// Copyright 2010-2017 Google
// 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/table.h"

#include <algorithm>
#include <memory>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <utility>

#include "ortools/base/int_type.h"
#include "ortools/base/logging.h"
#include "ortools/base/map_util.h"
#include "ortools/base/stl_util.h"
#include "ortools/sat/sat_solver.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

namespace {

// Transposes the given "matrix".
std::vector<std::vector<int64>> Transpose(
    const std::vector<std::vector<int64>>& tuples) {
  CHECK(!tuples.empty());
  const int n = tuples.size();
  const int m = tuples[0].size();
  std::vector<std::vector<int64>> transpose(m, std::vector<int64>(n));
  for (int i = 0; i < n; ++i) {
    CHECK_EQ(m, tuples[i].size());
    for (int j = 0; j < m; ++j) {
      transpose[j][i] = tuples[i][j];
    }
  }
  return transpose;
}

// Converts the vector representation returned by FullDomainEncoding() to a map.
std::unordered_map<IntegerValue, Literal> GetEncoding(IntegerVariable var,
                                                      Model* model) {
  std::unordered_map<IntegerValue, Literal> encoding;
  IntegerEncoder* encoder = model->GetOrCreate<IntegerEncoder>();
  for (const auto& entry : encoder->FullDomainEncoding(var)) {
    encoding[entry.value] = entry.literal;
  }
  return encoding;
}

void FilterValues(IntegerVariable var, Model* model,
                  std::unordered_set<int64>* values) {
  const Domain domain = model->Get<IntegerTrail>()->InitialVariableDomain(var);
  for (auto it = values->begin(); it != values->end();) {
    const int64 v = *it;
    auto copy = it++;
    // TODO(user): quadratic! improve.
    if (!domain.Contains(v)) {
      values->erase(copy);
    }
  }
}

// Add the implications and clauses to link one column of a table to the Literal
// controling if the lines are possible or not. The column has the given values,
// and the Literal of the column variable can be retrieved using the encoding
// map.
void ProcessOneColumn(const std::vector<Literal>& line_literals,
                      const std::vector<IntegerValue>& values,
                      const std::unordered_map<IntegerValue, Literal>& encoding,
                      Model* model) {
  CHECK_EQ(line_literals.size(), values.size());
  std::unordered_map<IntegerValue, std::vector<Literal>>
      value_to_list_of_line_literals;

  // If a value is false (i.e not possible), then the tuple with this value
  // is false too (i.e not possible).
  for (int i = 0; i < values.size(); ++i) {
    const IntegerValue v = values[i];
    if (!gtl::ContainsKey(encoding, v)) {
      model->Add(ClauseConstraint({line_literals[i].Negated()}));
    } else {
      value_to_list_of_line_literals[v].push_back(line_literals[i]);
      model->Add(Implication(gtl::FindOrDie(encoding, v).Negated(),
                             line_literals[i].Negated()));
    }
  }

  // If all the tuples containing a value are false, then this value must be
  // false too.
  for (const auto& entry : value_to_list_of_line_literals) {
    std::vector<Literal> clause = entry.second;
    clause.push_back(gtl::FindOrDie(encoding, entry.first).Negated());
    model->Add(ClauseConstraint(clause));
  }
}

}  // namespace

// Makes a static decomposition of a table constraint into clauses.
// This uses an auxiliary vector of Literals tuple_literals.
// For every column col, and every value val of that column,
// the decomposition uses clauses corresponding to the equivalence:
// (\/_{row | tuples[row][col] = val} tuple_literals[row]) <=> (vars[col] = val)
std::function<void(Model*)> TableConstraint(
    const std::vector<IntegerVariable>& vars,
    const std::vector<std::vector<int64>>& tuples) {
  return [=](Model* model) {
    const int n = vars.size();

    // Compute the set of possible values for each variable (from the table).
    std::vector<std::unordered_set<int64>> values_per_var(n);
    for (const std::vector<int64>& tuple : tuples) {
      for (int i = 0; i < n; ++i) {
        values_per_var[i].insert(tuple[i]);
      }
    }

    // Filter each values_per_var entries using the current variable domain.
    for (int i = 0; i < n; ++i) {
      FilterValues(vars[i], model, &values_per_var[i]);
    }

    // Remove the unreachable tuples.
    std::vector<std::vector<int64>> new_tuples;
    for (const std::vector<int64>& tuple : tuples) {
      bool keep = true;
      for (int i = 0; i < n; ++i) {
        if (!gtl::ContainsKey(values_per_var[i], tuple[i])) {
          keep = false;
          break;
        }
      }
      if (keep) {
        new_tuples.push_back(tuple);
      }
    }

    if (new_tuples.empty()) {
      model->GetOrCreate<SatSolver>()->NotifyThatModelIsUnsat();
      return;
    }

    // Remove duplicates if any.
    gtl::STLSortAndRemoveDuplicates(&new_tuples);

    // Create one Boolean variable per tuple to indicate if it can still be
    // selected or not. Note that we don't enforce exactly one tuple to be
    // selected because these variables are just used by this constraint, so
    // only the information "can't be selected" is important.
    //
    // TODO(user): If a value in one column is unique, we don't need to create a
    // new BooleanVariable corresponding to this line since we can use the one
    // corresponding to this value in that column.
    //
    // Note that if there is just one tuple, there is no need to create such
    // variables since they are not used.
    std::vector<Literal> tuple_literals;
    tuple_literals.reserve(new_tuples.size());
    if (new_tuples.size() == 2) {
      tuple_literals.emplace_back(model->Add(NewBooleanVariable()), true);
      tuple_literals.emplace_back(tuple_literals[0].Negated());
    } else if (new_tuples.size() > 2) {
      for (int i = 0; i < new_tuples.size(); ++i) {
        tuple_literals.emplace_back(model->Add(NewBooleanVariable()), true);
      }
    }

    // Fully encode the variables using all the values appearing in the tuples.
    IntegerTrail* integer_trail = model->GetOrCreate<IntegerTrail>();
    const std::vector<std::vector<int64>> tr_tuples = Transpose(new_tuples);
    for (int i = 0; i < n; ++i) {
      const int64 first = tr_tuples[i].front();
      if (std::all_of(tr_tuples[i].begin(), tr_tuples[i].end(),
                      [first](int64 v) { return v == first; })) {
        model->Add(Equality(vars[i], first));
      } else {
        integer_trail->UpdateInitialDomain(vars[i],
                                           Domain::FromValues(tr_tuples[i]));
        model->Add(FullyEncodeVariable(vars[i]));
        ProcessOneColumn(
            tuple_literals,
            std::vector<IntegerValue>(tr_tuples[i].begin(), tr_tuples[i].end()),
            GetEncoding(vars[i], model), model);
      }
    }
  };
}

std::function<void(Model*)> NegatedTableConstraint(
    const std::vector<IntegerVariable>& vars,
    const std::vector<std::vector<int64>>& tuples) {
  return [=](Model* model) {
    const int n = vars.size();
    std::vector<std::unordered_map<int64, Literal>> mapping(n);
    for (int i = 0; i < n; ++i) {
      for (const auto pair : model->Add(FullyEncodeVariable(vars[i]))) {
        mapping[i][pair.value.value()] = pair.literal;
      }
    }

    // For each tuple, forbid the variables values to be this tuple.
    std::vector<Literal> clause(n);
    for (const std::vector<int64>& tuple : tuples) {
      bool add_tuple = true;
      for (int i = 0; i < n; ++i) {
        if (gtl::ContainsKey(mapping[i], tuple[i])) {
          clause[i] = gtl::FindOrDie(mapping[i], tuple[i]).Negated();
        } else {
          add_tuple = false;
          break;
        }
      }
      if (add_tuple) model->Add(ClauseConstraint(clause));
    }
  };
}

std::function<void(Model*)> NegatedTableConstraintWithoutFullEncoding(
    const std::vector<IntegerVariable>& vars,
    const std::vector<std::vector<int64>>& tuples) {
  return [=](Model* model) {
    const int n = vars.size();
    IntegerEncoder* encoder = model->GetOrCreate<IntegerEncoder>();
    std::vector<Literal> clause;
    for (const std::vector<int64>& tuple : tuples) {
      clause.clear();
      bool add = true;
      for (int i = 0; i < n; ++i) {
        const int64 value = tuple[i];
        const int64 lb = model->Get(LowerBound(vars[i]));
        const int64 ub = model->Get(UpperBound(vars[i]));
        // TODO(user): test the full initial domain instead of just checking
        // the bounds.
        if (value < lb || value > ub) {
          add = false;
          break;
        }
        if (value > lb) {
          clause.push_back(encoder->GetOrCreateAssociatedLiteral(
              IntegerLiteral::LowerOrEqual(vars[i], IntegerValue(value - 1))));
        }
        if (value < ub) {
          clause.push_back(encoder->GetOrCreateAssociatedLiteral(
              IntegerLiteral::GreaterOrEqual(vars[i],
                                             IntegerValue(value + 1))));
        }
      }
      if (add) model->Add(ClauseConstraint(clause));
    }
  };
}

std::function<void(Model*)> LiteralTableConstraint(
    const std::vector<std::vector<Literal>>& literal_tuples,
    const std::vector<Literal>& line_literals) {
  return [=](Model* model) {
    CHECK_EQ(literal_tuples.size(), line_literals.size());
    const int num_tuples = line_literals.size();
    if (num_tuples == 0) return;
    const int tuple_size = literal_tuples[0].size();
    if (tuple_size == 0) return;
    for (int i = 1; i < num_tuples; ++i) {
      CHECK_EQ(tuple_size, literal_tuples[i].size());
    }

    std::unordered_map<LiteralIndex, std::vector<LiteralIndex>>
        line_literals_per_literal;
    for (int i = 0; i < num_tuples; ++i) {
      const LiteralIndex selected_index = line_literals[i].Index();
      for (const Literal l : literal_tuples[i]) {
        line_literals_per_literal[l.Index()].push_back(selected_index);
      }
    }

    // line_literals[i] == true => literal_tuples[i][j] == true.
    // literal_tuples[i][j] == false => line_literals[i] == false.
    for (int i = 0; i < num_tuples; ++i) {
      const Literal line_is_selected = line_literals[i];
      for (const Literal lit : literal_tuples[i]) {
        model->Add(Implication(line_is_selected, lit));
      }
    }

    // Exactly one selected literal is true.
    model->Add(ExactlyOneConstraint(line_literals));

    // If all selected literals of the lines containing a literal are false,
    // then the literal is false.
    for (const auto& p : line_literals_per_literal) {
      std::vector<Literal> clause;
      for (const auto& index : p.second) {
        clause.push_back(Literal(index));
      }
      clause.push_back(Literal(p.first).Negated());
      model->Add(ClauseConstraint(clause));
    }
  };
}

std::function<void(Model*)> TransitionConstraint(
    const std::vector<IntegerVariable>& vars,
    const std::vector<std::vector<int64>>& automata, int64 initial_state,
    const std::vector<int64>& final_states) {
  return [=](Model* model) {
    IntegerTrail* integer_trail = model->GetOrCreate<IntegerTrail>();
    const int n = vars.size();
    CHECK_GT(n, 0) << "No variables in TransitionConstraint().";

    // Test precondition.
    {
      std::set<std::pair<int64, int64>> unique_transition_checker;
      for (const std::vector<int64>& transition : automata) {
        CHECK_EQ(transition.size(), 3);
        const std::pair<int64, int64> p{transition[0], transition[1]};
        CHECK(!gtl::ContainsKey(unique_transition_checker, p))
            << "Duplicate outgoing transitions with value " << transition[1]
            << " from state " << transition[0] << ".";
        unique_transition_checker.insert(p);
      }
    }

    // Construct a table with the possible values of each vars.
    std::vector<std::unordered_set<int64>> possible_values(n);
    for (int time = 0; time < n; ++time) {
      const auto domain = integer_trail->InitialVariableDomain(vars[time]);
      for (const std::vector<int64>& transition : automata) {
        // TODO(user): quadratic algo, improve!
        if (domain.Contains(transition[1])) {
          possible_values[time].insert(transition[1]);
        }
      }
    }

    // Compute the set of reachable state at each time point.
    std::vector<std::set<int64>> reachable_states(n + 1);
    reachable_states[0].insert(initial_state);
    reachable_states[n] = {final_states.begin(), final_states.end()};

    // Forward.
    //
    // TODO(user): filter using the domain of vars[time] that may not contain
    // all the possible transitions.
    for (int time = 0; time + 1 < n; ++time) {
      for (const std::vector<int64>& transition : automata) {
        if (!gtl::ContainsKey(reachable_states[time], transition[0])) continue;
        if (!gtl::ContainsKey(possible_values[time], transition[1])) continue;
        reachable_states[time + 1].insert(transition[2]);
      }
    }

    // Backward.
    for (int time = n - 1; time > 0; --time) {
      std::set<int64> new_set;
      for (const std::vector<int64>& transition : automata) {
        if (!gtl::ContainsKey(reachable_states[time], transition[0])) continue;
        if (!gtl::ContainsKey(possible_values[time], transition[1])) continue;
        if (!gtl::ContainsKey(reachable_states[time + 1], transition[2]))
          continue;
        new_set.insert(transition[0]);
      }
      reachable_states[time].swap(new_set);
    }

    // We will model at each time step the current automata state using Boolean
    // variables. We will have n+1 time step. At time zero, we start in the
    // initial state, and at time n we should be in one of the final states. We
    // don't need to create Booleans at at time when there is just one possible
    // state (like at time zero).
    std::unordered_map<IntegerValue, Literal> encoding;
    std::unordered_map<IntegerValue, Literal> in_encoding;
    std::unordered_map<IntegerValue, Literal> out_encoding;
    for (int time = 0; time < n; ++time) {
      // All these vector have the same size. We will use them to enforce a
      // local table constraint representing one step of the automata at the
      // given time.
      std::vector<Literal> tuple_literals;
      std::vector<IntegerValue> in_states;
      std::vector<IntegerValue> transition_values;
      std::vector<IntegerValue> out_states;
      for (const std::vector<int64>& transition : automata) {
        if (!gtl::ContainsKey(reachable_states[time], transition[0])) continue;
        if (!gtl::ContainsKey(possible_values[time], transition[1])) continue;
        if (!gtl::ContainsKey(reachable_states[time + 1], transition[2]))
          continue;

        // TODO(user): if this transition correspond to just one in-state or
        // one-out state or one variable value, we could reuse the corresponding
        // Boolean variable instead of creating a new one!
        tuple_literals.push_back(
            Literal(model->Add(NewBooleanVariable()), true));
        in_states.push_back(IntegerValue(transition[0]));

        transition_values.push_back(IntegerValue(transition[1]));

        // On the last step we don't need to distinguish the output states, so
        // we use zero.
        out_states.push_back(time + 1 == n ? IntegerValue(0)
                                           : IntegerValue(transition[2]));
      }

      // Fully instantiate vars[time].
      // Tricky: because we started adding constraints that can propagate, the
      // possible values returned by encoding might not contains all the value
      // computed in transition_values.
      {
        std::vector<IntegerValue> s = transition_values;
        gtl::STLSortAndRemoveDuplicates(&s);

        encoding.clear();
        if (s.size() > 1) {
          std::vector<int64> values;
          values.reserve(s.size());
          for (IntegerValue v : s) values.push_back(v.value());
          integer_trail->UpdateInitialDomain(vars[time],
                                             Domain::FromValues(values));
          model->Add(FullyEncodeVariable(vars[time]));
          encoding = GetEncoding(vars[time], model);
        } else {
          // Fix vars[time] to its unique possible value.
          CHECK_EQ(s.size(), 1);
          const int64 unique_value = s.begin()->value();
          model->Add(LowerOrEqual(vars[time], unique_value));
          model->Add(GreaterOrEqual(vars[time], unique_value));
        }
      }

      // For each possible out states, create one Boolean variable.
      {
        std::vector<IntegerValue> s = out_states;
        gtl::STLSortAndRemoveDuplicates(&s);

        out_encoding.clear();
        if (s.size() == 2) {
          const BooleanVariable var = model->Add(NewBooleanVariable());
          out_encoding[s.front()] = Literal(var, true);
          out_encoding[s.back()] = Literal(var, false);
        } else if (s.size() > 1) {
          for (const IntegerValue state : s) {
            const Literal l = Literal(model->Add(NewBooleanVariable()), true);
            out_encoding[state] = l;
          }
        }
      }

      // Now we link everything together.
      //
      // Note that we do not need the ExactlyOneConstraint(tuple_literals)
      // because it is already implicitely encoded since we have exactly one
      // transition value.
      if (!in_encoding.empty()) {
        ProcessOneColumn(tuple_literals, in_states, in_encoding, model);
      }
      if (!encoding.empty()) {
        ProcessOneColumn(tuple_literals, transition_values, encoding, model);
      }
      if (!out_encoding.empty()) {
        ProcessOneColumn(tuple_literals, out_states, out_encoding, model);
      }
      in_encoding = out_encoding;
    }
  };
}

}  // namespace sat
}  // namespace operations_research