ortools-clone/ortools/sat/python/linear_expr.h

// 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.

#ifndef OR_TOOLS_SAT_PYTHON_LINEAR_EXPR_H_
#define OR_TOOLS_SAT_PYTHON_LINEAR_EXPR_H_

#include <cstdint>
#include <memory>
#include <string>
#include <utility>
#include <vector>

#include "absl/container/btree_map.h"
#include "absl/container/fixed_array.h"
#include "absl/log/check.h"
#include "absl/strings/str_cat.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research::sat::python {

class BoundedLinearExpression;
class FlatFloatExpr;
class FloatExprVisitor;
class LinearExpr;
class IntExprVisitor;
class LinearExpr;
class BaseIntVar;
class NotBooleanVariable;

/**
 * A class to hold an integer or floating point linear expression.
 *
 * A linear expression is built from (integer or floating point) constants and
 * variables. For example, `x + 2 * (y - z + 1)`.
 *
 * Linear expressions are used in CP-SAT models in constraints and in the
 * objective.
 *
 * Note that constraints only accept linear expressions with integral
 * coefficients and constants. On the other hand, The objective can be a linear
 * expression with floating point coefficients and constants.
 *
 * You can define linear constraints as in:
 *
 * ```
 * model.add(x + 2 * y <= 5)
 * model.add(sum(array_of_vars) == 5)
 * ```
 *
 * - In CP-SAT, the objective is a linear expression:
 *
 * ```
 * model.minimize(x + 2 * y + z)
 * ```
 *
 * - For large arrays, using the LinearExpr class is faster that using the
 * python `sum()` function. You can create constraints and the objective from
 * lists of linear expressions or coefficients as follows:
 *
 * ```
 * model.minimize(cp_model.LinearExpr.sum(expressions))
 * model.add(cp_model.LinearExpr.weighted_sum(expressions, coefficients) >= 0)
 * ```
 */
class LinearExpr : public std::enable_shared_from_this<LinearExpr> {
 public:
  virtual ~LinearExpr() = default;
  virtual void VisitAsFloat(FloatExprVisitor& /*lin*/, double /*c*/) = 0;
  virtual bool VisitAsInt(IntExprVisitor& /*lin*/, int64_t /*c*/) = 0;
  bool IsInteger();
  virtual std::string ToString() const = 0;
  virtual std::string DebugString() const = 0;

  /// Returns expr * coeff.
  static std::shared_ptr<LinearExpr> TermInt(std::shared_ptr<LinearExpr> expr,
                                             int64_t coeff);
  /// Returns expr * coeff.
  static std::shared_ptr<LinearExpr> TermFloat(std::shared_ptr<LinearExpr> expr,
                                               double coeff);
  /// Returns expr * coeff + offset.
  static std::shared_ptr<LinearExpr> AffineInt(std::shared_ptr<LinearExpr> expr,
                                               int64_t coeff, int64_t offset);
  /// Returns expr * coeff + offset.
  static std::shared_ptr<LinearExpr> AffineFloat(
      std::shared_ptr<LinearExpr> expr, double coeff, double offset);
  /// Returns a new LinearExpr that holds the given constant.
  static std::shared_ptr<LinearExpr> ConstantInt(int64_t value);
  /// Returns a new LinearExpr that holds the given constant.
  static std::shared_ptr<LinearExpr> ConstantFloat(double value);

  /// Returns (this) + (expr).
  std::shared_ptr<LinearExpr> Add(std::shared_ptr<LinearExpr> expr);
  /// Returns (this) + (cst).
  std::shared_ptr<LinearExpr> AddInt(int64_t cst);
  /// Returns (this) + (cst).
  std::shared_ptr<LinearExpr> AddFloat(double cst);
  /// Returns (this) - (expr).
  std::shared_ptr<LinearExpr> Sub(std::shared_ptr<LinearExpr> expr);
  /// Returns (this) - (cst).
  std::shared_ptr<LinearExpr> SubInt(int64_t cst);
  /// Returns (this) - (cst).
  std::shared_ptr<LinearExpr> SubFloat(double cst);
  /// Returns (cst) - (this).
  std::shared_ptr<LinearExpr> RSubInt(int64_t cst);
  /// Returns (cst) - (this).
  std::shared_ptr<LinearExpr> RSubFloat(double cst);
  /// Returns (this) * (cst).
  std::shared_ptr<LinearExpr> MulInt(int64_t cst);
  /// Returns (this) * (cst).
  std::shared_ptr<LinearExpr> MulFloat(double cst);
  /// Returns -(this).
  std::shared_ptr<LinearExpr> Neg();

  /// Returns (this) == (rhs).
  std::shared_ptr<BoundedLinearExpression> Eq(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) == (rhs).
  std::shared_ptr<BoundedLinearExpression> EqCst(int64_t rhs);
  /// Returns (this) != (rhs).
  std::shared_ptr<BoundedLinearExpression> Ne(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) != (rhs).
  std::shared_ptr<BoundedLinearExpression> NeCst(int64_t rhs);
  /// Returns (this) >= (rhs).
  std::shared_ptr<BoundedLinearExpression> Ge(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) >= (rhs).
  std::shared_ptr<BoundedLinearExpression> GeCst(int64_t rhs);
  /// Returns (this) <= (rhs).
  std::shared_ptr<BoundedLinearExpression> Le(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) <= (rhs).
  std::shared_ptr<BoundedLinearExpression> LeCst(int64_t rhs);
  /// Returns (this) < (rhs).
  std::shared_ptr<BoundedLinearExpression> Lt(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) < (rhs).
  std::shared_ptr<BoundedLinearExpression> LtCst(int64_t rhs);
  /// Returns (this) > (rhs).
  std::shared_ptr<BoundedLinearExpression> Gt(std::shared_ptr<LinearExpr> rhs);
  /// Returns (this) > (rhs).
  std::shared_ptr<BoundedLinearExpression> GtCst(int64_t rhs);
};

/// Compare the indices of variables.
struct BaseIntVarComparator {
  bool operator()(std::shared_ptr<BaseIntVar> lhs,
                  std::shared_ptr<BaseIntVar> rhs) const;
};

/// A visitor class to process a floating point linear expression.
class FloatExprVisitor {
 public:
  void AddToProcess(std::shared_ptr<LinearExpr> expr, double coeff);
  void AddConstant(double constant);
  void AddVarCoeff(std::shared_ptr<BaseIntVar> var, double coeff);
  double Process(std::shared_ptr<LinearExpr> expr,
                 std::vector<std::shared_ptr<BaseIntVar>>* vars,
                 std::vector<double>* coeffs);

 private:
  std::vector<std::pair<std::shared_ptr<LinearExpr>, double>> to_process_;
  absl::btree_map<std::shared_ptr<BaseIntVar>, double, BaseIntVarComparator>
      canonical_terms_;
  double offset_ = 0;
};

/**
 * A flattened and optimized floating point linear expression.
 *
 * It flattens the linear expression passed to the constructor to a sum of
 * products of variables and coefficients plus an offset. It can be used to
 * cache complex expressions as parsing them is only done once.
 */
class FlatFloatExpr : public LinearExpr {
 public:
  /// Builds a flattened floating point linear expression from the given
  /// expression.
  explicit FlatFloatExpr(std::shared_ptr<LinearExpr> expr);
  /// Returns the array of variables of the flattened expression.
  const std::vector<std::shared_ptr<BaseIntVar>>& vars() const { return vars_; }
  /// Returns the array of coefficients of the flattened expression.
  const std::vector<double>& coeffs() const { return coeffs_; }
  /// Returns the offset of the flattened expression.
  double offset() const { return offset_; }

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  std::string ToString() const override;
  std::string DebugString() const override;
  bool VisitAsInt(IntExprVisitor& /*lin*/, int64_t /*c*/) override {
    return false;
  }

 private:
  std::vector<std::shared_ptr<BaseIntVar>> vars_;
  std::vector<double> coeffs_;
  double offset_ = 0;
};

/// A visitor class to process an integer linear expression.
class IntExprVisitor {
 public:
  void AddToProcess(std::shared_ptr<LinearExpr> expr, int64_t coeff);
  void AddConstant(int64_t constant);
  void AddVarCoeff(std::shared_ptr<BaseIntVar> var, int64_t coeff);
  bool ProcessAll();
  bool Process(std::vector<std::shared_ptr<BaseIntVar>>* vars,
               std::vector<int64_t>* coeffs, int64_t* offset);
  bool Evaluate(std::shared_ptr<LinearExpr> expr,
                const CpSolverResponse& solution, int64_t* value);

 private:
  std::vector<std::pair<std::shared_ptr<LinearExpr>, int64_t>> to_process_;
  absl::btree_map<std::shared_ptr<BaseIntVar>, int64_t, BaseIntVarComparator>
      canonical_terms_;
  int64_t offset_ = 0;
};

/**
 * A flattened and optimized integer linear expression.
 *
 * It flattens the linear expression passed to the constructor to a sum of
 * products of variables and coefficients plus an offset. It can be used to
 * cache complex expressions as parsing them is only done once.
 */
class FlatIntExpr : public LinearExpr {
 public:
  /// Builds a flattened integer linear expression from the given
  /// expression.
  explicit FlatIntExpr(std::shared_ptr<LinearExpr> expr);
  /// Returns the array of variables of the flattened expression.
  const std::vector<std::shared_ptr<BaseIntVar>>& vars() const { return vars_; }
  /// Returns the array of coefficients of the flattened expression.
  const std::vector<int64_t>& coeffs() const { return coeffs_; }
  /// Returns the offset of the flattened expression.
  int64_t offset() const { return offset_; }
  /// Returns true if the expression is integer.
  bool ok() const { return ok_; }

  void VisitAsFloat(FloatExprVisitor& lin, double c) override {
    for (int i = 0; i < vars_.size(); ++i) {
      lin.AddVarCoeff(vars_[i], coeffs_[i] * c);
    }
    lin.AddConstant(offset_ * c);
  }

  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override {
    for (int i = 0; i < vars_.size(); ++i) {
      lin.AddVarCoeff(vars_[i], coeffs_[i] * c);
    }
    lin.AddConstant(offset_ * c);
    return true;
  }

  std::string ToString() const override;
  std::string DebugString() const override;

 private:
  std::vector<std::shared_ptr<BaseIntVar>> vars_;
  std::vector<int64_t> coeffs_;
  int64_t offset_ = 0;
  bool ok_ = true;
};

/**
 * A class to hold a sum of linear expressions, and optional integer and
 * double offsets.
 */
class SumArray : public LinearExpr {
 public:
  explicit SumArray(std::vector<std::shared_ptr<LinearExpr>> exprs,
                    int64_t int_offset = 0, double double_offset = 0.0);
  ~SumArray() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override;
  std::string ToString() const override;
  std::string DebugString() const override;

  void AddInPlace(std::shared_ptr<LinearExpr> expr);
  void AddIntInPlace(int64_t cst) { int_offset_ += cst; }
  void AddFloatInPlace(double cst) { double_offset_ += cst; }
  int num_exprs() const { return exprs_.size(); }
  int64_t int_offset() const { return int_offset_; }
  double double_offset() const { return double_offset_; }

 private:
  std::vector<std::shared_ptr<LinearExpr>> exprs_;
  int64_t int_offset_;
  double double_offset_;
};

/// A class to hold a weighted sum of floating point linear expressions.
class FloatWeightedSum : public LinearExpr {
 public:
  FloatWeightedSum(const std::vector<std::shared_ptr<LinearExpr>>& exprs,
                   const std::vector<double>& coeffs, double offset);
  ~FloatWeightedSum() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  std::string ToString() const override;
  std::string DebugString() const override;

  bool VisitAsInt(IntExprVisitor& /*lin*/, int64_t /*c*/) override {
    return false;
  }

 private:
  const absl::FixedArray<std::shared_ptr<LinearExpr>, 2> exprs_;
  const absl::FixedArray<double, 2> coeffs_;
  double offset_;
};

/// A class to hold a weighted sum of integer linear expressions.
class IntWeightedSum : public LinearExpr {
 public:
  IntWeightedSum(const std::vector<std::shared_ptr<LinearExpr>>& exprs,
                 const std::vector<int64_t>& coeffs, int64_t offset);
  ~IntWeightedSum() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override;

  std::string ToString() const override;
  std::string DebugString() const override;

 private:
  const absl::FixedArray<std::shared_ptr<LinearExpr>, 2> exprs_;
  const absl::FixedArray<int64_t, 2> coeffs_;
  int64_t offset_;
};

/// A class to hold linear_expr * a = b (a and b are floating point numbers).
class FloatAffine : public LinearExpr {
 public:
  FloatAffine(std::shared_ptr<LinearExpr> expr, double coeff, double offset);
  ~FloatAffine() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  bool VisitAsInt(IntExprVisitor& /*lin*/, int64_t /*c*/) override {
    return false;
  }
  std::string ToString() const override;
  std::string DebugString() const override;

  std::shared_ptr<LinearExpr> expression() const { return expr_; }
  double coefficient() const { return coeff_; }
  double offset() const { return offset_; }

 private:
  std::shared_ptr<LinearExpr> expr_;
  double coeff_;
  double offset_;
};

/// A class to hold linear_expr * a = b (a and b are integers).
class IntAffine : public LinearExpr {
 public:
  IntAffine(std::shared_ptr<LinearExpr> expr, int64_t coeff, int64_t offset);
  ~IntAffine() override = default;

  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override;
  void VisitAsFloat(FloatExprVisitor& lin, double c) override;

  std::string ToString() const override;
  std::string DebugString() const override;

  /// Returns the linear expression.
  std::shared_ptr<LinearExpr> expression() const { return expr_; }
  /// Returns the coefficient.
  int64_t coefficient() const { return coeff_; }
  /// Returns the offset.
  int64_t offset() const { return offset_; }

  std::shared_ptr<LinearExpr> AddInt(int64_t cst);
  std::shared_ptr<LinearExpr> SubInt(int64_t cst);
  std::shared_ptr<LinearExpr> RSubInt(int64_t cst);
  std::shared_ptr<LinearExpr> MulInt(int64_t cst);
  std::shared_ptr<LinearExpr> Neg();

 private:
  std::shared_ptr<LinearExpr> expr_;
  int64_t coeff_;
  int64_t offset_;
};

/// A class to hold a floating point constant as a linear expression.
class FloatConstant : public LinearExpr {
 public:
  explicit FloatConstant(double value) : value_(value) {}
  ~FloatConstant() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;
  bool VisitAsInt(IntExprVisitor& /*lin*/, int64_t /*c*/) override {
    return false;
  }
  std::string ToString() const override;
  std::string DebugString() const override;

 private:
  double value_;
};

/// A class to hold an integer constant as a linear expression.
class IntConstant : public LinearExpr {
 public:
  explicit IntConstant(int64_t value) : value_(value) {}
  ~IntConstant() override = default;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override {
    lin.AddConstant(value_ * c);
  }

  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override {
    lin.AddConstant(value_ * c);
    return true;
  }

  std::string ToString() const override { return absl::StrCat(value_); }

  std::string DebugString() const override {
    return absl::StrCat("IntConstant(", value_, ")");
  }

 private:
  int64_t value_;
};

/**
 * A class to hold a Boolean literal.
 *
 * A literal is a Boolean variable or its negation.
 *
 * Literals are used in CP-SAT models in constraints and in the objective.
 *
 * - You can define literal as in:
 *
 * ```
 * b1 = model.new_bool_var()
 * b2 = model.new_bool_var()
 * # Simple Boolean constraint.
 * model.add_bool_or(b1, b2.negated())
 * # We can use the ~ operator to negate a literal.
 * model.add_bool_or(b1, ~b2)
 * # Enforcement literals must be literals.
 * x = model.new_int_var(0, 10, 'x')
 * model.add(x == 5).only_enforced_if(~b1)
 * ```y
 *
 * - Literals can be used directly in linear constraints or in the objective:
 *
 * ```
 *     model.minimize(b1  + 2 * ~b2)
 * ```
 */
class Literal : public LinearExpr {
 public:
  ~Literal() override = default;
  /// Returns the index of the current literal.
  virtual int index() const = 0;

  /**
   * Returns the negation of a literal (a Boolean variable or its negation).
   *
   * This method implements the logical negation of a Boolean variable.
   * It is only valid if the variable has a Boolean domain (0 or 1).
   *
   * Note that this method is nilpotent: `x.negated().negated() == x`.
   *
   * Returns:
   *   The negation of the current literal.
   */
  virtual std::shared_ptr<Literal> negated() = 0;
};

/**
 * A class to hold a variable index. It is the base class for Integer
 * variables.
 */
class BaseIntVar : public Literal {
 public:
  explicit BaseIntVar(int index) : index_(index), is_boolean_(false) {
    DCHECK_GE(index, 0);
  }
  BaseIntVar(int index, bool is_boolean);

  ~BaseIntVar() override = default;

  int index() const override { return index_; }

  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override {
    std::shared_ptr<BaseIntVar> var =
        std::static_pointer_cast<BaseIntVar>(shared_from_this());
    lin.AddVarCoeff(var, c);
    return true;
  }

  void VisitAsFloat(FloatExprVisitor& lin, double c) override {
    std::shared_ptr<BaseIntVar> var =
        std::static_pointer_cast<BaseIntVar>(shared_from_this());
    lin.AddVarCoeff(var, c);
  }

  std::string ToString() const override {
    if (negated_ != nullptr) {
      return absl::StrCat("BooleanBaseIntVar(", index_, ")");
    } else {
      return absl::StrCat("BaseIntVar(", index_, ")");
    }
  }

  std::string DebugString() const override {
    return absl::StrCat("BaseIntVar(index=", index_,
                        ", is_boolean=", negated_ != nullptr, ")");
  }

  /// Returns the negation of the current variable.
  std::shared_ptr<Literal> negated() override;

  /// Returns true if the variable has a Boolean domain (0 or 1).
  bool is_boolean() const { return is_boolean_; }

  bool operator<(const BaseIntVar& other) const {
    return index_ < other.index_;
  }

 protected:
  const int index_;
  const bool is_boolean_;
  std::shared_ptr<Literal> negated_;
};

template <typename H>
H AbslHashValue(H h, std::shared_ptr<BaseIntVar> i) {
  return H::combine(std::move(h), i->index());
}

/// A class to hold a negated variable index.
class NotBooleanVariable : public Literal {
 public:
  explicit NotBooleanVariable(std::shared_ptr<BaseIntVar> var) : var_(var) {}
  ~NotBooleanVariable() override = default;

  /// Returns the index of the current literal.
  int index() const override;

  bool ok() const { return !var_.expired(); }

  /**
   * Returns the negation of the current literal, that is the original Boolean
   * variable.
   */
  std::shared_ptr<Literal> negated() override;

  bool VisitAsInt(IntExprVisitor& lin, int64_t c) override;

  void VisitAsFloat(FloatExprVisitor& lin, double c) override;

  std::string ToString() const override;

  std::string DebugString() const override;

 private:
  // We keep a weak ptr to the base variable to avoid a circular dependency.
  // The base variable holds a shared pointer to the negated variable.
  // Any call to a risky method is checked at the pybind11 level to raise a
  // python exception before the call is made.
  std::weak_ptr<BaseIntVar> var_;
};

/// A class to hold a linear expression with bounds.
class BoundedLinearExpression {
 public:
  /// Creates a BoundedLinearExpression representing `expr in domain`.
  BoundedLinearExpression(std::shared_ptr<LinearExpr> expr,
                          const Domain& bounds);

  /// Creates a BoundedLinearExpression representing `pos - neg in domain`.
  BoundedLinearExpression(std::shared_ptr<LinearExpr> pos,
                          std::shared_ptr<LinearExpr> neg,
                          const Domain& bounds);

  ~BoundedLinearExpression() = default;

  /// Returns the bounds constraining the expression passed to the constructor.
  const Domain& bounds() const;
  /// Returns the array of variables of the flattened expression.
  const std::vector<std::shared_ptr<BaseIntVar>>& vars() const;
  /// Returns the array of coefficients of the flattened expression.
  const std::vector<int64_t>& coeffs() const;
  /// Returns the offset of the flattened expression.
  int64_t offset() const;
  /// Returns true if the bounded linear expression is valid.
  bool ok() const;
  std::string ToString() const;
  std::string DebugString() const;
  bool CastToBool(bool* result) const;

 private:
  std::vector<std::shared_ptr<BaseIntVar>> vars_;
  std::vector<int64_t> coeffs_;
  int64_t offset_;
  const Domain bounds_;
  bool ok_ = true;
};

}  // namespace operations_research::sat::python

#endif  // OR_TOOLS_SAT_PYTHON_LINEAR_EXPR_H_