An Introduction to Computational Combinatorics
By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.
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adjacency matrix algorithm B-list backtrack program begin integer branch and bound cells chapter choice list classical assignment problem column combinations Combinatorial complete vector compositions Consider contains correct successors cost matrix derive difference equation distinct representatives dynamic programming elements end end enumerator Euler circuit Euler path example expression factor factorial representation Ferrers graph give given graph G Hence incidence matrix indicial equation integer array integer value lexicographical order machine male optimal stable method minimum n+1 n n n+2 n+1 Newcastle node number of lines number of partitions number of permutations obtained operations optimal stable solution optimum order equation pair particular solution path points polynomial positive integers possible procedure proposal r-combinations r-permutations Ramsey's theorem random permutation recurrence relation result root selected sequence solve spanning tree stable marriage stage Step subsets symbols systems of distinct theorem undirected graph unknown function variable zeros