let h = 4
let w = 4
let grid = [|
  [| 0; 0; 0; 0 |];
  [| 0; 1; 0; 0 |];
  [| 0; 0; 0; 1 |];
  [| 1; 0; 0; 0 |]
|]

let paths_with_obs () =
  let dp = Array.init h (fun _ -> Array.make w 0) in
  if grid.(0).(0) = 0 then dp.(0).(0) <- 1;
  for j = 1 to w - 1 do
    if grid.(0).(j) = 0 then dp.(0).(j) <- dp.(0).(j - 1)
  done;
  for i = 1 to h - 1 do
    if grid.(i).(0) = 0 then dp.(i).(0) <- dp.(i - 1).(0)
  done;
  for i = 1 to h - 1 do
    for j = 1 to w - 1 do
      if grid.(i).(j) = 0 then
        dp.(i).(j) <- dp.(i - 1).(j) + dp.(i).(j - 1)
    done
  done;
  dp.(h - 1).(w - 1)
;;

paths_with_obs ()