# Re: Surrogates and character representation

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```William D Clinger wrote:
```
```Alex Shinn quoting me:
> > I acknowledged that the algorithm will still work.  My point
> > is that its asymptotic complexity may be degraded.
>
> I'm sorry, perhaps I'm just misunderstanding, but if the exact
> same algorithm, in fact the exact same code, can be used,
> how is the asymptotic complexity affected?

The different representations for the string being searched
(UTF-8 vs UTF-32) change the problem.  The main difference
is that UTF-32 admits random access of characters, while
UTF-8 does not.  UTF-8 admits random access of bytes, but
there is no way to convert a byte value obtained by random
access into a UTF-8 string into the character offset on
which the Boyer-Moore algorithm depends,
```
```
I don't claim to understand Boyer-Moore, beyond what I gather
is the key insight: if you're searching for "ABC" and character
N is "D" there is no point in checking characters N+1 or N+2.
(Hence the non-obvious part of building the appropriate delta
tables before you start.)

But I'm puzzled, since I think Alex's point is this:  A Boyer-Moore
implementation that works on 8-bits characters (e.g. Latin-1) will
work unchanged on UTF-8 characters.  Naively, one would think it
would have the same performance characteristics.  I guess that
statistics of multi-byte characters might throw off the "delta"
tables so they delta will tend to be smaller.  (However, don't
go into details for my sake: I suspect t would take me too much
effort to delve into it.)

```
```As Per Bothner agreed, that can degrade the asympototic
complexity of the algorithm from O(n/m) to O(n).
```
```
I did?
--
--Per Bothner
per@xxxxxxxxxxx   http://per.bothner.com/

```