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numrange.py
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"""
Compiles ranges of integers into a regular expression that matches only them:
>>> numrange_to_regex(0, 5)
r"[0-5]"
>>> numrange_to_regex(0, 255)
r"\d|[1-9]\d|1\d\d|2[0-4]\d|25[0-5]"
The regex will be composed of "single ranges" separated by the "|" operator
"""
def replace_with(a, i, digit):
s = str(a)
above = s[: -i - 1]
below = s[-i:] if i > 0 else ""
return int(above + str(digit) + below)
assert replace_with(0, 0, 9) == 9
assert replace_with(10, 0, 9) == 19
assert replace_with(10, 1, 9) == 90
assert replace_with(8000, 0, 9) == 8009
assert replace_with(8000, 2, 9) == 8900
assert replace_with(8000, 3, 9) == 9000
assert replace_with(8999, 3, 9) == 9999
assert replace_with(8999, 4, 9) == 98999
assert replace_with(3, 0, 5) == 5
assert replace_with(8999, 4, 5) == 58999
def digit_at(x, i):
return int(str(x)[-i - 1])
assert digit_at(0, 0) == 0
assert digit_at(9, 0) == 9
assert digit_at(10, 0) == 0
assert digit_at(10, 1) == 1
def try_to_replace_lowest_nonzero_digit(a, b, index):
# otherwise when a > 0 and b == 0, _try_replace will return falsy 0 to mean "use this" :(
assert a <= b
digit = min(9, digit_at(b, 0)) if index == 0 else max(1, digit_at(b, index) - 1)
return _try_replace(a, b, index, 9) or _try_replace(a, b, index, digit) or a
def _try_replace(a, b, index, digit):
replaced = replace_with(a, index, digit)
if replaced <= b:
return replaced
return None
assert try_to_replace_lowest_nonzero_digit(0, 0, 0) == 0
assert try_to_replace_lowest_nonzero_digit(0, 5, 0) == 5
assert try_to_replace_lowest_nonzero_digit(0, 9, 0) == 9
assert try_to_replace_lowest_nonzero_digit(0, 100, 0) == 9
assert try_to_replace_lowest_nonzero_digit(1, 1, 0) == 1
assert try_to_replace_lowest_nonzero_digit(1, 5, 0) == 5
assert try_to_replace_lowest_nonzero_digit(1, 9, 0) == 9
assert try_to_replace_lowest_nonzero_digit(1, 100, 0) == 9
assert try_to_replace_lowest_nonzero_digit(11, 9999, 0) == 19
assert try_to_replace_lowest_nonzero_digit(11, 19, 0) == 19
assert try_to_replace_lowest_nonzero_digit(11, 15, 0) == 15
assert try_to_replace_lowest_nonzero_digit(199, 199, 2) == 199
assert try_to_replace_lowest_nonzero_digit(199, 299, 2) == 199
assert try_to_replace_lowest_nonzero_digit(199, 399, 2) == 299
assert try_to_replace_lowest_nonzero_digit(119, 999, 1) == 199
assert try_to_replace_lowest_nonzero_digit(109, 109, 1) == 109
def sequence_of_nines_instead_of_zeros(a):
replaced = a
nine = 9
while a % 10 == 0:
replaced += nine
yield replaced
a //= 10
nine *= 10
assert list(sequence_of_nines_instead_of_zeros(1000)) == [1009, 1099, 1999]
assert list(sequence_of_nines_instead_of_zeros(1)) == []
assert list(sequence_of_nines_instead_of_zeros(200100)) == [200109, 200199]
assert list(sequence_of_nines_instead_of_zeros(100100000)) == [
100100009,
100100099,
100100999,
100109999,
100199999,
]
def replace_all_zero_digits_staying_smaller_than_b(a, b):
if a == 0:
return 0, a
i = 0
for replaced in sequence_of_nines_instead_of_zeros(a):
if replaced <= b:
a = replaced
i += 1
else:
break
return i, a
assert replace_all_zero_digits_staying_smaller_than_b(100, 999) == (2, 199)
assert replace_all_zero_digits_staying_smaller_than_b(100, 108) == (0, 100)
assert replace_all_zero_digits_staying_smaller_than_b(100, 109) == (1, 109)
assert replace_all_zero_digits_staying_smaller_than_b(0, 999) == (0, 0)
assert replace_all_zero_digits_staying_smaller_than_b(9, 999) == (0, 9)
assert replace_all_zero_digits_staying_smaller_than_b(10, 999) == (1, 19)
assert replace_all_zero_digits_staying_smaller_than_b(11, 999) == (0, 11)
def max_single_range_below(a, b):
assert a <= b
index, a = replace_all_zero_digits_staying_smaller_than_b(a, b)
return try_to_replace_lowest_nonzero_digit(a, b, index)
assert max_single_range_below(0, 0) == 0
assert max_single_range_below(0, 5) == 5
assert max_single_range_below(0, 9) == 9
assert max_single_range_below(0, 10) == 9
assert max_single_range_below(0, 99) == 9
assert max_single_range_below(0, 39) == 9
assert max_single_range_below(1, 39) == 9
assert max_single_range_below(1, 5) == 5
assert max_single_range_below(10, 99) == 99
assert max_single_range_below(11, 99) == 19
assert max_single_range_below(100, 999) == 999
assert max_single_range_below(109, 999) == 109
assert max_single_range_below(100, 200) == 199
assert max_single_range_below(100, 210) == 199
assert max_single_range_below(100, 199) == 199
assert max_single_range_below(100, 198) == 189
assert max_single_range_below(110, 999) == 199
assert max_single_range_below(100, 109) == 109
assert max_single_range_below(101010000, 999999999999) == 101099999
assert max_single_range_below(101010020, 999999999999) == 101010099
assert max_single_range_below(101010020, 101010025) == 101010025
assert max_single_range_below(101010020, 101010315) == 101010099
def single_range_to_regex(a, b):
if a == b:
return str(a)
below = ""
while a // 10 != b // 10:
a //= 10
b //= 10
below += r"\d"
digit_a = a % 10
digit_b = b % 10
if digit_a == digit_b:
character_class = digit_a
elif digit_a == 0 and digit_b == 9:
character_class = r"\d"
else:
character_class = f"[{digit_a}-{digit_b}]"
if a // 10:
above = str(a // 10)
else:
above = ""
return f"{above}{character_class}{below}"
assert single_range_to_regex(5, 5) == "5"
assert single_range_to_regex(3, 4) == "[3-4]"
assert single_range_to_regex(5, 8) == "[5-8]"
assert single_range_to_regex(9, 9) == "9"
assert single_range_to_regex(0, 9) == r"\d"
assert single_range_to_regex(2, 9) == "[2-9]"
assert single_range_to_regex(21, 29) == "2[1-9]"
assert single_range_to_regex(21, 27) == "2[1-7]"
assert single_range_to_regex(20, 99) == r"[2-9]\d"
assert single_range_to_regex(100, 999) == r"[1-9]\d\d"
assert single_range_to_regex(200, 999) == r"[2-9]\d\d"
assert single_range_to_regex(988, 989) == r"98[8-9]"
assert single_range_to_regex(998, 999) == "99[8-9]"
assert single_range_to_regex(12000, 12599) == r"12[0-5]\d\d"
def number_range_to_regex(a, b):
assert a <= b
assert a >= 0 and b >= 0
if a == b:
return str(a)
max_a = max_single_range_below(a, b)
if max_a == b:
return single_range_to_regex(a, b)
return "|".join(
[single_range_to_regex(a, max_a), number_range_to_regex(max_a + 1, b)]
)
assert number_range_to_regex(3, 3) == "3"
assert number_range_to_regex(3, 4) == "[3-4]"
assert number_range_to_regex(0, 9) == r"\d"
assert number_range_to_regex(13, 14) == "1[3-4]"
assert number_range_to_regex(993, 998) == "99[3-8]"
assert number_range_to_regex(988, 993) == "98[8-9]|99[0-3]"
assert number_range_to_regex(0, 14) == r"\d|1[0-4]"
assert number_range_to_regex(0, 100) == r"\d|[1-9]\d|100"
assert number_range_to_regex(0, 10000) == r"\d|[1-9]\d|[1-9]\d\d|[1-9]\d\d\d|10000"
assert number_range_to_regex(100, 123) == r"1[0-1]\d|12[0-3]"
assert number_range_to_regex(23, 367) == r"2[3-9]|[3-9]\d|[1-2]\d\d|3[0-5]\d|36[0-7]"
assert number_range_to_regex(0, 255) == r"\d|[1-9]\d|1\d\d|2[0-4]\d|25[0-5]"