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The travelling salesman problem (TSP) asks the following question: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.

Quick Sort

http://en.wikipedia.org/wiki/Quicksort

Insertion Sort

Counting Sort

http://en.wikipedia.org/wiki/Counting_sort

Selection Algorithm

Finds the kth largest item in a sequence.

Heap Sort

The longest common subsequence

The longest common subsequence (LCS) problem is to find the longest subsequence common to all sequences in a set of sequences (often just two). (Note that a subsequence is different from a substring, for the terms of the former need not be consecutive terms of the original sequence.) It is a classic computer science problem, the basis of file comparison programs such as diff, and has applications in bioinformatics.