9/23/2013. Chapter 2. Objectives. Introduction. Objectives (continued) Representing Algorithms. Representing Algorithms

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1 Chapter 2 The Algorithmic Foundations of Computer Science Objectives After studying this chapter, students will be able to: Explain the benefits of pseudocode over natural language or a programming language Represent algorithms using pseudocode Identify algorithm statements as sequential, conditional, or iterative Define abstraction and top-down design, and explain their use in breaking down complex problems INVITATION TO Computer Science 1 Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Objectives After studying this chapter, students will be able to: Illustrate the operation of sample algorithms multiplication by repeated addition sequential search of a collection of values finding the maximum element in a collection finding a pattern string in a larger piece of text Introduction Algorithms for everyday may not be suitable for computers to perform (as in Chapter 1) Algorithmic problem solving focuses on algorithms suitable for computers Pseudocode is a tool for designing algorithms This chapter will use a set of problems to illustrate algorithmic problem solving Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Natural language Language spoken and written in everyday life Examples: English, Spanish, Arabic, etc. Problems with using natural language for algorithms Verbose Imprecise Relies on context and experiences to give precise meaning to a word or phrase High-level programming language Examples: C++, Java Problem with using a high-level programming language for algorithms During the initial phases of design, we are forced to deal with detailed language issues 1

2 Pseudocode English language constructs modeled to look like statements available in most programming languages Steps presented in a structured manner (numbered, indented, etc.) No fixed syntax for most operations is required Less ambiguous, more readable than natural language Emphasis is on process, not notation Well-understood forms allow logical reasoning about algorithm behavior Can be easily translated into a programming language Pseudocode is used to design algorithms Natural language is: expressive, easy to use verbose, unstructured, and ambiguous Programming languages are: structured, designed for computers Formal syntax, grammar grammatically fussy, cryptic Pseudocode lies somewhere between these two Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Types of algorithmic operations Sequential step by step Conditional if Iterative - loop Sequential operations perform a single task Input: gets data values from outside the algorithm Computation: a single numeric calculation Output: sends data values to the outside world A variable is a named location to hold a value A sequential algorithm is made up only of sequential operations Example: computing average miles per gallon Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

3 Control operation: changes the normal flow of control Conditional statement: asks a question and selects among alternative options 1. Evaluate the true/false condition 2. If the condition is true, then do the first set of operations and skip the second set 3. If the condition is false, skip the first set of operations and do the second set Example: check for good or bad gas mileage Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Iteration: an operation that causes looping, repeating a block of instructions While statement repeats while a condition remains true continuation condition: a test to see if while loop should continue loop body: instructions to perform repeatedly Example: repeated mileage calculations Iterative Operations [ loops] Components of a loop Continuation condition Loop body Infinite loop (avoid) The continuation condition never becomes false An error Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

4 Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Do/while, repeat/until alternate iterative operation continuation condition appears at the end loop body always performed at least once post-test loop Primitive operations: sequential, conditional, and iterative are all that is needed Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 1: Go Forth and Multiply Given two nonnegative integer values, a 0, b 0, compute and output the product (a b) using the technique of repeated addition. That is, determine the value of the sum a + a + a a (b times). Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

5 Example 1: Go Forth and Multiply Example 1: Go Forth and Multiply Get input values Get values for a and b Compute the answer Loop b times, adding each time* Output the result Print the final value* * steps need elaboration Loop b times, adding each time Set the value of count to 0 While (count < b) do the rest of the loop* Set the value of count to count + 1 End of loop * steps need elaboration Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 1: Go Forth and Multiply Loop b times, adding each time Set the value of count to 0 Set the value of product to 0 While (count < b) do Set the value of product to (product + a) Set the value of count to count + 1 End of loop Output the result Print the value of product Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 2: Looking, Looking, Looking Examples of algorithmic problem solving: Searching 2. Sequential search: find a particular value in an unordered collection 3. Find maximum: find the largest value in a collection of data 4. Pattern matching: determine if and where a particular pattern occurs in a piece of text Example 2: Looking, Looking, Looking Assume that we have a list of 10,000 names that we define as N 1, N 2, N 3,..., N 10,000, along with the 10,000 telephone numbers of those individuals, denoted as T 1, T 2, T 3,..., T 10,000. To simplify the problem, we initially assume that all names in the book are unique and that the names need not be in alphabetical order. Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

6 Example 2: Looking, Looking, Looking Finding the correct solution to a problem is called algorithm discovery and is the most challenging and creative part of the problem-solving process. Three versions here illustrate algorithm discovery, working toward a correct, efficient solution A sequential algorithm (no loops or conditionals) An incomplete iterative algorithm A correct algorithm Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 2: Looking, Looking, Looking Correct sequential search algorithm Uses iteration to simplify the task Refers to a value in the list using an index (or pointer) Handles special cases (like a name not found in the collection) Uses the variable Found to exit the iteration as soon as a match is found Example 3: Big, Bigger, Biggest Task Find the largest value from a list of values Algorithm outline 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 6

7 Example 3: Big, Bigger, Biggest A building-block algorithm used in many libraries Library: A collection of pre-defined useful algorithms Example 3: Big, Bigger, Biggest Find Largest algorithm Uses iteration and indices like previous example Given a value n 1 and a list containing exactly n unique numbers called A 1, A 2,..., A n, find and print out both the largest value in the list and the position in the list where that largest value occurred. Updates location and largest so far when needed in the loop Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 4: Meeting Your Match Task Find if and where a pattern string occurs within a longer piece of text Algorithm outline Try each possible location of pattern string in turn At each location, compare pattern characters against string characters Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 4: Meeting Your Match Pattern-matching: common across many applications word processor search, web search, image analysis, human genome project You will be given some text composed of n characters that will be referred to as T 1 T 2... T n. You will also be given a pattern of m characters, m n, that will be represented as P 1 P 2... P m. The algorithm must locate every occurrence of the given pattern within the text. The output of the algorithm is the location in the text where each match occurred. Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Example 4: Meeting Your Match Algorithm has two parts: 1. Sliding the pattern along the text, aligning it with each position in turn 2. Given a particular alignment, determine if there is a match at that location Solve parts separately and use Abstraction, focus on high level, not details Top-down design, start with big picture, gradually elaborate parts Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

8 Example 4: Meeting Your Match Abstraction Separating high-level view from low-level details Key concept in computer science Makes difficult problems intellectually manageable Allows piece-by-piece development of algorithms Example 4: Meeting Your Match Top-down design When solving a complex problem: Create high-level operations in first draft of an algorithm After drafting the outline of the algorithm, return to the high-level operations and elaborate each one Repeat until all operations are primitives Example 3: Meeting Your Match Pattern-matching algorithm Contains a loop within a loop External loop iterates through possible locations of matches to pattern Internal loop iterates through corresponding characters of pattern and string to evaluate match Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Pattern Matching Some applications Matching phrases in Literature or text Find a pattern and replace it with another Web search ( Google )- matching strings Patterns in X-rays, CAT scans, etc. Patterns in the human genome whole new field of bioinformatics Invitation to Computer Science, 6th Editionm, modified by SJF, Fall

9 Summary Pseudocode is used for algorithm design: structured like code, but allows English and math phrasing and notation Pseudocode is made up of: sequential, conditional, and iterative operations Algorithmic problem solving involves: Step-by-step development of algorithm pieces Use of abstraction, and top-down design Invitation to Computer Science, 6th Editionm, modified by SJF, Fall Important Algorithms Sequential search ( Get values) and Start at the beginning of list Set found = false Repeat until found or end of list Look at each element If element = target set found = true and print desired element else move pointer to next element End loop If found = false then print message not on list Stop Important Algorithms Find Largest ( Get values) and Start at the beginning of list Set found = false and Largest to first element Repeat until end of list Look at each element If element > largest set (found = true) and (largest = element) and (location = i) move pointer to next element End loop Print largest and location Stop Important Algorithms Pattern matching in text Location Text A man and a woman Pattern an Output There is a match at position 4, etc. Patterns in genes Gene: TCAGGCTAATCGGAAGT Probe: TAATC Match: Yes! Definitions Algorithm Discovery finding a correct and efficient solution to a problem Library collection of useful algorithms Iteration repeated operations Index the position of an element in a list Abstraction- ability to separate the high level view of an object from the low level details Top-Down Design viewing an operation at a high level of abstraction and later adding the details in steps ( stepwise refinement) Research Write an algorithm that generates a Caesar cipher (See p. 86, #21) and Chapter 13 Investigate the field of bioinformatics Basic Explanations htthttp://en.wikipedia.org/wiki/bioinformatics BLAST tool used to search protein databases ation3.html 9