them. Array: [7, 6, 5, 4, 8]

- First Position of 8

At this point, 8 has reached the end of the array. Array: [7, 6, 5, 4, 8]

Key concepts

Sorting Algorithms

When dealing with data, sorting algorithms are essential to arrange the data in a specific order. Bubble sort is one of the simplest sorting algorithms. It repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.
Despite its simplicity, bubble sort is not frequently used for large datasets as it has a time complexity of \(O(n^2)\). However, it's an excellent way to introduce basic sorting concepts and get familiar with algorithmic thinking.

Bubble sort can work for arrays or linked lists and ensures the largest element moves to the end of the list in each pass, but many rounds are often required to fully sort the list.

Array Manipulation

Manipulating an array to sort it using bubble sort involves multiple swaps. These swaps are necessary to place elements in the right order step by step. In the given exercise, here's how the array changes in each step:

• Initial Array: [8, 7, 6, 5, 4]
• After 1st Swap: [7, 8, 6, 5, 4]
• After 2nd Swap: [7, 6, 8, 5, 4]
• After 3rd Swap: [7, 6, 5, 8, 4]
• After 4th Swap: [7, 6, 5, 4, 8]
• First Position of 8: [7, 6, 5, 4, 8]

Each of these steps involves comparing elements and swapping them only if the previous element is greater than the next one. By swapping adjacent elements repeatedly, bubble sort pushes larger elements to the end of the array first.

Step-by-step Guide

Understanding bubble sort through a step-by-step guide can make it much easier.

Let's break down each step for clarity:

• Step 1: Start with the initial array: [8, 7, 6, 5, 4]
• Step 2: Compare the first two elements (8 and 7). Since 8 is greater than 7, swap them. Now the array is [7, 8, 6, 5, 4]
• Step 3: Compare the next pair (8 and 6). Since 8 is greater than 6, swap them. Now the array is [7, 6, 8, 5, 4]
• Step 4: Compare the next pair (8 and 5). Since 8 is greater than 5, swap them. Now the array is [7, 6, 5, 8, 4]
• Step 5: Compare the last pair (8 and 4). Since 8 is greater than 4, swap them. Now the array is [7, 6, 5, 4, 8]

At this point, the largest number, 8, has reached its final position at the end of the array, demonstrating the fundamental principle of bubble sorting.