include "alldifferent.mzn";


string: Name; % name of datafile
int: n = length(Demand); % n - number of customers
int: NumVehicles; % - number of vehicles available
int: Cap; % capacity of a vehicle. Each vehicle has the same capacity
array [int] of int: Demand; % each customers demand
array [1..n+1] of float: locX; % each customer location (x coordinate)
array [1..n+1] of float: locY; % each customer location (y coordinate)
float: DepotX = locX[n+1]; % x coordinate of depot
float: DepotY = locY[n+1]; % y coordinate of depot


function int: calculate_distance(float: x1, float: y1, float: x2, float: y2) = let {
  float: diff_x = coords_dist(x1, x2);
  float: diff_y = coords_dist(y1, y2);
  } in round(sqrt(diff_x*diff_x + diff_y*diff_y) * 1000);
function float: coords_dist(float: x, float: y) = if x > 0 /\ y > 0 then abs(x-y) else
  if x < 0 /\ y < 0 then abs(abs(x) - abs(y)) else
  abs(x) + abs(y) endif endif;

array[1..n+1, 1..n+1] of int: distanceMatrix = array2d(1..n+1, 1..n+1, [
    if i = j then 0 else calculate_distance(locX[i], locY[i], locX[j], locY[j]) endif | i, j in 1..n+1
]);

array [1..n] of var 1..n: order :: domain;
constraint alldifferent(order);

var int: total_distance =
  sum([
    distanceMatrix[order[i], order[i+1]] | i in 1..n-1
  ]);

solve minimize total_distance;

output ["objective_function = \(total_distance)\n"]