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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- *//* * Main authors: * Christian Schulte <schulte@gecode.org> * * Copyright: * Christian Schulte, 2007 * * This file is part of Gecode, the generic constraint * development environment: * http://www.gecode.org * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * */
namespace Gecode { namespace Int { namespace Circuit {
template<class View, class Offset> forceinline Base<View,Offset>::Base(Home home, ViewArray<View>& x, Offset& o0) : NaryPropagator<View,Int::PC_INT_DOM>(home,x), start(0), y(home,x), o(o0) { home.notice(*this,AP_WEAKLY); }
template<class View, class Offset> forceinline Base<View,Offset>::Base(Space& home, Base<View,Offset>& p) : NaryPropagator<View,Int::PC_INT_DOM>(home,p), start(p.start) { o.update(p.o); y.update(home,p.y); }
/// Information required for non-recursive checking for a single scc template<class View> class NodeInfo { public: int min, low, pre; Int::ViewValues<View> v; };
/// Information for performing a recorded tell template<class View> class TellInfo { public: View x; int n; };
template<class View, class Offset> ExecStatus Base<View,Offset>::connected(Space& home) { int n = x.size();
/// First non-assigned node reachable from start { int v = start; /// Number of nodes not yet visited int m = n; while (x[v].assigned()) { m--; v = o(x[v]).val(); // Reached start node again, check whether all nodes have been visited if (start == v) return (m == 0) ? home.ES_SUBSUMED(*this) : ES_FAILED; } start = v; }
/// Information needed for checking scc's Region r; typedef typename Offset::ViewType OView; NodeInfo<OView>* si = r.alloc<NodeInfo<OView> >(n); unsigned int n_edges = 0; for (int i=0; i<n; i++) { n_edges += x[i].size(); si[i].pre=-1; }
// Stack to remember which nodes have not been processed completely Support::StaticStack<int,Region> next(r,n);
// Array to remember which mandatory tells need to be done TellInfo<OView>* eq = r.alloc<TellInfo<OView> >(n); int n_eq = 0;
// Array to remember which edges need to be pruned TellInfo<OView>* nq = r.alloc<TellInfo<OView> >(n_edges); int n_nq = 0;
/* * Check whether there is a single strongly connected component. * This is a downstripped version of Tarjan's algorithm as * the computation of sccs proper is not needed. In addition, it * checks a mandatory condition for a graph to be Hamiltonian * (due to Mats Carlsson). * * To quote Mats: Suppose you do a depth-first search of the graph. * In that search, the root node will have a number of child subtrees * T1, ..., Tn. By construction, if i<j then there is no edge from * Ti to Tj. The necessary condition for Hamiltonianicity is that * there be an edge from Ti+1 to Ti, for 0 < i < n. * * In addition, we do the following: if there is only a single edge * from Ti+1 to Ti, then it must be mandatory and the variable must * be assigned to that value. * * The same holds true for a back edge from T0 to the root node. * * Then, all edges that reach from Ti+k+1 to Ti can be pruned. * */
{ // Start always at node start int i = start; // Counter for scc int cnt = 0; // Smallest preorder number of last subtree (initially, the root node) int subtree_min = 0; // Largest preorder number of last subtree (initially, the root node) int subtree_max = 0; // Number of back edges into last subtree or root int back = 0; start: si[i].min = si[i].pre = si[i].low = cnt++; si[i].v.init(o(x[i])); do { if (si[si[i].v.val()].pre < 0) { next.push(i); i=si[i].v.val(); goto start; } else if ((subtree_min <= si[si[i].v.val()].pre) && (si[si[i].v.val()].pre <= subtree_max)) { back++; eq[n_eq].x = o(x[i]); eq[n_eq].n = si[i].v.val(); } else if (si[si[i].v.val()].pre < subtree_min) { nq[n_nq].x = o(x[i]); nq[n_nq].n = si[i].v.val(); n_nq++; } cont: if (si[si[i].v.val()].low < si[i].min) si[i].min = si[si[i].v.val()].low; ++si[i].v; } while (si[i].v()); if (si[i].min < si[i].low) { si[i].low = si[i].min; } else if (i != start) { // If it is not the first node visited, there is more than one SCC return ES_FAILED; } if (!next.empty()) { i=next.pop(); if (i == start) { // No back edge if (back == 0) return ES_FAILED; // Exactly one back edge, make it mandatory (keep topmost entry) if (back == 1) n_eq++; back = 0; subtree_min = subtree_max+1; subtree_max = cnt-1; } goto cont; }
// Whether all nodes have been visited if (cnt != n) return ES_FAILED;
/* * Whether there is more than one subtree * * This propagation rule is taken from: Kathryn Glenn Francis, * Peter Stuckey, Explaining Circuit Propagation, * Constraints (2014) 19:1-29. * */ if (subtree_min > 1) { for (Int::ViewValues<OView> v(o(x[start])); v(); ++v) if (si[v.val()].pre < subtree_min) { nq[n_nq].x = o(x[v.val()]); nq[n_nq].n = v.val(); n_nq++; } }
ExecStatus es = ES_FIX; // Assign all mandatory edges while (n_eq-- > 0) { ModEvent me = eq[n_eq].x.eq(home,eq[n_eq].n); if (me_failed(me)) return ES_FAILED; if (me_modified(me)) es = ES_NOFIX; }
// Remove all edges that would require a non-simple cycle while (n_nq-- > 0) { ModEvent me = nq[n_nq].x.nq(home,nq[n_nq].n); if (me_failed(me)) return ES_FAILED; if (me_modified(me)) es = ES_NOFIX; }
// Move start to different node for next run start = o(x[start]).min();
return es; } }
template<class View, class Offset> ExecStatus Base<View,Offset>::path(Space& home) { // Prunes that partial assigned paths are not completed to cycles
int n=x.size();
Region r;
// The path starting at assigned x[i] ends at x[end[j]] which is // not assigned. int* end = r.alloc<int>(n); for (int i=0; i<n; i++) end[i]=-1;
// A stack that records all indices i such that end[i] != -1 Support::StaticStack<int,Region> tell(r,n);
typedef typename Offset::ViewType OView; for (int i=0; i<y.size(); i++) { assert(!y[i].assigned()); // Non-assigned views serve as starting points for assigned paths Int::ViewValues<OView> v(o(y[i])); // Try all connected values do { int j0=v.val(); // Starting point for not yet followed assigned path found if (x[j0].assigned() && (end[j0] < 0)) { // Follow assigned path until non-assigned view: // all assigned view on the paths can be skipped, as // if x[i] is assigned to j, then x[j] will only have // x[i] as predecessor due to propagating distinct. int j = j0; do { j=o(x[j]).val(); } while (x[j].assigned()); // Now there cannot be a cycle from x[j] to x[v.val()]! // However, the tell cannot be done here as j might be // equal to i and might hence kill the iterator v! end[j0]=j; tell.push(j0); } ++v; } while (v()); }
// Now do the tells based on the end information while (!tell.empty()) { int i = tell.pop(); assert(end[i] >= 0); GECODE_ME_CHECK(o(x[end[i]]).nq(home,i)); } return ES_NOFIX; }
template<class View, class Offset> forceinline size_t Base<View,Offset>::dispose(Space& home) { home.ignore(*this,AP_WEAKLY); (void) NaryPropagator<View,Int::PC_INT_DOM>::dispose(home); return sizeof(*this); }
}}}
// STATISTICS: int-prop