Python and Algorithms

218 Pages·2013·5.03 MB·English

♥ Python and Algorithms ♥
Mari Wahl, [email protected]
University of New York at Stony Brook
May 24, 2013
“There’s nothing to fear but the fear itself.
That’s called recursion, and that would lead you
to infinite fear.”
Hello, human! Welcome to my book on Python and algorithms! If you
are reading this you probably agree with me that those two can be a
lot of fun together (or you might be lost, and in this case I
suggest you give it a try anyway!). Also, many of the examples
shown here are available in my git repository, together with several
other (more advanced) examples for abstract data structures, trees,
graphs, and solutions for the Euler Project and the Topcoder
website. Don’t forget to check them out!
This text was written purely for fun (I know, I know, this is a
broad definition of the word fun...) with no pretensions for
anything big, so please forgive me (or better, let me know) if you
find any typo or mistake. I am not a computer scientist by
formation (I am actually an almost-I-swear-it-is-close-Ph.D. in
Physics) so this maybe makes things a little less usual (or risky?).
I hope you have fun!
Mari, Stony Brook, NY
Summer/2013
4
Contents
I Flying with Python 9
1 Numbers 11
1.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Floats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 The fractions Module . . . . . . . . . . . . . . . . . . . . . 14
1.5 The decimal Module . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Other Representations . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 16
2 Built-in Sequence Types 25
2.1 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Bytes and Byte Arrays . . . . . . . . . . . . . . . . . . . . . . 43
3 Collection Data Structures 45
3.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 Python’s collection Data Types . . . . . . . . . . . . . . . 54
3.4 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 58
4 Python’s Structure and Modules 63
4.1 Modules in Python . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Control Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 File Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Multiprocessing and Threading . . . . . . . . . . . . . . . . . 79
4.5 Error Handling in Python . . . . . . . . . . . . . . . . . . . . 81
4.6 Debugging and Profiling . . . . . . . . . . . . . . . . . . . . . 83
5
6 CONTENTS
4.7 Unit Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5 Object-Oriented Design 89
5.1 Classes and Objects . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 Principles of OOP . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 Python Design Patterns . . . . . . . . . . . . . . . . . . . . . 94
5.4 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 96
II Algorithms are Fun 99
6 Additional Abstract Data Structures 101
6.1 Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.3 Deques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.4 Priority Queues and Heaps . . . . . . . . . . . . . . . . . . . 110
6.5 Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.6 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 120
7 Asymptotic Analysis 133
7.1 Complexity Classes . . . . . . . . . . . . . . . . . . . . . . . . 133
7.2 Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3 Runtime in Functions . . . . . . . . . . . . . . . . . . . . . . 136
8 Sorting 139
8.1 Quadratic Sort . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.2 Linear Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.3 Loglinear Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Comparison Between Sorting Methods . . . . . . . . . . . . . 148
8.5 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 149
9 Searching 153
9.1 Sequential Search . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.2 Binary Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.3 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 156
10 Dynamic Programming 163
10.1 Memoization . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
10.2 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 165
CONTENTS 7
III Climbing Graphs and Trees 169
11 Introduction to Graphs 171
11.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.2 The Neighborhood Function . . . . . . . . . . . . . . . . . . . 173
11.3 Introduction to Trees . . . . . . . . . . . . . . . . . . . . . . . 176
12 Binary Trees 179
12.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 179
12.2 Representing Binary Trees . . . . . . . . . . . . . . . . . . . . 179
12.3 Binary Search Trees . . . . . . . . . . . . . . . . . . . . . . . 183
12.4 Self-Balancing BST . . . . . . . . . . . . . . . . . . . . . . . . 186
12.5 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 193
13 Traversals and Problems on Graphs and Trees 207
13.1 Depth-First Search . . . . . . . . . . . . . . . . . . . . . . . . 207
13.2 Breadth-First Search . . . . . . . . . . . . . . . . . . . . . . 208
13.3 Representing Tree Traversals . . . . . . . . . . . . . . . . . . 209
13.4 Additional Exercises . . . . . . . . . . . . . . . . . . . . . . . 211
8 CONTENTS
Part I
Flying with Python
9