CS 107 Introduction to Computer Science Lecture 2

CS 107 Introduction to Computer Science Lecture 2

Administrativia • Lab access – Searles 128: daily until 4 pm unless class in progress – Searles 117: 6 -10 pm, Sat-Sun 12 -10 pm • Office hours – M, W 4 -5 pm – Quick questions: Anytime I am in the office – Email to set up appointment • My office: Searles 219 • Study group – Mondays 8 -9 pm in Searles 224

Last time – What is (not) Computer Science – Algorithms, properties and examples – Expressing algorithms: Pseudocode • Who was Alan Turing and what is he famous for? • Today – More pseudocode elements – Algorithm examples

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 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 • Repeat operations – Execute a block of operation multiple times until a certain condition is met

Basic operations – Read the input from user • Get x • Get a, b, c – Print the output to the user • Print x • Print “Your mileage is ” x – Cary out basic arithmetical computations • Set x to 10 • Set y to x*x/3

Conditional statements Specify 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 0 else set the vale of a to a+1

Loop statements 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 Variables: count 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

Pseudocode examples Equivalent: – Set the value of a to 1 – Set a to 1 – a=1 Equivalent – – Add 1 to count Set count to count + 1 Increment the value of count by 1 count = count + 1 Writing in pseudocode gives you the freedom to choose any of these!

• Incorrect – Set 1 to a – Add a + b (what do you do with the result? ) – Set a+b +3 • Note: not the same – set a to b – set b to a • Example: what is the output of the following algorithms? set a to 2 set b to 4 set a to b set b to a print a, b

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

Algorithm for computing MPG (Fig 2. 5) Write a pseudocode algorithm to compute the distance traveled and the average miles per gallon on a trip when given as input the number of gallons used and the starting and ending mileage readings on the odometer. Variables: response, gallons, start, end, distance, mpg 0 Set response to “Yes” 1 Repeat steps 2 -8 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 print “You are getting good gas mileage” else print “You are NOT getting good gas mileage” 7 Print “Do you want to do this again, Yes or No? ” 8 Get response 9 Stop

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)

Designing Algorithms: A Methodology 1. Read the problem, identifying the input and the output. 2. What variables are needed? 3. What computations are required to achieve the output? 4. Usually, the first steps in your algorithm bring input values to the variables. 5. Usually, the last steps display the output 6. So, the middle steps will do the computation. 7. If the process is to be repeated, add loops.

How was the MPG program (Fig 2. 5) designed? Problem statement: Write a pseudocode algorithm to compute the distance traveled and the average miles per gallon on a trip when given as input the number of gallons used and the starting and ending mileage readings on the odometer. Input: number of gallons, starting mileage, ending mileage Output: distance traveled, average miles per gallon Variables: gallons, start, end, distance, mpg Calculate: distance = end - start mpg = distance / gallons Put the steps in order: input, calculate, output (steps 2 -8) Determine if a loop is needed (steps 0, 1, 9, 10)

Problem • Adding two n-digit numbers 7597831 + 1287525 ---------8885356 How would you write an algorithm to solve this problem? Assume the basic operation is adding one-digit numbers.

Computing the sum 1+2+…. +n Problem: Write an algorithm which reads a positive integer from the user and computes the sum of all positive integers smaller than or equal to te number entered by the user. – Example: if the user enters 10, the algorithm should compute 1+2+3+…+10

Gauss formula • Find a formula for 1 + 2 + ……. + n Gauss noticed that • 1 + n = n+1 • 2 + (n-1) = n+1 • …. ==> 1 + 2 + … + (n-1) + n = n(n+1)/2