How do I decompose a number into powers of 2?

Question

I\'m trying to create a function that receives a number as an argument and performs actions on that number to find out its closest powers of 2 that will then add up to that

Answer 1

Rather than solve the problem, how about some information to help you solve it? Take a look at a few examples, and solve them. Here are a few,

Suppose N=2, then the answer is = {2=2^1}.

Suppose N=3, then the answer is = {2=2^1,1=2^0} (note that 2**0=1)

Suppose N=4, then the answer is = {4=2^2}

...

Suppose N=63, then the answer is = {32=2^5, 16=2^4, 8=2^3, 4=2^2, 2=2^1, 1=2^0}

Suppose N=64, then the answer is = {64=2^6}

...

Suppose N=259, then the answer is = {256=2^8, 2=2^1, 1=2^0}

Do you see the pattern?

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Want an algorithm?

Think about these simple steps, and combine them together in a loop,

Can you check if the number is odd? When the number is odd, then you have detected a bit 'on'. Subtract one (make the number even).

Can you divide by 2? What do you do with the result?

Answer 2

The best and fastest way to do this is, of course, with binary numbers, but here's a way with a generator:

def powers_finder(num):
    d = []
    while sum(d) < num:
        p = powers_of_2()
        a=b=1
        while sum(d)+a<=num:
            b=a
            a = next(p)
        d.append(b)
    d.reverse()
    return d

def powers_of_2():
    n=1
    while 1:
        yield n
        n*=2

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>>> print(powers_finder(5))
[1, 4]
>>> print(powers_finder(8))
[8]
>>> print(powers_finder(9))
[1, 8]
>>> print(powers_finder(14))
[2, 4, 8]