Paul LaFollette wrote:
Thank you all for your thoughtful and useful comments. Since this has
largely morphed into a discussion of my 3rd question, perhaps it would
interest you to hear my reason for asking it.
John is just about spot on. Part of my research involves the
enumeration and generation of various combinatorial objects using what
are called "loopless" or "constant time" algorithms. (This means that
the time required to move from one object to the next is bounded by a
constant that is independent of the size of the object. It is related
to following idea: If I generate all of the possible patterns
expressible with N bits by simply counting in binary, as many as N
bits may change from one pattern to the next. On the other hand if I
use Gray code only one bit changes from each pattern to the next.
But the number of bits you must examine to determine which to change is
bounded by N and increases with N.
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