determining state space based on area

views:

answers:

determining state space based on area

+5 A:

First of all, the number of "points" (as defined in mathematics - the only relevant definition) in a rectangle of any size (non-zero area) is infinity. Why? Because a point does not necessarily have to have integer coordinates - there can be a point at (0,0), (0,0.1), (0.001), (0,0.0001) and so on. I think what you mean by points in your question is that all points must have integer coordinates (i.e. lattice points), or alternately, "cells" in a rectangular grid (like cells on a chess board). Please let me know if I misunderstood your question.

There are 600 rows and 300 coloumns. This means that there are 600 * 300 = 180,000 different cells. It follows that there are nCr(180,000,2) = 16,199,910,000 unique pairs in the grid. I am assuming you consider the pair ((1,1),(2,2)) and ((2,2),(1,1)) equivalent. Otherwise, there are 180,000*180,000 = 32,400,000,000 pairs.

MAK 2010-09-12 18:14:11

I guess (!) means (factorial) in the question.

belisarius 2010-09-12 21:03:18

@belisarius: I thought so too. Doesn't make sense as punctuation :).

MAK 2010-09-12 21:04:48

@MAK sorry if it was trivial. I just don't understand what is a "state" for the OP.

belisarius 2010-09-12 21:11:08

@belisarius: From what I understand of the question, the state space is the set of pairs of cells in the grid. Each state is a pair of the form ((x1,y1),(x2,y2)).

MAK 2010-09-12 21:23:56

@MAK: That is what I read too, but how is such a vector/move a 'State' ?

Henk Holterman 2010-09-12 21:41:32

@Henk Holterman: It appears that the OP wants to run some sort of procedure on this state space (probably a search algorithm like BFS/DFS/Dijkstra etc.). I think the pair represents the state used in the algorithm. Probably something like the position of two objects on the screen, like the 'state' of a chess board is the positions of the pieces. But I think this answer can be best answered by the OP himself. I'm just saying what I thought.

MAK 2010-09-12 22:01:00

@MAK you would be correct in your assumptions. Also (!) was factorial, as I was under the impression that was the only way to really show it. Thanks for the link to lattice points, I will take a look into this and most likely mark this as the answer.

Woot4Moo 2010-09-13 12:29:59

ansaurus

tags:

views:

answers:

determining state space based on area

related questions