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
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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.
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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.
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.”
This exercise asks the student to expand on their concept of an integer representation.
A good answer is described by Project , 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.
A sample ADT for character strings might look as follows (with the normal interpretation of the function names assumed).
Chap. 1 Data Structures and Algorithms
Some
In C++, this is 1
for s1int strcmp(String s1, String s2)
One’s compliment stores the binary representation of positive numbers, and stores the binary representation of a negative number with the bits inverted. Two’s compliment is the same, except t hat a negative number has its bits inverted and then one is added (for reasons of efficiency in hardware implementation).
This representation is the physical implementation of an ADT
defined by the normal arithmetic operations, declarations, and other support given by the programming language for integers.
An ADT for two-dimensional arrays might look as follows.
Matrix add(Matrix M1, Matrix M2);
Matrix multiply(Matrix M1, Matrix M2);
Matrix transpose(Matrix M1);
void setvalue(Matrix M1, int row, int col, int val);
int getvalue(Matrix M1, int row, int col);
List getrow(Matrix M1, int row);
One implementation for the sparse matrix is described in Section Another implementation
is a hash table whose search key is a concatenation of the matrix coordinates.
Every problem certainly does not have an algorithm. As discussed in Chapter 15,
