How does the insertion sort algorithm function?

The insertion sort algorithm sorts a list by building a sorted array one item at a time.

The insertion sort algorithm is a simple sorting algorithm that works similarly to how you might sort playing cards in your hand. It starts with the second element in the list, comparing it with the first. If the second element is smaller, it swaps places with the first. The algorithm then moves to the next element, comparing it with all the elements before it, and swapping places until it finds its correct position. This process is repeated until the entire list is sorted.

The algorithm can be visualised as dividing the list into a sorted and an unsorted region. The sorted region starts with the first element, and with each iteration, one element from the unsorted region is placed into its correct position within the sorted region. This continues until there are no more elements in the unsorted region, and the entire list is sorted.

The insertion sort algorithm is efficient for small lists or for lists that are already partially sorted. However, for larger lists, the time complexity of insertion sort can be a disadvantage. The worst-case scenario, where the list is sorted in reverse order, has a time complexity of O(n^2), as each element must be compared with every other element. The best-case scenario, where the list is already sorted, has a time complexity of O(n), as each element only needs to be compared once.

In terms of space complexity, insertion sort is very efficient, as it only requires a single additional memory space for the element being sorted. This makes it an in-place sorting algorithm, as it does not require any extra space proportional to the size of the input list.

In conclusion, while insertion sort may not be the most efficient sorting algorithm for large lists, its simplicity and efficiency for small or partially sorted lists make it a useful tool in a programmer's toolkit.