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　　曆經十年數百所高校教學實踐的算法入門經典。算法是思維的藝術，是數學之美的完美體現，是計算機和信息科學的靈魂，更是優秀程序員的安身立命之本。《算法設計與分析基礎 (第3版）（影印版）》將算法視為解決問題的工具，通過作者獨創的、具有裏程碑意義的新型分類法彌補瞭傳統算法設計技術分類法的缺陷，用深入淺齣的語言和新穎的實例與謎題，詮釋瞭何為算法、算法的分類、算法幕後的思想、算法的效率，抽絲剝繭、條分縷析地探索瞭算法設計與分析過程。

內容簡介

　　《算法設計與分析基礎 （第3版）（影印版）》在講述算法設計技術時采用瞭新的分類方法，在討論分析方法時條分縷析，形成瞭連貫有序、耳目一新的風格。為便於學生掌握，本書涵蓋算法入門課程的全部內容，更注重對概念(而非形式)的理解。書中通過一些流行的謎題來激發學生的興趣，幫助他們加強和提高解決算法問題的能力。每章小結、習題提示和詳細解答，形成瞭非常鮮明的教學特色。

作者簡介

　　Anany Levitin博士，美國維拉諾瓦大學教授，畢業於莫斯科國立大學並獲得數學碩士學位。他擁有耶路撒冷希伯來大學數學博士學位和美國肯塔基大學計算機科學碩士學位。他的著作《算法設計與分析基礎》已經被翻譯為中文、俄文、希臘文和韓文，並被全球數百所高校廣泛用作教材。目前，Levitin博士在美國維拉諾瓦大學講授“算法設計與分析”課程。他的另一本著作《算法謎題》已經於2011年鞦齣版。
　　Anany Levitin，美籍猶太人，維拉諾瓦大學（Villanova）計算機科學係教授。他的論文“算法設計技術新途徑：彌補傳統分類法的缺憾”(A New Road Mpa of Algorithm Design Techniques： Picking Up Where the Traditional Classfication Leaves Off)深受業內好評，並享有廣泛的聲譽。他提齣的這種新分類方法涵蓋眾多經典算法，開創瞭傳統分類無法以一緻方式介紹這些算法的先河。作為通用的問題解決工具，算法設計技術的應用很廣，尤其適用於解決“狼，羊，白菜”問題和旅行商問題之類的流行謎題。
　　因為他對算法教育所做齣的傑齣貢獻，Levitin教授曾多次受邀在SIGCSE(Computer Science Education，計算機教育) 全球大會上發錶演講，此大會每三年纔舉行一次。
　　Anany Levitin教授目前的研究課題為“Do We Teach the Right Algorithm Design Techniques ？”

目錄

New to the Third Edition xvii
Preface xix
1Introduction
1.1 What Is an Algorithm?
Exercises 1.1
1.2 Fundamentals of Algorithmic Problem Solving
Understanding the Problem
Ascertaining the Capabilities of the Computational Device
Choosing between Exact and Approximate Problem Solving
Algorithm Design Techniques
Designing an Algorithm and Data Structures
Methods of Specifying an Algorithm
Proving an Algorithm's Correctness
Analyzing an Algorithm
Coding an Algorithm
Exercises 1.2
1.3 Important Problem Types
Sorting
Searching
String Processing
Graph Problems
Combinatorial Problems
Geometric Problems
Numerical Problems
Exercises 1.3
1.4 Fundamental Data Structures
Linear Data Structures
Graphs
Trees
Sets and Dictionaries
Exerises 1.4
Summary
2 Fundamentals of the Analysis of Algorithm Efficiency
2.1 The Analysis Framework
Measuring an Input's Size
Units for Measuring Running Time
Orders of Growth
Worst-Case, Best-Case, and Average-Case Efficiencies
Recapitulation of the Analysis Framework
Exercises 2.1
2.2 Asymptotic Notations and Basic Efficiency Classes
Informal Introduction
O-notation
-notation
-notation
Useful Property Involving the Asymptotic Notations
Using Limits for Comparing Orders of Growth
Basic Efficiency Classes
Exercises 2.2
2.3 Mathematical Analysis of Nonrecursive Algorithms
Exercises 2.3
2.4 Mathematical Analysis of Recursive Algorithms
Exercises 2.4
2.5 Example: Computing the nth Fibonacci Number
Exercises 2.5
2.6 Empirical Analysis of Algorithms
Exercises 2.6
2.7 Algorithm Visualization
Summary
3 Brute Force and Exhaustive Search
3.1 Selection Sort and Bubble Sort
Selection Sort
Bubble Sort
Exercises 3.1
3.2 Sequential Search and Brute-Force String Matching
Sequential Search
Brute-Force String Matching
Exercises 3.2
3.3 Closest-Pair and Convex-Hull Problems by Brute Force
Closest-Pair Problem
Convex-Hull Problem
Exercises 3.3
3.4 Exhaustive Search
Traveling Salesman Problem
Knapsack Problem
Assignment Problem
Exercises 3.4
3.5 Depth-First Search and Breadth-First Search
Depth-First Search
Breadth-First Search
Exercises 3.5
Summary
4 Decrease-and-Conquer
4.1 Insertion Sort
Exercises 4.1
4.2 Topological Sorting
Exercises 4.2
4.3 Algorithms for Generating Combinatorial Objects
Generating Permutations
Generating Subsets
Exercises 4.3
4.4 Decrease-by-a-Constant-Factor Algorithms
Binary Search
Fake-Coin Problem
Russian Peasant Multiplication
Josephus Problem
Exercises 4.4
4.5 Variable-Size-Decrease Algorithms
Computing a Median and the Selection Problem
Interpolation Search
Searching and Insertion in a Binary Search Tree
The Game of Nim
Exercises 4.5
Summary
5 Divide-and-Conquer
5.1 Mergesort
Exercises 5.1
5.2 Quicksort
Exercises 5.2
5.3 Binary Tree Traversals and Related Properties
Exercises 5.3
5.4 Multiplication of Large Integers and
Strassen's Matrix Multiplication
Multiplication of Large Integers
Strassen's Matrix Multiplication
Exercises 5.4
5.5 The Closest-Pair and Convex-Hull Problems
by Divide-and-Conquer
The Closest-Pair Problem
Convex-Hull Problem
Exercises 5.5
Summary
6 Transform-and-Conquer
6.1 Presorting
Exercises 6.1
6.2 Gaussian Elimination
LU Decomposition
Computing a Matrix Inverse
Computing a Determinant
Exercises 6.2
6.3 Balanced Search Trees
AVL Trees
2-3 Trees
Exercises 6.3
6.4 Heaps and Heapsort
Notion of the Heap
Heapsort
Exercises 6.4
6.5 Horner's Rule and Binary Exponentiation
Horner's Rule
Binary Exponentiation
Exercises 6.5
6.6 Problem Reduction
Computing the Least Common Multiple
Counting Paths in a Graph
Reduction of Optimization Problems
Linear Programming
Reduction to Graph Problems
Exercises 6.6
Summary
7 Space and Time Trade-Offs
7.1 Sorting by Counting
Exercises 7.1
7.2 Input Enhancement in String Matching
Horspool's Algorithm
Boyer-Moore Algorithm
Exercises 7.2
7.3 Hashing
Open Hashing (Separate Chaining)
Closed Hashing (Open Addressing)
Exercises 7.3
7.4 B-Trees
Exercises 7.4
Summary
8 Dynamic Programming
8.1 Three Basic Examples
Exercises 8.1
8.2 The Knapsack Problem and Memory Functions
Memory Functions
Exercises 8.2
8.3 Optimal Binary Search Trees
Exercises 8.3
8.4 Warshall's and Floyd's Algorithms
Warshall's Algorithm
Floyd's Algorithm for the All-Pairs Shortest-Paths Problem
Exercises 8.4
Summary
9 Greedy Technique
9.1 Prim's Algorithm
Exercises 9.1
9.2 Kruskal's Algorithm
Disjoint Subsets and Union-Find Algorithms
Exercises 9.2
9.3 Dijkstra's Algorithm
Exercises 9.3
9.4 Huffman Trees and Codes
Exercises 9.4
Summary
10 Iterative Improvement
10.1 The Simplex Method
Geometric Interpretation of Linear Programming
An Outline of the Simplex Method
Further Notes on the Simplex Method
Exercises 10.1
10.2 The Maximum-Flow Problem
Exercises 10.2
10.3 Maximum Matching in Bipartite Graphs
Exercises 10.3
10.4 The Stable Marriage Problem
Exercises 10.4
Summary
11 Limitations of Algorithm Power
11.1 Lower-Bound Arguments
Trivial Lower Bounds
Information-Theoretic Arguments
Adversary Arguments
Problem Reduction
Exercises 11.1
11.2 Decision Trees
Decision Trees for Sorting
Decision Trees for Searching a Sorted Array
Exercises 11.2
11.3 P, NP, and NP-Complete Problems
P and NP Problems
NP-Complete Problems
Exercises 11.3
11.4 Challenges of Numerical Algorithms
Exercises 11.4
Summary
12 Coping with the Limitations of Algorithm Power
12.1 Backtracking
n-Queens Problem
Hamiltonian Circuit Problem
Subset-Sum Problem
General Remarks
Exercises 12.1
12.2 Branch-and-Bound
Assignment Problem
Knapsack Problem
Traveling Salesman Problem
Exercises 12.2
12.3 Approximation Algorithms for NP-Hard Problems
Approximation Algorithms for the Traveling Salesman Problem
Approximation Algorithms for the Knapsack Problem
Exercises 12.3
12.4 Algorithms for Solving Nonlinear Equations
Bisection Method
Method of False Position
Newton's Method
Exercises 12.4
Summary
Epilogue
APPENDIX A
Useful Formulas for the Analysis of Algorithms
Properties of Logarithms
Combinatorics
Important Summation Formulas
Sum Manipulation Rules
Approximation of a Sum by a Definite Integral
Floor and Ceiling Formulas
Miscellaneous
APPENDIX B
Short Tutorial on Recurrence Relations
Sequences and Recurrence Relations
Methods for Solving Recurrence Relations
Common Recurrence Types in Algorithm Analysis
References
Hints to Exercises
Index

前言/序言

　　“一個人接受科技教育時所能獲得的最珍貴的收獲，是那些能夠受用終身的通用智能工具 。”
　　——George Forsythe，What to do till the computer scientist comes，1968
　　無論是計算科學還是計算實踐，算法都在其中扮演著重要角色。因此，這門學科中齣現瞭大量的教材。它們在介紹算法的時候，基本上都選擇瞭以下兩種方案中的一種。第一種方案是按照問題的類型對算法分類。這類教材安排瞭不同的章節分彆討論排序、查找、圖等算法。這種做法的優點是，對於解決同一問 算法設計與分析基礎 （第3版）（影印版） 下載 mobi epub pdf txt 電子書

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