One algorithm we can talk about is the mergesort algorithm. It is an algorithm that uses a technique known as divide-and-conquer which breaks down a problem into smaller pieces. This breaking down process makes it more efficient in solving each individual problem separately.

It is a recursive algorithm which continuously splits an array in half until it cannot be further divided. So this means The base case to stop the recursion is when there is either no elements in the array or at least one element. However if the array has multiple elements, split the array into halves and recursively invoke the merge sort on each of the halves. Lastly, when both halves are sorted, the merge operation is applied. Merge operation is a action of taking two smaller sorted arrays and combining them to eventually make a larger one. In the end each piece merges to create a new sorted array.

Merge sort has a time complexity of O(n log n), making it a good choice for sorting large lists. It is a stable sort, meaning that the relative order of elements with equal keys is preserved by the sort. Merge sort is also an example of a divide-and-conquer algorithm.

Quicksort is an efficient sorting algorithm that like mergesort uses a divide-and-conquer approach to sort a list of items. It works by selecting a "pivot" element from the list, and partitioning the other elements into two lists based on whether they are less than or greater than the pivot. The two sublists are then recursively sorted using the same quicksort algorithm.

Quicksort has a time complexity of O(n log n), making it a fast and efficient sorting algorithm for large lists. However, it is not a stable sort, meaning that the relative order of elements with equal keys may be changed by the sort. Read about Stable Sorts at FreeCodeCamp

Selection sort works by repeatedly finding the minimum element from the unsorted part of the list and adding it to the sorted part of the list. In every iteration of selection sort, the minimum element (given ascending order) from the unsorted subarray is picked and moved to the beginning of unsorted subarray. After every iteration the sorted subarray size increases by one and the unsorted subarray size decrease by one.

Selection sort has a time complexity of O(n^2), making it less efficient than other sorting algorithms for large lists. However, it has the advantage of being simple to implement and requiring a small amount of additional memory. Selection sort is not a stable sort, meaning that the relative order of elements with equal keys may be changed by the sort.

A linked list is a linear data structure in which each element is a separate object, consisting of a node and a reference (link) to the next node in the sequence. The main advantage of linked lists over arrays is that elements can be inserted or removed from the list without reallocation or reorganization of the entire structure. However, linked lists require more memory overhead to store the references, so they are less efficient for cases where the size of the list is fixed or the majority of operations are element access rather than insertion or deletion. The size flexibility in linked lists can make them use less memory overall. This is useful when there is uncertainty about size or there are large variations in the size of data elements.