def __init__(self, numbers: List[int]):
"""Initialize a new EliasFano data structure for given monotone sequence.
numbers:List[int], sequence to convert into an EliasFano data structure.
"""
self._size = ceil(log2(max(numbers) / len(numbers)))
superiors, inferiors = list(
zip(*[divmod(n, 1 << self._size) for n in numbers]))
self._inferiors = "".join(
[f"{{0:0{self._size}b}}".format(n) for n in inferiors])
self._superiors = "".join([
inverted_unary(n - superiors[i - 1] if i else n)
for i, n in enumerate(superiors)
])
def test_inverted_unary():
tests = {
0: "1", # 0 -> 0
1: "01", # 1 -> 10
2: "001", # 10 -> 110
3: "0001", # 11 -> 1110
4: "00001", # 100 -> 11110
5: "000001", # 101 -> 111110
11: "000000000001", # 1011 -> 111111111110
}
for n, u in tests.items():
assert u == inverted_unary(n)
def test_is_prefix_code():
positive = [[unary(i) for i in range(100)],
[inverted_unary(i) for i in range(100)],
[minimal_binary_coding(i, 100) for i in range(100)],
[gamma_coding(i) for i in range(100)],
[delta_coding(i) for i in range(100)],
[omega_coding(i) for i in range(1, 100)],
[levenshtein_coding(i) for i in range(100)],
[nibble_coding(i) for i in range(100)],
[byte_coding(i) for i in range(100)],
[golomb_coding(i, 5) for i in range(100)]]
negative = [
interpolative_coding(list(range(0, 100)), 0, 100),
[reduced_binary_coding(i) for i in range(100)]
]
assert all([is_prefix_code(p) for p in positive])
assert not any([is_prefix_code(n) for n in negative])
def gamma_coding(n: int) -> str:
"""Return string representing given number in gamma coding.
n:int, number to convert to unary.
"""
rbc = reduced_binary_coding(n)
return inverted_unary(len(rbc)) + rbc
def golomb_coding(n: int, b: int) -> str:
"""Return string representing given number in golomb coding.
n:int, number to convert to golomb coding.
b:int, module.
"""
return inverted_unary(n // b) + minimal_binary_coding(n % b, b)