Python数据结构与算法实战指南

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"《Data Structures and Algorithms Using Python》是一本以Python语言讲解数据结构与算法的教程，由Rance D. Necaise撰写，属于College of William and Mary的计算机科学系。该书由John Wiley & Sons, Inc.出版，旨在帮助读者理解和应用Python中的核心数据结构和算法。" 在Python编程中，数据结构是存储和组织数据的关键工具，而算法则是解决问题和执行任务的有效方法。本书涵盖了以下几个重要的知识点： 1. **列表(Lists)**：Python的基础数据结构，支持动态大小调整，可以存储任意类型的对象。它提供了索引访问、切片操作、append、extend、insert、remove等方法，以及排序功能。 2. **元组(Tuples)**：不可变的数据结构，用于存储有序的元素集合。元组比列表更高效，适用于数据交换和作为字典键。 3. **字典(Dictionaries)**：基于哈希表的无序数据结构，以键值对形式存储数据。字典的查找、插入和删除操作通常具有O(1)的时间复杂度。 4. **集合(Sets)**：不包含重复元素的无序集合，支持基本的数学运算，如并集、交集和差集。 5. **堆(Heap)**：Python的heapq模块实现了优先队列，常用于处理最小或最大的元素，是实现优先级队列的常见数据结构。 6. **栈(Stack)**：后进先出（LIFO）的数据结构，Python中可通过列表模拟栈的操作，如push和pop。 7. **队列(Queue)**：先进先出（FIFO）的数据结构，Python的collections模块提供了deque（双端队列）来实现。 8. **链表(Linked Lists)**：非连续存储的数据结构，每个节点包含数据和指向下一个节点的引用。虽然Python中没有内置链表，但可以通过类来实现。 9. **树(Tree)**：包括二叉树、二叉搜索树、平衡树（如AVL树和红黑树）等，它们在搜索、排序和组织数据方面有广泛应用。 10. **图(Graph)**：由节点和边构成的数据结构，可以表示各种复杂关系。Python中可以通过邻接矩阵或邻接表来实现。 11. **排序算法**：包括冒泡排序、选择排序、插入排序、快速排序、归并排序、堆排序等，分析其时间复杂度和稳定性。 12. **查找算法**：如线性查找、二分查找、哈希查找等。 13. **递归(Recursion)**：函数调用自身的技术，常用于解决分治问题和树形结构的问题。 14. **动态规划(Dynamic Programming)**：通过将问题分解成子问题，避免重复计算，以优化解决方案。 15. **贪心算法(Greedy Algorithm)**：每一步都采取当前最优决策，但不保证全局最优解。 16. **回溯法(Backtracking)**：在解决问题时尝试所有可能的解决方案，遇到错误就退回一步，尝试其他路径。本书不仅讲解了这些基础概念，还可能深入探讨算法的实现、性能分析、复杂度分析以及如何在实际项目中应用这些概念。通过学习，读者能够提升编程能力，更好地解决复杂问题，并为面试和专业开发工作做好准备。

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.

2 CHAPTER 1 Abstract Data Types

contain multiple values, are all examples of complex types. The primitive types

provided by a language may not be suﬃcient for solving large complex problems.

Thus, most languages allow for the construction of additional data types, known

as user-deﬁned types since they are deﬁned by the programmer and not the

language. Some of these data types can themselves be very complex.

1.1.1 Abstractions

To help manage complex problems and complex data types, computer scientists

typically work with abstractions. An abstraction is a mechanism for separat-

ing the properties of an object and restricting the focus to those relevant in the

current context. The user of the abstraction does not have to understand all of

the details in order to utilize the object, but only those relevant to the current task

or problem.

Two common types of abstractions encountered in computer science are proce-

dural, or functional, abstraction and data abstraction. Procedural abstraction

is the use of a function or method knowing what it does but ignoring how it’s

accomplished. Consider the mathematical square root function which you have

probably used at some point. You know the function will compute the square root

of a given number, but do you know how the square root is computed? Does it

matter if you know how it is computed, or is simply knowing how to correctly use

the function suﬃcient? Data abstraction is the separation of the properties of a

data type (its values and operations) from the implementation of that data type.

You have used strings in Python many times. But do you know how they are

implemented? That is, do you know how the data is structured internally or how

the various operations are implemented?

Typically, abstractions of complex problems occur in layers, with each higher

layer adding more abstraction than the previous. Consider the problem of repre-

senting integer values on computers and performing arithmetic operations on those

values. Figure 1.1 illustrates the common levels of abstractions used with integer

arithmetic. At the lowest level is the hardware with little to no abstraction since it

includes binary representations of the values and logic circuits for performing the

arithmetic. Hardware designers would deal with integer arithmetic at this level

and be concerned with its correct implementation. A higher level of abstraction

for integer values and arithmetic is provided through assembly language, which in-

volves working with binary values and individual instructions corresponding to the

underlying hardware. Compiler writers and assembly language programmers would

work with integer arithmetic at this level and must ensure the proper selection of

assembly language instructions to compute a given mathematical expression. For

example, suppose we wish to compute x = a + b − 5. At the assembly language

level, this expression must be split into multiple instructions for loading the values

from memory, storing them into registers, and then performing each arithmetic

operation separately, as shown in the following psuedocode:

loadFromMem( R1,

)

loadFromMem( R2,

)

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