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August 14th, 2019, 09:33 AM   #1
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Need help solving a problem

(@Mods: I'm not sure what section this question belongs to, so feel free to move it to another forum as you see fit)

Hi,

Assume you can only represent any value (V) with a combination of the four integers 1, 2, 4, 8 (J).

Based on a value V, and the number of integers (P) of type J it is made up of, it possible to calculate the exact Js the value V consists of? Specifically, for any V and P, I would like to check if it comprised of the integer J.


Examples:
Code:
V=8, P=2    ->  J=4, 4
V=8, P=1    ->  J=8
V=11, P=5  ->  J=4, 2, 2, 2, 1
V=11, P=3  ->  J=8, 2, 1
V=4, P=4    ->  J=1, 1, 1, 1
In other words: knowing V and P, we want to arrive on the single correct answer for the Js it is made up of.

Is this possible at all with a simple "one liner" algorithm/function?
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August 14th, 2019, 11:24 PM   #2
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The 3rd example could also be 4, 4, 1, 1, 1
I'm not sure a one-liner is going to be easy to find, especially given multiple possible answers. A short algorithm is possible, I have one in my head which I used to find the alternative answer to the 3rd example.
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August 15th, 2019, 12:03 AM   #3
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You are right about the 3rd example, of course. Good catch!

However, since I am really only interested in the smallest value of J, it might still be a valid approach, though I suspect that the higher the value V, the more chances there are of "collisions". There would also likely be alternative answers that don't include the smallest J.

Still, I'd be curios to see your algorithm.
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August 15th, 2019, 06:04 AM   #4
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Smallest possible value of P is easy to determine. Express V in binary, and min(P) is the sum of the last three digits plus the remaining digits right-shifted three places.
n1 = V mod 2; n2 = floor(V/2) mod 2; n4 = floor(V/4) mod 4; n8 = floor(V/8); Pmin = n1 + n2 + n4 + n8
where the n1 is the number of 1s, etc..
Then by splitting the larger numbers, you can build ANY value of P from Pmin up to V.
Not exactly one line, but you could write a code that fits on a computer screen to form valid J values.
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August 15th, 2019, 11:27 PM   #5
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My algorithym which I did in my head goes something like this: (This doesn't check that if V<P, which can't yield a result)
Code:
V = 11
P = 5

Dim R[P]    ;R[] holds the result
for i = 1 to P    ;loop P times
    if V > 8 + P - i then    ;if V is big enough to have an 8 and the remaining amount can still fit as all 1's
        R[i] = 8    ;store the number
        V = V - 8    ;the remaining V is reduced
    else if V > 4 + P - i then    ;if V is big enough to have a 4 and the remaining amount can still fit as all 1's
        R[i] = 4    ;store the number
        V = V - 4    ;the remaining V is reduced
    else if V > 2 + P - i then    ;if V is big enough to have a 2 and the remaining amount can still fit as all 1's
        R[i] = 2    ;store the number
        V=V - 2    ;the remaining V is reduced
    else
        R[i] = 1    ;store the number
        V=V - 1    ;the remaining V is reduced
    end if
next i
;R[] now contains the result!
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August 16th, 2019, 09:54 AM   #6
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Thanks for the ideas, I have enough info input now to solve it!
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