type position = Plain | Water | Wall | Home
type board = position array array

type location = int * int

let find_home board = 
  let ans = ref (-1,-1) in 
  for i=0 to Array.length board - 1 do
    for j=0 to Array.length board.(0) - 1 do 
      if board.(i).(j) = Home then ans := (i,j)
    done
  done;
  !ans
  
(* returns all valid neighboring positions which are not water or wall *)
let compute_neighbors board (i,j) = 
  let r = Array.length board in 
  let c = Array.length board.(0) in 
  let ns = [(i,j-1); (i,j+1); (i-1,j); (i+1,j)] in
  let valid_ns = List.filter (fun (x,y) -> x>=0 && x<r && y>=0 && y<c) ns in
  List.filter (fun (x,y) -> board.(x).(y) = Plain || board.(x).(y) = Home) valid_ns

let b1 = 
  let b = Array.make_matrix 5 7 Plain in 
  b.(2).(1) <- Home;
  b.(0).(5) <- Water; b.(1).(5) <- Water; b.(2).(5) <- Water;
  b.(0).(3) <- Wall; b.(1).(3) <- Wall; b.(2).(3) <- Wall;
  b

let b2 = 
  let b = Array.make_matrix 5 7 Plain in 
  b.(2).(1) <- Home;
  b.(1).(5) <- Water; b.(2).(5) <- Water;
  b.(1).(3) <- Wall; b.(2).(3) <- Wall;
  b