forum-msg-id-131441-edit

Original date:2017-10-12 09:40:13 Edited by: petelomax Subject: Index Problem

I am trying my hand at implementing walking distance instead of manhattan distance for the 15-puzzle.
(For the terminally curious only, see this page.)
In short, you count the number of tiles in each row (and column, but ignore that) vs. goal position, eg:

  1  2  3  0 
  5  6  7  8 
  9 10 11 12 
 13 14 15  4 
 
 Row 1 contains 3 tiles from row 1. 
 Row 2 contains 4 tiles from row 2. 
 Row 3 contains 4 tiles from row 3. 
 Row 4 contains 1 tile from row 1 and 3 tiles from row 4. 

and the (horizontal) "key" is therefore

    3 0 0 0 
    0 4 0 0 
    0 0 4 0 
    1 0 0 3 

Each line (and column, but again you can completely ignore that part) adds up to 3 or 4.
A naive base-5 approach would give me an index space of 62,500,000,000 - way too much.
But there are, I think, only 32 sum-4 numbers (0004,0013,..1111,1120,..4000) and 19 sum-3 numbers (0003..3000).
If I use find() [4 times] on a 51-element sequence, the subsequent index space drops to just 6,765,201 - much more reasonable.

My question (finally): is there a better way to convert those sum-4 and sum-3 digits to an index 1..51? Or something not drastically larger (unlike the 3..500 that base 5 gives me).

I should mention that with 24,964 tables a dictionary based approach is also quite feasible, but I suspect a plain old sequence subscript would be at least 10x faster.

Pete

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