Patience sorting

In computer science, patience sorting is a sorting algorithm inspired by, and named after, the card game patience. A variant of the algorithm efficiently computes the length of a longest increasing subsequence in a given array.

Overview

The algorithm's name derives from a simplified variant of the patience card game. This game begins with a shuffled deck of cards. These cards are dealt one by one into a sequence of piles on the table, according to the following rules.

This card game is turned into a two-phase sorting algorithm, as follows. Given an array of n elements from some totally ordered domain, consider this array as a collection of cards and simulate the patience sorting game. When the game is over, recover the sorted sequence by repeatedly picking off the minimum visible card; in order words, perform an p-way merge of the p piles, each of which is internally sorted.