# Lecture 6 — Decisions¶

## 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

but we will not explore this until Lecture 9.

## 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 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 spacesThe

`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¶

Suppose we want to input the heights of two siblings and output the name and height of the taller of them.

We could write two consecutive

`if`

statements: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

Since the two

`if`

statements are (seemingly) exclusive, we can use the`if-else`

structure to simplify this: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,)) max_height = 0; 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

Note that none of the blank lines are required for these programs to have correct syntax.

Note also that 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 can use multiple
`elif`

conditions and blocks - 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

## 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`

.

- the left relational expression is
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 omlet.

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*.

- This is called the

## 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 is inside the rectangle if

- Write a Python boolean expression using
`and`

that is`True`

if a point is inside the rectangle. - Write a Python boolean expression using
`or`

that is`True`

if a point is outside the rectangle.

- Write a Python boolean expression using

## 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`==`

- Be careful of the distinction between
- In Lecture 9 we will review boolean logic and discuss more complex if structures.