% measure-command {minizinc -s .\newgraph.mzn .\ConvertedInstances03\path100.dzn}
include "alldifferent.mzn";

int: maxDegree;           % graph degree
int: lb;                         % upward rounding of maxdegree/2
int: ub;                        % min of 
                                  %   -graph bandwidth (type cyclic bandwith but the 
                                  %    distance is different, only the absolute value)
                                  %   -downward rounding of order/2

int: order;                     % number of vertices
int: nedges;                  % number of edges 
int: d_max=order-1;       % max possible distance

set of int: node = 1..order;             % vertices labels
set of int: distance = 1..d_max;         % distance range
var 1..d_max: bandwidth;           % bandwidth is a distance
% var lb..d_max: cyclicbandwidth;        % with a better simple bound
% var lb..ub: cyclicbandwidth;           % simple lb, but complex ub
array[node] of var node: g;              % graph labels
array[1..nedges,1..2] of int: edges;     % array of nedeges edges
array[1..nedges] of var distance: dist;        % distances associated to each edge


   
          
% constraints for distances between connected vertices
constraint forall (i in 1..nedges)  
  (
   let {var int: v1=edges[i,1], var int: v2=edges[i,2]} in 
       let {var int: d=abs(g[v2]-g[v1])} in 
                      dist[i] = d
  );
  
  
constraint all_different(g);
           
constraint bandwidth = max(dist);
                                                                       

                   
% search strategy               
solve :: seq_search ([

int_search([bandwidth],first_fail,indomain_min,complete),

int_search(g,first_fail,indomain_min,complete)%,

%int_search(dist,first_fail,indomain_min,complete)

       
])   minimize bandwidth;