Lecture 6 — Decisions¶

Initial Example:¶

Suppose we have a height measurements for two people, Chris and Sandy. We have the tools to write a program that determines which height measurement is greater:

chris_height = float(raw_input("Enter Chris's height (in cm): "))
sandy_height = float(raw_input("Enter Sandy's height (in cm): "))
print "The greater height is", max(chris_height,sandy_height)

But, we don’t have the tools yet to decide who has the greater height. For this we need if statements:

chris_height = float(raw_input("Enter Chris's height (in cm): "))
sandy_height = float(raw_input("Enter Sandy's height (in cm): "))
if chris_height > sandy_height:
    print "Chris is taller"
else:
    print "Sandy is taller"

This is the first of many lectures exploring logic, if statement and decision making.

Overview — Logic and Decision Making¶

Boolean logic
Use in decision making
Use in branching and alternatives

Reading: Sections 6.1 and 6.2 of Practical Programming. We’ll return to the rest of this chapter later in the semester.

Part 1: Boolean Values¶

Yet another type
Values are True and False
We’ll see a large series of operations that either produce or use boolean values, including relational operators such as <, <=, etc. and logical operations such as and and or.
We can assign them to variables, as in,
```
x = True
```
although we will not explore this much during the current lecture.

Relational Operators — Less Than and Greater Than¶

Comparisons between values, perhaps values associated with variables, to produce a boolean outcome.

For numerical values, <, <=, >, >= are straightforward:

>>> x = 17
>>> y = 15.1
>>> x < y
False
>>> x <= y
False
>>> x <= 17
True
>>> y < x
True

The comparison operators <, <=, >, >= may also be used for strings but the results are sometimes a bit surprising:

>>> s1 = 'art'
>>> s2 = 'Art'
>>> s3 = 'Music'
>>> s4 = 'music'
>>> s1 < s2
False
>>> s2 < s3
True
>>> s2 < s4
True
>>> s1 < s3
False

With strings, the ordering is what’s called lexicographic rather than purely alphabetical order:
- All capital letters come before small letters, so strict alphabetical ordering can only be ensured when there is no mixing of caps and smalls.

Relational Operators: Equality and Inequality¶

Testing if two values are equal uses the combined, double-equal symbol == rather than the single =, which is reserved for assignment.
- Getting accustomed to this convention requires practice, and it is a common source of mistakes
Inequality is indicated by !=.
We will play with a few examples in class.

Part 1 Exercises¶

What are the values of the following boolean expressions?

a = 1.6
b = -1.7
c = 15
s = 'hi'
t = "good"
u = "Bye"
v = "GOOD"
w = "Bye"

a < b             # A
a < abs(b)        # B
a >= c            # C
s < t             # D
t == v            # E
u == w            # F
b < y             # G

What happens with the following?
```
u == w
u = v
u == w
```

Part 2: if Statements¶

General form of what we saw in the example we explored at the start of lecture:
```
if condition:
   block1
else:
   block2
```
where
- condition is the result of a logical expression, such as the result of computing the value of a relational operation
- block1 is Python code executed when the condition is True
- block2 is Python code executed when the condition is False
All statements in the block1 and block2 must be indented the same number of spaces
The block continues until the indentation stops, and returns to the same level of indentation as the statement starting with if
The else: and block2 are optional, as the following example shows.

Example: Heights of Siblings¶

Here is a more extensive version of our initial example, implemented using two consecutive if statements and not using an else:

name1 = "Dale"
print "Enter the height of %s in cm ==> " %name1,
height1 = int(raw_input())

name2 = "Erin"
print "Enter the height of %s in cm ==> " %name2,
height2 = int(raw_input())

if height1 < height2:
    print "%s is taller" %name2
    max_height = height2

if height1 >= height2:
    print "%s is taller" %name1
    max_height = height1

print "The max height is %d" %max_height

This is not a good idea because we need to read the code carefully to believe those two if statements produce mutually exclusive results. Instead we go back to using else

name1 = "Dale"
height1 = int(raw_input("Enter the height of %s in cm ==> " %name1))

name2 = "Erin"
height2 = int(raw_input("Enter the height of %s in cm ==> " %name2,))

if height1 < height2:
    print "%s is taller" %name2
    max_height = height2
else:
    print "%s is taller" %name1
    max_height = height1

print "The max height is %d" %max_height

Notes:
- The blank lines are added for clarity; they are not required for these programs to have correct syntax.
- Neither program handles the case of Dale and Erin being the same height. For this we need the next Python construct.

Elif¶

Recall the kids guessing game where someone thinks of a number and you have to guess it. The only information you are given is that the person who knows the number tells you if your guess is too high, too low, or if you got it correct.

When we have three or more alternatives to consider we use the if-elif-else structure:

if condition1:
    block1
elif condition2:
    block2
else:
    block3

We’ll write the solution and discuss the flow of Python execution in class.
Notes:
- You do NOT need to have an else block.
- Exactly one block of code (block1, block2, block3) is executed!
- If we leave off the else: and block3, then it is possible that none of the blocks are executed.
- You can use multiple elif conditions and blocks.

Part 2 Exercise¶

Rewrite the height example to use elif to handle the case of Dale and Erin having the same height.

Part 3: More Complex Boolean Expressions, Starting with and¶

Consider the following piece of Python code:

if cel > 0 and cel < 100:
    print "At %dC water is liquid" %cel

A boolean expression involving and is True if and only if both the relational operations produce the value True

More Complex Boolean Expressions — or¶

Consider the following:

if cel < 0 or cel > 100:
    print "At %dC water is not a liquid" %cel

The boolean expression is True if ANY of the following occurs
- the left relational expression is True,
- the right relational expression is True,
- both the left and right relational expression are True.
This is called the inclusive or and it is somewhat different from common use of the word or in English.
For examples, in the sentence

You may order the pancakes or the omelet.

usually means you may choose pancakes, or you may choose an omelet, but you may not choose both (unless you pay extra).
- This is called the exclusive-or; it is only used in logic and computer science in very special cases.
- Hence, or always means inclusive-or.

Boolean Logic — not¶

We can also “logically negate” a boolean expression using not.

a = 15
b = 20
if not a<b:
    print "a is not less than b"
else:
    print "a is less than b"

Part 3 Exercises¶

What are the results of the following Python boolean expressions:

>>> x = 15
>>> y = -15
>>> z = 32
>>> x == y and y < z        #A
>>> x == y or y < z         #B
>>> x == abs(y) and y < z   #C
>>> x == abs(y) or y < z    #D
>>> not x == abs(y)         #E
>>> not x != abs(y)         #F

Suppose the bounds of a rectangle are defined by
```
x0 = 10
x1 = 16
y0 = 32
y1 = 45
```
Note that a point at location $x,y$ is inside the rectangle if

$x0 \leq x \leq x1 \qquad \text{and} \qquad y0 \leq y \leq y1.$
1. Write a Python boolean expression using and that is True if a point is inside the rectangle.
2. Write a Python boolean expression using or that is True if a point is outside the rectangle.

Summary and Looking Ahead¶

if-else and if-elif-else are tools for making decisions and creative alternative computations and results
The conditional tests involve relationship operators and logical operators
- Be careful of the distinction between = and ==
In Lecture 11 we will review boolean logic and discuss more complex if structures.