I've been looking for stuff on this for a while now, but I can't seem to find anything. All I'm asking is for a link to some wiki page or something for a possible solution.

Say I have the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192.

Since the sums of any of them are not equal to the sums of any others, I've been using them for a variety of error codes in my programs, however, figuring up what the sums are made of has proven a little difficult.

So, I'm looking for a way to say, for example, that 1153 = 128 + 1024. Or more complex ones like 8800 = 16 + 32 + 128 + 512 + 8192.

I've honestly no idea where to start with this, and I've looked up stuff about various geometric sequences, but they don't mention figuring out this sort of thing. Any ideas would be greatly appreciated

# Sequence composition algorithm

Page 1 of 1## 8 Replies - 1112 Views - Last Post: 18 September 2011 - 09:27 AM

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**Replies To:** Sequence composition algorithm

### #2

## Re: Sequence composition algorithm

Posted 17 September 2011 - 08:02 PM

I would start by generating the sequence of terms <= the number n. While n > 0, subtract the largest element in the sequence from n, so long as that number does not exceed n.

### #3

## Re: Sequence composition algorithm

Posted 17 September 2011 - 08:24 PM

I'd go with dynamic programming on this one. If you know know how to calculate the sequence up to n. Then apply the subset sum algorithm. Ofcourse you may wanna generate the sequence in advance up to a sufficient number to avoid having to generate it for each in.

### #4

## Re: Sequence composition algorithm

Posted 18 September 2011 - 07:19 AM

This is just bitwise comparrison and we do it a lot for flags and enumerations.

Enum Modes { UNKNOWN = 0, CLERK = 1, MANAGER = 2, SUPERVISOR = 4, OWNER = 8 } Modes myMode = Modes.MANAGER; // Thus equal to 2 bool IsManager() { if ((myModes & MODES.Manager) == (MODES.Manager)) return true; return false; // Only reaches this line if not true }

### #5

## Re: Sequence composition algorithm

Posted 18 September 2011 - 08:38 AM

I hate to be the newb here, but if someone could kindly explain what you're all 'on about' I'd be greatly appreciative!

### #6

## Re: Sequence composition algorithm

Posted 18 September 2011 - 08:59 AM

I'd have to agree with macosxnerd101 and mostyfriedman. I'll post what I end up with when I get around to making it.

And to tlhIn`toq, yeah, that's how you'd normally do something like that... However, I'm using a system similar to errno, and one that I decided could hold multiple values at a time for the fun of it, for if multiple things happen in one function, etc(not the best reasons to do so, but it makes things interesting and fun). So preset comparisons or even a small lookup table would be a little less 'clean and beautiful' than I'd like.

To RetardedGenius, Imma just trying to figure out that given the sequence I listed above, how could you figure out that a number such as 1152 is made up of 128 and 1024. Something like that, for any value that is a sum of any of those numbers.

And to tlhIn`toq, yeah, that's how you'd normally do something like that... However, I'm using a system similar to errno, and one that I decided could hold multiple values at a time for the fun of it, for if multiple things happen in one function, etc(not the best reasons to do so, but it makes things interesting and fun). So preset comparisons or even a small lookup table would be a little less 'clean and beautiful' than I'd like.

To RetardedGenius, Imma just trying to figure out that given the sequence I listed above, how could you figure out that a number such as 1152 is made up of 128 and 1024. Something like that, for any value that is a sum of any of those numbers.

### #7

## Re: Sequence composition algorithm

Posted 18 September 2011 - 09:11 AM

novacrazy, on 18 September 2011 - 09:59 AM, said:

And to tlhIn`toq, yeah, that's how you'd normally do something like that... However, I'm using a system similar to errno, and one that I decided could hold multiple values at a time for the fun of it, for if multiple things happen in one function, etc

I have no idea what 'errno' is.

Just to be sure you realize, but you can hold multiple values with flags. That's sort of the point. YOu just 'or' them together with |

myModes = Modes.CLERK | Modes.OWNER;

Then when you need to know if they have permissions as a Clerk or an Owner you check.

if (IsClerk || IsOwner) console.WriteLine("You have permission"); bool IsClerk() { if ((myModes & Modes.CLERK) == (Modes.CLERK)) return true; return false; // Only reaches this line if not true } bool IsOwner() { if ((myModes & Modes.OWNER) == (Modes.OWNER)) return true; return false; // Only reaches this line if not true }

I do things like this all the time for logging.

Enum LogEvents { UNKNOWN = 0, DRIVES = 1, PORTS = 2, VIDEO = 4, CAMERA = 8, // 16, // 32, // 64 // 128 VERBOSE = 256 }

Then set the event catagories I'd like to log with:

LogEvents LogTheseThings = LogEvents.DRIVES | LogEvents.VIDEO;

Usually set by a series of checkboxes on a preferences control.

### #8

## Re: Sequence composition algorithm

Posted 18 September 2011 - 09:18 AM

I think this is a math modeling problem, not an instance of checking permissions. I can't imagine the sequence for 2^n would be great for flags.

### #9

## Re: Sequence composition algorithm

Posted 18 September 2011 - 09:27 AM

macosxnerd101, on 18 September 2011 - 10:18 AM, said:

I think this is a math modeling problem, not an instance of checking permissions. I can't imagine the sequence for 2^n would be great for flags.

It's kind of both No, it's not that great for flags and such, but I'm finding it fun to try to use it like that. Though this particular question was mostly for the math.

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