{
  Solutions to the Advent Of Code.
  Copyright (C) 2024  Stefan Müller

  This program is free software: you can redistribute it and/or modify it under
  the terms of the GNU General Public License as published by the Free Software
  Foundation, either version 3 of the License, or (at your option) any later
  version.

  This program is distributed in the hope that it will be useful, but WITHOUT
  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.

  You should have received a copy of the GNU General Public License along with
  this program.  If not, see <http://www.gnu.org/licenses/>.
}

unit UPolynomialRoots;

{$mode ObjFPC}{$H+}

interface

uses
  Classes, SysUtils, UPolynomial, UBigInt;

type

  { TRootIsolation }

  TRootIsolation = class
  private
    function CalcSimpleRootBound(constref APolynomial: TBigIntPolynomial): TBigInt;
  public
    function Bisect(constref APolynomial: TBigIntPolynomial): Int64;
  end;

implementation

{ TRootIsolation }

function TRootIsolation.CalcSimpleRootBound(constref APolynomial: TBigIntPolynomial): TBigInt;
var
  i, sign: Integer;
  a: TBigInt;
begin
  // We need a_n > 0 here, so we use -sign(a_n) instead of actually flipping the polynomial.
  // Sign is not 0 because a_n is not 0.
  sign := -APolynomial.Coefficient[APolynomial.Degree].Sign;

  // This is a simplification of Cauchy's bound to avoid division.
  // https://en.wikipedia.org/wiki/Geometrical_properties_of_polynomial_roots#Bounds_of_positive_real_roots
  Result := TBigInt.Zero;
  for i := 0 to APolynomial.Degree - 1 do begin
    a := sign * APolynomial.Coefficient[i];
    if Result < a then
      Result := a;
  end;
  Result := Result + 1;
end;

function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial): Int64;
var
  bound: TBigInt;
  p: TBigIntPolynomial;
begin
  bound := CalcSimpleRootBound(APolynomial);
  p := APolynomial.ScaleVariable(bound);
end;

end.