CS 107 Introduction to Computer Science Lecture 2

CS 107: Introduction to Computer Science Lecture 2 Jan 29 th

• Last time – What is not Computer Science – What is Computer Science – Algorithms, properties and examples • Today – Expressing algorithms: Pseudocode – Examples • Algorithm for adding two m-digit numbers • Algorithm for computing miles-per-gallon

What is Computer Science? The study of algorithms: – their formal properties • correctness, limits • efficiency/cost (Chapters 2, 3, 10) – their hardware realizations • computer design (Chapters 4 -6) – their linguistic realizations • programming languages (Chapters 7 -9) – their applications • network design, ocean modeling, bioinformatics, . . .

What is an algorithm? Algorithm = well-defined procedure that allows an agent to solve a problem. Algorithms must: 1. Be well-ordered and unambiguous 2. Be executable (understandable), 3. Solve the problem, and 4. Terminate. Note: often the agent is a computer or a robot…

Example Algorithms • • • Cooking a dish Making a peanut-butter jelly sandwich Shampooing hair Adding two numbers (p 7) Programming a VCR (p 6) Making a pie (p 13)

Designing Algorithms We need: • A problem for which an effective algorithm can be written (i. e. , one that is tractable), • A language (e. g. , “pseudocode” or C++), A methodology for translating the problem into an algorithm, and • A computing “agent” that can understand execute such algorithms.

Expressing algorithms • Is natural language good? – For daily life, yes…but for CS is lacks structure and would be hard to follow – Too rich, ambiguous, depends on context • How about a programming language? – Good, but not when we try to solve a problem. . we want to think at an abstract level – It shifts the emphasis from how to solve the problem to tedious details of syntax and grammar.

Pseudocode • Pseudocode = English but looks like programming • Good compromise – Simple, readable, no rules, don’t worry about punctuation. Lets you think at an abstract level about the problem. – Contains only instructions that have a well-defined structure and resemble programming languages

Pseudocode elements Basic (primitive) operations – Read the input from user – Print the output to the user – Cary out basic arithmetical computations • Conditional operations – Execute an operation if a condition is true • Sequential operations • Repeat operations – Execute a block of operation multiple times until a certain condition is met

Variables Variable – A named memory location that can store a value – Think of it as a box into which you can store a value, and from which you can retrieve a value Examples: i carry – List variables: used when the input comes as a list of elements am-1 am-2 … … a 1 a 0 a 1 a 2 a m-1 am … …

Expression and assignment statements Function: change the value of a variable by evaluating arithmetic expressions • can use any arithmetic expression, just like on a typical calculator: +. -. *, /, … Examples set the value of m to 2 set the value of i to 6. set the value of carry to i+2*m set the value of ai to 0 a 1 a 2 a m-1 am … …

Input/Output Statements Function: transfer values from the user to a variable, or viceversa get values for <variable> print value of <variable> • Examples – Get the value of n from the user – Get value of the list of elements a 1, a 2, …, am from the user – Print the value of result to the user

Sequential statements The steps of an algorithm are carried out in the order they are written. Conditional statements Function: specifying a statement that may or may not be done: if <condition> then <statement to be done> else <statement to be done otherwise> Example if the value of carry is 0 then set the value of a to else set the vale of a to a+1 0

Loop statements Function: specify a group of statements that may be done several times (repeated): repeat until <condition> < statements to be repeated > • How does this work? – Condition is evaluated – If it is true than the loop terminates and the next instruction to be executed will be the instruction immediately following the loop – If it is false, then the algorithm executes the <statements to be repeated> in order, one by one

Example Step 1: set count to 1 Step 2: repeat step 3 to step 5 until count is > 10 Step 3: set square to count *count Step 4: print value of square and value of count Step 5: add 1 to count Step 6: end • What does this algorithm do? • Note: indentation – Not necessary, but makes reading/understanding algorithms easier

An example pseudocode algorithm (Fig 1. 2) Given: m ≥ 1 and two positive numbers a and b, each containing m digits, compute the sum c = a + b. 0 Get values for m, am-1 … a 0 and bm-1 … b 0 1 Set the value of carry to 0. 2 Set the value of i to 0. 3 Repeat steps 4 -6 until i > m-1 4 Set the value of ci to ai + bi + carry 5 if ci ≥ 10 then subtract 10 from ci and set the value of carry to 1 else set the value of carry to 0 6 Add 1 to i 7 Set the value of cm to carry

So, how does this work? ? ? For example, the input is m = 4, a = 3276, and b = 7345. After step 0, the variables m, a, and b have those values: m 4 3 2 a 3 a 2 7 6 a 1 a 0 7 3 b 2 4 5 b 1 b 0 After steps 1 and 2, the variables i and carry are initialized. i 0 carry 0 Next, steps 4 -6 are repeated until the value of i > 3. Each repetition computes a single digit of c. c 4 c 3 c 2 c 1 c 0

A model for visualizing an algorithm’s behavior Computer Input (keyboard) Algorithm Variables Output (screen)

E. g. , Visualizing Fig 1. 2 Computer Input (keyboard) 4 3276 7345 0 Get values for … … 8 Print value of … m 4 i 0 3 2 a 3 a 2 7 3 b 2 c 4 c 3 c 2 carry 7 6 a 1 a 0 4 5 b 1 b 0 c 1 c 0 Output (screen) 0

Another example: computing MPG (Fig 2. 5) Set response to “Yes” Repeat steps 2 -10 until response = “No” 2 Get gallons, start, end 3 Set distance to end - start 4 Set mpg to distance ÷ gallons 5 Print mpg 6 if mpg > 25. 0 then 7 print “You are getting good gas mileage” 8 else print “You are NOT getting good gas mileage” 9 Print “Do you want to do this again, Yes or No? ” 10 Get response 11 Stop 0 1

So, how does this work? ? ? For example, suppose we use 25 gallons, beginning at 12000 and ending at 13000 on the odometer. Then, after step 2, some variables have the following values: Yes 25 12000 13000 response gallons start end After step 4, the variables distance and mpg are computed. distance 1000 mpg 40 Steps 5 -9 displays these results on the output screen: 40 You are getting good gas mileage Do you want to do this again, Yes or No?

Visualizing Fig 2. 5 Computer Input (keyboard) 25 12000 13000 0 Set response … … 11 Stop response Yes gallons start distance end mpg Output (screen)

Summary • Pseudocode – – Get/print statements (input/output statements) Conditional statements Sequential statements Loops • Algoritms – Compute sum of two m-digit numbers – Compute miles-per-gallon

Over the weekend… 1. Get the textbook. 2. Read Chapter 1, 2. 1 and 2. 2 3. Discuss and solve the problems in the Lab 1 (in groups or individually). Lab 1 is due on Monday in class. If you have questions we’ll discuss them in class on Monday. 4. Bring a digital picture for the lab tomorrow. You will need it for your website.