算法导论

Introduction to Algorithms（MIT教材）

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本书自第一版出版以来，已经成为世界范围内广泛使用的大学教材和专业人员的标准参考手册。本书全面论述了算法的内容，从一定深度上涵盖了算法的诸多方面，同时其讲授和分析方法又兼顾了各个层次读者的接受能力。各章内容自成体系，可作为独立单元学习。所有算法都用英文和伪码描述，使具备初步编程经验的人也可读懂。全书讲解通俗易懂，且不失深度和数学上的严谨性。

Topics covered: Overview of algorithms (including algorithms as a technology); designing and analyzing algorithms; asymptotic notation; recurrences and recursion; probabilistic analysis and randomized algorithms; heapsort algorithms; priority queues; quicksort algorithms; linear time sorting (including radix and bucket sort); medians and order statistics (including minimum and maximum); introduction to data structures (stacks, queues, linked lists, and rooted trees); hash tables (including hash functions); binary search trees; red-black trees; augmenting data structures for custom applications; dynamic programming explained (including assembly-line scheduling, matrix-chain multiplication, and optimal binary search trees); greedy algorithms (including Huffman codes and task-scheduling problems); amortized analysis (the accounting and potential methods); advanced data structures (including B-trees, binomial and Fibonacci heaps, representing disjoint sets in data structures); graph algorithms (representing graphs, minimum spanning trees, single-source shortest paths, all-pairs shortest paths, and maximum flow algorithms); sorting networks; matrix operations; linear programming (standard and slack forms); polynomials and the Fast Fourier Transformation (FFT); number theoretic algorithms (including greatest common divisor, modular arithmetic, the Chinese remainder theorem, RSA public-key encryption, primality testing, integer factorization); string matching; computational geometry (including finding the convex hull); NP-completeness (including sample real-world NP-complete problems and their insolvability); approximation algorithms for NP-complete problems (including the traveling salesman problem); reference sections for summations and other mathematical notation, sets, relations, functions, graphs and trees, as well as counting and probability backgrounder (plus geometric and binomial distributions).