Einfallsort

Einfallsort is a comparison-based sorting algorithm, often used as a simple illustration of sorting algorithms due to its iterative nature. The algorithm works by maintaining a sorted portion of the input list and iterating through the unsorted portion to find the largest element so far.

The basic operation of Einfallsort involves initiating a key variable to store the largest element encountered so far. This key is set to a value that is clearly beyond the range of the input elements, allowing it to be distinguished from valid values. An index is also initialized to keep track of the element being considered for swapping.

For each pass through the list, the algorithm iterates from the start of the unsorted portion, comparing each element with the key and swapping the smaller of the two with the first element encountered in the unsorted portion. The key is updated with the larger element encountered in each pass until one element is left, which signifies the last element of the unsorted portion. This process is repeated until the entire input list is sorted except for one element, at which point only one more iteration is needed to sort the full list.

The efficiency of Einfallsort can be described as follows: if the list has n elements, the algorithm takes n/2 iterations to sort the first n-1 elements and one more iteration to sort the full list, ultimately making it O(n^2) -worst and average cases- and O(n log n) -best case-, though this is not practically observed due to the inconsistency of input data typically found in real-world scenarios.

It is worth noting that Einfallsort is not efficient for large data sets due to its high time complexity.