(*我們先假設 P (i,j)，意思是當裡面有 i 行文，j 張圖的時候，存放的分頁資訊，其型別為 Pagination*)
type pagination = {mutable isPagizable : bool; mutable noOfPages : int; mutable predecessor : int * int};;



let t = 300;; (* 行數 *)
let f = 25;; (* 圖數 *)

let maxHeight = 27.0;;
let minHeight = 20.0;;

(*行屬性：height 高度，spaceHeight 其後空白高度，isPagizable 其後空白是否可分頁*)
type line = {height : float; spaceHeight : float; mutable isPagizable : bool};;

let tArray = Array.make (t+1) {height = 0.8; spaceHeight = 0.7; isPagizable = true};;

let fArray = Array.make (f+1) {height = 12.0; spaceHeight = 1.1; isPagizable = true};;

(*tArray與fArray 第0行是空行*)
let _ = tArray.(0) <- {height = 0.0; spaceHeight = 0.0; isPagizable = false} in
let _ = fArray.(0) <- {height = 0.0; spaceHeight = 0.0; isPagizable = false} in
for i = 1 to t do
  if i / 9 == 3 then
    let _ = tArray.(i).isPagizable <- false in ()
  else
  ()
done

(*連 p 0 0 都要加進去所以需要輸入 t+1 和 f+1 的矩陣*)
let p = Array.init (t+1) (fun x -> (Array.init (f+1) (fun x -> {isPagizable = false; noOfPages = -1; predecessor=(-1,-1)})) );;

let nil = -1;; (*condition value*)


(* 圖片 k 對到哪一個文字*)
let referId k = 
if k <= 1 then 1
else if k <= 3 then 9
else if k <= 6 then 40
else if k==7 then 42
else if k <= 10 then 70
else if k == 11 then 80
else if k <= 15 then 112
else if k == 16 then 120
else if k == 17 then 130
else if k <= 22 then 179
else 180

(*組頁*)
let makeOnePage (p : pagination array array) a b i j = 
  if a == i && b == j then false
  else if p.(a).(b).isPagizable == false then false
  else if (referId j) > i || (referId j) == 0 then false
  else 
    let textAndSpaceHeight = 
    if a == i then 0.0
    else
      let textHeight = Array.fold_right (+.) (Array.map (fun x -> x.height) (Array.sub tArray (a+1) (i-a))) 0.0 in
      let textSpaceHeight = Array.fold_right (+.)  (Array.map (fun x -> x.spaceHeight) (Array.sub tArray (a+1) (i-a-1))) 0.0 in
      textHeight +. textSpaceHeight in
    let figAndSpaceHeight = 
    if b == j then 0.0
    else
      let figHeight = Array.fold_right (+.)  (Array.map (fun x -> x.height) (Array.sub fArray (b+1) (j-b))) 0.0  in
      let figSpaceHeight = Array.fold_right (+.)  (Array.map (fun x -> x.spaceHeight) (Array.sub fArray (b+1) (j-b-1))) 0.0 in
      figHeight +. figSpaceHeight in
  let inputHeight = textAndSpaceHeight +. figAndSpaceHeight in
  if inputHeight > maxHeight then false
  else if inputHeight < minHeight then false
  else true;;


(*以下是分頁程式*)
let pagize p = 
let _ = p.(0).(0) <- {isPagizable = true; noOfPages = 0;  predecessor = (nil , nil)} in
for i=0 to t do
for j=0 to f do
    for a = 0 to i do
    for b = 0 to j do
        if i != 0 || j != 0 then
        let canMakeOnePage =  makeOnePage p a b i j in
        if canMakeOnePage then
        let _ = p.(i).(j).isPagizable <- true in
        let _ = p.(i).(j).predecessor <- (a, b) in
        let _ = p.(i).(j).noOfPages <- p.(i).(j).noOfPages + 1 in
        ()
        else
        ()
    done
    done
done
done;;

pagize p;;


for i=0 to  t do
  for j=0 to f do
  let x1,y1 = p.(i).(j).predecessor in
  Printf.printf "%d\t%d->%d\t%d\n" i j x1 y1
  done
  done;;







let costFuncOfPredecessor p i j pred = 
  let  tracePage = ref [(i, j)] in
  let movablePred = ref pred in

  let _ =
     while !movablePred != (-1, -1) do
     let _ = tracePage := !movablePred :: !tracePage in
     let (x, y) = !movablePred in
     let _ = movablePred := p.(x).(y).predecessor in Printf.printf "%d\t%d\n" x y
     done
  in  !tracePage;;

(*costFuncOfPredecessor p 100 15 (98, 15);;*)