Considering a deck of N playing cards with X different rankings and Y different suits (i.e. there are Y cards with X ranking, thus N=X*Y). What is the fastest algorithm to sort them assuming that X, Y, and N will be known at run-time and may be passed as parameters into the algorithm? Can we beat the performance of quicksort or heapsort given that we already know everything about the data being sorted in advance? Of the fastest algorithms which one(s) require the least amount of memory?Motivations & ApplicationIn response to the comments, obviously, in software if we already know what we want the final arrangement to look like, sorting becomes trivial because we can just generate a new deck. However, I'm asking this question specifically because I'm interested in the means, not the goal. This problem can pop up when trying to generate a list of instructions for sorting a physical deck, or when each card contains a data structure with pointers to unique data that must be sorted along with the cards that can't be derived from the card's suit and rank.
What algorithm would have the fastest average run time and least memory requirements for sorting a deck of playing cards?
algorithms
You should be able to so this with a form of Bucket Sort in O(N) time.  Create an array of cards with N elements (buckets), with each bucket initialized to empty1Iterate the cardsexamine card calculate bucket number as card rank + X * card suitput card into bucketIn one pass, you can place all cards into the correct bucket.  The sort time is O(N).You can also do the sorting in-place with O(1) additional memory.  Like the old Clock Patience game ...1 - Initialization is not strictly necessary, provided that the card deck is complete.