01 Introduction to programming, Introduction to Python (Chapter 1, 2)

Weighting marks of 84, 61 and 73 into one number

The course counts labs as 20 per cent, the midterm as 40 and the final as 40. A student has 84, 61 and 73. Write the algorithm first, in words, then the program.

The algorithm, with every step doing exactly one thing:

1. Name the three marks and give each its value.
2. Multiply each mark by its weight as a decimal: 0.2, 0.4, 0.4.
3. Add the three products into one name.
4. Show that name.

Now the same four steps as Python, which is the only part that would change if the course switched language:

lab_average = 84
midterm = 61
final = 73

overall = 0.2 * lab_average + 0.4 * midterm + 0.4 * final
print('overall:', overall)

Output:

overall: 70.4

overall: 70.4

The same three marks, averaged instead of weighted

Here is a second program for the same task. It runs, it prints a believable mark, and it is wrong. Find the step of the algorithm it fails to carry out.

lab_average = 84
midterm = 61
final = 73

overall = (lab_average + midterm + final) / 3
print('overall: {:.1f}'.format(overall))

Output:

overall: 72.7

Two broken files: one prints nothing, one prints a line first

Both files below are wrong. Before reading the outputs, decide which one gets to print something.

First file.

print('this line is fine')
print 'this line is not'
print('this line never runs')

What the screen shows:

  File "broken.py", line 2
    print 'this line is not'
SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?

The first line is flawless and it still never ran. Python read the file, found a line it could not even parse, and refused the whole file. That is why the screen has no this line is fine on it.

Second file.

print('this line is fine')
total = 5
print('total is ' + total)
print('this line never runs')

What the screen shows:

this line is fine
Traceback (most recent call last):
  File "broken.py", line 3, in <module>
    print('total is ' + total)
TypeError: can only concatenate str (not "int") to str

Here the first line did run, and its output is sitting above the report. Python only discovered the problem when it tried to join a piece of text to the number 5.

A till that never complains and is ten per cent wrong

Three items at 80 lira each, with a ten per cent discount on the bill. The program below runs to the end and prints a number with no complaint at all.

price = 80
quantity = 3
discount = 10

total = price * quantity - discount / 100
print('total:', total)

Output:

total: 239.9

The discount was meant to take ten per cent off 240, which is 24, leaving 216. What came out was 239.9, which is 240 minus ten hundredths. The program subtracted discount / 100, a tenth of a lira, instead of that fraction of the total.

Asking five different values what they are

type is the tool that settles arguments. Here it is used on one value of each kind, including the odd one out.

print(type(7))
print(type(7.0))
print(type('7'))
print(type(True))
print(type(None))

Output:

<class 'int'>
<class 'float'>
<class 'str'>
<class 'bool'>
<class 'NoneType'>

The output names the class of each object. bool has a class name of its own, and None has a type all to itself with exactly one value in it.

The conversions are the same four names used as functions:

print(float(7))
print(int(7.9))
print(int(-7.9))
print(str(7) , type(str(7)))
print(bool(7), bool(0), bool(0.0))

Output:

7.0
7
-7
7 <class 'str'>
True False False

Line four is the one to look at twice. The screen shows 7 and then says the thing printed was a str. A number and the text of a number look identical once they are on the screen, which is exactly why the earlier till program could break.

Why int(9.99) * 2 and int(9.99 * 2) differ by one

Same value, same conversion, same multiplication, and two answers one apart, because the brackets decide which happens first.

value = 9.99
print(int(value) * 2)
print(int(value * 2))
print(float(int(value)))

Output:

18
19
9.0

Cut first and the 0.99 never gets doubled, so the answer is 18. Double first and the 0.99 becomes 1.98, which pushes the value past 19 before the cut, so the answer is 19. The third line shows how permanent the loss is: converting to int and back to float gives 9.0, and the 0.99 is not coming back.

18
19
9.0

radius changes from 2.0 to 3.0 and area does not follow

The classic first week trap, and the reason the memory diagram above exists. Read the code, decide what the second print shows, then look.

pi = 3.14
radius = 2.0
area = pi * radius ** 2

radius = 3.0
print('radius:', radius)
print('area:', area)

Output:

radius: 3.0
area: 12.56

The first line of output moved and the second did not. If you want the area of the bigger circle you have to say so:

pi = 3.14
radius = 2.0
area = pi * radius ** 2

radius = 3.0
area = pi * radius ** 2
print('radius:', radius)
print('area:', area)

Output:

radius: 3.0
area: 28.26

One extra line, the same expression as before, and now both numbers belong to the same circle.

Swapping two names in one line, and the two line version that fails

Two names, and the job is to exchange their values. Python has a one line way to do it, and the obvious two line way is broken.

x, y = 2, 3
x, y = y, x
print('x =', x)
print('y =', y)

Output:

x = 3
y = 2

Both right hand sides are worked out before either name moves, so the pair on the right is the old pair, 3 and 2. Now the two line attempt:

x, y = 2, 3
x = y
y = x
print('x =', x)
print('y =', y)

Output:

x = 3
y = 3

The first line pointed x at 3 and nothing is left pointing at the old 2, so the second line can only copy 3 back. Both names end at 3 and one value is gone.

197 minutes as hours and minutes, first with the wrong slash

A duration in minutes has to come out as whole hours and whole minutes. Here is the attempt almost everybody writes first.

minutes_total = 197

hours = minutes_total / 60
minutes = minutes_total % 60
print('{:d} h {:d} min'.format(hours, minutes))

What the screen shows:

Traceback (most recent call last):
  File "clock.py", line 5, in <module>
    print('{:d} h {:d} min'.format(hours, minutes))
ValueError: Unknown format code 'd' for object of type 'float'

Read the error name rather than the sentence: a value that should have been a whole number is a float. 197 / 60 is 3.283333333333333, and a field that says d refuses it.

The fix is one character.

minutes_total = 197

hours = minutes_total // 60
minutes = minutes_total % 60
print('{:d} h {:d} min'.format(hours, minutes))

Output:

3 h 17 min

3 h 17 min

Evaluating 2 + 3 * 4 ** 2 // 5 without a calculator

Four operators, no brackets, one right answer. Work through it with the tier ladder rather than left to right.

print(2 + 3 * 4)
print((2 + 3) * 4)
print(2 + 3 * 4 ** 2 // 5)
print(2 ** 3 ** 2)
print(-2 ** 2)
print((-2) ** 2)

Output:

14
20
11
512
-4
4

The first two lines are the plain precedence check, the third is the four operator expression, and the last three are the two associativity traps that turn up in every exam: the power tower and the leading minus.

A three line receipt whose numbers line up on the last digit

Three prices, an 18 per cent tax, and the answer that opened this section: the line that was asked for against the line that came out.

# bill.py - subtotal, VAT and total for three items.
price_1 = 24.5
price_2 = 9.9
price_3 = 130.0
vat_rate = 0.18

subtotal = price_1 + price_2 + price_3
vat = subtotal * vat_rate
total = subtotal + vat

print('subtotal:{:10.2f}'.format(subtotal))
print('vat:     {:10.2f}'.format(vat))
print('total:   {:10.2f}'.format(total))
print('exact total:', total)

Output:

subtotal:    164.40
vat:          29.59
total:       193.99
exact total: 193.99200000000002

The first three lines are the receipt. Each label is different in length, so the widths after the labels are different too, and the effect is one column of numbers whose last digits agree. The fourth line is the same total with no field at all, and it is the number the hook complained about: the value really is 193.99200000000002, and only the printed text was ever 193.99.

subtotal:    164.40
vat:          29.59
total:       193.99
exact total: 193.99200000000002

The same mark printed three ways, and the value left untouched

One float, three printings, and the proof that a field is not a change.

mark = 61.276
print('{:.1f}'.format(mark))
print(mark)
print(mark * 2)

Output:

61.3
61.276
122.552

The first line is the field, the second is the value, and the third doubles it. If the field had rounded anything the third line would read 122.6.

The same two lines can be written with a different tool, and they produce the same text:

name = 'Ada'
mark = 61.276
print(f'{name:s} scored {mark:.1f}')
print('{:s} scored {:.1f}'.format(name, mark))

Output:

Ada scored 61.3
Ada scored 61.3

The first form puts the name straight inside the string, the second passes the values to format. The part after the colon is identical in both, which is the part worth learning; a closed book exam sheet lists format, so that is the form used throughout these notes.

61.3
61.276
122.552

The same area calculation, written twice

Both programs below compute the same number and print it. One of them you can hand to a lab assistant.

Written for the machine.

p=3.14
r=2.0
a=p*r**2
print(a)

Output:

12.56

Three names of one letter each, no spaces around the operators, no unit anywhere, and an answer with fourteen digits in it. Nothing here is wrong and nothing here can be checked either.

Written for a reader.

# Area of a circular flower bed, in square metres.
PI = 3.14
radius = 2.0

area = PI * radius ** 2
print('area: {:.2f}'.format(area))

Output:

area: 12.56

The same arithmetic. The names now say what the numbers are, the constant is in capitals because it does not change, one comment gives the unit, and the output has the two decimals money and measurements normally get.

Two comments, and only one of them earns its line

A comment costs a line and buys nothing automatically. Here are one of each kind in the same file.

# Add 1 to counter.
counter = 41 + 1

# The till sends the amount in kurus, so it is turned into lira
# once, here, and every later line can trust the unit.
total_kurus = 19399
total_lira = total_kurus / 100

print(counter, total_lira)

Output:

42 193.99

The first comment says what the line already says, word for word. If the line changes and the comment does not, it becomes a lie, and it was never informative anyway.

The second says something the code cannot: which unit the number arrived in and why the division happens once, here, rather than in three places later. That is a choice, and a choice is the kind of thing a comment is for.

42 193.99