I'm working on a function to perform a 'true' binary expansion of a positive odd number by using powers of 2 with coefficients of 1 or -1 instead of the usual 0 or 1. The goal is to return this expansion as an array, starting from the most significant bit. For example, for the number 25, the expected output should be [1, 1, 1, -1, -1].
I've implemented a solution, but while it works correctly, it tends to slow down significantly with larger numbers. I'm looking for ways to optimize the code to make it run faster. Here's the code I've written:
```python
def true_binary(n):
num_list = []
final_list = []
final_number = 0
check_sum = 0
j = 1
while final_number < n:
check_number = j
final_number += check_number
num_list.append(check_number)
j *= 2
if final_number == n:
return [1] * len(num_list)
for i in reversed(num_list):
if check_sum == n:
break
if check_sum < n:
check_sum += i
final_list.append(1)
else:
check_sum -= i
final_list.append(-1)
return final_list
```
3 Answers
Just a heads up, your original code seemed to return a list of 1s for certain inputs. Make sure you double-check it to avoid potential issues. Also, focus on bit operations; they'll really reduce your processing time.
It looks like you're doing some bitwise manipulation, which is a great idea! Consider using bit operators to streamline your code. Here's a more efficient version:
```python
def true_binary(n):
b = n.bit_length()
p = ((1 <> 1
return [(p >> i & 1) * 2 - 1 for i in range(b - 1, -1, -1)]
```
This should significantly speed things up by taking advantage of Python's bit manipulation capabilities.
Have you thought about using built-in methods? Python has a .to_bytes() method for integers that gives you their binary representation. You can leverage that alongside some properties of binary numbers to convert the [0, 1] representation into [1, -1]. This can lead to O(log n) efficiency, making it much faster for large numbers.
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