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@xr1s
Created Oct 19, 2022
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from typing import List, Sequence, TypeVar, overload
T = TypeVar("T")
@overload
def de_bruijn(alphabet: str, n: int) -> str:
...
@overload
def de_bruijn(alphabet: Sequence[T], n: int) -> List[T]:
...
def de_bruijn(alphabet: Sequence[T], n: int) -> str | List[T]:
"""
从 alphabet 生成窗口长度 n 的 de Bruijn 序列
摘自维基百科,对参数类型和返回类型稍作修改
"""
size = len(alphabet)
a = [0] * size * n
sequence: List[int] = []
def search(t, p):
if t > n:
if n % p == 0:
sequence.extend(a[1 : p + 1])
return
a[t] = a[t - p]
search(t + 1, p)
for k in range(a[t - p] + 1, size):
a[t] = k
search(t + 1, t)
search(1, 1)
if isinstance(alphabet, str):
return "".join(alphabet[k] for k in sequence)
return [alphabet[k] for k in sequence]
def pretty_print_binary_de_bruijn_table(bits: int):
magic = int(de_bruijn("01", bits), 2)
size = 1 << bits
mask = size - 1
bit_perm = [0] * size
for k in range(size):
bit_perm[magic << k >> size - bits & mask] = k
digits = len(str(size))
print(f"int ctz{size}(uint{size}_t x) {{")
print(f" static const int bit_perm[{size}] = {{")
for l in range(0, size, 16):
print(
" " * 7, "".join(f"{index:>{digits}}, " for index in bit_perm[l : l + 16])
)
print(" };")
print(f" return bit_perm[{magic:#X} * (x & ~x + 1) >> {size - bits}];")
print("}")
def main():
pretty_print_binary_de_bruijn_table(7)
if __name__ == "__main__":
main()
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