数据结构与算法分析 C++版答案

Data Structures and Algorithm 习题答案

Preface ii

1 Data Structures and Algorithms 1

2 Mathematical Preliminaries 5

3 Algorithm Analysis 17

4 Lists, Stacks, and Queues 23

5 Binary Trees 32

6 General Trees 40

7 Internal Sorting 46

8 File Processing and External Sorting 54 9Searching 58

10 Indexing 64

11 Graphs 69

12 Lists and Arrays Revisited 76

13 Advanced Tree Structures 82

i

ii Contents

14 Analysis Techniques 88

15 Limits to Computation 94

Preface

Contained herein are the solutions to all exercises from the textbook A Practical Introduction to Data Structures and Algorithm Analysis, 2nd edition.

For most of the problems requiring an algorithm I have given actual code. In

a few cases I have presented pseudocode. Please be aware that the code presented in this manual has not actually been compiled and tested. While I believe the algorithms

to be essentially correct, there may be errors in syntax as well as semantics. Most importantly, these solutions provide a guide to the instructor as to the intended

answer, rather than usable programs.

1

Data Structures and Algorithms

Instructor’s note: Unlike the other chapters, many of the questions in this chapter are not really suitable for graded work. The questions are mainly intended to get students thinking about data structures issues.

1.1

This question does not have a specific right answer, provided the student keeps to the spirit of the question. Students may have trouble with the concept of “operations.”

1.2

This exercise asks the student to expand on their concept of an integer representation.

A good answer is described by Project 4.5, where a singly-linked

list is suggested. The most straightforward implementation stores each digit

in its own list node, with digits stored in reverse order. Addition and multiplication

are implemented by what amounts to grade-school arithmetic. For

addition, simply march down in parallel through the two lists representing

the operands, at each digit appending to a new list the appropriate partial sum and bringing forward a carry bit as necessary. For multiplication, combine the addition function with a new function that multiplies a single digit

by an integer. Exponentiation can be done either by repeated multiplication (not really practical) or by the traditional Θ(log n)-time algorithm based on the binary representation of the exponent. Discovering this faster algorithm will be beyond the reach of most students, so should not be required.

1.3

A sample ADT for character strings might look as follows (with the normal interpretation of the function names assumed).