include "globals.mzn";

int: n;
int: k;
int: EndTime;
int: ConstTime;
array[1..n] of var 0..EndTime: Begins;
array[1..n] of var 0..EndTime: Ends;
array[1..n] of 0..EndTime: Durations;
array[1..n] of var 0..EndTime: NeedEnds;
array[1..n] of var 0..1: TimeCondition;
array[1..n] of 0..EndTime: Start_time;
array[1..k] of 0..EndTime: B;
array[1..k] of 0..EndTime: E;
array[1..n] of var 0..1: NeedCh;

array[1..n] of var 1..n: x;

array[1..n] of 0..EndTime: FirstTime;
array[1..n,1..n] of 0..EndTime: Time;
% No overlapping
predicate no_overlap(var int:s1, var int:d1, var int:z1, int:h1, var int:s2, var int:d2, var int:z2, int:h2) =
    s1 + d1 + z1 + h1 <= s2 / s2 + d2 + z2 + h2 <= s1;

predicate in_interval(var int:c, int:k,
var int:b,
var int:s,
array[int] of var int:B_int,
array[int] of var int:E_int) =
(let {
      array[1..k] of var 0..1: res,
      int: i = 1
    } in
        forall(i in 1..k) (res[i] = (if (b >=B_int[i]
        / b+s <=E_int[i]) / c = 0
                                    then 1 else 0 endif ))
                                    /
                                    sum(res) > 0);

 % general constraints
constraint
        all_different(x)
        /
        forall(i in 1..n) (Ends[x[i]] = Begins[x[i]] + ConstTime + Start_time[x[i]] + Durations[x[i]])
        /
        forall(i,j in 1..n  where i < j) (
              no_overlap(Begins[x[i]], Durations[x[i]], Start_time[x[i]], ConstTime, Begins[x[j]], Durations[x[j]], Start_time[x[j]], ConstTime)
        /
        forall(i in 1..n) (in_interval(NeedCh[x[i]], k, Begins[x[i]]+ConstTime, Start_time[x[i]], B, E))
        /
        forall(i in 1..n) (TimeCondition[x[i]] = (NeedEnds[x[i]] >= Ends[x[i]]))
        )
;

solve :: int_search(x ++ Begins, first_fail,
   indomain_split,
   complete) maximize sum(i in 1..n) (TimeCondition[i]);

output [
   "               [A1, A2, A3, A4n",
   "x:             ", show(x), "n",
   "Begins:        ", show(Begins), "n",
   "First time:    ", show(FirstTime), "n",
   "Start times:   ", show(Start_time), "n",
   "Durations:     ", show(Durations), "n",
   "Ends:          ", show(Ends), "n",
   "Need:          ", show(NeedEnds), "n",
   "TimeCondition: ", show(TimeCondition), "n",
];


n = 4;
k = 1;
Durations = [6,5,10,7];
NeedEnds = [20,20,10,30];
EndTime = 40000000000;
Start_time = [1,2,1,4];
B = [100];
E = [200];
NeedCh = [0,0,0,0];
ConstTime = 5;
           %[A1, A2, A3, A4
FirstTime = [1,   2,  3,  4];

Time = [|    0,   12, 13, 14,   %A1
        |    21,  0,  23, 24,   %A2
        |    31,  32,  0, 34,   %A3
        |    41,  42, 43,  0|]; %A4