Today - interpreter, math int/float, style, black box examples, boolean logic, string introduction, string +=, string for/i/range loop

Big Picture Strategy - Divide and Conquer

• Q: What is the main technique for solving big problems?
• A: Divide and Conquer
• Divide the big program into functions
• Work on one function at a time
• aka decomposition
• As we build up CS techniques ...
  Many techniques are in service of the big-picture goal

Data Flow Picture

Here is a way of looking at a program.

You have some files with data in them. You write code to lode the data into Python in one form. Then compute a transform into another form. Then a further computation produces an "answer" form. You publish the answer and get tweets of praise - the coding lifecycle! You can think of this as a sort of "data flow", from the original data to the final output.

Today: Black Box Function

• We have seen functions thus far, mainly we call them to run their code
• Today we will start using functions as data flow
• Each function is like a little box of some computation, with data-in and data-out
• One stage in the picture above might be one function

"Black Box" Function Model

Black-box model of a function: function runs with parameters as input, returns a value. All the complexity of its code is sealed inside.

The black box model makes it easy to call the function - provide data you have as the input, call the function, get back an answer.

Strategy - One Function at a Time

For Divide and Conquer, want to be able to work on each function separately, one at a time. We need to keep the functions sealed off from each other as much as possible. The black box model works well for this, narrowing the interactions to just the input and output data for each function.

Write Black Box Code - Cases

Here we'll work through the code for first black-box examples. There are in the logic 1 section on the experimental server.

We'll think about the various cases for the input, since ultimately the code needs to handle all possible input cases. Thinking about the various cases is an easy way to get started with the code for a function.

1. winnings1() Example

> winnings1()

• This is a first, simple example, just showing the mechanics
• Say we are writing a function for a lottery game
• Rules: input is an int score 0..10 inclusive
• score 0-4 -> winnings is score * 10
• score 5-10 -> winnings is score * 12
• Can make a table showing output for each input

score   winnings
0       0
1       10
2       20
3       30
4       40
5       60  # 12x kicks in here
6       72
7       84
8       96
9       108
10      120

1. Function Input: Parameter

def winnings1(score):
    ...

• The parameters to a function are its inputs
  Left side of black-box picture
• e.g. score is the input here
• Each parameter is like a variable with a value in it
• Code inside the function just uses the parameter value - easy

2. Function Output: return result

def winnings1(score):
    return score * 10

• When a return line runs in a function
• 1. It exits the run of the function immediately
• 2. It specifies the return value that will go back to the caller
  Often called the "result" of the function
• So the return statement makes the output of the function

Experiment 1 - winnings1()

You can type these in and hit the Run button as we go or just watch as we go. The results are pretty easy to follow.

def winnings1(score):
    return score * 10

• Try 1 line for the function:
  return score * 10
• Look at the table of output
• See the basic roles of parameter/return
• But this output is wrong half the time

Experimental Server Output Format

• Run function on experimental server, generates table of outputs
• It calls the function with many inputs
• Shows the function result one per row
• First "call" column is the input
• Second "got" column is what the function returned
• Easy to see the function's behavior this way
• Black box model: think of function as its inputs and outputs

if-return Pick-Off Strategy

• The function needs to handle all possible input cases
• Have if-logic to detect one case
  Return the answer for that case
  Exiting the function
• Lines below have if-return logic for other cases
• Code is "picking off" the cases one by one
• As we get past if-checks .. input must be a remaining case
• Analogy: coin sorting machine
  Coin rolls past holes, smallest to largest
  1st hole dime, 2nd hole penny, 3rd nickel, 4th quarter
  A dime never makes it to the quarter-hole
  The dime is picked-off earlier

Experiment 2

def winnings1(score):
    if score < 5:
        return score * 10

Add if-logic to pick off the < 5 case. Run it. We can see that it's right for half the cases.

None Result

• None is the default return value of a function
• None is returned if there is no explicit return value
• This can happen by "falling off the end" of the function
  All its lines have run and the function is finished
• Above example, we see None if score >= 5
• If you see None like this
  Look at your code: how is it not doing a return?

Experiment 3 - Very Close

def winnings1(score):
    if score < 5:
        return score * 10

    if score >= 5:
        return score * 12

Add pick-off code for the score >= 5 case. This code returns the right result in all cases. There is just at tiny logical flaw.

Experiment 4 - Perfect

def winnings1(score):
    if score < 5:
        return score * 10
    
    # Run gets here: we know score >= 5
    return score * 12

• Each pick-off recognizes a case and exits the function
• Therefore for lines below the pick-off, the picked-off case is excluded
• That is, the score >= 5 test is unnecessary
• This helps with your one-at-a-time attention
  Work on code for case-1
  When that's done, put it out of mind
  Work on case-2, knowing case-1 is out of the picture

winnings1() Observations

• Thinking about cases, if-logic to pick off one case at a time
• Try changing <= to < to make Off By One errors
• Be careful right at the boundary

What About This Code?

What about this solution...

def winnings1(score):
    if score < 5:
        return score * 10
        return score * 12

That does not work. The second return is in the control of the if because of the indentation. It never runs because the line above exits the function. Obviously indentation is very significant for what code means in Python.

Think Like A Programmer - Systematic Cases

• Think like a programmer, you know the code needs to work on all the cases
• Natural to think about case-1, then case-2, ...
• This is helpful when you are staring at a blank screen
• Think .. ok, what's one case, write code to pick-off that one

2. Winnings2 Example

Extra practice example.

> winnings2()

Say there are 3 cases. Use a series of if-return to pick them off. Need to think about the order. Need to put the == 10 case early.

Winnings2: The int score number is in the range 0..10 inclusive. Bonus! if score is 10 exactly, winnings is score * 15. If score is between 4 and 9 inclusive, winnings is score * 12. if score is 3 or less, winnings is score * 10. Given int score, compute and return the winnings.

Solution

def winnings2(score):
    if score == 10:
        return score * 15
  
    if score >= 4:  # score <= 9 is implicit
        return score * 12
    
    # All score >= 4 cases have been picked off.
    # so score < 4 here.
    return score * 10

    # Here the cases are handled from 10 to 0.
    # The opposite order would be fine too.

Boolean Values

For more detail, see guide Python Boolean

• "boolean" value in code - True or False
• if-test and while-test work with boolean inputs
• e.g. bit.front_clear() returns a boolean
• So we have if bit.front_clear():

Ways to Get a Boolean

• == operator to compare two things
  2 == 1 + 1 returns True
  Two equal signs
  Since single = is used for var assignment
• != - not-equal test
  2 != 10 returns True
• Compare greater-than / less-than
• < is strict less-than
• <= is less-or-equal
  6 < 10 returns True
6 < 6 returns False (strict)
  6 <= 6 returns True
• > is strict greater-than
• >= is greater-or-equal
• These all work with ints, floats, other types of data

Try this in the interpreter (or Hack Mode button at bottom experimental server)

>>> n = 5   # assign to n to start
>>> n == 6
False
>>> n == 5
True
>>> n != 6
True
>>> 
>>> n < 10
True
>>> n < 5  # < is strict
False
>>> 
>>> n <= 5  # less-or-equal
True
>>> 
>>> n > 0
True

Boolean Operators: and or not

• An operator combines values in an expression
  e.g. + operator, 1 + 2 returns 3
• Boolean operators combine True False values
• Boolean operators: and or not
• Suppose here that xxx and yyy are boolean values
• xxx and yyy - if both sides are True, then it is True
  aka all the inputs must be True
• xxx or yyy - if either side or both sides are True, it is True
  aka some input must be True
• not xxx = inverts True/False
  Why does not go to the left?
  It's like the - for a negative number
  e.g. -6

Weather Examples - and or not

Say we have temp variable is a temperature, and is_raining is a Boolean indicating if it's raining or not. Here are some examples to demonstrate and or not:

# OR: either or both are true
# Say we don't want to go outside if
# if it's cold or raining.
if temp < 50 or is_raining:
    print('not going outside!')


# AND
# We want to go outside if it's snowing.
if temp < 32 and is_raining:
    print('yay snow!')

Boolean Exercise

What is the code to detect if the temp is over 70 and it's not raining?

if -what goes here?-:
    print('Sunny and nice!')

if temp > 70 and not is_raining:
    print('Sunny and nice!')

# Style note: don't use == False or == True
# to form a test. See above how "is_raining"
# is used directly in the test, or with a "not"
# in front of it.

Numeric and Example

Suppose we have this code, and n holds an int value.

if n > 0 and n < 10:
   # get here if test is True

What must n be inside the if-statement? Try values like 0 1 2 3 . 8 9 10

You can work out that n must be a an int value in the range 1..9 inclusive.

3. is_teen(n) Example

> is_teen()

is_teen(n): Given an int n which is 0 or more. Return True if n is a "teenager", in the range 13..19 inclusive. Otherwise return False. Write a boolean test to pick off the teenager case.

Solution

def is_teen(n):
    # Use and to check
    if n >= 13 and n <= 19:
        return True

    return False

    # Future topic: possible to write this
    # as one-liner: return n >= 13 and n <= 19

4. Lottery Scratcher Example

> scratcher()

An extra example for practice.

Lottery scratcher game: We have three icons called a, b, and c. Each is an int in the range 0..10 inclusive. If all three are the same, winnings is 100. Otherwise if 2 are the same, winnings is 50. Otherwise winnings is 0. Given a, b and c inputs, compute and return the winnings. Use and/or/== to make the tests.

Solution:

def scratcher(a, b, c):
    # 1. All 3 the same
    if a == b and b == c:
        return 100
    
    # 2. Pair the same (3 same picked off above)
    if a == b or b == c or a == c:
        return 50
    
    # 3. Run gets to here, nothing matched
    return 0

Strings

For more detail, see guide Python Strings

• A very widely used data type
• e.g. a string: 'Hello'
• String is a sequence of "characters" or "chars"
• e.g. urls, paragraphs
• A string written in code is called a "literal"
• e.g. 'This is a string'
• Python string literals written on one line with single quotes ' (prefer)
• Double quote also works " - two ways of writing the same string:
  'Hello'
"Hello"

len() function

• Returns number of chars in string
• Works on other collections too
• Not noun.verb style

>>> len('Hello')
5
>>> s = 'Hello'   # Equivalently
>>> len(s)
5
>>> len('x')
1
>>> len('')
0

Empty String ''

• The "empty string" is the string of 0 chars
• Written like: '' or ""
• This is a valid string, its len is 0
• A common edge case to think about with string algorithms
• Does the code need to work on the empty string?
• Probably yes

Zero Based Indexing - Super Common

• Characters in strings are indexed starting with 0 for the first char
  Index numbers are: 0, 1, 2 .... (length-1)
• Everything in computers uses this zero-based indexing scheme
• Pixels within an image used this, x/y vs. width/height
• Index number addresses each char in the string
• Foreshadow: we'll use index numbers, [ ], and len()...
  For many many linear type data arrangements
  But for today strings

String Square Bracket Index

• Use square bracket to access a char by index number
• Valid index numbers: 0..len-1
• Get out of bounds error for too large index number

>>> s = 'Python'
>>> s[0]
'P'
>>> s[1]
'y'
>>> s[4]
'o'
>>> s[5]
'n'
>>> s[6]
IndexError: string index out of range

String Immutable

• A string in memory is not editable
• "Immutable" is the official word for this
• e.g. square bracket cannot change a string

>>> s = 'Python'
>>> s[0]        # read ok
'P'
>>> s[0] = 'X'  # write not ok
TypeError: 'str' object does not support item assignment

String +

• Plus operator + combines 2 strings to make a new, bigger string
  aka "concatenate"
• Uses new memory to hold the result
• Does not change the original strings

>>> a = 'Hello'
>>> b = 'there'
>>> a + b
'Hellothere'
>>> a
'Hello'

1. Set Var With =

We've already used = to set a variable to point to a value. The code below sets s to point to the string 'hello'.

s = 'hello'

2. Change Var With =

What if we use = to set an existing variable to point to a new value? This just changes the variable to point to the latest value, forgetting the previous value. The assignment = could be translated to English as "now points to".

s = 'hello'
# change s to point to 'bye'
s = 'bye'

Useful Pattern: s = s + something

• Use + to add something at the end of a string, yielding a new bigger string
• Use = to assign the new string back to the variable
• e.g. s = s + 'xxx'
• The += operator works here too
• We are constructing a new, bigger string with each step

>>> s = 'hello'
>>> s = s + '!'
>>> # Q: What is s now?

Answer: s is 'hello!' after the two lines. So s = s + xxx is a way of adding something to the right side of a string. The following form does the exactly the same thing using += as a shorthand:

>>> s = 'hello'
>>> s += '!'

String += Strategy

Use a series of += to add on the end.

>>> s = 'hello'
>>> s = s + '!'
>>> s = s + '!'
>>> s
'hello!!'

Recall: String Index Numbers

Here is our string, using zero-based index numbers to refer to the individual chars..

>>> s = 'Python'
>>> s[0]
'P'
>>> s[1]
'y'
>>>

How To Loop Over Those Index Numbers?

The length of the string is 6. The index numbers are 0, 1, 2, 3, 4, 5. How to write a loop that generates those numbers? It's the same loop we used to, say, loop over the x values of an image. If the image width was 100, we wanted the index numbers 0, 1, 2.. 99. Strings work the same way, use range(len(s)) to generate the index numbers.

Standard loop: for i in range(len(s)):

This is the standard, idiomatic loop to go through all the index numbers. It's traditional to use a loop variable with the simple name i with this loop. Inside the loop, use s[i] to access each char of the string.

• The standard loop to go through all the index numbers
• e.g. s = 'Python'
• Length is 6
• Want index numbers 0, 1, 2, 3, 4, 5
• Recall range(n) goes 0 .. n-1
• So use range(6) aka range(len(s))
• for i in range(len(s)):
• Use s[i] to access each char in the loop
• Standard to use the variable name i for this loop
• This loop is so common, it's idiomatic
• We'll see another way to do this later

# have string s, loop over its chars
for i in range(len(s)):
    # access s[i] in here

1. double_char() Example

double_char(s): Given string s. Return a new string that has 2 chars for every char in s. So 'Hello' returns 'HHeelllloo'. Use a for/i/range loop.

> double_char

Also, see the experimental server section string2 for many problems like double_char()

• Standard for/i/range loop to look at every char
• Initialize result = '' variable before loop
• Update in loop: result = result + xxxx
• Use s[i] to access each char in loop
• Return result at end
• Could use += shortcut
• Q: does it work on empty string input?

Solution code

def double_char(s):
    result = ''
    for i in range(len(s)):
        result = result + s[i] + s[i]
    return result

Exercise/Example - not_ab()

not_ab(s): Given string s. Return a new string made of all the chars in s which are not lowercase 'a' or 'b'. Use a for/i/range loop.

Try to solve using for/i/range loop with the += pattern like double_char(). Test each char to see if it is 'a' or 'b' using !=.

> not_ab