linear_constraint.cc

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// Copyright 2010-2025 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/linear_constraint.h"
 
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <string>
#include <utility>
#include <vector>
 
#include "absl/base/attributes.h"
#include "absl/container/flat_hash_set.h"
#include "absl/log/check.h"
#include "absl/strings/str_cat.h"
#include "absl/types/span.h"
#include "ortools/base/mathutil.h"
#include "ortools/base/strong_vector.h"
#include "ortools/sat/integer.h"
#include "ortools/sat/integer_base.h"
#include "ortools/sat/sat_base.h"
#include "ortools/util/saturated_arithmetic.h"
#include "ortools/util/strong_integers.h"
 
namespace operations_research {
namespace sat {
 
void LinearConstraintBuilder::AddTerm(IntegerVariable var, IntegerValue coeff) {
  if (coeff == 0) return;
  // We can either add var or NegationOf(var), and we always choose the
  // positive one.
  if (VariableIsPositive(var)) {
    terms_.push_back({var, coeff});
  } else {
    terms_.push_back({NegationOf(var), -coeff});
  }
}
 
void LinearConstraintBuilder::AddTerm(AffineExpression expr,
                                      IntegerValue coeff) {
  if (coeff == 0) return;
  // We can either add var or NegationOf(var), and we always choose the
  // positive one.
  if (expr.var != kNoIntegerVariable) {
    if (VariableIsPositive(expr.var)) {
      terms_.push_back({expr.var, coeff * expr.coeff});
    } else {
      terms_.push_back({NegationOf(expr.var), -coeff * expr.coeff});
    }
  }
  DCHECK(!ProdOverflow(coeff, expr.constant));
  offset_ += coeff * expr.constant;
}
 
void LinearConstraintBuilder::AddLinearExpression(
    const LinearExpression& expr) {
  AddLinearExpression(expr, IntegerValue(1));
}
 
void LinearConstraintBuilder::AddLinearExpression(const LinearExpression& expr,
                                                  IntegerValue coeff) {
  for (int i = 0; i < expr.vars.size(); ++i) {
    // We must use positive variables.
    if (VariableIsPositive(expr.vars[i])) {
      terms_.push_back({expr.vars[i], expr.coeffs[i] * coeff});
    } else {
      terms_.push_back({NegationOf(expr.vars[i]), -expr.coeffs[i] * coeff});
    }
  }
  offset_ += expr.offset * coeff;
}
 
ABSL_MUST_USE_RESULT bool LinearConstraintBuilder::AddDecomposedProduct(
    absl::Span<const LiteralValueValue> product) {
  if (product.empty()) return true;
 
  IntegerValue product_min = kMaxIntegerValue;
  // TODO(user): Checks the value of literals.
  for (const LiteralValueValue& term : product) {
    product_min = std::min(product_min, term.left_value * term.right_value);
  }
 
  for (const LiteralValueValue& term : product) {
    IntegerValue coeff = term.left_value * term.right_value - product_min;
    if (coeff == 0) continue;
    if (!AddLiteralTerm(term.literal, coeff)) {
      return false;
    }
  }
  AddConstant(product_min);
  return true;
}
 
void LinearConstraintBuilder::AddQuadraticLowerBound(
    AffineExpression left, AffineExpression right, IntegerTrail* integer_trail,
    bool* is_quadratic) {
  if (integer_trail->IsFixed(left)) {
    AddTerm(right, integer_trail->FixedValue(left));
  } else if (integer_trail->IsFixed(right)) {
    AddTerm(left, integer_trail->FixedValue(right));
  } else {
    const IntegerValue left_min = integer_trail->LowerBound(left);
    const IntegerValue right_min = integer_trail->LowerBound(right);
    AddTerm(left, right_min);
    AddTerm(right, left_min);
    // Substract the energy counted twice.
    AddConstant(-left_min * right_min);
    if (is_quadratic != nullptr) *is_quadratic = true;
  }
}
 
void LinearConstraintBuilder::AddConstant(IntegerValue value) {
  offset_ += value;
}
 
ABSL_MUST_USE_RESULT bool LinearConstraintBuilder::AddLiteralTerm(
    Literal lit, IntegerValue coeff) {
  DCHECK(encoder_ != nullptr);
  IntegerVariable var = kNoIntegerVariable;
  bool view_is_direct = true;
  if (!encoder_->LiteralOrNegationHasView(lit, &var, &view_is_direct)) {
    return false;
  }
 
  if (view_is_direct) {
    AddTerm(var, coeff);
  } else {
    AddTerm(var, -coeff);
    offset_ += coeff;
  }
  return true;
}
 
LinearConstraint LinearConstraintBuilder::Build() {
  return BuildConstraint(lb_, ub_);
}
 
LinearConstraint LinearConstraintBuilder::BuildConstraint(IntegerValue lb,
                                                          IntegerValue ub) {
  LinearConstraint result;
  result.lb = lb > kMinIntegerValue ? lb - offset_ : lb;
  result.ub = ub < kMaxIntegerValue ? ub - offset_ : ub;
  CleanTermsAndFillConstraint(&terms_, &result);
  return result;
}
 
bool LinearConstraintBuilder::BuildIntoConstraintAndCheckOverflow(
    IntegerValue lb, IntegerValue ub, LinearConstraint* ct) {
  ct->lb = lb > kMinIntegerValue ? lb - offset_ : lb;
  ct->ub = ub < kMaxIntegerValue ? ub - offset_ : ub;
  return MergePositiveVariableTermsAndCheckForOverflow(&terms_, ct);
}
 
LinearExpression LinearConstraintBuilder::BuildExpression() {
  LinearExpression result;
  CleanTermsAndFillConstraint(&terms_, &result);
  result.offset = offset_;
  return result;
}
 
double LinearConstraint::NormalizedViolation(
    const util_intops::StrongVector<IntegerVariable, double>& lp_values) const {
  const double activity = ComputeActivity(*this, lp_values);
  const double violation =
      std::max(activity - ToDouble(ub), ToDouble(lb) - activity);
  if (violation <= 0.0) return 0.0;
 
  const double l2_norm = ComputeL2Norm(*this);
  return violation / l2_norm;
}
 
double ComputeActivity(
    const LinearConstraint& constraint,
    const util_intops::StrongVector<IntegerVariable, double>& values) {
  int i = 0;
  const int size = constraint.num_terms;
  const int shifted_size = size - 3;
  double a0 = 0.0;
  double a1 = 0.0;
  double a2 = 0.0;
  double a3 = 0.0;
  const double* view = values.data();
  for (; i < shifted_size; i += 4) {
    a0 += static_cast<double>(constraint.coeffs[i].value()) *
          view[constraint.vars[i].value()];
    a1 += static_cast<double>(constraint.coeffs[i + 1].value()) *
          view[constraint.vars[i + 1].value()];
    a2 += static_cast<double>(constraint.coeffs[i + 2].value()) *
          view[constraint.vars[i + 2].value()];
    a3 += static_cast<double>(constraint.coeffs[i + 3].value()) *
          view[constraint.vars[i + 3].value()];
  }
  double activity = a0 + a1 + a2 + a3;
  if (i < size) {
    activity += static_cast<double>(constraint.coeffs[i].value()) *
                view[constraint.vars[i].value()];
    if (i + 1 < size) {
      activity += static_cast<double>(constraint.coeffs[i + 1].value()) *
                  view[constraint.vars[i + 1].value()];
      if (i + 2 < size) {
        activity += static_cast<double>(constraint.coeffs[i + 2].value()) *
                    view[constraint.vars[i + 2].value()];
      }
    }
  }
  return activity;
}
 
double ComputeL2Norm(const LinearConstraint& ct) {
  double sum = 0.0;
  for (int i = 0; i < ct.num_terms; ++i) {
    sum += ToDouble(ct.coeffs[i]) * ToDouble(ct.coeffs[i]);
  }
  return std::sqrt(sum);
}
 
IntegerValue ComputeInfinityNorm(const LinearConstraint& ct) {
  IntegerValue result(0);
  for (int i = 0; i < ct.num_terms; ++i) {
    result = std::max(result, IntTypeAbs(ct.coeffs[i]));
  }
  return result;
}
 
double ScalarProduct(const LinearConstraint& ct1, const LinearConstraint& ct2) {
  if (ct1.num_terms == 0 || ct2.num_terms == 0) return 0.0;
  DCHECK(std::is_sorted(ct1.vars.get(), ct1.vars.get() + ct1.num_terms));
  DCHECK(std::is_sorted(ct2.vars.get(), ct2.vars.get() + ct2.num_terms));
  double scalar_product = 0.0;
  int index_1 = 0;
  int index_2 = 0;
  IntegerVariable var1 = ct1.vars[index_1];
  IntegerVariable var2 = ct2.vars[index_2];
  while (true) {
    if (var1 == var2) {
      scalar_product += static_cast<double>(ct1.coeffs[index_1].value()) *
                        static_cast<double>(ct2.coeffs[index_2].value());
      if (++index_1 == ct1.num_terms) break;
      if (++index_2 == ct2.num_terms) break;
      var1 = ct1.vars[index_1];
      var2 = ct2.vars[index_2];
    } else if (var1 > var2) {
      if (++index_2 == ct2.num_terms) break;
      var2 = ct2.vars[index_2];
    } else {
      if (++index_1 == ct1.num_terms) break;
      var1 = ct1.vars[index_1];
    }
  }
  return scalar_product;
}
 
namespace {
 
// TODO(user): Template for any integer type and expose this?
IntegerValue ComputeGcd(absl::Span<const IntegerValue> values) {
  if (values.empty()) return IntegerValue(1);
  int64_t gcd = 0;
  for (const IntegerValue value : values) {
    gcd = MathUtil::GCD64(gcd, std::abs(value.value()));
    if (gcd == 1) break;
  }
  if (gcd < 0) return IntegerValue(1);  // Can happen with kint64min.
  return IntegerValue(gcd);
}
 
}  // namespace
 
void DivideByGCD(LinearConstraint* constraint) {
  if (constraint->num_terms == 0) return;
  const IntegerValue gcd = ComputeGcd(
      {constraint->coeffs.get(), static_cast<size_t>(constraint->num_terms)});
  if (gcd == 1) return;
 
  if (constraint->lb > kMinIntegerValue) {
    constraint->lb = CeilRatio(constraint->lb, gcd);
  }
  if (constraint->ub < kMaxIntegerValue) {
    constraint->ub = FloorRatio(constraint->ub, gcd);
  }
  for (int i = 0; i < constraint->num_terms; ++i) {
    constraint->coeffs[i] /= gcd;
  }
}
 
void RemoveZeroTerms(LinearConstraint* constraint) {
  int new_size = 0;
  const int size = constraint->num_terms;
  for (int i = 0; i < size; ++i) {
    if (constraint->coeffs[i] == 0) continue;
    constraint->vars[new_size] = constraint->vars[i];
    constraint->coeffs[new_size] = constraint->coeffs[i];
    ++new_size;
  }
  constraint->resize(new_size);
}
 
void MakeAllCoefficientsPositive(LinearConstraint* constraint) {
  const int size = constraint->num_terms;
  for (int i = 0; i < size; ++i) {
    const IntegerValue coeff = constraint->coeffs[i];
    if (coeff < 0) {
      constraint->coeffs[i] = -coeff;
      constraint->vars[i] = NegationOf(constraint->vars[i]);
    }
  }
}
 
void MakeAllVariablesPositive(LinearConstraint* constraint) {
  const int size = constraint->num_terms;
  for (int i = 0; i < size; ++i) {
    const IntegerVariable var = constraint->vars[i];
    if (!VariableIsPositive(var)) {
      constraint->coeffs[i] = -constraint->coeffs[i];
      constraint->vars[i] = NegationOf(var);
    }
  }
}
 
double LinearExpression::LpValue(
    const util_intops::StrongVector<IntegerVariable, double>& lp_values) const {
  double result = ToDouble(offset);
  for (int i = 0; i < vars.size(); ++i) {
    result += ToDouble(coeffs[i]) * lp_values[vars[i]];
  }
  return result;
}
 
IntegerValue LinearExpression::LevelZeroMin(IntegerTrail* integer_trail) const {
  IntegerValue result = offset;
  for (int i = 0; i < vars.size(); ++i) {
    DCHECK_GE(coeffs[i], 0);
    result += coeffs[i] * integer_trail->LevelZeroLowerBound(vars[i]);
  }
  return result;
}
 
IntegerValue LinearExpression::Min(const IntegerTrail& integer_trail) const {
  IntegerValue result = offset;
  for (int i = 0; i < vars.size(); ++i) {
    if (coeffs[i] > 0) {
      result += coeffs[i] * integer_trail.LowerBound(vars[i]);
    } else {
      result += coeffs[i] * integer_trail.UpperBound(vars[i]);
    }
  }
  return result;
}
 
IntegerValue LinearExpression::Max(const IntegerTrail& integer_trail) const {
  IntegerValue result = offset;
  for (int i = 0; i < vars.size(); ++i) {
    if (coeffs[i] > 0) {
      result += coeffs[i] * integer_trail.UpperBound(vars[i]);
    } else {
      result += coeffs[i] * integer_trail.LowerBound(vars[i]);
    }
  }
  return result;
}
 
std::string LinearExpression::DebugString() const {
  if (vars.empty()) return absl::StrCat(offset.value());
  std::string result;
  for (int i = 0; i < vars.size(); ++i) {
    absl::StrAppend(&result, i > 0 ? " " : "",
                    IntegerTermDebugString(vars[i], coeffs[i]));
  }
  if (offset != 0) {
    absl::StrAppend(&result, " + ", offset.value());
  }
  return result;
}
 
bool NoDuplicateVariable(const LinearConstraint& ct) {
  absl::flat_hash_set<IntegerVariable> seen_variables;
  const int size = ct.num_terms;
  for (int i = 0; i < size; ++i) {
    if (VariableIsPositive(ct.vars[i])) {
      if (!seen_variables.insert(ct.vars[i]).second) return false;
    } else {
      if (!seen_variables.insert(NegationOf(ct.vars[i])).second) return false;
    }
  }
  return true;
}
 
LinearExpression CanonicalizeExpr(const LinearExpression& expr) {
  LinearExpression canonical_expr;
  canonical_expr.offset = expr.offset;
  for (int i = 0; i < expr.vars.size(); ++i) {
    if (expr.coeffs[i] < 0) {
      canonical_expr.vars.push_back(NegationOf(expr.vars[i]));
      canonical_expr.coeffs.push_back(-expr.coeffs[i]);
    } else {
      canonical_expr.vars.push_back(expr.vars[i]);
      canonical_expr.coeffs.push_back(expr.coeffs[i]);
    }
  }
  return canonical_expr;
}
 
// TODO(user): Avoid duplication with PossibleIntegerOverflow() in the checker?
// At least make sure the code is the same.
bool ValidateLinearConstraintForOverflow(const LinearConstraint& constraint,
                                         const IntegerTrail& integer_trail) {
  int64_t positive_sum(0);
  int64_t negative_sum(0);
  for (int i = 0; i < constraint.num_terms; ++i) {
    const IntegerVariable var = constraint.vars[i];
    const IntegerValue coeff = constraint.coeffs[i];
    const IntegerValue lb = integer_trail.LevelZeroLowerBound(var);
    const IntegerValue ub = integer_trail.LevelZeroUpperBound(var);
 
    int64_t min_prod = CapProd(coeff.value(), lb.value());
    int64_t max_prod = CapProd(coeff.value(), ub.value());
    if (min_prod > max_prod) std::swap(min_prod, max_prod);
 
    positive_sum = CapAdd(positive_sum, std::max(int64_t{0}, max_prod));
    negative_sum = CapAdd(negative_sum, std::min(int64_t{0}, min_prod));
  }
 
  const int64_t limit = std::numeric_limits<int64_t>::max();
  if (positive_sum >= limit) return false;
  if (negative_sum <= -limit) return false;
  if (CapSub(positive_sum, negative_sum) >= limit) return false;
 
  return true;
}
 
LinearExpression NegationOf(const LinearExpression& expr) {
  LinearExpression result;
  result.vars = NegationOf(expr.vars);
  result.coeffs = expr.coeffs;
  result.offset = -expr.offset;
  return result;
}
 
LinearExpression PositiveVarExpr(const LinearExpression& expr) {
  LinearExpression result;
  result.offset = expr.offset;
  for (int i = 0; i < expr.vars.size(); ++i) {
    if (VariableIsPositive(expr.vars[i])) {
      result.vars.push_back(expr.vars[i]);
      result.coeffs.push_back(expr.coeffs[i]);
    } else {
      result.vars.push_back(NegationOf(expr.vars[i]));
      result.coeffs.push_back(-expr.coeffs[i]);
    }
  }
  return result;
}
 
IntegerValue GetCoefficient(const IntegerVariable var,
                            const LinearExpression& expr) {
  for (int i = 0; i < expr.vars.size(); ++i) {
    if (expr.vars[i] == var) {
      return expr.coeffs[i];
    } else if (expr.vars[i] == NegationOf(var)) {
      return -expr.coeffs[i];
    }
  }
  return IntegerValue(0);
}
 
IntegerValue GetCoefficientOfPositiveVar(const IntegerVariable var,
                                         const LinearExpression& expr) {
  CHECK(VariableIsPositive(var));
  for (int i = 0; i < expr.vars.size(); ++i) {
    if (expr.vars[i] == var) {
      return expr.coeffs[i];
    }
  }
  return IntegerValue(0);
}
 
bool PossibleOverflow(const IntegerTrail& integer_trail,
                      const LinearConstraint& constraint) {
  IntegerValue min_activity(0);
  IntegerValue max_activity(0);
  const int size = constraint.num_terms;
  for (int i = 0; i < size; ++i) {
    const IntegerVariable var = constraint.vars[i];
    const IntegerValue coeff = constraint.coeffs[i];
    CHECK_NE(coeff, 0);
    const IntegerValue lb = integer_trail.LevelZeroLowerBound(var);
    const IntegerValue ub = integer_trail.LevelZeroUpperBound(var);
    if (coeff > 0) {
      if (!AddProductTo(lb, coeff, &min_activity)) return true;
      if (!AddProductTo(ub, coeff, &max_activity)) return true;
    } else {
      if (!AddProductTo(ub, coeff, &min_activity)) return true;
      if (!AddProductTo(lb, coeff, &max_activity)) return true;
    }
  }
  return AtMinOrMaxInt64(CapSub(max_activity.value(), min_activity.value()));
}
 
}  // namespace sat
}  // namespace operations_research