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You do deliberate practice to improve
your ability to perform a task. It’s about
skill and technique.
Deliberate practice means repetition.
You do deliberate practice to master the
task, not to complete the task.
Jon Jagger
Do Lots of Deliberate Practice

Rien n’est plus dangereux
qu’une idée, quand on n’a
qu’une idée.
Émile-Auguste Chartier

Nothing is more dangerous
than an idea, when you
have only one idea.
Émile-Auguste Chartier

c2
½ab
½ab ½ab
½ab
c2 + 2ab

Fizz buzz is a group word
game for children to teach
them about division.
http://en.wikipedia.org/wiki/Fizz_buzz

Players generally sit in a circle. The player
designated to go first says the number "1", and
each player thenceforth counts one number in
turn. However, any number divisible by three is
replaced by the word fizz and any divisible by five
by the word buzz. Numbers divisible by both
become fizz buzz. A player who hesitates or
makes a mistake is eliminated from the game.

Adults may play Fizz buzz as a
drinking game, where making
a mistake leads to the player
having to make a drinking-
related forfeit.
[citation needed]

Fizz buzz has been used as an
interview screening device for
computer programmers.

FizzBuzz was invented to avoid
the awkwardness of realising
that nobody in the room can
binary search an array.
https://twitter.com/richardadalton/status/591534529086693376

public class FizzBuzzTests
{
@Test
public void testFizzBuzz()
{
...
}
}

{
@Test
public void testFizzBuzzIsOK()
{
...
}
}

{
@Test
public void fizzBuzzOf1Is1()
{
...
}
}

{
@Test
{
...
}
@Test
{
...
}
}

{
@Test
{
...
}
@Test
{
...
}
@Test
public void fizzBuzzOf3IsFizz()
{
...
}
}

{
@Test
{
...
}
@Test
{
...
}
@Test
public void fizzBuzzOf3IsFizz()
{
...
}
...
}

public class FizzBuzzCalculator
{
...
}

I have yet to see any problem,
however complicated, which,
when you looked at it in the
right way, did not become still
more complicated.
Anderson's Law

public class FizzBuzzCalculator
{
private static final String FIZZ = "Fizz";
private static final String BUZZ = "Buzz";
private static final String FIZZBUZZ = "FizzBuzz";
private int fizzMultipleValue;
private int buzzMultipleValue;
private int fizzBuzzMultipleValue;
public FizzBuzzCalculator(int fizzMultipleValue, int buzzMultipleValue)
{
this.fizzMultipleValue = fizzMultipleValue;
this.buzzMultipleValue = buzzMultipleValue;
calculateFizzBuzzMultipleValue();
}
private void calculateFizzBuzzMultipleValue()
{
fizzBuzzMultipleValue = fizzMultipleValue * buzzMultipleValue;
}
public int getFizzMultipleValue()
{
return fizzMultipleValue;
}
public void setFizzMultipleValue(int fizzMultipleValue)
{
this.fizzMultipleValue = fizzMultipleValue;
}
public int getBuzzMultipleValue()
{
return buzzMultipleValue;
}
public void setBuzzMultipleValue(int buzzMultipleValue)
{
this.buzzMultipleValue = buzzMultipleValue;
}
public String returnFizzBuzzOrNumber(int n)
{
if (isFizzBuzz(n))
return FIZZBUZZ;
if (isFizz(n))
return FIZZ;
if (isBuzz(n))
return BUZZ;
return new Integer(n).toString();
}
private static boolean isFizz(int n)
{
return n % fizzMultipleValue == 0;
}
private static boolean isBuzz(int n)
{
return n % buzzMultipleValue == 0;
}
private static boolean isFizzBuzz(int n)
{
return n % fizzBuzzMultipleValue == 0;
}
}

def fizzbuzz(n)
{
result = ''
if (n % 3 == 0)
result += 'Fizz'
if (n % 5 == 0)
result += 'Buzz'
if (!result)
result += n
result
}

def fizzbuzz(n)
{
if (n % 15 == 0)
'FizzBuzz'
else if (n % 3 == 0)
'Fizz'
else if (n % 5 == 0)
'Buzz'
else
n.toString()
}

def fizzbuzz(n)
{
n % 15 == 0 ? 'FizzBuzz' :
n % 3 == 0 ? 'Fizz' :
n % 5 == 0 ? 'Buzz' :
n.toString()
}

def fizzbuzz(n)
{
n in (0..100).step(15) ? 'FizzBuzz' :
n in (0..100).step(3) ? 'Fizz' :
n in (0..100).step(5) ? 'Buzz' :
n.toString()
}

fizzes = [''] + ([''] * 2 + ['Fizz']) * 33 + ['']
buzzes = [''] + ([''] * 4 + ['Buzz']) * 20
numbers = (0..100)*.toString()
def fizzbuzz(n)
{
fizzes[n] + buzzes[n] ?: numbers[n]
}

$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }

echo {1..100} | tr ' ' 'n' | awk '
$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }
'

echo {1..100} | tr ' ' 'n' | awk '
$0 % 3 == 0 { printf "Fizz" }
$0 % 5 == 0 { printf "Buzz" }
$0 % 3 != 0 && $0 % 5 != 0 { printf $0 }
{ printf "n" }
' | diff - expected && echo Pass

1
2
Fizz
4
Buzz
Fizz
7
8
Fizz
Buzz
11
Fizz
13
14
FizzBuzz

We instituted a rigorous regression
test for all of the features of AWK. Any
of the three of us who put in a new
feature into the language [...], first
had to write a test for the new feature.
Alfred Aho
http://www.computerworld.com.au/article/216844/a-z_programming_languages_awk/

Red
Write a failing test for
a new feature
Green
Write enough code to
pass the test
Refactor
Refine code and tests
Test-First Cycle

Red
Write a failing test for
a new feature
Green
Write enough code to
pass the test
Test-First Dumbed Down

assert fizzbuzz(1) == '1'
def fizzbuzz(n):
return '1'

def fizzbuzz(n):
if n == 1: return '1'
return '2'

assert fizzbuzz(3) == 'Fizz'
def fizzbuzz(n):
return 'Fizz'

assert fizzbuzz(5) == 'Buzz'
assert fizzbuzz(15) == 'FizzBuzz'
def fizzbuzz(n):
if n == 3: return 'Fizz'
if n == 5: return 'Buzz'
if n == 11: return '11'
if n == 13: return '13'
if n == 14: return '14'
return 'FizzBuzz'

assert fizzbuzz(15) == 'FizzBuzz'
...
def fizzbuzz(n):
if n == 11: return '11'
if n == 13: return '13'
if n == 14: return '14'
if n == 15: return 'FizzBuzz'
...
if n == 98: return '98'
return 'Buzz'

def fizzbuzz(n):
if n == 11: return '11'
if n == 13: return '13'
if n == 14: return '14'
if n == 15: return 'FizzBuzz'
...
if n == 98: return '98'

def fizzbuzz(n):
return {
1: lambda: '1',
2: lambda: '2',
3: lambda: 'Fizz',
4: lambda: '4',
5: lambda: 'Buzz',
6: lambda: 'Fizz',
7: lambda: '7',
8: lambda: '8',
9: lambda: 'Fizz',
10: lambda: 'Buzz',
11: lambda: '11',
12: lambda: 'Fizz',
13: lambda: '13',
14: lambda: '14',
15: lambda: 'FizzBuzz',
...
98: lambda: '98',
99: lambda: 'Fizz',
100: lambda: 'Buzz'
}[n]()

def fizzbuzz(n):
return {
1: '1',
2: '2',
3: 'Fizz',
4: '4',
5: 'Buzz',
6: 'Fizz',
7: '7',
8: '8',
9: 'Fizz',
10: 'Buzz',
11: '11',
12: 'Fizz',
13: '13',
14: '14',
15: 'FizzBuzz',
...
98: '98',
99: 'Fizz',
100: 'Buzz'
}[n]

def fizzbuzz(n):
return [
'1',
'2',
'Fizz',
'4',
'Buzz',
'Fizz',
'7',
'8',
'Fizz',
'Buzz',
'11',
'Fizz',
'13',
'14',
'FizzBuzz',
...
'98',
'Fizz',
'Buzz'
][n-1]

Plan
Establish hypothesis,
goal or work tasks
Do
Carry out plan
Study
Review what has
been done against
plan (a.k.a. Check)
Act
Revise approach
or artefacts based
on study
Deming/Shewhart Cycle

Write
Create or extend a test
case for new
behaviour — as it's
new, the test fails
Reify
Implement so that
the test passes
Reflect
Is there something in
the code or tests that
could be improved?
Refactor
Make it so!
Test-First Cycle

actual = [fizzbuzz(n) for n in range(1, 101)]
truths = [
every result is 'Fizz', 'Buzz', 'FizzBuzz' or a decimal string,
every decimal result corresponds to its ordinal position,
every third result contains 'Fizz',
every fifth result contains 'Buzz',
every fifteenth result is 'FizzBuzz',
the ordinal position of every 'Fizz' result is divisible by 3,
the ordinal position of every 'Buzz' result is divisible by 5,
the ordinal position of every 'FizzBuzz' result is divisible by 15
]
assert all(truths)

actual = [fizzbuzz(n) for n in range(1, 101)]
truths = [
all(a in {'Fizz', 'Buzz', 'FizzBuzz'} or a.isdecimal() for a in actual),
all(int(a) == n for n, a in enumerate(actual, 1) if a.isdecimal()),
all('Fizz' in a for a in actual[2::3]),
all('Buzz' in a for a in actual[4::5]),
all(a == 'FizzBuzz' for a in actual[14::15]),
all(n % 3 == 0 for n, a in enumerate(actual, 1) if a == 'Fizz'),
all(n % 5 == 0 for n, a in enumerate(actual, 1) if a == 'Buzz'),
all(n % 15 == 0 for n, a in enumerate(actual, 1) if a == 'FizzBuzz')
]
assert all(truths)

A work of art is the
unique result of a
unique temperament.
Oscar Wilde

https://twitter.com/wm/status/7206700352

bi-quinary coded decimal, noun
▪ A system of representing numbers based on counting in fives,
with an additional indicator to show whether the count is in the
first or second half of the decimal range, i.e., whether the number
represented is in the range 0–4 or 5–9 (or in the range 1–5 or 6–10).
▪ This system is found in many abacus systems, with paired
columns of counters (normally aligned) representing each bi-
quinary range.
▪ The Roman numeral system is also a form of bi-quinary coded
decimal.

proc roman numerals = (int year) string:
skip;

assert (roman numerals (1) = “I”)

“I”;

assert (roman numerals (1) = “I”);
assert (roman numerals (5) = “V”)

if year = 5 then “V” else “I” fi;

assert (roman numerals (5) = “V”);
assert (roman numerals (10) = “X”)

if year = 10 then “X”
elif year = 5 then “V”
else “I”
fi;

assert (roman numerals (5) = “V”);
assert (roman numerals (10) = “X”);
assert (roman numerals (50) = “L”);
assert (roman numerals (100) = “C”);
assert (roman numerals (500) = “D”);
assert (roman numerals (1000) = “M”)

if year = 1000 then “M”
elif year = 500 then “D”
elif year = 100 then “C”
elif year = 50 then “L”
elif year = 10 then “X”
elif year = 5 then “V”
else “I”
fi;

[] struct (int value, string letters) mapping =
(
(1000, “M”),
(500, “D”),
(100, “C”),
(50, “L”),
(10, “X”),
(5, “V”),
(1, “I”)
);

begin
string result := "";
for entry from lwb mapping to upb mapping do
if value of mapping[entry] = year then
result := letters of mapping[entry]
fi
od;
result
end;

(
if value of mapping[entry] = year then
result := letters of mapping[entry]
fi
od;
result
);

[] proposition roman numerals spec =
(
("Decimal positions correspond to numerals",
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
("Quinary values correspond to numerals",
((5, "V"), (50, "L"), (500, "D")))
);

(
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
("Quinary intervals correspond to numerals",
((5, "V"), (50, "L"), (500, "D")))
);
test (roman numerals, roman numerals spec)

mode test = struct (int input, string expected);
mode proposition = struct (string name, flex [1:0] test tests);

proc test = (proc (int) string function, [] proposition spec) void:
for entry from lwb spec to upb spec do
print (name of spec[entry]);
string report := "", separator := " failed:";
[] test tests = tests of spec[entry];
for test from lwb tests to upb tests do
int input = input of tests[test];
string expected = expected of tests[test];
string actual = function (input);
if actual /= expected then
report +:=
separator + " for " + whole (input, 0) +
" expected " + expected + " but was " + actual
separator := “,”
fi
od;
print (if report = "" then (new line) else (new line, report, new line) fi)
od;

(
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
((5, "V"), (50, "L"), (500, "D"))),
("Multiples of decimals are additive",
((2, "II"), (30, "XXX"), (200, "CC"), (4000, "MMMM")))
);

(
int value = year;
if value mod value of mapping[entry] = 0 then
while value > 0 do
result +:= letters of mapping[entry];
value -:= value of mapping[entry]
od
fi
od;
result
);

(
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
((5, "V"), (50, "L"), (500, "D"))),
((2, "II"), (30, "XXX"), (200, "CC"), (4000, "MMMM"))),
("Non-multiples of decimals are additive",
((6, "VI"), (23, "XXIII"), (273, "CCLXXIII"), (1500, "MD")))
);

(
int value = year;
while value >= value of mapping[entry] do
result +:= letters of mapping[entry];
value -:= value of mapping[entry]
od
od;
result
);

(
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
((5, "V"), (50, "L"), (500, "D"))),
((2, "II"), (30, "XXX"), (200, "CC"), (4000, "MMMM"))),
((6, "VI"), (23, "XXIII"), (273, "CCLXXIII"), (1500, "MD"))),
("Numeral predecessors are subtractive",
((4, "IV"), (9, "IX"), (40, "XL"), (90, "XC"), (400, "CD"), (900, "CM")))
);

[] struct (int value, string letters) mapping =
(
(1000, "M"), (900, "CM"),
(500, "D"), (400, "CD"),
(100, "C"), (90, "XC"),
(50, "L"), (40, "XL"),
(10, "X"), (9, "IX"),
(5, "V"), (4, "IV"),
(1, "I")
);

(
((1, "I"), (10, "X"), (100, "C"), (1000, "M"))),
((5, "V"), (50, "L"), (500, "D"))),
((2, "II"), (30, "XXX"), (200, "CC"), (4000, "MMMM"))),
((6, "VI"), (23, "XXIII"), (273, "CCLXXIII"), (1500, "MD"))),
("Numeral predecessors are subtractive",
((4, "IV"), (9, "IX"), (40, "XL"), (90, "XC"), (400, "CD"), (900, "CM"))),
("Subtractive predecessors are additive",
((14, "XIV"), (42, "XLII"), (1968, "MCMLXVIII")))
);

We could, of course, use any notation
we want; do not laugh at notations;
invent them, they are powerful. In
fact, mathematics is, to a large extent,
invention of better notations.
Richard Feynman

$ ./roman 42
XLII
$ cat roman
printf %$1s |
tr ' ' 'I' |
sed '
s/IIIII/V/g
s/IIII/IV/
s/VV/X/g
s/VIV/IX/
s/XXXXX/L/g
s/XXXX/XL/
s/LL/C/g
s/LXL/XC/
s/CCCCC/D/g
s/CCCC/CD/
s/DD/M/g
s/DCD/CM/
'
echo

Style is time’s fool.
Form is time’s student.
Stewart Brand

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