let h = 4
let w = 4

let cost = [|
  [| 1; 3; 1; 2 |];
  [| 1; 5; 1; 3 |];
  [| 4; 2; 1; 4 |];
  [| 1; 6; 2; 3 |]
|]

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

;;

min_cost_path ()