Python编程：数据结构与算法解析

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"数据结构与算法python版是Rance D. Necaise编著的一本英文教材，主要针对计算机科学领域，由John Wiley & Sons, Inc. 出版。该书涵盖了数据结构和算法的核心概念，并使用Python编程语言进行实现和解释。" 在计算机科学中，数据结构与算法是两个至关重要的概念，它们是编程和软件开发的基础。数据结构是指组织、存储和管理数据的方式，而算法是一系列解决问题或执行特定任务的精确步骤。Python作为一种流行的高级编程语言，因其简洁的语法和强大的库支持，常被用于教学和实践数据结构与算法。本书的内容可能包括以下部分： 1. **基础数据结构**：如数组、链表、栈、队列、散列表（哈希表）、树（二叉树、AVL树、红黑树等）和图。这些数据结构各有特点，适用于不同的场景，例如，栈用于回溯操作，队列处理先进先出（FIFO）的问题，哈希表提供快速查找功能，树和图则用于表示层次关系或网络连接。 2. **算法分析**：包括时间复杂度和空间复杂度分析，帮助读者理解算法运行效率。这涉及到大O符号表示法，用来描述算法运行时间随输入规模增长的趋势。 3. **排序和搜索算法**：如冒泡排序、选择排序、插入排序、快速排序、归并排序、堆排序以及二分查找、广度优先搜索（BFS）、深度优先搜索（DFS）等。这些算法在实际问题中广泛应用，如数据库查询优化、数据排序和问题求解。 4. **递归与动态规划**：递归是一种解决问题的方法，它将问题分解成更小的子问题，而动态规划则是通过储存和重用子问题的解来避免重复计算，提高效率。 5. **图论算法**：如最短路径问题（Dijkstra算法、Bellman-Ford算法）、最小生成树（Prim算法、Kruskal算法）等，这些算法在路由选择、网络优化等领域有广泛的应用。 6. **数据结构的实现**：通过Python代码演示如何创建和操作上述数据结构，使读者能够动手实践，加深理解。 7. **案例研究和应用**：可能包含实际问题的案例，展示如何运用数据结构和算法来解决这些问题，从而提升读者的编程和问题解决能力。通过阅读和学习这本书，读者不仅可以掌握数据结构与算法的基本概念，还能学会如何用Python高效地实现和应用它们，这对于提升编程技能和解决复杂问题的能力至关重要。此外，书中可能还包括习题和练习，帮助巩固理论知识并提高实战技能。

xiv PREFACE

basics” approach to learning data structures and algorithms without overwhelming

the reader with all of the OOP terminology and concepts, which is especially

important when the instructor has no plans to cover such topics. Second, diﬀerent

instructors take diﬀerent approaches with Python in their ﬁrst course. Our aim is

to provide an excellent text to the widest possible audience. We do this by placing

the focus on the data structures and algorithms, while designing the examples to

allow the introduction of object-oriented programming if so desired.

The text also introduces the concept of algorithm analysis and explores the

eﬃciency of algorithms and data structures throughout the text. The major pre-

sentation of complexity analysis is contained in a single chapter, which allows it to

be omitted by instructors who do not normally cover such material in their data

structures course. Additional evaluations are provided throughout the text as new

algorithms and data structures are introduced, with the major details contained in

individual sections. When algorithm analysis is covered, examples of the various

complexity functions are introduced, including amortized cost. The latter is im-

portant when using Python since many of the list operations have a very eﬃcient

amortized cost.

Prerequisites

This book assumes that the student has completed the standard introduction to

programming and problem-solving course using the Python language. Since the

contents of the ﬁrst course can diﬀer from college to college and instructor to

instructor, we assume the students are familiar with or can do the following:



Design and implement complete programs in Python, including the use of

modules and namespaces



Apply the basic data types and constructs, including loops, selection state-

ments, and subprograms (functions)



Create and use the built-in list and dictionary structures



Design and implement basics classes, including the use of helper methods and

private attributes

Contents and Organization

The text is organized into fourteen chapters and four appendices. The basic con-

cepts related to abstract data types, data structures, and algorithms are presented

in the ﬁrst four chapters. Later chapters build on these earlier concepts to present

more advanced topics and introduce the student to additional abstract data types

and more advanced data structures. The book contains several topic threads that

run throughout the text, in which the topics are revisited in various chapters as

appropriate. The layout of the text does not force a rigid outline, but allows for the

PREFACE xv

reordering of some topics. For example, the chapters on recursion and hashing can

be presented at any time after the discussion of algorithm analysis in Chapter 4.

Chapter 1: Abstract Data Types. Introduces the concept of abstract data types

(ADTs) for both simple types, those containing individual data ﬁelds, and the more

complex types, those containing data structures. ADTs are presented in terms

of their deﬁnition, use, and implementation. After discussing the importance of

abstraction, we deﬁne several ADTs and then show how a well-deﬁned ADT can

be used without knowing how its actually implemented. The focus then turns to

the implementation of the ADTs with an emphasis placed on the importance of

selecting an appropriate data structure. The chapter includes an introduction to

the Python iterator mechanism and provides an example of a user-deﬁned iterator

for use with a container type ADT.

Chapter 2: Arrays. Introduces the student to the array structure, which is im-

portant since Python only provides the list structure and students are unlikely to

have seen the concept of the array as a ﬁxed-sized structure in a ﬁrst course using

Python. We deﬁne an ADT for a one-dimensional array and implement it using a

hardware array provided through a special mechanism of the C-implemented ver-

sion of Python. The two-dimensional array is also introduced and implemented

using a 1-D array of arrays. The array structures will be used throughout the text

in place of the Python’s list when it is the appropriate choice. The implementa-

tion of the list structure provided by Python is presented to show how the various

operations are implemented using a 1-D array. The Matrix ADT is introduced and

includes an implementation using a two-dimensional array that exposes the stu-

dents to an example of an ADT that is best implemented using a structure other

than the list or dictionary.

Chapter 3: Sets and Maps. This chapter reintroduces the students to both

the Set and Map (or dictionary) ADTs with which they are likely to be familiar

from their ﬁrst programming course using Python. Even though Python provides

these ADTs, they both provide great examples of abstract data types that can be

implemented in many diﬀerent ways. The chapter also continues the discussion of

arrays from the previous chapter by introducing multi-dimensional arrays (those

of two or more dimensions) along with the concept of physically storing these

using a one-dimensional array in either row-major or column-major order. The

chapter concludes with an example application that can beneﬁt from the use of a

three-dimensional array.

Chapter 4: Algorithm Analysis. Introduces the basic concept and importance

of complexity analysis by evaluating the operations of Python’s list structure and

the Set ADT as implemented in the previous chapter. This information will be used

to provide a more eﬃcient implementation of the Set ADT in the following chapter.

The chapter concludes by introducing the Sparse Matrix ADT and providing a more

eﬃcient implementation with the use of a list in place of a two-dimensional array.

xvi PREFACE

Chapter 5: Searching and Sorting. Introduces the concepts of searching and

sorting and illustrates how the eﬃciency of some ADTs can be improved when

working with sorted sequences. Search operations for an unsorted sequence are

discussed and the binary search algorithm is introduced as a way of improving this

operation. Three of the basic sorting algorithms are also introduced to further

illustrate the use of algorithm analysis. A new implementation of the Set ADT is

provided to show how diﬀerent data structures or data organizations can change

the eﬃciency of an ADT.

Chapter 6: Linked Structures. Provides an introduction to dynamic structures

by illustrating the construction and use of the singly linked list using dynamic

storage allocation. The common operations — traversal, searching, insertion, and

deletion — are presented as is the use of a tail reference when appropriate. Several

of the ADTs presented in earlier chapters are reimplemented using the singly linked

list, and the run times of their operations are compared to the earlier versions.

A new implementation of the Sparse Matrix is especially eye-opening to many

students as it uses an array of sorted linked lists instead of a single Python list as

was done in an earlier chapter.

Chapter 7: Stacks. Introduces the Stack ADT and includes implementations

using both a Python list and a linked list. Several common stack applications

are then presented, including balanced delimiter veriﬁcation and the evaluation of

postﬁx expressions. The concept of backtracking is also introduced as part of the

application for solving a maze. A detailed discussion is provided in designing a

solution and a partial implementation.

Chapter 8: Queues. Introduces the Queue ADT and includes three diﬀerent

implementations: Python list, circular array, and linked list. The priority queue

is introduced to provide an opportunity to discuss diﬀerent structures and data

organization for an eﬃcient implementation. The application of the queue presents

the concept of discrete event computer simulations using an airline ticket counter

as the example.

Chapter 9: Advanced Linked Lists. Continues the discussion of dynamic struc-

tures by introducing a collection of more advanced linked lists. These include the

doubly linked, circularly linked, and multi linked lists. The latter provides an

example of a linked structure containing multiple chains and is applied by reimple-

menting the Sparse Matrix to use two arrays of linked lists, one for the rows and

one for the columns. The doubly linked list is applied to the problem of designing

and implementing an Edit Buﬀer ADT for use with a basic text editor.

Chapter 10: Recursion. Introduces the use of recursion to solve various pro-

gramming problems. The properties of creating recursive functions are presented

along with common examples, including factorial, greatest common divisor, and

the Towers of Hanoi. The concept of backtracking is revisited to use recursion for

solving the eight-queens problem.

PREFACE xvii

Chapter 11: Hash Tables. Introduces the concept of hashing and the use of hash

tables for performing fast searches. Diﬀerent addressing techniques are presented,

including those for both closed and open addressing. Collision resolution techniques

and hash function design are also discussed. The magic behind Python’s dictionary

structure, which uses a hash table, is exposed and its eﬃciency evaluated.

Chapter 12: Advanced Sorting. Continues the discussion of the sorting problem

by introducing the recursive sorting algorithms—merge sort and quick sort—along

with the radix distribution sort algorithm, all of which can be used to sort se-

quences. Some of the common techniques for sorting linked lists are also presented.

Chapter 13: Binary Trees. Presents the tree structure and the general binary

tree speciﬁcally. The construction and use of the binary tree is presented along

with various properties and the various traversal operations. The binary tree is

used to build and evaluate arithmetic expressions and in decoding Morse Code

sequences. The tree-based heap structure is also introduced along with its use in

implementing a priority queue and the heapsort algorithm.

Chapter 14: Search Trees. Continues the discussion from the previous chapter

by using the tree structure to solve the search problem. The basic binary search

tree and the balanced binary search tree (AVL) are both introduced along with

new implementations of the Map ADT. Finally, a brief introduction to the 2-3

multi-way tree is also provided, which shows an alternative to both the binary

search and AVL trees.

Appendix A: Python Review. Provides a review of the Python language and

concepts learned in the traditional ﬁrst course. The review includes a presentation

of the basic constructs and built-in data structures.

Appendix B: User-Deﬁned Modules. Describes the use of modules in creating

well structured programs. The diﬀerent approaches for importing modules is also

discussed along with the use of namespaces.

Appendix C: Exceptions. Provides a basic introduction to the use of exceptions

for handling and raising errors during program execution.

Appendix D: Classes. Introduces the basic concepts of object-oriented program-

ming, including encapsulation, inheritance, and polymorphism. The presentation

is divided into two main parts. The ﬁrst part presents the basic design and use

of classes for those instructors who use a “back to basics” approach in teaching

data structures. The second part brieﬂy explores the more advanced features of

inheritance and polymorphism for those instructors who typically include these

topics in their course.

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