Quickly assigning an id to a given combination of bits

Question

the context behind my issue is not important, as my question itself is fairly self-contained.

Im currently trying to assign numbers to sequences of bits. Such that, if i ask functionA for bit sequence 42, it would return the corresponding bits, say "0110101011…" (not correct, just an example), and if i gave functionB the sequence "0110101011…", it could give me the number 42.

Currently, the way im assigning each sequence’s number is through the pattern

  bits   val  
| 0    | 0    |
| 1    | 1    |
| 00   | 2    |
| 10   | 3    |
| 01   | 4    |
| 11   | 5    |
| 000  | 6    |
| 100  | 7    |

and so on and so fourth. Currently, the functions i have created to do this work as such

from itertools import product


def bit_lookup_num(lookup):
  if lookup == '':
    return -1
    
  bits=[]
  current_len=1
  while lookup not in bits:
    bits.extend(["".join(perm[::-1]) for perm in product(["0","1"],repeat=current_len)])
    current_len+=1
  return bits.index(lookup)

def num_lookup_bit(lookup):
  if lookup == -1:
    return ''
    
  bits=[]
  current_len=1
  while len(bits)-1<lookup:
    bits.extend(["".join(perm[::-1]) for perm in product(["0","1"],repeat=current_len)])
    current_len+=1
  return bits[lookup]

Where num_lookup_bit functions as my prior example’s functionA, and bit_lookup_num serves as functionB. However, my implementation becomes quite slow for large bit sequences, and its due to my use of the product() function from itertools. There surely must be a faster way to accomplish this than generating every possibility using product() and checking its position in the list, alas i have yet to discover this workaround.

How can i improve upon these functions by avoiding brute-force algorithms?

Asked By: Jacob

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Source

Answer 1

Incremental approach:

def num_lookup_bit(num):
    x = 2
    bits = ''
    while num >= 0:
        bits += '0' if num%x < x/2 else '1'
        num -= x
        x *= 2
    return bits

def bit_lookup_num(bits):
    x = 2
    num = 0
    for b in bits:
        num += x//2 if b == '0' else x
        x *= 2
    return num-1

Answered By: Woodford

Answer 2

Here is an inelegant way to do this:

import math

def num_lookup_bit(lookup: int) -> str:
    log = int(math.log2(lookup))
    diff = lookup - sum(2**i for i in range(1, log))
    return f"{diff:0{log}b}"

def bit_lookup_num(lookup: str) -> int:
    length = len(lookup)
    return sum(2**i for i in range(1, length)) + int(lookup, 2)

They key thing to understand is that you first index into a "bin" which corresponds to the binary digit, then you count from there!

There’s probably a super obvious elegant way to do this, but the above seems to work for me.

Answered By: juanpa.arrivillaga

Answer 3

Your bit sequences are just, take the binary representation of val+2, chop off the leading 1, and reverse what’s left:

def bit_sequence(val):
    # [3:] removes the '0b1'
    return bin(val+2)[3:][::-1]
    # return bin(val+2)[:2:-1] would be a bit faster, but a bit harder to understand

def val_for_bit_sequence(bits):
    binary = '1' + bits[::-1]
    return int(binary, 2) - 2

Answered By: user2357112

Quickly assigning an id to a given combination of bits

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