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mudder.py
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mudder.py
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import math
from decimal import Decimal, ROUND_HALF_UP
from functools import partial
from itertools import chain, cycle
from operator import add
from typing import Dict, Iterable, List, Optional, Reversible, Tuple, Union
__all__ = [
"SymbolTable",
"decimal",
"base36",
"base62",
"alphabet",
]
def is_prefix_code(strings: Iterable[str]) -> bool:
strings = list(strings)
strings.sort()
for i in range(1, len(strings)):
prev, current = strings[i - 1 : i + 1]
if prev == current:
continue
if current.startswith(prev):
return False
return True
class SymbolTable:
def __init__(
self, symbols: Iterable[str], symbol_map: Optional[Dict[str, int]] = None
):
symbols = list(symbols)
if not symbol_map:
symbol_map = dict((c, i) for i, c in enumerate(symbols))
symbol_values = set(symbol_map.values())
for i in range(len(symbols)):
if i not in symbol_values:
raise ValueError(
f"{len(symbols)} symbols given but {i} not found in symbol table"
)
self.num2sym = symbols
self.sym2num = symbol_map
self.max_base = len(symbols)
self.is_prefix_code = is_prefix_code(symbols)
def number_to_digits(self, num: int, base: Optional[int] = None) -> List[int]:
base = base or self.max_base
digits: List[int] = []
while num >= 1:
digits.append(num % base)
num = num // base
digits.reverse()
if digits:
return digits
return [0]
def digits_to_string(self, digits: Iterable[int]) -> str:
return "".join([self.num2sym[n] for n in digits])
def string_to_digits(self, string: Iterable[str]) -> List[int]:
if isinstance(string, str):
if not self.is_prefix_code:
raise ValueError(
"Parsing without prefix code is unsupported. "
"Pass in array of stringy symbols?"
)
string = (c for c in string if c in self.sym2num)
return [self.sym2num[c] for c in string]
def digits_to_number(
self, digits: Reversible[int], base: Optional[int] = None
) -> int:
base = base or self.max_base
current_base = 1
accum = 0
for current in reversed(digits):
accum += current * current_base
current_base *= base
return accum
def number_to_string(self, num: int, base: Optional[int] = None) -> str:
return self.digits_to_string(self.number_to_digits(num, base=base))
def string_to_number(self, num: Iterable[str], base: Optional[int] = None) -> int:
return self.digits_to_number(self.string_to_digits(num), base=base)
def round_fraction(
self, numerator: int, denominator: int, base: Optional[int] = None
) -> List[int]:
base = base or self.max_base
places = math.ceil(math.log(denominator) / math.log(base))
scale = pow(base, places)
scaled = int(
Decimal(numerator / denominator * scale).to_integral_value(
rounding=ROUND_HALF_UP
)
)
digits = self.number_to_digits(scaled, base)
return left_pad(digits, places)
def mudder(
self,
a: Union[Iterable[str], int] = "",
b: Iterable[str] = "",
num_strings: int = 1,
base: Optional[int] = None,
num_divisions: Optional[int] = None,
) -> List[str]:
if isinstance(a, int):
num_strings = a
a = ""
b = ""
a = a or self.num2sym[0]
b = b or self.num2sym[-1] * (len(list(a)) + 6)
base = base or self.max_base
num_divisions = num_divisions or num_strings + 1
ad = self.string_to_digits(a)
bd = self.string_to_digits(b)
intermediate_digits = long_linspace(ad, bd, base, num_strings, num_divisions)
final_digits = [
v + self.round_fraction(rem, den, base)
for v, rem, den in intermediate_digits
]
final_digits.insert(0, ad)
final_digits.append(bd)
return [
self.digits_to_string(v) for v in chop_successive_digits(final_digits)[1:-1]
]
def long_div(
numerator: List[int], denominator: int, base: int
) -> Tuple[List[int], int]:
result = []
remainder = 0
for current in numerator:
new_numerator = current + remainder * base
result.append(new_numerator // denominator)
remainder = new_numerator % denominator
return result, remainder
def long_sub_same_len( # noqa: C901
a: List[int],
b: List[int],
base: int,
remainder: Optional[Tuple[int, int]] = None,
denominator=0,
) -> Tuple[List[int], int]:
if len(a) != len(b):
raise ValueError("a and b should have same length")
a = a.copy() # pre-emptively copy
if remainder:
a.append(remainder[0])
b = b.copy()
b.append(remainder[1])
ret = [0] * len(a)
for i in reversed(range(len(a))):
if a[i] >= b[i]:
ret[i] = a[i] - b[i]
continue
if i == 0:
raise ValueError("Cannot go negative")
do_break = False
# look for a digit to the left to borrow from
for j in reversed(range(i)):
if a[j] > 0:
# found a non-zero digit. Decrement it
a[j] -= 1
# increment all digits to the right by `base-1`
for k in range(j + 1, i):
a[k] += base - 1
# until you reach the digit you couldn't subtract
ret[i] = (
a[i]
+ (denominator if remainder and i == len(a) - 1 else base)
- b[i]
)
do_break = True
break
if do_break:
continue
raise ValueError("Failed to find digit to borrow from")
if remainder:
# result, remainder
return ret[:-1], ret[-1]
return ret, 0
def long_add_same_len(
a: List[int], b: List[int], base: int, remainder: int, denominator: int
) -> Tuple[List[int], bool, int, int]:
if len(a) != len(b):
raise ValueError("a and b should have same length")
carry = remainder >= denominator
res = b.copy()
if carry:
remainder -= denominator
for i, ai in reversed(list(enumerate(a))):
result = ai + b[i] + int(carry)
carry = result >= base
res[i] = result - base if carry else result
return res, carry, remainder, denominator
def right_pad(arr: List[int], to_length: int, val: int = 0) -> List[int]:
pad_len = to_length - len(arr)
if pad_len > 0:
return arr + [val] * pad_len
return arr
def long_linspace(
a: List[int], b: List[int], base: int, n: int, m: int
) -> List[Tuple[List[int], int, int]]:
if len(a) < len(b):
a = right_pad(a, len(b))
elif len(b) < len(a):
b = right_pad(b, len(a))
if a == b:
raise ValueError("Start and end strings are lexicographically inseperable")
a_div, a_div_rem = long_div(a, m, base)
b_div, b_div_rem = long_div(b, m, base)
a_prev, a_prev_rem = long_sub_same_len(a, a_div, base, (0, a_div_rem), m)
b_prev, b_prev_rem = b_div, b_div_rem
ret = []
for _i in range(1, n + 1):
sum_, _carry, rem, den = long_add_same_len(
a_prev, b_prev, base, a_prev_rem + b_prev_rem, m
)
ret.append((sum_, rem, den))
a_prev, a_prev_rem = long_sub_same_len(
a_prev, a_div, base, (a_prev_rem, a_div_rem), m
)
b_prev, _carry, b_prev_rem, _den = long_add_same_len(
b_prev, b_div, base, b_prev_rem + b_div_rem, m
)
return ret
def left_pad(arr: List[int], to_length: int, val: int = 0) -> List[int]:
pad_len = to_length - len(arr)
if pad_len > 0:
return [val] * pad_len + arr
return arr
def chop_digits(rock: List[int], water: List[int]) -> List[int]:
for i in range(len(water)):
if water[i] and (i >= len(rock) or rock[i] != water[i]):
return water[: i + 1]
return water
def lexicographic_less_than_array(a: List[int], b: List[int]) -> bool:
n = min(len(a), len(b))
for i in range(n):
if a[i] == b[i]:
continue
return a[i] < b[i]
return len(a) < len(b)
def chop_successive_digits(strings: List[List[int]]) -> List[List[int]]:
reversed_ = not lexicographic_less_than_array(strings[0], strings[1])
if reversed_:
strings.reverse()
result = strings[:1]
for i in range(1, len(strings)):
result.append(chop_digits(result[-1], strings[i]))
if reversed_:
result.reverse()
return result
digits = "0123456789"
alpha_lower = "abcdefghijklmnopqrstuvwxyz"
alpha_upper = alpha_lower.upper()
decimal = SymbolTable(digits)
base62 = SymbolTable(digits + alpha_upper + alpha_lower)
base36 = SymbolTable(
digits + alpha_lower,
dict(
zip(
digits + alpha_lower + alpha_upper,
# 0-9, then 10-35 repeating (for upper and lower case)
chain(range(10), cycle(map(partial(add, 10), range(26)))),
)
),
)
alphabet = SymbolTable(
alpha_lower, dict(zip(alpha_lower + alpha_upper, cycle(range(26))))
)