/** @group globals.graph
   Constrains the subgraph \a ns and \a es of a given directed graph to be a path from \a s to \a t of weight \a K.

   @param N: the number of nodes in the given graph
   @param E: the number of edges in the given graph
   @param from: the leaving node 1..\a N for each edge
   @param to: the entering node 1..\a N for each edge
   @param w: the weight of each edge
   @param s: the source node (which may be variable)
   @param t: the dest node (which may be variable)
   @param ns: a Boolean for each node whether it is in the subgraph
   @param es: a Boolean for each edge whether it is in the subgraph
   @param K: the cost of the path
*/
predicate bounded_dpath(int: N, int: E, array[int] of int: from, array[int] of int: to, array[int] of int: w,
                    var int: s, var int: t, array[int] of var bool: ns, array[int] of var bool: es, var int: K) =
   assert(index_set(from) = 1..E,"bounded_dpath: index set of from must be 1..\(E)") /\
   assert(index_set(to) = 1..E,"bounded_dpath: index set of to must be 1..\(E)") /\
   assert(index_set(ns) = 1..N,"bounded_dpath: index set of ns must be 1..\(N)") /\
   assert(index_set(es) = 1..E,"bounded_dpath: index set of es must be 1..\(E)") /\
   assert(index_set(w) = 1..E,"bounded_dpath: index set of w must be 1..\(E)") /\
   fzn_bounded_dpath(N,E,from,to,w,s,t,ns,es,K);

/** @group globals.graph
   Constrains the subgraph \a ns and \a es of a given directed graph to be a path from \a s to \a t of weight \a K.

   @param from: the leaving node for each edge
   @param to: the entering node for each edge
   @param w: the weight of each edge
   @param s: the source node (which may be variable)
   @param t: the dest node (which may be variable)
   @param ns: a Boolean for each node whether it is in the subgraph
   @param es: a Boolean for each edge whether it is in the subgraph
   @param K: the cost of the path
*/
predicate bounded_dpath(array[int] of $$N: from, array[int] of $$N: to, array[int] of int: w,
                    var $$N: s, var $$N: t, array[$$N] of var bool: ns, array[int] of var bool: es, var int: K) =
   assert(index_set(from) = index_set(to),"bounded_dpath: index set of from and to must be identical") /\
   assert(index_set(from) = index_set(es),"bounded_dpath: index set of from and es must be identical") /\
   assert(index_set(w) = index_set(es),"bounded_dpath: index set of w and es must be identical") /\
   assert(dom_array(from) subset index_set(ns),"bounded_dpath: nodes in from must be in index set of ns") /\
   assert(dom_array(to) subset index_set(ns),"bounded_dpath: nodes in to must be in index set of ns") /\
   fzn_bounded_dpath(from,to,w,s,t,ns,es,K);
   

/** @group globals.graph
   Constrains the subgraph \a ns and \a es of a given undirected graph to be a path from \a s to \a t of weight \a K.

   @param N: the number of nodes in the given graph
   @param E: the number of edges in the given graph
   @param from: the leaving node 1..\a N for each edge
   @param to: the entering node 1..\a N for each edge
   @param w: the weight of each edge
   @param s: the source node (which may be variable)
   @param t: the dest node (which may be variable)
   @param ns: a Boolean for each node whether it is in the subgraph
   @param es: a Boolean for each edge whether it is in the subgraph
   @param K: the cost of the path
*/   
predicate bounded_path(int: N, int: E, array[int] of int: from, array[int] of int: to, array[int] of int: w,
                   var int: s, var int: t, array[int] of var bool: ns, array[int] of var bool: es, var int: K) =
   assert(index_set(from) = 1..E,"bounded_path: index set of from must be 1..\(E)") /\
   assert(index_set(to) = 1..E,"bounded_path: index set of to must be 1..\(E)") /\
   assert(index_set(ns) = 1..N,"bounded_path: index set of ns must be 1..\(N)") /\
   assert(index_set(es) = 1..E,"bounded_path: index set of es must be 1..\(E)") /\
   assert(index_set(w) = 1..E,"bounded_path: index set of w must be 1..\(E)") /\
   fzn_bounded_path(N,E,from,to,w,s,t,ns,es,K);


/** @group globals.graph
   Constrains the subgraph \a ns and \a es of a given undirected graph to be a path from \a s to \a t of weight \a K.

   @param from: the leaving node for each edge
   @param to: the entering node for each edge
   @param w: the weight of each edge
   @param s: the source node (which may be variable)
   @param t: the dest node (which may be variable)
   @param ns: a Boolean for each node whether it is in the subgraph
   @param es: a Boolean for each edge whether it is in the subgraph
   @param K: the cost of the path
*/
predicate bounded_path(array[int] of $$N: from, array[int] of $$N: to, array[int] of int: w,
                    var $$N: s, var $$N: t, array[$$N] of var bool: ns, array[int] of var bool: es, var int: K) =
   assert(index_set(from) = index_set(to),"bounded_path: index set of from and to must be identical") /\
   assert(index_set(from) = index_set(es),"bounded_path: index set of from and es must be identical") /\
   assert(index_set(w) = index_set(es),"bounded_path: index set of w and es must be identical") /\
   assert(dom_array(from) subset index_set(ns),"bounded_path: nodes in from must be in index set of ns") /\
   assert(dom_array(to) subset index_set(ns),"bounded_path: nodes in to must be in index set of ns") /\
   fzn_bounded_path(from,to,w,s,t,ns,es,K);

include "fzn_bounded_path_int.mzn";
include "fzn_bounded_path_int_reif.mzn";
include "fzn_bounded_path_enum.mzn";
include "fzn_bounded_path_enum_reif.mzn";
include "fzn_bounded_dpath_int.mzn";
include "fzn_bounded_dpath_int_reif.mzn";
include "fzn_bounded_dpath_enum.mzn";
include "fzn_bounded_dpath_enum_reif.mzn";
   
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