circuit.cc

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// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
 
#include "ortools/sat/circuit.h"
 
#include <algorithm>
 
#include "absl/container/flat_hash_map.h"
#include "ortools/base/map_util.h"
#include "ortools/sat/sat_solver.h"
 
namespace operations_research {
namespace sat {
 
CircuitPropagator::CircuitPropagator(const int num_nodes,
                                     const std::vector<int>& tails,
                                     const std::vector<int>& heads,
                                     const std::vector<Literal>& literals,
                                     Options options, Model* model)
    : num_nodes_(num_nodes),
      options_(options),
      trail_(model->GetOrCreate<Trail>()),
      assignment_(trail_->Assignment()) {
  CHECK(!tails.empty()) << "Empty constraint, shouldn't be constructed!";
  next_.resize(num_nodes_, -1);
  prev_.resize(num_nodes_, -1);
  next_literal_.resize(num_nodes_);
  must_be_in_cycle_.resize(num_nodes_);
  absl::flat_hash_map<LiteralIndex, int> literal_to_watch_index;
 
  const int num_arcs = tails.size();
  graph_.reserve(num_arcs);
  self_arcs_.resize(num_nodes_,
                    model->GetOrCreate<IntegerEncoder>()->GetFalseLiteral());
  for (int arc = 0; arc < num_arcs; ++arc) {
    const int head = heads[arc];
    const int tail = tails[arc];
    const Literal literal = literals[arc];
    if (assignment_.LiteralIsFalse(literal)) continue;
 
    if (tail == head) {
      self_arcs_[tail] = literal;
    } else {
      graph_[{tail, head}] = literal;
    }
 
    if (assignment_.LiteralIsTrue(literal)) {
      if (next_[tail] != -1 || prev_[head] != -1) {
        VLOG(1) << "Trivially UNSAT or duplicate arcs while adding " << tail
                << " -> " << head;
        model->GetOrCreate<SatSolver>()->NotifyThatModelIsUnsat();
        return;
      }
      AddArc(tail, head, kNoLiteralIndex);
      continue;
    }
 
    // Tricky: For self-arc, we watch instead when the arc become false.
    const Literal watched_literal = tail == head ? literal.Negated() : literal;
    int watch_index = gtl::FindWithDefault(literal_to_watch_index,
                                           watched_literal.Index(), -1);
    if (watch_index == -1) {
      watch_index = watch_index_to_literal_.size();
      literal_to_watch_index[watched_literal.Index()] = watch_index;
      watch_index_to_literal_.push_back(watched_literal);
      watch_index_to_arcs_.push_back(std::vector<Arc>());
    }
    watch_index_to_arcs_[watch_index].push_back({tail, head});
  }
 
  for (int node = 0; node < num_nodes_; ++node) {
    if (assignment_.LiteralIsFalse(self_arcs_[node])) {
      // For the multiple_subcircuit_through_zero case, must_be_in_cycle_ will
      // be const and only contains zero.
      if (node == 0 || !options_.multiple_subcircuit_through_zero) {
        must_be_in_cycle_[rev_must_be_in_cycle_size_++] = node;
      }
    }
  }
}
 
void CircuitPropagator::RegisterWith(GenericLiteralWatcher* watcher) {
  const int id = watcher->Register(this);
  for (int w = 0; w < watch_index_to_literal_.size(); ++w) {
    watcher->WatchLiteral(watch_index_to_literal_[w], id, w);
  }
  watcher->RegisterReversibleClass(id, this);
  watcher->RegisterReversibleInt(id, &propagation_trail_index_);
  watcher->RegisterReversibleInt(id, &rev_must_be_in_cycle_size_);
 
  // This is needed in case a Literal is used for more than one arc, we may
  // propagate it to false/true here, and it might trigger more propagation.
  //
  // TODO(user): come up with a test that fail when this is not here.
  watcher->NotifyThatPropagatorMayNotReachFixedPointInOnePass(id);
}
 
void CircuitPropagator::SetLevel(int level) {
  if (level == level_ends_.size()) return;
  if (level > level_ends_.size()) {
    while (level > level_ends_.size()) {
      level_ends_.push_back(added_arcs_.size());
    }
    return;
  }
 
  // Backtrack.
  for (int i = level_ends_[level]; i < added_arcs_.size(); ++i) {
    const Arc arc = added_arcs_[i];
    next_[arc.tail] = -1;
    prev_[arc.head] = -1;
  }
  added_arcs_.resize(level_ends_[level]);
  level_ends_.resize(level);
}
 
void CircuitPropagator::FillReasonForPath(int start_node,
                                          std::vector<Literal>* reason) const {
  CHECK_NE(start_node, -1);
  reason->clear();
  int node = start_node;
  while (next_[node] != -1) {
    if (next_literal_[node] != kNoLiteralIndex) {
      reason->push_back(Literal(next_literal_[node]).Negated());
    }
    node = next_[node];
    if (node == start_node) break;
  }
}
 
// If multiple_subcircuit_through_zero is true, we never fill next_[0] and
// prev_[0].
void CircuitPropagator::AddArc(int tail, int head, LiteralIndex literal_index) {
  if (tail != 0 || !options_.multiple_subcircuit_through_zero) {
    next_[tail] = head;
    next_literal_[tail] = literal_index;
  }
  if (head != 0 || !options_.multiple_subcircuit_through_zero) {
    prev_[head] = tail;
  }
}
 
bool CircuitPropagator::IncrementalPropagate(
    const std::vector<int>& watch_indices) {
  for (const int w : watch_indices) {
    const Literal literal = watch_index_to_literal_[w];
    for (const Arc arc : watch_index_to_arcs_[w]) {
      // Special case for self-arc.
      if (arc.tail == arc.head) {
        must_be_in_cycle_[rev_must_be_in_cycle_size_++] = arc.tail;
        continue;
      }
 
      // Get rid of the trivial conflicts: At most one incoming and one outgoing
      // arc for each nodes.
      if (next_[arc.tail] != -1) {
        std::vector<Literal>* conflict = trail_->MutableConflict();
        if (next_literal_[arc.tail] != kNoLiteralIndex) {
          *conflict = {Literal(next_literal_[arc.tail]).Negated(),
                       literal.Negated()};
        } else {
          *conflict = {literal.Negated()};
        }
        return false;
      }
      if (prev_[arc.head] != -1) {
        std::vector<Literal>* conflict = trail_->MutableConflict();
        if (next_literal_[prev_[arc.head]] != kNoLiteralIndex) {
          *conflict = {Literal(next_literal_[prev_[arc.head]]).Negated(),
                       literal.Negated()};
        } else {
          *conflict = {literal.Negated()};
        }
        return false;
      }
 
      // Add the arc.
      AddArc(arc.tail, arc.head, literal.Index());
      added_arcs_.push_back(arc);
    }
  }
  return Propagate();
}
 
// This function assumes that next_, prev_, next_literal_ and must_be_in_cycle_
// are all up to date.
bool CircuitPropagator::Propagate() {
  processed_.assign(num_nodes_, false);
  for (int n = 0; n < num_nodes_; ++n) {
    if (processed_[n]) continue;
    if (next_[n] == n) continue;
    if (next_[n] == -1 && prev_[n] == -1) continue;
 
    // TODO(user): both this and the loop on must_be_in_cycle_ might take some
    // time on large graph. Optimize if this become an issue.
    in_current_path_.assign(num_nodes_, false);
 
    // Find the start and end of the path containing node n. If this is a
    // circuit, we will have start_node == end_node.
    int start_node = n;
    int end_node = n;
    in_current_path_[n] = true;
    processed_[n] = true;
    while (next_[end_node] != -1) {
      end_node = next_[end_node];
      in_current_path_[end_node] = true;
      processed_[end_node] = true;
      if (end_node == n) break;
    }
    while (prev_[start_node] != -1) {
      start_node = prev_[start_node];
      in_current_path_[start_node] = true;
      processed_[start_node] = true;
      if (start_node == n) break;
    }
 
    // TODO(user): we can fail early in more case, like no more possible path
    // to any of the mandatory node.
    if (options_.multiple_subcircuit_through_zero) {
      // Any cycle must contain zero.
      if (start_node == end_node && !in_current_path_[0]) {
        FillReasonForPath(start_node, trail_->MutableConflict());
        return false;
      }
 
      // An incomplete path cannot be closed except if one of the end-points
      // is zero.
      if (start_node != end_node && start_node != 0 && end_node != 0) {
        const auto it = graph_.find({end_node, start_node});
        if (it == graph_.end()) continue;
        const Literal literal = it->second;
        if (assignment_.LiteralIsFalse(literal)) continue;
 
        std::vector<Literal>* reason = trail_->GetEmptyVectorToStoreReason();
        FillReasonForPath(start_node, reason);
        if (!trail_->EnqueueWithStoredReason(literal.Negated())) {
          return false;
        }
      }
 
      // None of the other propagation below are valid in case of multiple
      // circuits.
      continue;
    }
 
    // Check if we miss any node that must be in the circuit. Note that the ones
    // for which self_arcs_[i] is kFalseLiteralIndex are first. This is good as
    // it will produce shorter reason. Otherwise we prefer the first that was
    // assigned in the trail.
    bool miss_some_nodes = false;
    LiteralIndex extra_reason = kFalseLiteralIndex;
    for (int i = 0; i < rev_must_be_in_cycle_size_; ++i) {
      const int node = must_be_in_cycle_[i];
      if (!in_current_path_[node]) {
        miss_some_nodes = true;
        extra_reason = self_arcs_[node].Index();
        break;
      }
    }
 
    if (miss_some_nodes) {
      // A circuit that miss a mandatory node is a conflict.
      if (start_node == end_node) {
        FillReasonForPath(start_node, trail_->MutableConflict());
        if (extra_reason != kFalseLiteralIndex) {
          trail_->MutableConflict()->push_back(Literal(extra_reason));
        }
        return false;
      }
 
      // We have an unclosed path. Propagate the fact that it cannot
      // be closed into a cycle, i.e. not(end_node -> start_node).
      if (start_node != end_node) {
        const auto it = graph_.find({end_node, start_node});
        if (it == graph_.end()) continue;
        const Literal literal = it->second;
        if (assignment_.LiteralIsFalse(literal)) continue;
 
        std::vector<Literal>* reason = trail_->GetEmptyVectorToStoreReason();
        FillReasonForPath(start_node, reason);
        if (extra_reason != kFalseLiteralIndex) {
          reason->push_back(Literal(extra_reason));
        }
        const bool ok = trail_->EnqueueWithStoredReason(literal.Negated());
        if (!ok) return false;
        continue;
      }
    }
 
    // If we have a cycle, we can propagate all the other nodes to point to
    // themselves. Otherwise there is nothing else to do.
    if (start_node != end_node) continue;
    BooleanVariable variable_with_same_reason = kNoBooleanVariable;
    for (int node = 0; node < num_nodes_; ++node) {
      if (in_current_path_[node]) continue;
      if (assignment_.LiteralIsTrue(self_arcs_[node])) continue;
 
      // This shouldn't happen because ExactlyOnePerRowAndPerColumn() should
      // have executed first and propagated self_arcs_[node] to false.
      CHECK_EQ(next_[node], -1);
 
      // We should have detected that above (miss_some_nodes == true). But we
      // still need this for corner cases where the same literal is used for
      // many arcs, and we just propagated it here.
      if (assignment_.LiteralIsFalse(self_arcs_[node])) {
        FillReasonForPath(start_node, trail_->MutableConflict());
        trail_->MutableConflict()->push_back(self_arcs_[node]);
        return false;
      }
 
      // Propagate.
      const Literal literal(self_arcs_[node]);
      if (variable_with_same_reason == kNoBooleanVariable) {
        variable_with_same_reason = literal.Variable();
        FillReasonForPath(start_node, trail_->GetEmptyVectorToStoreReason());
        const bool ok = trail_->EnqueueWithStoredReason(literal);
        if (!ok) return false;
      } else {
        trail_->EnqueueWithSameReasonAs(literal, variable_with_same_reason);
      }
    }
  }
  return true;
}
 
CircuitCoveringPropagator::CircuitCoveringPropagator(
    std::vector<std::vector<Literal>> graph,
    const std::vector<int>& distinguished_nodes, Model* model)
    : graph_(std::move(graph)),
      num_nodes_(graph_.size()),
      trail_(model->GetOrCreate<Trail>()) {
  node_is_distinguished_.resize(num_nodes_, false);
  for (const int node : distinguished_nodes) {
    node_is_distinguished_[node] = true;
  }
}
 
void CircuitCoveringPropagator::RegisterWith(GenericLiteralWatcher* watcher) {
  const int watcher_id = watcher->Register(this);
 
  // Fill fixed_arcs_ with arcs that are initially fixed to true,
  // assign arcs to watch indices.
  for (int node1 = 0; node1 < num_nodes_; node1++) {
    for (int node2 = 0; node2 < num_nodes_; node2++) {
      const Literal l = graph_[node1][node2];
      if (trail_->Assignment().LiteralIsFalse(l)) continue;
      if (trail_->Assignment().LiteralIsTrue(l)) {
        fixed_arcs_.emplace_back(node1, node2);
      } else {
        watcher->WatchLiteral(l, watcher_id, watch_index_to_arc_.size());
        watch_index_to_arc_.emplace_back(node1, node2);
      }
    }
  }
  watcher->RegisterReversibleClass(watcher_id, this);
}
 
void CircuitCoveringPropagator::SetLevel(int level) {
  if (level == level_ends_.size()) return;
  if (level > level_ends_.size()) {
    while (level > level_ends_.size()) {
      level_ends_.push_back(fixed_arcs_.size());
    }
  } else {
    // Backtrack.
    fixed_arcs_.resize(level_ends_[level]);
    level_ends_.resize(level);
  }
}
 
bool CircuitCoveringPropagator::IncrementalPropagate(
    const std::vector<int>& watch_indices) {
  for (const int w : watch_indices) {
    const auto& arc = watch_index_to_arc_[w];
    fixed_arcs_.push_back(arc);
  }
  return Propagate();
}
 
void CircuitCoveringPropagator::FillFixedPathInReason(
    int start, int end, std::vector<Literal>* reason) {
  reason->clear();
  int current = start;
  do {
    DCHECK_NE(next_[current], -1);
    DCHECK(trail_->Assignment().LiteralIsTrue(graph_[current][next_[current]]));
    reason->push_back(graph_[current][next_[current]].Negated());
    current = next_[current];
  } while (current != end);
}
 
bool CircuitCoveringPropagator::Propagate() {
  // Gather next_ and prev_ from fixed arcs.
  next_.assign(num_nodes_, -1);
  prev_.assign(num_nodes_, -1);
  for (const auto& arc : fixed_arcs_) {
    // Two arcs go out of arc.first, forbidden.
    if (next_[arc.first] != -1) {
      *trail_->MutableConflict() = {
          graph_[arc.first][next_[arc.first]].Negated(),
          graph_[arc.first][arc.second].Negated()};
      return false;
    }
    next_[arc.first] = arc.second;
    // Two arcs come into arc.second, forbidden.
    if (prev_[arc.second] != -1) {
      *trail_->MutableConflict() = {
          graph_[prev_[arc.second]][arc.second].Negated(),
          graph_[arc.first][arc.second].Negated()};
      return false;
    }
    prev_[arc.second] = arc.first;
  }
 
  // For every node, find partial path/circuit in which the node is.
  // Use visited_ to visit each path/circuit only once.
  visited_.assign(num_nodes_, false);
  for (int node = 0; node < num_nodes_; node++) {
    // Skip if already visited, isolated or loop.
    if (visited_[node]) continue;
    if (prev_[node] == -1 && next_[node] == -1) continue;
    if (prev_[node] == node) continue;
 
    // Find start of path/circuit.
    int start = node;
    for (int current = prev_[node]; current != -1 && current != node;
         current = prev_[current]) {
      start = current;
    }
 
    // Find distinguished node of path. Fail if there are several,
    // fail if this is a non loop circuit and there are none.
    int distinguished = node_is_distinguished_[start] ? start : -1;
    int current = next_[start];
    int end = start;
    visited_[start] = true;
    while (current != -1 && current != start) {
      if (node_is_distinguished_[current]) {
        if (distinguished != -1) {
          FillFixedPathInReason(distinguished, current,
                                trail_->MutableConflict());
          return false;
        }
        distinguished = current;
      }
      visited_[current] = true;
      end = current;
      current = next_[current];
    }
 
    // Circuit with no distinguished nodes, forbidden.
    if (start == current && distinguished == -1) {
      FillFixedPathInReason(start, start, trail_->MutableConflict());
      return false;
    }
 
    // Path with no distinguished node: forbid to close it.
    if (current == -1 && distinguished == -1 &&
        !trail_->Assignment().LiteralIsFalse(graph_[end][start])) {
      auto* reason = trail_->GetEmptyVectorToStoreReason();
      FillFixedPathInReason(start, end, reason);
      const bool ok =
          trail_->EnqueueWithStoredReason(graph_[end][start].Negated());
      if (!ok) return false;
    }
  }
  return true;
}
 
std::function<void(Model*)> ExactlyOnePerRowAndPerColumn(
    const std::vector<std::vector<Literal>>& graph) {
  return [=](Model* model) {
    const int n = graph.size();
    std::vector<Literal> exactly_one_constraint;
    exactly_one_constraint.reserve(n);
    for (const bool transpose : {false, true}) {
      for (int i = 0; i < n; ++i) {
        exactly_one_constraint.clear();
        for (int j = 0; j < n; ++j) {
          exactly_one_constraint.push_back(transpose ? graph[j][i]
                                                     : graph[i][j]);
        }
        model->Add(ExactlyOneConstraint(exactly_one_constraint));
      }
    }
  };
}
 
std::function<void(Model*)> SubcircuitConstraint(
    int num_nodes, const std::vector<int>& tails, const std::vector<int>& heads,
    const std::vector<Literal>& literals,
    bool multiple_subcircuit_through_zero) {
  return [=](Model* model) {
    const int num_arcs = tails.size();
    CHECK_GT(num_arcs, 0);
    CHECK_EQ(heads.size(), num_arcs);
    CHECK_EQ(literals.size(), num_arcs);
 
    // If a node has no outgoing or no incoming arc, the model will be unsat
    // as soon as we add the corresponding ExactlyOneConstraint().
    auto sat_solver = model->GetOrCreate<SatSolver>();
 
    std::vector<std::vector<Literal>> exactly_one_incoming(num_nodes);
    std::vector<std::vector<Literal>> exactly_one_outgoing(num_nodes);
    for (int arc = 0; arc < num_arcs; arc++) {
      const int tail = tails[arc];
      const int head = heads[arc];
      exactly_one_outgoing[tail].push_back(literals[arc]);
      exactly_one_incoming[head].push_back(literals[arc]);
    }
    for (int i = 0; i < exactly_one_incoming.size(); ++i) {
      if (i == 0 && multiple_subcircuit_through_zero) continue;
      model->Add(ExactlyOneConstraint(exactly_one_incoming[i]));
      if (sat_solver->IsModelUnsat()) return;
    }
    for (int i = 0; i < exactly_one_outgoing.size(); ++i) {
      if (i == 0 && multiple_subcircuit_through_zero) continue;
      model->Add(ExactlyOneConstraint(exactly_one_outgoing[i]));
      if (sat_solver->IsModelUnsat()) return;
    }
 
    CircuitPropagator::Options options;
    options.multiple_subcircuit_through_zero = multiple_subcircuit_through_zero;
    CircuitPropagator* constraint = new CircuitPropagator(
        num_nodes, tails, heads, literals, options, model);
    constraint->RegisterWith(model->GetOrCreate<GenericLiteralWatcher>());
    model->TakeOwnership(constraint);
  };
}
 
std::function<void(Model*)> CircuitCovering(
    const std::vector<std::vector<Literal>>& graph,
    const std::vector<int>& distinguished_nodes) {
  return [=](Model* model) {
    CircuitCoveringPropagator* constraint =
        new CircuitCoveringPropagator(graph, distinguished_nodes, model);
    constraint->RegisterWith(model->GetOrCreate<GenericLiteralWatcher>());
    model->TakeOwnership(constraint);
  };
}
 
}  // namespace sat
}  // namespace operations_research