Question

I am reading Section 9.3 of Jon Bentley’s Programming Pearls, 2nd Edition.

On page 94, Jon gave an implementation of an improved binary search algorithm, utilizing the fact that n is 1000 (search 1000 numbers to find the target).

At the end of the program, it is:

if p > 1000 || x[p] != t
    p = -1

My question is that, what if p is exactly 1000? It seems like the when p is 1000, it should also error out, like:

if p >= 1000 || x[p] != t
    p = -1

Anyway, this part of code is translated from the code on page 93, at the end of wich:

if p >= n || x[p] != t
    p = -1

Is my understanding correct? I am just wondering if this is a typo, or it is really not necessary to include the case p is 1000 in the condtion.

Another question is, in lines 5~6 from bottom up on page 94, it says: When the first test fails and l stays zero, the program computes the bits of p in order, most significant bit first.

What does it mean here? And when the first test fails, shoudn’t l be -1, rather than 0?

Anyone can elaborate on this statement?

P.S. I can’t find Jon’s email address, otherwise, I’ll field these questions to him. 🙁

Answer 1

It is typo. Maxvalue of l is 999 (1000 – 512 + 256 + .. + 1, ), so maxvalue of p = l+1 is 1000. It is clear for hardcoded version of binsearch (listing 9.8).

And we can see real C code (not pseudocode) here (Alg.4) with if (p >= n ||