def dec_to_unary(num):
"""Tally representation e.g. | = 1, / = 5"""
result = ''
rounds = num // 5
fives = 1
if rounds < 5:
result = '|' * num
else:
for round in range(0, rounds + 1):
# Reset tally "five" marker every time it gets to five.
if fives == 5:
result += '/'
fives = 0
else:
result += '|'
fives += 1
print_h4('Base 1', desc='aka "tally"')
print('{} base 1 = {}'.format(num, result))
def dec_to_unary(num):
"""Tally representation e.g. | = 1, / = 5"""
result = ''
rounds = num // 5
fives = 1
if rounds < 5:
result = '|' * num
else:
for round in range(0, rounds + 1):
# Reset tally "five" marker every time it gets to five.
if fives == 5:
result += '/'
fives = 0
else:
result += '|'
fives += 1
print_h4('Base 1', desc='aka "tally"')
print('{} base 1 = {}'.format(num, result))
return a**a
def g(b):
return b * 2
def f_g(a, b, arg):
return a(b(arg))
if DEBUG:
with Section('Category Theory basics'):
"""Challenge ideas taken from bartoszmilewski.com/2014/11/04
/category-the-essence-of-composition/ "Challenges" section."""
print_h4('Identity function')
for thing in ['cat', 1, 'dog', 2, range(0, 3), 0.03]:
assert thing == id(thing)
print(thing, id(thing))
print_h4('Function composition')
res = compose_hybrid('composition is neat!', f=dictify, g=listify)
print(res)
print_h4('Random funcs')
print(listify('foo'))
print(dictify('foo'))
print_h4('Higher order function composition')
f2 = compose_hybrid_hof(f=listify, g=dictify)
print(f2('composition yay!'))
print_h4('Function composition on a "stream" or incoming set')
binval = encoders.dec_to_bin(int(digit))
binval = BaseDataType.add(str(binval), bias)
binary += '{}{}'.format(binval, ' ' * (4 - len(binval) + 1))
if len(binval) < 4:
binval = binval.zfill(4)
bcd += '{} '.format(binval)
decimals += digit + (' ' * 4)
_show_bcd(num, decimals, binary, bcd)
return bcd
if DEBUG:
with Section('Numerical encoding: Binary Coded Decimal (BCD)'):
"""More exist, but are not covered here.
See books.google.com/books?id=0f-6diYBV0wC&lpg
=PA48&ots=jG6NiHY3he&dq=bcd%207421&pg
=PA51#v=onepage&q=bcd%207421&f=false For more examples."""
print('D = Decimal, B = Binary, C = Binary Coded Decimal')
nums = [
1, 2, 4, 16, 32, 64, 128, 256, 512, 1024, 2048, 1234, 12345,
123456, 1234567, 12345678, 123456789
]
print_h4('BCD', desc='8421 encoding')
for num in nums:
dec_to_bcd_8421(num)
print_h4('BCD', desc='Excess-3 (bias) encoding')
for num in nums:
dec_to_bcd_excess3(num)
@trials._test_speed
def trial_exp(func, max=10):
print('Testing function: "{}"'.format(func.__name__))
rounds = []
for x in range(max):
round = []
for n in range(max):
round.append(func(x, n))
rounds.append(round)
ppr(rounds)
return rounds
def test_matrix_with_exp(matrix):
"""Test the exponentiation function with a bonafide matrix."""
ppr(matrix)
for row in matrix:
for k in row:
print(k, exp_by_squaring(k, 2))
if DEBUG:
with Section('Matrix Processing algorithms'):
print_h4('Trials with different squaring functions')
res = trial_exp(exp_by_squaring)
res2 = trial_exp(exp_by_convential)
assert res == res2
print_h4('Trials with squaring function on matrices')
test_matrix_with_exp(random_matrix(rows=3, columns=3))
result += '|'
fives += 1
print_h4('Base 1', desc='aka "tally"')
print('{} base 1 = {}'.format(num, result))
if DEBUG:
with Section('Numerical encoding: "N-ary" (positional) - extended'):
"""I thought I had the extent of the positional number systems,
but much more exist, and many can be found at:
http://www.calculand.com/unit-converter/zahlen.php"""
print_h2('N to Decimal',
desc='Conversion to decimal from a given base')
for n in range(4):
print_h4('Convert base {}'.format(n))
n_to_dec(999, n)
print_h2(
'Decimal to N',
desc='Conversion of numbers to any base with divide-by technique.')
for base_info in BASES:
base, title = base_info['base'], base_info['name']
print_h4('Base {}'.format(base), desc='aka "{}"'.format(title))
test_base(base_info)
for num in [4, 256, 512]:
dec_to_unary(num)
'edges': [],
'parent': 1
},
4: {
'edges': [],
'parent': 2
},
5: {
'edges': [],
'parent': 2
},
}
btree = BinaryTree(data)
print(btree)
print_h4('Binary trees',
desc=('They can have no more than two nodes, '
'so adding new edges that do not conform'
' should throw an error.'))
try:
btree[6] = {'edges': [7, 8, 9], 'parent': 3}
except InvalidChildNodeCount:
cmd_title('Error called successfully', newlines=False)
bst = NaiveBinarySearchTree(data)
print(bst)
bst.add_child(5, 6)
bst.add_siblings(5, [10, 11])
print(bst)
if DEBUG:
with Section('Set Abstract Data Type'):
set_adt = SetADT()
frozen_set_adt = FrozenSetADT([1, 2, 3, 4, True, False, 'A', 'B', 'C'])
for n in range(6):
set_adt[n] = rr(0, 10)
set_adt[n] = ''.join(randchars(1))
set_adt[n] = choice([True, False])
try:
frozen_set_adt[n] = rr(0, 10)
except ImmutableSetError:
print('Frozen set cannot be modified after creation.')
print_h4('Set/Frozen set items', '')
ppr(set_adt.items)
ppr(frozen_set_adt.items)
dynam_set = DynamicSet.create([1, 2, 3, 4], capacity=4)
print('Capacity', dynam_set.set_capacity(4))
print('Room left', dynam_set.room_left())
dynam_set.add(range(100))
print_h4('Multiset example', 'Allowing multiple items of the same')
multiset = MultiSet()
multiset['cat'] = {'name': 'lily', 'type': 'persian'}
multiset['cat'] = {'name': 'radical', 'type': 'calico', 'age': 23}
multiset['cat'] = {'name': 'jadore', 'type': 'siamese'}
multiset['cat'] = {'name': 'tutu', 'type': 'abyssinian'}
super(Word, self).__init__(value)
def update_animation(steps, func, instance):
for _ in range(steps):
sleep(0.05)
instance.value = func(instance.value)
bin_inc = BaseDataType.increment
bin_dec = BaseDataType.decrement
if __name__ == '__main__':
with Section('Computer organization - Data types'):
print_h4('Bit', desc='The simplest unit of information.')
bit = Bit('0')
assert bit.get_max_binvals() == 2
print_h3('Nibble', desc='4 bits = 1/2 byte.')
nibble = Nibble('0000')
print(nibble)
assert nibble.get_max_binvals() == 24
print_h3('Byte', desc='8 bits = one byte.')
byte = Byte('00000000')
print(byte)
assert byte.get_max_binvals() == 40320
orig = byte.value
# Flip bits then reverse and check the value to test things
tdpl.test_grammar(5, '1', **kwargs)
wikipedia_kwargs = {
'ruleset': {
'S': 'AS/T',
'T': 'BS/E',
'A': 'a',
'B': 'b',
'E': '', # Epsilon string
}
}
tdpl.test_grammar(10, 'S', **wikipedia_kwargs)
# NOTE: For simplicity, slashes are not implemented as fallbacks,
# as seen in the example.
for left, right in wikipedia_kwargs['ruleset'].iteritems():
print_h4('Testing wikipedia example '
'with starting rule: {}'.format(left))
tdpl.test_grammar(10, left, **wikipedia_kwargs)
wikipedia_kwargs2 = {
'ruleset': {
'S': 'OT/E',
'T': 'SU/F',
'U': 'CS/F',
'O': '{',
'C': '}',
'E': '', # Epsilon string
'F': 'f',
}
}
for left, right in wikipedia_kwargs2['ruleset'].iteritems():
print_h4('Testing wikipedia example 2 '
"""
data = {
0: {"edges": [1, 2], "is_root": True},
1: {"edges": [3], "parent": 0},
2: {"edges": [4, 5], "parent": 0},
3: {"edges": [], "parent": 1},
4: {"edges": [], "parent": 2},
5: {"edges": [], "parent": 2},
}
btree = BinaryTree(data)
print(btree)
print_h4(
"Binary trees",
desc=(
"They can have no more than two nodes, "
"so adding new edges that do not conform"
" should throw an error."
),
)
try:
btree[6] = {"edges": [7, 8, 9], "parent": 3}
except InvalidChildNodeCount:
cmd_title("Error called successfully", newlines=False)
bst = NaiveBinarySearchTree(data)
print(bst)
bst.add_child(5, 6)
bst.add_siblings(5, [10, 11])
print(bst)
"""A visualization of the powers of ten technique for a given `num`"""
value = 0
digits = list(reversed(unicode(num)))
places = len(digits)
values = []
mapping = {}
for index in reversed(range(places)):
place_index = '1{}'.format('0' * index)
place = int(digits[index]) * int(place_index)
value += place
values.append(place)
mapping[place] = (int(digits[index]), int(place_index))
print('{} * {} = {}'.format(digits[index], place_index, place, value))
print('{} = {}'.format(' + '.join(map(unicode, values)), num))
print('\n')
return mapping
if DEBUG:
with Section('Computer organization - Numerical encoding'):
groups = {
'General': genr,
'Hexadecimal': hexa,
'Octal': octa,
'Binary': bina,
'Decimal': deca,
}
for title, func in groups.iteritems():
print_h4(title, desc='The {} encoding scheme.'.format(title))
func()
tdpl.test_grammar(5, '1', **kwargs)
wikipedia_kwargs = {
'ruleset': {
'S': 'AS/T',
'T': 'BS/E',
'A': 'a',
'B': 'b',
'E': '', # Epsilon string
}
}
tdpl.test_grammar(10, 'S', **wikipedia_kwargs)
# NOTE: For simplicity, slashes are not implemented as fallbacks,
# as seen in the example.
for left, right in wikipedia_kwargs['ruleset'].iteritems():
print_h4('Testing wikipedia example '
'with starting rule: {}'.format(left))
tdpl.test_grammar(10, left, **wikipedia_kwargs)
wikipedia_kwargs2 = {
'ruleset': {
'S': 'OT/E',
'T': 'SU/F',
'U': 'CS/F',
'O': '{',
'C': '}',
'E': '', # Epsilon string
'F': 'f',
}
}
for left, right in wikipedia_kwargs2['ruleset'].iteritems():
print_h4('Testing wikipedia example 2 '
return a ** a
def g(b):
return b * 2
def f_g(a, b, arg):
return a(b(arg))
if DEBUG:
with Section('Category Theory basics'):
"""Challenge ideas taken from bartoszmilewski.com/2014/11/04
/category-the-essence-of-composition/ "Challenges" section."""
print_h4('Identity function')
for thing in ['cat', 1, 'dog', 2, range(0, 3), 0.03]:
assert thing == id(thing)
print(thing, id(thing))
print_h4('Function composition')
res = compose_hybrid('composition is neat!', f=dictify, g=listify)
print(res)
print_h4('Random funcs')
print(listify('foo'))
print(dictify('foo'))
print_h4('Higher order function composition')
f2 = compose_hybrid_hof(f=listify, g=dictify)
print(f2('composition yay!'))
print_h4('Function composition on a "stream" or incoming set')
@trials.test_speed
def trial_exp(func, max=10):
print('Testing function: "{}"'.format(func.__name__))
rounds = []
for x in range(max):
round = []
for n in range(max):
round.append(func(x, n))
rounds.append(round)
ppr(rounds)
return rounds
def test_matrix_with_exp(matrix):
"""Test the exponentiation function with a bonafide matrix."""
ppr(matrix)
for row in matrix:
for k in row:
print(k, exp_by_squaring(k, 2))
if DEBUG:
with Section('Matrix Processing algorithms'):
print_h4('Trials with different squaring functions')
res = trial_exp(exp_by_squaring)
res2 = trial_exp(exp_by_convential)
assert res == res2
print_h4('Trials with squaring function on matrices')
test_matrix_with_exp(random_matrix(rows=3, columns=3))
result += '|'
fives += 1
print_h4('Base 1', desc='aka "tally"')
print('{} base 1 = {}'.format(num, result))
if DEBUG:
with Section('Numerical encoding: "N-ary" (positional) - extended'):
"""I thought I had the extent of the positional number systems,
but much more exist, and many can be found at:
http://www.calculand.com/unit-converter/zahlen.php"""
print_h2('N to Decimal', desc='Conversion to decimal from a given base')
for n in range(4):
print_h4('Convert base {}'.format(n))
n_to_dec(999, n)
print_h2(
'Decimal to N',
desc='Conversion of numbers to any base with divide-by technique.')
for base_info in BASES:
base, title = base_info['base'], base_info['name']
print_h4('Base {}'.format(base), desc='aka "{}"'.format(title))
test_base(base_info)
for num in [4, 256, 512]:
dec_to_unary(num)
for digit in str(num):
binval = encoders.dec_to_bin(int(digit))
binval = BaseDataType.add(str(binval), bias)
binary += '{}{}'.format(binval, ' ' * (4 - len(binval) + 1))
if len(binval) < 4:
binval = binval.zfill(4)
bcd += '{} '.format(binval)
decimals += digit + (' ' * 4)
_show_bcd(num, decimals, binary, bcd)
return bcd
if DEBUG:
with Section('Numerical encoding: Binary Coded Decimal (BCD)'):
"""More exist, but are not covered here.
See books.google.com/books?id=0f-6diYBV0wC&lpg
=PA48&ots=jG6NiHY3he&dq=bcd%207421&pg
=PA51#v=onepage&q=bcd%207421&f=false For more examples."""
print('D = Decimal, B = Binary, C = Binary Coded Decimal')
nums = [
1, 2, 4, 16, 32, 64, 128, 256, 512, 1024, 2048, 1234,
12345, 123456, 1234567, 12345678, 123456789]
print_h4('BCD', desc='8421 encoding')
for num in nums:
dec_to_bcd_8421(num)
print_h4('BCD', desc='Excess-3 (bias) encoding')
for num in nums:
dec_to_bcd_excess3(num)
"""A visualization of the powers of ten technique for a given `num`"""
value = 0
digits = list(reversed(unicode(num)))
places = len(digits)
values = []
mapping = {}
for index in reversed(range(places)):
place_index = '1{}'.format('0' * index)
place = int(digits[index]) * int(place_index)
value += place
values.append(place)
mapping[place] = (int(digits[index]), int(place_index))
print('{} * {} = {}'.format(digits[index], place_index, place, value))
print('{} = {}'.format(' + '.join(map(unicode, values)), num))
print('\n')
return mapping
if DEBUG:
with Section('Computer organization - Numerical encoding'):
groups = {
'General': genr,
'Hexadecimal': hexa,
'Octal': octa,
'Binary': bina,
'Decimal': deca,
}
for title, func in groups.iteritems():
print_h4(title, desc='The {} encoding scheme.'.format(title))
func()