### 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.
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