#16683: gray code for integer vectors and combinations
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16683 | 4d2136a6d0505c15c0b1af4fb4c7ea22aa4980f6
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:8 ncohen]:
> If I make no mistake :
You did.
> With a gray code that makes you change two coordinates for each vector,
you need to do `2n^k` to enumerate the elements of `n^k`
It is only one change at a time. So it is `n^k`.
Result :
{{{
sage: n^k # number of changes with a gray code
810000
sage: (1-n^(k+1))/(1-n)-1 # number of changes with addition
837930
}}}
> Thus if you really care about those changes, may you should build a
function which outputs the changes that must be performed at each run,
based on stupid addition ? Or did I make a mistake somewhere ?
The point is not really the gain in the number of changes but rather the
simplicity with which you can adapt more complicated stuff. If you have to
iterate through the number of changes you need a for loop. With a gray
code, you need nothing, just do your change!
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16683#comment:9>
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