[英]Combinaison of 1, 2, 3, 4 bits as 0 in 5bits
我正在嘗試獲得所有可能的組合,其中 1 位為 0,2 位為 0,...,4 位為 5 位中的 0
例如 1 位應該是這樣的: [11110, 11101, 11011, 10111, 01111]
我正在使用列表理解:
five_mask = int('11111', 2)
# for 1 bit
[five_mask ^ 2**i for i in range(0, 5)]
# for 2 bits
[five_mask ^ (2**i | 2**j) for i in range(0, 5) for j in range(i+1, 5)]
# for 3 bits
[five_mask ^ (2**i | 2**j | 2**k) for i in range(0, 5) for j in range(i+1, 5) for k in range(j+1, 5)]
...
它有效,但我認為有一種不那么重復且漂亮的方法,知道嗎?
從 Python 3.10 開始,我們可以使用int.bit_count
(在舊版本中,我們可以使用bin(i).count('1')
)。
n = 5
a = [[] for _ in range(n+1)]
for i in range(2**n):
a[i.bit_count()].append(i)
結果:
[[0],
[1, 2, 4, 8, 16], # for 4 bits
[3, 5, 6, 9, 10, 12, 17, 18, 20, 24], # for 3 bits
[7, 11, 13, 14, 19, 21, 22, 25, 26, 28], # for 2 bits
[15, 23, 27, 29, 30], # for 1 bit
[31]]
嘗試使用itertools.product
:
import itertools
output = dict()
for i in itertools.product(("0","1"),repeat=5):
key = i.count("0")
value = int("".join(i), 2)
if key not in output:
output[key] = list()
output[key].append(value)
>>> output
{5: [0],
4: [1, 2, 4, 8, 16],
3: [3, 5, 6, 9, 10, 12, 17, 18, 20, 24],
2: [7, 11, 13, 14, 19, 21, 22, 25, 26, 28],
1: [15, 23, 27, 29, 30],
0: [31]}
一種不錯的方法是使用 itertools 中的組合 function。
from itertools import combinations
d = {k:[sum(t) for t in combinations([2**i for i in range(5)],5-k)] for k in range(6)}
結果字典:
{0: [31],
1: [15, 23, 27, 29, 30],
2: [7, 11, 19, 13, 21, 25, 14, 22, 26, 28],
3: [3, 5, 9, 17, 6, 10, 18, 12, 20, 24],
4: [1, 2, 4, 8, 16],
5: [0]}
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