Lecture 4 8/24/18. Expressing Procedural Knowledge. Procedural Knowledge. What are we going to cover today? Computational Constructs

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1 What are we going to cover today? Lecture 4 Conditionals and Boolean Expressions What is procedural knowledge? Boolean expressions The if-else and if-elif-else statements s Procedural Knowledge We differentiate our knowledge of facts from our knowledge of how to do things Procedural knowledge Where do you see procedural knowledge? Instructions Recipes Programming is the act of describing a process for the computer to follow Expressing Procedural Knowledge If the process is identical for all situations, then it can be linear step 1 -> step 2 -> step 3 -> -> step N Most recipes are like this The sequential steps we ve been seeing are like this But if the process varies depending on the situation, it will have branches like a tree step 1 -> step 2 -> step 3 (for some cases) step 1 -> step 2 -> step 4 (for other cases) We want to make our program adapt to a variety of use situations To create branches in programs, we describe the conditions for each Conditions are assessed as Boolean (true/false) variables and expressions Computational Constructs After this lesson, we ll have 2 ways of organizing computation: Sequential Conditional Boolean Expressions To have a conditional, we need a Boolean value Remember that Booleans are values that can be True or False But, how can we create a Boolean? There are many ways, but the most common are relational operators 1

2 Relational Operators Allow us to compare two values. We generally have comparisons for Equality: == [note the two equal signs, instead of one. One is assignment!] Inequality:!= [note the!] Less Than: < Greater Than: > Less Than or Equal To: <= [note that =< is not allowed] Greater Than or Equal To: >= [note that => is not allowed] The result of a relational operator is a Boolean value It can be assigned to a variable or used in an expression Relational Operators For example, we might want to determine if a variable is: zero (variable1 == 0) not zero (variable1!= 0) positive (variable1 > 0) negative (variable1 < 0) greater than or equal to zero (variable1 >= 0) less than or equal to zero (variable1 <= 0) If we have variables: JohnAge : the age of John JoeAge: the age of Joe And we want a Boolean variable: JohnOlderThanJoe : True if, and only if, John is older than Joe How would we set that variable? If we have variables: JohnAge : the age of John JoeAge: the age of Joe And we want a Boolean variable: JohnOlderThanJoe : True if, and only if, John is older than Joe How would we set that variable? JohnOlderThanJoe = JohnAge > JoeAge Boolean Operators Boolean Operators are operators for 1 or 2 Booleans The Boolean operators are and, or, and not A and B : true if both A and B are true, false otherwise A or B : true if A is true or B is true (or both are true), false otherwise not A : reverses A, so true if A is false, false if A is true Boolean operators can be combined to create almost any logical decision There are often many ways to combine Booleans and get the same result e.g. A and B is equivalent to: not ((not A) or (not B)) Same is true for larger Boolean/Relational Expressions ((A > B) and (B < C)) is equivalent to: not ((B>=A) or (B>=C)) Boolean Operators s: To test if a variable is between 0 and 100, inclusive ((variable1 >= 0) and (variable1 <= 100)) To test if two variables are equal and positive ((variable1 == variable2) and (variable1 > 0)) Notice: don t need to test for variable2 > 0 since we know variable1 must equal variable2 Alternative versions of the above tests: not ((variable1 < 0) or (variable1 > 100)) not ((variable1!= variable2) or (variable1 <= 0)) 2

3 Given a temperature in Fahrenheit stored in the variable F, set a variable that tells whether water at that temperature is in liquid form or not. Given a temperature in Fahrenheit stored in the variable F, set a variable that tells whether water at that temperature is in liquid form or not. is_liquid = (F >= 32) and (F <= 212) Order of Operation and Boolean Expressions Boolean order of operations not before and before or Relational operators before Boolean operators not a == b is evaluated not (a == b) rather than (not a) == b You should use parentheses rather than relying on order of operation to avoid bugs in your code to improve comprehensibility Reminder of order of operations for assignment operators Convention Description ( ) Items within parentheses are evaluated first ** Exponentiation operators are evaluated next. The right side of the exponentiation is computed first * / // % to be evaluated are *, /, //, and %. + - Finally come + and - with equal precedence. left-to-right If more than one operator of equal precedence could be evaluated, evaluation occurs left to right. What would be the output of the following code? a = 10 b = 10 c = 20 d = ((a>b) and (b<=c)) or (not((((c<=a+b) and (a==10)) or ((b==10) and c!=10)))) print(d) What would be the output of the following code? a = 10 b = 10 c = 20 d = ((a>b) and (b<=c)) or (not((((c<=a+b) and (a==10)) or ((b==10) and c!=10)))) print(d) False Why? a = 10 b = 10 c = 20 d = ((a>b) and (b<=c)) or (not((((c<=a+b) and (a==10)) or ((b==10) and (c!=10))))) (False and True ) or (not((( True and True ) or ( True and True )))) ( False ) or (not(( True or True ))) ( False ) or (not( True )) ( False ) or ( False ) False 3

4 Start with the keyword if is the condition: a Boolean literal, variable, or expression There is a colon at the end of the line Then the following line(s) are indented. It is common practice to indent 4 spaces. Finally are the commands to actually perform, if and only if the condition is true 4

5 Indenting It is important to indent the code that should happen if (and only if) the condition is true. The indentation should be consistent through the program, and must be the same for every line in the conditional block 4 spaces is common Often, the editor in your IDE will do this for you automatically. (1) if True: print("howdy") print("world") Howdy World Note: unlike most other programming languages, the indentation is required in Python. (2) (3) if False: print("howdy") print("world") Notice that only the indented portion is subject to the conditional. World if True: print("one") print("two") if False: print("three") print("four") print("five") Notice that more than one line can be part of the conditional One Two Five (4) (5) Temperature = 100 is_hot = (Temperature > 85) if is_hot: print("it's hot") if not is_hot: print("it's not hot") The condition can be a Boolean variable It's hot Temperature = 100 if Temperature > 85: print("it's hot") if Temperature <= 85: print("it's not hot") The condition can be a Boolean expression It's hot 5

6 The if-else and if-elif-else statements s When there are two possibilities if (boolean-expression): do this when expression is true do this when expression is false The FIRST Boolean expression that is true will be the only one followed: When there are more than two alternative paths if (boolean-expression1): do this when expression1 is true elif (boolean-expression2): do this if expression1 is false but expression 2 is true elif (boolean-expression3): do this if all above expressions are false walking_speed = 3 biking_speed = 10 if walking: speed = walking_speed speed = biking_speed time-taken = distance / speed if major == "CSCE": office = 'HRBB 302' elif major == "ECEN": office = 'WEB 301' elif major == "MEEN": office = 'MEOB 100' office = 'unknown' Test the first condition First condition was false, so skip indentation Test the second condition Second condition was false, so skip indentation Test the third condition 6

7 Third condition was true, so go to indented section This line was executed, so there was output. Execution continues from after the rest of the if-elif-else statement Few Few Several What input can produce None for an output? Nested Branches What input can produce None for an output? Nothing! The elif cases handle all the situations, so there is never a chance to encounter the else clause. If we wanted to handle an input of 0, we would need to modify the (how_many < 10) condition. Complex condition statements can become hard to understand And hard to maintain We can nest condition statements Place an if/if-else/if-elif-else statement inside of a conditional block The new statement is nested inside the first one Remember to be consistent with indentation it is required by Python if (animal == 'bird'): if (animal_name == 'penguin'): moves_by= 'walking' else moves_by = 'flying' elif (animal == 'fish'): moves_by = 'swimming' elif (animal == 'snake'): moves_by = 'slithering' moves_by = 'walking' 7

8 Why would we nest conditions? To better match our understanding of the problem Helps the programmer reflect the logic of the situation better We don t always know all of the various options at the time of the first condition e.g. we might get input based on the first condition, then need another condition to respond to the input To make the code easier to comprehend Long, complex Boolean expressions can be hard to comprehend Nested statements can make the logic easier to follow We will see other examples of nesting in the future When should we use each type? Use if-elif- When you have multiple cases of the same type Generally, the conditionals in the if-elif statements should be very similar to one another Use nested statements: When you have a clear order of checks: checking A then B When a single conditional would appear too complicated Use separate if statements: When your conditions are checking different concepts Or, when you potentially have things matching more than one condition, and want to deal with both Problem Taken from Your Own Life One of the most important skills engineering students need is to be able to effectively allocate their time to their studies. What questions do we want to answer? How effective are many short, a middle number of medium-length, or a few long study sessions? How might other aspects of us affect the outcome? What characteristics effect the outcome? The length of study sessions The number of study sessions How tired, stressed, hungry, etc. you are Start by just considering study session length We can model how much a student learns in a study session if we have a model of how the student s capture of knowledge changes through the session. We can think of this using the following graph. Rate of Learning 2. But perhaps there is a warm-up period where we remember what we had learned before Time since start of study session 1. We might assume a constant learning rate 3. And, maybe when we get fatigued we learn worse The number of concepts/skills learned in a session is the area under the curve. Conditionals and Boolean Expressions Consider computing the number of concepts learned in a study session of a given length using a learning rate model that involves a warm-up period Rate of Learning (concepts per minute) observed-learning-rate [observation] 15 Time since start of study session (minutes) We could implement this as a single line of code, but it would not be very comprehensible So, we will create variables to store intermediate values needed in the computation For example: warmup_slope = ( ) / 15 of if-else To compute the learned concepts, we need different paths if the length of the session is less than 15 minutes if (session_length < 15): warmup_slope = (( ) / 15) end_learning_rate = (warmup_slope * session_length) concepts_learned = session_length * ((0.1 + end_learning_rate) / 2) avg_warmup_learning-rate = ( ) / 2 concepts_learned = 15 * avg-warmup_learning_rate + ((session_length 15) * 0.2) Rate of Learning (concepts per minute) Time since start of study session (minutes) We are computing the area under the above function. 8

9 of if-elif-else Rate of Learning (concepts Now we need three different computations if (session_length < 15): warmup_slope = (( ) / 15) end-learning-rate = (warmup_slope * session_length) concepts_learned = session_length * 0.2 per minute) ((0.1 + end_learning_rate) / 2) Time since start of study session (minutes) elif (session_length <= 30): avg_warmup_learning_rate = ( ) / 2 concepts_learned = 15 * avg_warmup_learning_rate + ((session_length 15) * 0.2) avg_warmup_learning_rate = ( ) / 2 cooldown_slope = ( ) / (120 30) end_learning_rate = 0.2 (cooldown_slope * (session_length 30)) concepts_learned = 15 * avg_warmup_learning_rate + (30 15) * (session_length 30) * ((0.2 + end_learning_rate) / 2) 9