sat/util.h

Go to the documentation of this file.

// 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.
 
#ifndef OR_TOOLS_SAT_UTIL_H_
#define OR_TOOLS_SAT_UTIL_H_
 
#include <cstdint>
#include <deque>
#include <vector>
 
#include "ortools/base/logging.h"
#if !defined(__PORTABLE_PLATFORM__)
#include "google/protobuf/descriptor.h"
#endif  // __PORTABLE_PLATFORM__
#include "absl/container/btree_set.h"
#include "absl/random/bit_gen_ref.h"
#include "absl/random/random.h"
#include "absl/types/span.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_base.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/random_engine.h"
#include "ortools/util/time_limit.h"
 
namespace operations_research {
namespace sat {
 
// Returns a in [0, m) such that a * x = 1 modulo m.
// If gcd(x, m) != 1, there is no inverse, and it returns 0.
//
// This DCHECK that x is in [0, m).
// This is integer overflow safe.
//
// Note(user): I didn't find this in a easily usable standard library.
int64_t ModularInverse(int64_t x, int64_t m);
 
// Just returns x % m but with a result always in [0, m).
int64_t PositiveMod(int64_t x, int64_t m);
 
// If we know that X * coeff % mod = rhs % mod, this returns c such that
// PositiveMod(X, mod) = c.
//
// This requires coeff != 0, mod !=0 and gcd(coeff, mod) == 1.
// The result will be in [0, mod) but there is no other condition on the sign or
// magnitude of a and b.
//
// This is overflow safe, and when rhs == 0 or abs(mod) == 1, it returns 0.
int64_t ProductWithModularInverse(int64_t coeff, int64_t mod, int64_t rhs);
 
// Returns true if the equation a * X + b * Y = cte has some integer solutions.
// For now, we check that a and b are different from 0 and from int64_t min.
//
// There is actually always a solution if cte % gcd(|a|, |b|) == 0. And because
// a, b and cte fit on an int64_t, if there is a solution, there is one with X
// and Y fitting on an int64_t.
//
// We will divide everything by gcd(a, b) first, so it is why we take reference
// and the equation can change.
//
// If there are solutions, we return one of them (x0, y0).
// From any such solution, the set of all solutions is given for Z integer by:
// X = x0 + b * Z;
// Y = y0 - a * Z;
//
// Given a domain for X and Y, it is possible to compute the "exact" domain of Z
// with our Domain functions. Note however that this will only compute solution
// where both x-x0 and y-y0 do fit on an int64_t:
// DomainOf(x).SubtractionWith(x0).InverseMultiplicationBy(b).IntersectionWith(
//     DomainOf(y).SubtractionWith(y0).InverseMultiplicationBy(-a))
bool SolveDiophantineEquationOfSizeTwo(int64_t& a, int64_t& b, int64_t& cte,
                                       int64_t& x0, int64_t& y0);
 
// The argument must be non-negative.
int64_t FloorSquareRoot(int64_t a);
int64_t CeilSquareRoot(int64_t a);
 
// Returns the multiple of base closest to value. If there is a tie, we return
// the one closest to zero. This way we have ClosestMultiple(x) =
// -ClosestMultiple(-x) which is important for how this is used.
int64_t ClosestMultiple(int64_t value, int64_t base);
 
// Given a linear equation "sum coeff_i * X_i <= rhs. We can rewrite it using
// ClosestMultiple() as "base * new_terms + error <= rhs" where error can be
// bounded using the provided bounds on each variables. This will return true if
// the error can be ignored and this equation is completely equivalent to
// new_terms <= new_rhs.
//
// This is useful for cases like 9'999 X + 10'0001 Y <= 155'000 where we have
// weird coefficient (maybe due to scaling). With a base of 10K, this is
// equivalent to X + Y <= 15.
//
// Preconditions: All coeffs are assumed to be positive. You can easily negate
// all the negative coeffs and corresponding bounds before calling this.
bool LinearInequalityCanBeReducedWithClosestMultiple(
    int64_t base, const std::vector<int64_t>& coeffs,
    const std::vector<int64_t>& lbs, const std::vector<int64_t>& ubs,
    int64_t rhs, int64_t* new_rhs);
 
// The model "singleton" random engine used in the solver.
//
// In test, we usually set use_absl_random() so that the sequence is changed at
// each invocation. This way, clients do not relly on the wrong assumption that
// a particular optimal solution will be returned if they are many equivalent
// ones.
class ModelRandomGenerator : public absl::BitGenRef {
 public:
  // We seed the strategy at creation only. This should be enough for our use
  // case since the SatParameters is set first before the solver is created. We
  // also never really need to change the seed afterwards, it is just used to
  // diversify solves with identical parameters on different Model objects.
  explicit ModelRandomGenerator(Model* model)
      : absl::BitGenRef(deterministic_random_) {
    const auto& params = *model->GetOrCreate<SatParameters>();
    deterministic_random_.seed(params.random_seed());
    if (params.use_absl_random()) {
      absl_random_ = absl::BitGen(absl::SeedSeq({params.random_seed()}));
      absl::BitGenRef::operator=(absl::BitGenRef(absl_random_));
    }
  }
 
  // This is just used to display ABSL_RANDOM_SALT_OVERRIDE in the log so that
  // it is possible to reproduce a failure more easily while looking at a solver
  // log.
  //
  // TODO(user): I didn't find a cleaner way to log this.
  void LogSalt() const {}
 
 private:
  random_engine_t deterministic_random_;
  absl::BitGen absl_random_;
};
 
// The model "singleton" shared time limit.
class ModelSharedTimeLimit : public SharedTimeLimit {
 public:
  explicit ModelSharedTimeLimit(Model* model)
      : SharedTimeLimit(model->GetOrCreate<TimeLimit>()) {}
};
 
// Randomizes the decision heuristic of the given SatParameters.
void RandomizeDecisionHeuristic(absl::BitGenRef random,
                                SatParameters* parameters);
 
// Context: this function is not really generic, but required to be unit-tested.
// It is used in a clause minimization algorithm when we try to detect if any of
// the clause literals can be propagated by a subset of the other literal being
// false. For that, we want to enqueue in the solver all the subset of size n-1.
//
// This moves one of the unprocessed literal from literals to the last position.
// The function tries to do that while preserving the longest possible prefix of
// literals "amortized" through the calls assuming that we want to move each
// literal to the last position once.
//
// For a vector of size n, if we want to call this n times so that each literal
// is last at least once, the sum of the size of the changed suffixes will be
// O(n log n). If we were to use a simpler algorithm (like moving the last
// unprocessed literal to the last position), this sum would be O(n^2).
//
// Returns the size of the common prefix of literals before and after the move,
// or -1 if all the literals are already processed. The argument
// relevant_prefix_size is used as a hint when keeping more that this prefix
// size do not matter. The returned value will always be lower or equal to
// relevant_prefix_size.
int MoveOneUnprocessedLiteralLast(
    const absl::btree_set<LiteralIndex>& processed, int relevant_prefix_size,
    std::vector<Literal>* literals);
 
// ============================================================================
// Implementation.
// ============================================================================
 
// Manages incremental averages.
class IncrementalAverage {
 public:
  // Initializes the average with 'initial_average' and number of records to 0.
  explicit IncrementalAverage(double initial_average)
      : average_(initial_average) {}
  IncrementalAverage() {}
 
  // Sets the number of records to 0 and average to 'reset_value'.
  void Reset(double reset_value);
 
  double CurrentAverage() const { return average_; }
  int64_t NumRecords() const { return num_records_; }
 
  void AddData(double new_record);
 
 private:
  double average_ = 0.0;
  int64_t num_records_ = 0;
};
 
// Manages exponential moving averages defined as
// new_average = decaying_factor * old_average
//               + (1 - decaying_factor) * new_record.
// where 0 < decaying_factor < 1.
class ExponentialMovingAverage {
 public:
  explicit ExponentialMovingAverage(double decaying_factor)
      : decaying_factor_(decaying_factor) {
    DCHECK_GE(decaying_factor, 0.0);
    DCHECK_LE(decaying_factor, 1.0);
  }
 
  // Returns exponential moving average for all the added data so far.
  double CurrentAverage() const { return average_; }
 
  // Returns the total number of added records so far.
  int64_t NumRecords() const { return num_records_; }
 
  void AddData(double new_record);
 
 private:
  double average_ = 0.0;
  int64_t num_records_ = 0;
  const double decaying_factor_;
};
 
// Utility to calculate percentile (First variant) for limited number of
// records. Reference: https://en.wikipedia.org/wiki/Percentile
//
// After the vector is sorted, we assume that the element with index i
// correspond to the percentile 100*(i+0.5)/size. For percentiles before the
// first element (resp. after the last one) we return the first element (resp.
// the last). And otherwise we do a linear interpolation between the two element
// around the asked percentile.
class Percentile {
 public:
  explicit Percentile(int record_limit) : record_limit_(record_limit) {}
 
  void AddRecord(double record);
 
  // Returns number of stored records.
  int64_t NumRecords() const { return records_.size(); }
 
  // Note that this is not fast and runs in O(n log n) for n records.
  double GetPercentile(double percent);
 
 private:
  std::deque<double> records_;
  const int record_limit_;
};
 
// This method tries to compress a list of tuples by merging complementary
// tuples, that is a set of tuples that only differ on one variable, and that
// cover the domain of the variable. In that case, it will keep only one tuple,
// and replace the value for variable by any_value, the equivalent of '*' in
// regexps.
//
// This method is exposed for testing purposes.
void CompressTuples(absl::Span<const int64_t> domain_sizes, int64_t any_value,
                    std::vector<std::vector<int64_t>>* tuples);
 
}  // namespace sat
}  // namespace operations_research
 
#endif  // OR_TOOLS_SAT_UTIL_H_