Part I Basic Concepts 1

Transcription

1 Introduction xiii Part I Basic Concepts 1 Chapter 1 Integer Arithmetic Example Program Computer Program Documentation Input Assignment Statement Basics of assignment statements Classification of errors Semantics of assignment statements Style guide for naming variables Built-in Types Integer types Boolean type Selection Backus-Naur Form The if statement Output Key Points Assignments 29 Chapter 2 Floating-Point Arithmetic Example Program Floating-point Type Floating-point representation Rounding errors Floating-point literals The built-in function float Floating-point operators and built-ins Built-in functions Library functions Key Points Assignment 42 Chapter 3 Informal Approach to Iteration Example Programs 45

2 vi Table of Contents 3.2 Algorithms High-level descriptions of algorithms Components of iterative algorithms Iterative Algorithms in Python Digit sum Square root Symbolic Constants Key Points Assignment 54 Chapter 4 Strings Example Program String Literals ASCII Unicode Indexing Slicing Comparison Operators and Functions Key Points Assignment 66 Part II Structuring Concepts 67 Chapter 5 Functions Example Function Function Definition Function heading Documentation string Function body Return statement A note on structured programming Function Invocation Testing Outline of a test suite Realization of test suite Key Points Assignment 84 Chapter 6 Tuples Example Function Design by Example Semantics of Sequences Tuple Literals 91

3 vii 6.5 Tuple Assignment Inspection of Sequences Indexing Slicing Comparison Concatenation Variable Number of Arguments Key Points Assignment 102 Chapter 7 Lists Example Function Selection Sort Semantics of Lists List Literals Operations Import Statement For Statement Ranges Key Points Assignment 122 Chapter 8 Matrices Example Functions Semantics of Matrices Matrix manipulation Matrix check Nested Loops List Comprehension Key Points Assignment 132 Chapter 9 Sets Example Function Semantics of Sets Set initialization Hashing Set Manipulation Set inspection Set computations Set mutation Iteration over Sets Key Points 149

4 viii Table of Contents 9.6 Assignment 149 Chapter 10 Dictionaries Example Code Semantics of Dictionaries Dictionary Initialization Dictionary Inspection Dictionary Mutation Iterating over Dictionaries Key Points Assignment 161 Chapter 11 Simple Recursion Example Function Recursion in Mathematics Recursive sets Recursive functions Fractals Recursion in Informatics Mathematical definition of factorials Recursive implementation of the factorial Execution of recursive functions Recursion versus Iteration Recursive version Iterative version Key Points Assignment 175 Chapter 12 Multiple Recursion Non-Tail Recursion Backtracking Eight queens problem General schemes Key Points Assignment 194 Chapter 13 Divide and Conquer Introduction Example: Elections Implementation Counting Votes Allocating Seats Assigning Candidates Key Points 207

5 ix Part III Advanced Topics 209 Chapter 14 Loop Invariants Example Functions Semantics of Loop Invariants Algorithm Design Integer sum Number of occurrences Strong versus weak tests Correctness of Algorithms Base step Induction step Epilogue Termination Loop variant Termination proof Correctness of Selection Sort Correctness of Binary Search Dutch National Flag Problem A humble programmer s version Dijkstra s version Proof of correctness Proof of finiteness Key Points Assignment 241 Chapter 15 Complexity Efficiency Iterative Algorithms Examples from previous chapters Insertion sort Recursive Algorithms Examples from previous chapters Heapsort Key Points Assignment 262 Chapter 16 Dynamic Programming Problem Statement Fibonacci Numbers Memoization The Knapsack Problem Brute Force Approach Greedy Approach Dynamic Programming Approach 275

6 x Table of Contents 16.4 Key Points Assignment 278 Chapter 17 Functional Programming Declarative Programming Imperative versus Declarative Iterative solution Recursive solution Solution with set comprehension Functions as First-Class Citizens Lambda Functions Definition Closures Higher-Order Functions Filter Map List comprehension and set comprehension Self-defined higher-order functions Key Points Assignment 308 Chapter 18 Object-Oriented Programming The Object-Oriented Paradigm Procedural Code Class Definition Class heading Attributes Methods Constructor Encapsulation Additional methods Key Points Assignment 339 Chapter 19 Inheritance Basics of inheritance Superclasses Subclasses Extending Subclasses Method Overriding Key Points Assignment 362

7 xi Solutions to Assignments 363 Chapter 1: Increment Time 363 Chapter 2: Quadratic Equation 365 Chapter 3: Mantissa 368 Chapter 4: Hexadecimal representation 370 Chapter 4: Palindrome 373 Chapter 5: Approximation of π 376 Chapter 6: Sorted Sequences 378 Chapter 7: Duplicates 382 Chapter 8: Encryption 385 Chapter 9: Set Cover 386 Chapter 10: Sparse Vectors 388 Chapter 11: Power 392 Chapter 11: Palindrome 393 Chapter 12: Quicksort 395 Chapter 12: Sudoku 398 Chapter 14: Longest Plateau 400 Chapter 15: Bubble Sort 404 Chapter 15: Merge Sort 406 Chapter 16: Shortest Route 410 Chapter 17: Suspicious Bank Accounts 412 Chapter 17: Flu Prediction 413 Chapter 18: Coordinates 414 Chapter 19: Junior Accounts 420 Index 425