Describe the strand sort algorithm.

The strand sort algorithm is a comparison-based sorting algorithm that operates by repeatedly extracting sorted subsequences from the input list and merging them together until the entire list is sorted. It was first proposed by Donald Knuth in 1973.

The algorithm begins by initializing an empty output list and a working list, which initially contains all the elements from the input list. It then proceeds with the following steps:

1. Find the longest increasing subsequence (LIS) in the working list. This can be done by iterating through the list and appending each element to a temporary subsequence if it is greater than the last element in the subsequence. If not, the subsequence is considered complete and is removed from the working list.

2. Append the LIS to the output list.

3. Remove the elements of the LIS from the working list.

4. Repeat steps 1-3 until the working list is empty.

5. The output list now contains the sorted elements.

The key idea behind the strand sort algorithm is to repeatedly find and extract the LIS from the working list, which guarantees that each subsequence appended to the output list is sorted. By merging these sorted subsequences together, the algorithm eventually produces a fully sorted list.

One advantage of the strand sort algorithm is that it is stable, meaning that the relative order of equal elements is preserved. This can be useful in certain applications where the original order of equal elements is important.

However, the strand sort algorithm has a time complexity of O(n^2), where n is the number of elements in the input list. This makes it less efficient than other sorting algorithms such as quicksort or mergesort, which have average time complexities of O(n log n). Therefore, the strand sort algorithm is not commonly used in practice for large datasets.

In summary, the strand sort algorithm is a comparison-based sorting algorithm that repeatedly extracts sorted subsequences from the input list and merges them together until the entire list is sorted. It is stable but less efficient than other sorting algorithms for large datasets.