Chapter 2 Algorithm Discovery and Design Invitation to

Chapter 2: Algorithm Discovery and Design Invitation to Computer Science, C++ Version, Fourth Edition Spring 2008 Invitation to Computer Science, C++ Version, Fourth Edition

Objectives In this chapter, you will learn about n Representing algorithms n Examples of algorithmic problem solving Invitation to Computer Science, C++ Version, Fourth Edition 2

Introduction n This chapter uses four problems to discuss algorithms and algorithmic problem solving q Multiplying two numbers q Searching lists q Finding maxima and minima q Matching patterns Invitation to Computer Science, C++ Version, Fourth Edition 3

Representing Algorithms n Natural language q Language spoken and written in everyday life q Examples: English, Spanish, Arabic, and so on q Problems with using natural language for algorithms n Verbose n Imprecise n Relies on context and experiences to give precise meaning to a word or phrase Invitation to Computer Science, C++ Version, Fourth Edition 4

Figure 2. 1 The Addition Algorithm of Figure 1. 2 Expressed in Natural Language Invitation to Computer Science, C++ Version, Fourth Edition 5

Representing Algorithms (continued) n High-level programming language q q Examples: C++, Java Problem with using a high-level programming language for algorithms n During the initial phases of design, we are forced to deal with detailed language issues Invitation to Computer Science, C++ Version, Fourth Edition 6

Figure 2. 2 The Beginning of the Addition Algorithm of Figure 1. 2 Expressed in a High-Level Programming Language Invitation to Computer Science, C++ Version, Fourth Edition 7

Pseudocode n English language constructs modeled to look like statements available in most programming languages n Steps presented in a structured manner (numbered, indented, and so on) n No fixed syntax for most operations is required Invitation to Computer Science, C++ Version, Fourth Edition 8

Pseudocode (continued) n Less ambiguous and more readable than natural language n Emphasis is on process, notation n Well-understood forms allow logical reasoning about algorithm behavior n Can be easily translated into a programming language Invitation to Computer Science, C++ Version, Fourth Edition 9

Sequential Operations n Types of algorithmic operations q Sequential q Conditional q Iterative Invitation to Computer Science, C++ Version, Fourth Edition 10

Sequential Operations (continued) n Computation operations q Example n q Set the value of “variable” to “arithmetic expression” Variable n Named storage location that can hold a data value Invitation to Computer Science, C++ Version, Fourth Edition 11

Sequential Operations (continued) n Input operations q To receive data values from the outside world q Example n n Get a value for r, the radius of the circle Output operations q To send results to the outside world for display q Example n Print the value of Area Invitation to Computer Science, C++ Version, Fourth Edition 12

Figure 2. 3 Algorithm for Computing Average Miles per Gallon Invitation to Computer Science, C++ Version, Fourth Edition 13

Conditional and Iterative Operations n Sequential algorithm q q n Also called straight-line algorithm Executes its instructions in a straight line from top to bottom and then stops Control operations q Conditional operations q Iterative operations Invitation to Computer Science, C++ Version, Fourth Edition 14

Conditional and Iterative Operations (continued) n Conditional operations q q Ask questions and choose alternative actions based on the answers Example n if x is greater than 25 then print x else print x times 100 Invitation to Computer Science, C++ Version, Fourth Edition 15

Conditional and Iterative Operations (continued) n Iterative operations q q Perform “looping” behavior, repeating actions until a continuation condition becomes false Loop n The repetition of a block of instructions Invitation to Computer Science, C++ Version, Fourth Edition 16

Conditional and Iterative Operations (continued) q Examples n while j > 0 do set s to s + aj set j to j - 1 n repeat print ak set k to k + 1 until k > n Invitation to Computer Science, C++ Version, Fourth Edition 17

Figure 2. 5 Second Version of the Average Miles per Gallon Algorithm Invitation to Computer Science, C++ Version, Fourth Edition 18

Conditional and Iterative Operations (continued) n n Components of a loop q Continuation condition q Loop body Infinite loop q The continuation condition never becomes false q An error Invitation to Computer Science, C++ Version, Fourth Edition 19

Figure 2. 7 Third Version of the Average Miles per Gallon Algorithm Invitation to Computer Science, C++ Version, Fourth Edition 20

Conditional and Iterative Operations (continued) n Pretest loop q q q Continuation condition tested at the beginning of each pass through the loop It is possible for the loop body to never be executed While loop Invitation to Computer Science, C++ Version, Fourth Edition 21

Conditional and Iterative Operations (continued) n Posttest loop q Continuation condition tested at the end of loop body q Loop body must be executed at least once q Do/While loop Invitation to Computer Science, C++ Version, Fourth Edition 22

Figure 2. 9 Summary of Pseudocode Language Instructions Invitation to Computer Science, C++ Version, Fourth Edition 23

Examples of Algorithmic Problem Solving q q Go Forth and Multiply: Multiply two numbers using repeated addition Sequential search: Find a particular value in an unordered collection Find maximum: Find the largest value in a collection of data Pattern matching: Determine if and where a particular pattern occurs in a piece of text Invitation to Computer Science, C++ Version, Fourth Edition 24

Example 1: Go Forth and Multiply n Task q n Implement an algorithm to multiply two numbers, a and b, using repeated addition Algorithm outline q Create a loop that executes exactly b times, with each execution of the loop adding the value of a to a running total Invitation to Computer Science, C++ Version, Fourth Edition 25

Figure 2. 10 Algorithm for Multiplication via Repeated Addition Invitation to Computer Science, C++ Version, Fourth Edition 26

Example 2: Looking, Looking n Task q n Find a particular person’s name from an unordered list of telephone subscribers Algorithm outline q Start with the first entry and check its name, then repeat the process for all entries Invitation to Computer Science, C++ Version, Fourth Edition 27

Example 2: Looking, Looking (continued) n Algorithm discovery q n Finding a solution to a given problem Naïve sequential search algorithm q q For each entry, write a separate section of the algorithm that checks for a match Problems n Only works for collections of exactly one size n Duplicates the same operations over and over Invitation to Computer Science, C++ Version, Fourth Edition 28

Example 2: Looking, Looking (continued) n Correct sequential search algorithm q q Uses iteration to simplify the task Refers to a value in the list using an index (or pointer) Handles special cases (such as a name not found in the collection) Uses the variable Found to exit the iteration as soon as a match is found Invitation to Computer Science, C++ Version, Fourth Edition 29

Figure 2. 13 The Sequential Search Algorithm Invitation to Computer Science, C++ Version, Fourth Edition 30

Example 2: Looking, Looking (continued) n The selection of an algorithm to solve a problem is greatly influenced by the way the data for that problem is organized Invitation to Computer Science, C++ Version, Fourth Edition 31

Example 3: Big, Bigger, Biggest n Task q n Find the largest value from a list of values Algorithm outline q q Keep track of the largest value seen so far (initialized to be the first in the list) Compare each value to the largest seen so far, and keep the larger as the new largest Invitation to Computer Science, C++ Version, Fourth Edition 32

Example 3: Big, Bigger, Biggest (continued) n Once an algorithm has been developed, it may itself be used in the construction of other, more complex algorithms n Library q q A collection of useful algorithms An important tool in algorithm design and development Invitation to Computer Science, C++ Version, Fourth Edition 33

Example 3: Big, Bigger, Biggest (continued) n Find Largest algorithm q q Uses iteration and indices as in previous example Updates location and largest so far when needed in the loop Invitation to Computer Science, C++ Version, Fourth Edition 34

Figure 2. 14 Algorithm to Find the Largest Value in a List Invitation to Computer Science, C++ Version, Fourth Edition 35

Example 4: Meeting Your Match n Task q n Find if and where a pattern string occurs within a longer piece of text Algorithm outline q q Try each possible location of pattern string in turn At each location, compare pattern characters against string characters Invitation to Computer Science, C++ Version, Fourth Edition 36

Example 4: Meeting Your Match (continued) n Abstraction q Separating high-level view from low-level details q Key concept in computer science q Makes difficult problems intellectually manageable q Allows piece-by-piece development of algorithms Invitation to Computer Science, C++ Version, Fourth Edition 37

Example 4: Meeting Your Match (continued) n Top-down design q When solving a complex problem n Create high-level operations in the first draft of an algorithm n After drafting the outline of the algorithm, return to the high-level operations and elaborate each one n Repeat until all operations are primitives Invitation to Computer Science, C++ Version, Fourth Edition 38

Example 4: Meeting Your Match (continued) n Pattern-matching algorithm q Contains a loop within a loop n External loop iterates through possible locations of matches to pattern n Internal loop iterates through corresponding characters of pattern and string to evaluate match Invitation to Computer Science, C++ Version, Fourth Edition 39

Figure 2. 16 Final Draft of the Pattern-Matching Algorithm Invitation to Computer Science, C++ Version, Fourth Edition 40

Summary n Algorithm design is a first step in developing an algorithm n Algorithm design must n q Ensure the algorithm is correct q Ensure the algorithm is sufficiently efficient Pseudocode is used to design and represent algorithms Invitation to Computer Science, C++ Version, Fourth Edition 41

Summary n Pseudocode is readable, unambiguous, and able to be analyzed n Algorithm design is a creative process; uses multiple drafts and top-down design to develop the best solution n Abstraction is a key tool for good design Invitation to Computer Science, C++ Version, Fourth Edition 42