Fortran 90 & 95 Array and Pointer Techniques

176 Pages·1998·0.55 MB·English

by  Loren P Meissner

Fortran 90 & 95
Array and Pointer
Techniques
Objects, Data Structures, and Algorithms
with subsets e-LF90 and F
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Loren P. Meissner
Computer Science Department
University of San Francisco

Fortran 90 & 95
Array and Pointer
Techniques
Objects, Data Structures, and Algorithms
with subsets e-LF90 and F
Loren P. Meissner
Computer Science Department
University of San Francisco
Copyright 1998, Loren P. Meissner
16 September 1998
Copyright © 1998 by Loren P. Meissner. All rights reserved. Except as permitted under the United States
Copyright Act of 1976, no part of this book may be reproduced or distributed in any form or by any
means, or stored in a database or retrieval system without the prior written permission of the author.

Contents
Contents
Preface
Chapter 1 Arrays and Pointers 1
1.1 WHAT IS AN ARRAY? 1
Subscripts
Multidimensional Arrays
Arrays as Objects
Whole Arrays and Array Sections
Whole Array Operations
Elemental Intrinsic Functions
Array Sections
Array Input and Output
Standard Array Element Sequence
Array Constructors and Array-Valued Constants
Vector Subscripts
1.2 ARRAY TECHNIQUES 11
Operation Counts and Running Time
Operation Counts for Swap Subroutine
The Invariant Assertion Method
Smallest Element in an Array Section
Operation Counts for Minimum_Location
Search in an Ordered Array
Linear Search in an Ordered Array
Binary Search in an Ordered Array
Operation Counts for Binary_Search
Solving Systems of Linear Algebraic Equations
Some Details of Gauss Elimination
Crout Factorization
Iterative Refinement
1.3 POINTERS 36
The Pointer Attribute
Association Status
Automatic Dereferencing
The deallocate Statement
Storage for Pointers and Allocated Targets
Management of Allocated Targets
Pointers as Derived Type Components
Pointers with Arrays
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Chapter 2 Introduction to Sorting 42
Computer Sorting
Operation Counts for Sort_3
2.1 SORTING BY SELECTION 44
Operation Counts for Selection Sort
Sorting an Array of Structures
Selection during Output
Duplicate Keys
Selection Sort is not Stable
2.2 SORTING BY INSERTION 52
Straight Insertion
Operation Counts for Straight Insertion
Initially Ordered Data
Straight Insertion Is Stable
Insertion Sort with Pointers
Insertion during Input
Expanding Array
Binary Insertion
Binary Insertion Is Not Stable
Operation Counts for Binary Insertion
2.3 SHELL SORT 62
Operation Counts for Shell Sort
Shell Sort with Array Sections
2.4 HEAPSORT 64
Binary Trees (Array Representation) and Heaps
The Procedure Peck
Building the Heap by Chain Insertion
Sorting the Heap by Selection
Operation Counts for Heapsort
2.5 OPERATION COUNTS FOR SORTING: SUMMARY 75
Sorting Methods Described So Far (Slower to Faster)
Chapter 3 Recursion and Quicksort 77
3.1 RECURSION 77
Recursion Compared with Iteration
A Good Example of Recursion: Towers of Hanoi
A Bad Example of Recursion: The Fibonacci Sequence
Application: Adaptive Quadrature (Numerical Integration)
Application: Recursive Selection Sort
Tail Recursion vs Iteration
Printing a List Forward
Factorial
3.2 QUICKSORT 76
Recursive Partitioning
Quicksort is Unstable for Duplicates
Choosing the Pivot
The Cutoff
Testing a Quicksort Implementation
Storage Space Considerations
Quicksort Operation Counts
iv
Chapter 4 Algorithm Analysis 94
4.1 WHAT IS AN ALGORITHM? 94
Computer Algorithms
4.2 WHAT MAKES A GOOD ALGORITHM? 95
From Thousands to Millions of Data Items
Operation Counts for Sorting
4.3 ASYMPTOTIC ANALYSIS 97
The Role of Constants
The Complexity of an Algorithm: Big Oh
Complexity of Sorting Methods
4.4 MATHEMATICAL INDUCTION 101
Chapter 5 Linked Lists 102
5.1 LINKED LIST NODE OPERATIONS 102
Create List
Insert Target Node
Delete Target Node
Print Target Node
Modify Target Node
5.2 OPERATIONS ON WHOLE LINKED LISTS 106
Making a Linked List by Insertion at the RootPrint List
Delete List
Searching in a Linked List
Maintaining a Large Ordered List
5.3 PROCESSING LINKED LISTS RECURSIVELY 109
5.4 LINKED LISTS WITH POINTERS TO POINTERS 113
5.5 APPLICATIONS WITH SEVERAL LINKED LISTS 118
Multiply Linked Lists
5.6 LINKED LISTS VS. ARRAYS 119
Array Implementation
Unordered Array
Ordered Array
Linked List Implementation
Unordered Linked List
Ordered Linked List
Summary
v
Chapter 6 Abstract Data Structures 121
6.1 STACKS 121
Applications of Stacks
Depth-First Search in a Graph
Stack Operations
Evaluating a Postfix Expression
Stacks and Recursion
Recursive Depth-First Search
Reversing a List
Abstraction, Encapsulation, and Information Hiding
Stack as an Object
Array Implementation of Stack
Linked List Implementation of Stack
A Stack of What?
Generic Stack Module
Stack Objects
6.2 QUEUES 137
Queue Objects
Linked List Implementation of Queue
Array Implementation of Queue
Special Considerations for High Efficiency
Chapter 7 Trees 145
7.1 BINARY SEARCH TREES 145
The Balance Problem
7.2 AVL TREES 149
Rotating a Subtree
7.3 B-TREES 153
7.4 SKIP LISTS 157
7.5 COMPARISON OF ALGORITHMS 162
Index 165
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Preface
This book covers modern Fortran array and pointer techniques, including facilities provided by Fortran
95, with attention to the subsets e-LF90 and F as well. It provides coverage of Fortran based data struc-
tures and algorithm analysis.
The principal data structure that has traditionally been provided by Fortran is the array. Data struc-
turing with Fortran has always been possible—although not always easy: one of the first textbooks on
the subject (by Berztiss, in 1971) used Fortran for its program examples. Fortran 90 significantly ex-
tended the array features of the language, especially with syntax for whole arrays and array sections
and with many new intrinsic functions. Also added were data structures, pointers, and recursion. Mod-
ern Fortran is second to none in its support of features required for efficient and reliable implementation
of algorithms and data structures employing linked lists and trees as well as arrays.
Examples shown in this book use some features of Fortran 95, notably derived type component
initialization, pointer initialization with null, and pure functions. Electronically distributed program
examples include the Fortran 95 versions printed in the book, as well as alternative versions acceptable
to the Fortran 90 subsets e-LF90 and F. Each of these subsets supports all essential features of Fortran 90
but omits obsolete features, storage association, and many redundancies that are present in the full
Fortran language; furthermore, they are available at a very reasonable price to students and educators.
Information concerning e-LF90 (“essential Lahey Fortran 90”) is available from Lahey Computer Sys-
tems, Inc.; 865 Tahoe Blvd.; Incline Village, NV 89450; [phone]; <www.lahey.com>;
<[email protected]>. Information concerning the F subset is available from Imagine1; 11930 Menaul
Blvd. NE, Suite 106; Albuquerque, NM 87112; [phone]; <www.imagine1.com/imagine1>;
<[email protected]>.
The programming style used in this book, and in all three electronically distributed variant versions
of the programming examples, is close to that required by F (the more restrictive of the two subsets). F
version examples conform to the “common subset” described in essential Fortran 90 & 95: Common Subset
Edition, by Loren P. Meissner (Unicomp, 1997), except that short-form read and print statements re-
place the more awkward form that common subset conformance requires. The e-LF90 version examples
incorporate extensions described in Appendix C of essential Fortran, namely: initialization and type defi-
nition in the main program, simple logical if statements, do while, and internal procedures. Fortran
95 version examples (including those printed in the text) do not employ any further extensions except
for facilities that are new in Fortran 95. All versions of the examples have been tested; the Fortran 95
versions were run under DIGITAL Visual Fortran v 5.0c: see <www.digital.com/ fortran>.
Bill Long, Clive Page, John Reid, and Chuckson Yokota reviewed earlier drafts of this material and
suggested many improvements.
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