Sorting algorithms are really helpful when we want to put data in a certain order, like from smallest to largest or from A to Z. Two of the simplest sorting methods are Bubble Sort and Selection Sort. Let’s take a closer look at how they work and how they are different!

Bubble Sort: The Basics

Bubble Sort is an easy sorting method. It checks two numbers that are next to each other in a list and swaps them if they are not in the right order. This keeps happening until everything is sorted.

Let’s say we have a list of numbers, like this:

Example:

[5, 3, 8, 4, 2]

1. First Round: Compare 5 and 3. Since 5 is bigger than 3, swap them.
   • New list: [3, 5, 8, 4, 2]
2. Compare 5 and 8. No swap needed.
3. Compare 8 and 4. Swap them.
   • New list: [3, 5, 4, 8, 2]
4. Compare 8 and 2. Swap them.
   • New list: [3, 5, 4, 2, 8]
5. Second Round: Keep doing this until the whole list is sorted.

Selection Sort: The Basics

Selection Sort works a bit differently. It splits the list into two parts: one part that is sorted and another that isn’t. The sorted part starts off empty. The algorithm picks the smallest number from the unsorted part and moves it to the end of the sorted part.

Example:
Using the same list

[5, 3, 8, 4, 2]

1. First, it looks for the smallest number (which is 2) and swaps it with the first number (5).

   • New list: [2, 3, 8, 4, 5]

2. Next, it finds the smallest number in the remaining unsorted part [3, 8, 4, 5] (which is 3) and leaves it there.

   • New list: [2, 3, 8, 4, 5]

3. This continues until everything is sorted.

Key Differences Between Bubble Sort and Selection Sort

1. How They Sort:

   • Bubble Sort: Keeps comparing next to each other and swapping when needed.
   • Selection Sort: Picks the smallest number and adds it to the sorted part.

2. Speed:

   • Bubble Sort: Usually slower and needs more swaps.
   • Selection Sort: Faster when it comes to swaps but can take longer because it has to find the smallest number over and over.

3. Complexity:

   • Both sorting methods have a time complexity of $O(n^2)$ if you look at the average and worst cases, but they work in very different ways.

4. Stability:

   • Bubble Sort: Is stable (if two numbers are the same, they keep their original order).
   • Selection Sort: Is not stable (equal numbers might change places).

In conclusion, while Bubble Sort and Selection Sort are both basic sorting methods great for beginners, each has its own way of sorting and speed. Choosing one over the other depends on what you need. Both are good ways to learn about algorithms. Happy sorting!