Data Structures and Algorithms 1: Sorting and Searching
The design and analysis of data structures and efficient algorithms has gained considerable importance in recent years. The concept of "algorithm" is central in computer science, and "efficiency" is central in the world of money. I have organized the material in three volumes and nine chapters. Vol. 1: Sorting and Searching (chapters I to III) Vol. 2: Graph Algorithms and NP-completeness (chapters IV to VI) Vol. 3: Multi-dimensional Searching and Computational G- metry (chapters VII and VIII) Volumes 2 and 3 have volume 1 as a common basis but are indepen dent from each other. Most of volumes 2 and 3 can be understood without knowing volume 1 in detail. A general kowledge of algorith mic principles as laid out in chapter 1 or in many other books on algorithms and data structures suffices for most parts of volumes 2 and 3. The specific prerequisites for volumes 2 and 3 are listed in the prefaces to these volumes. In all three volumes we present and analyse many important efficient algorithms for the fundamental computa tional problems in the area. Efficiency is measured by the running time on a realistic model of a computing machine which we present in chapter I. Most of the algorithms presented are very recent inven tions; after all computer science is a very young field. There are hardly any theorems in this book which are older than 20 years and at least fifty percent of the material is younger than 10 years.
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algorithm amortized analysis amortized cost analysis array assume b)-tree balanced trees binary tree bucket coin tosses computation Concatenate construct-tree D-trees data structure decision tree defined denote depth double rotation edge element example extendible hashing fusing hash table Heapsort height-balanced trees hence i-th induction input insertions and deletions integer j-node j-th keys labelled leaf lemma linear lists log log lower bound matrix Mergesort method Note number of leaves number of nodes O(log O(n log obtain operation Access perfect hash function pointer polynomial priority queue problem proof of theorem pushdown store queue Quicksort random randomized algorithm rebalancing operations red-black trees root root balance sequence sorting splay trees split storage locations subproblems subtree SYMORD TA(p tion tree for set tw║ Union union-find unit cost measure weighted path length worst