Added new unit for polynomial root finding algorithm

AdventOfCode.lpi

@@ -145,6 +145,10 @@
         <Filename Value="UPolynomial.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
+      <Unit>
+        <Filename Value="UPolynomialRoots.pas"/>
+        <IsPartOfProject Value="True"/>
+      </Unit>
     </Units>
   </ProjectOptions>
   <CompilerOptions>

UPolynomialRoots.pas

@@ -0,0 +1,72 @@
+{
+  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.
+

tests/AdventOfCodeFPCUnit.lpi

@@ -144,6 +144,10 @@
         <Filename Value="UPolynomialTestCases.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
+      <Unit>
+        <Filename Value="UPolynomialRootsTestCases.pas"/>
+        <IsPartOfProject Value="True"/>
+      </Unit>
     </Units>
   </ProjectOptions>
   <CompilerOptions>

tests/AdventOfCodeFPCUnit.lpr

@@ -9,7 +9,7 @@ uses
   UHotSpringsTestCases, UPointOfIncidenceTestCases, UParabolicReflectorDishTestCases, ULensLibraryTestCases,
   UFloorWillBeLavaTestCases, UClumsyCrucibleTestCases, ULavaductLagoonTestCases, UAplentyTestCases,
   UPulsePropagationTestCases, UStepCounterTestCases, USandSlabsTestCases, ULongWalkTestCases,
-  UNeverTellMeTheOddsTestCases, UPolynomialTestCases;
+  UNeverTellMeTheOddsTestCases, UPolynomialTestCases, UPolynomialRootsTestCases;
 
 {$R *.res}
 

tests/UPolynomialRootsTestCases.pas

@@ -0,0 +1,72 @@
+{
+  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 UPolynomialRootsTestCases;
+
+{$mode ObjFPC}{$H+}
+
+interface
+
+uses
+  Classes, SysUtils, fpcunit, testregistry, UPolynomial, UPolynomialRoots, UBigInt;
+
+type
+
+  { TPolynomialRootsTestCase }
+
+  TPolynomialRootsTestCase = class(TTestCase)
+  protected
+    FRootIsolation: TRootIsolation;
+    procedure SetUp; override;
+    procedure TearDown; override;
+  published
+    procedure TestBisectionRootIsolation;
+  end;
+
+implementation
+
+{ TPolynomialRootsTestCase }
+
+procedure TPolynomialRootsTestCase.SetUp;
+begin
+  inherited SetUp;
+  FRootIsolation := TRootIsolation.Create;
+end;
+
+procedure TPolynomialRootsTestCase.TearDown;
+begin
+  FRootIsolation.Free;
+  inherited TearDown;
+end;
+
+procedure TPolynomialRootsTestCase.TestBisectionRootIsolation;
+var
+  a: TBigIntPolynomial;
+  r: Int64;
+begin
+  // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
+  //   = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
+  a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
+  r := FRootIsolation.Bisect(a);
+  AssertEquals(0, r);
+end;
+
+initialization
+
+  RegisterTest(TPolynomialRootsTestCase);
+end.
+

tests/UPolynomialTestCases.pas

@@ -40,7 +40,6 @@ type
     procedure TestUnequalSameLength;
     procedure TestUnequalDifferentLength;
     procedure TestTrimLeadingZeros;
-    procedure TestBisectionRootIsolation;
   end;
 
 implementation
@@ -111,16 +110,6 @@ begin
   AssertTrue('Polynomials are not equal.', a = b);
 end;
 
-procedure TBigIntPolynomialTestCase.TestBisectionRootIsolation;
-var
-  a: TBigIntPolynomial;
-begin
-  // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
-  //   = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
-  a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
-  Fail('Not implemented');
-end;
-
 initialization
 
   RegisterTest(TBigIntPolynomialTestCase);