Understanding Sorting Algorithms

Sorting algorithms are methods used to arrange items, like numbers or words, in a certain order. Here are some important ideas about them:

1. Stability: A sorting algorithm is called stable if it keeps things that are the same in the same order they started with.

   For instance, if you have a list of names and two people have the same name, a stable sort will keep them in the order they were in before sorting.

   A common stable sort is Merge Sort, while Quick Sort is not stable.

2. Time Complexity: This helps us understand how fast a sorting algorithm works. It’s usually shown with a notation called "big O" that describes how the time changes as the number of items gets bigger.

   • $O(n \log n)$ represents faster algorithms. Examples include Merge Sort and Heap Sort.
   • $O(n^2)$ represents slower ones like Bubble Sort and Insertion Sort.

3. Space Complexity: This tells us how much extra memory a sorting algorithm needs to run.

   Some algorithms, like Quick Sort, only need a little extra memory, shown as $O(\log n)$.

   On the other hand, Merge Sort needs more extra memory, represented as $O(n)$.

4. Adaptability: Some sorting algorithms work better when the data is almost sorted.

   For example, Insertion Sort can be really fast, with a time of $O(n)$, when the list is nearly in order.

These key points can help you understand how different sorting algorithms work and what makes them unique!