hash design problem: both string and int[] keys

[Charles Hixson]

Charles Hixson wrote:
> Charles Hixson wrote:
>> Ali Çehreli wrote:
>>> On 11/20/2012 11:39 AM, Charles Hixson wrote:
>>>
>>> > I'm trying to figure out how to construct an associative array whose
>>> > keys will be a combination of strings and immutable int[]'s, but every
>>> > approach I've looked at has run into problems.
>>>
>>> Can you show some code?
>> Sorry, I'm still thinking about how to design it. BBFMI has definite
>> limitations, and that's all I could use to write code right now.
>>>
>>> > It should be relatively
>>> > easy, as strings are really just an immutable list of ints,
>>>
>>> A list of dchars is more accurate of course, but yes, dchar can be
>>> casted to int.
>> Well, longs anyway. Which is a minor problem, as I'd prefer to use ints,
>> which are smaller.
>>>
>>> > but I
>>> > haven't been able to find how strings are hashed. (It's looking as if
>>> > the details are handled in C...which makes it difficult.)
>>>
>>> I bet the algorithm considers all of the characters of the strings. The
>>> following has been mentioned in a recent forum thread:
>>>
>>> http://eternallyconfuzzled.com/tuts/algorithms/jsw_tut_hashing.aspx
>> For unicode strings? This causes a problem, though "considers" gives a
>> lot of room for alternatives. For ASCII there are several plausible
>> approaches, since all one needs to do is minimize collisions. But there
>> are too many plausible unicode chars for most of them to be reasonable.
>> I'd probably go for multiply by a medium size prime, add to the
>> accumulator, mod the accumulator by a large prime, stepping through the
>> loop. And I'd initialize the accumulator by the length of the current
>> string. (Note that this would apply equally to strings or int[]'s.) So
>> if that's what you mean by "considers all the characters", then, yes.
>>>
>>> > I could define
>>> > my own hash code, but I don't find it at all clear what would be
>>> > appropriate given that I don't know the size.
>> The above was a pseudo-code of the hash function I was considering.
>>>
>>> I wonder how much slow iterating over string would be, compared to
>>> directly accessing the elements of a dstring. (After all, strings must
>>> be decoded to produce dchars.)
>>>
>>> In any case, you don't need the length of the string; a loop would do:
>> The length isn't a problem. It just further differentiates the different
>> strings, and it's a convenient built-in function.
>>>
>>> while (!s.empty) {
>>> // ... use s.front and s.popFront() ...
>>> }
>>>
>>> Alternatively:
>>>
>>> foreach (c; stride(s, 1)) {
>>> // ... use c ...
>>> }
>>>
>>> UFCS looks better: :)
>>>
>>> foreach (c; s.stride(1)) {
>>> // ... use c ...
>>> }
>> Those are all good, but I might just use:
>> foreach (char c; lst) { ... }
>> A hash code doesn't need to reflect the chars of the string, merely to
>> separate different cases.
>>>
>>> > The data is rather sparse,
>>> > so a hash table seems appropriate. (My only other alternative is a
>>> > database, and that imposes the heavy slowdown of I/O ... even
>>> though it
>>> > does automate persistence it doesn't seem like a good tradeoff.)
>>> >
>>> > So far my best idea is to build two tables, and then look at the key
>>> > when a retrieval is attempted to figure out which table it's in. That
>>> > would probably work, but it feels like a kludge.
>>>
>>> How do you differentiate between the key type being int[] vs. string?
>>>
>>> Ali
>>>
>> I'd define the same access method (opIndex, opIndexAssign) with two
>> different parameter types.
>>
>> But as I said, that feels like a kludge. I'm just contemplating it
>> because I want rehash to work properly. So I'd have two indexes:
>> Items[string] stringKeys;
>> Items[int] listKeys;
>> This lets the compiler handle resizing the arrays properly, at the cost
>> of doubly hashing the listKeys variable. This isn't too bad, as I expect
>> all the lists to be 5 items or shorter, but it feels like a kludge.
> After a bit more thought, I couldn't use a hash function to merge the
> ints of the list, because if I did then any collision would cause the
> old value to be replaces...or would it if they didn't compare to equal?
> Which different items wouldn't, but the *keys* would compare to equal,
> so they probably would replace, which isn't at all what I desire. But if
> I just try to combine the ints, I can't guarantee unique
> keys...certainly not for any list longer than 2 items, as int.max * int
> would require a long, but adding a third term is a "can't do". BigInt
> defines opCmp, but doesn't seem to define toHash. So that seems to mean
> I need to convert the list to a string. UGH!!
>
> On the one hand, it allows me to get away with only using one hashtable,
> but on the other I've got this ugly key conversion...but maybe I won't
> need to convert both ways. But it's still ugly. Even the two table
> approach was nicer.

This is the approach I've decided to use, i.e., generate string keys 
from the list of ints.
/** Convert a list of non-negative ints into an invalid utf-8
  *  string.
  * \todo The generated string both begins and ends with 0xff ...
  * these aren't needed as a hash code, and could be trimmed.  Think
  * about removing them.	*/
string	lst2sbytes (int[] lst)
{  char[] retc;
    char[] num;
    retc	~=	0xff;
    foreach	(int i; lst)
    {  enforce (i >= 0, "only non-negative ints are allowed in an sbytes");
       int	val	=	i;
       num.length	=	0;
       while (val > 0)
       {  num	~=	val % 128;
          val	=	val / 128;
       }
       // N.B.:  the reverse is needed if you wish to decode the list
       // later, but is excess baggage when generating a hash code.
       // reverse (num);
       retc	~=	num ~ 0xff;
    }
    return	retc.idup;
}

A bit of a kludge, but it seems to work, and should be fairly fast and 
reasonably compact.  And it allows the components of the key to be any 
reasonable number.  (Well, reasonable for my purposes.  I don't want to 
handle anything but positive ints.  Even allowing 0 isn't really 
reasonable, it just doesn't cost anything.)