Added polynomials

AdventOfCode.lpi

@@ -141,6 +141,10 @@
         <Filename Value="UBigInt.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
+      <Unit>
+        <Filename Value="UPolynomial.pas"/>
+        <IsPartOfProject Value="True"/>
+      </Unit>
     </Units>
   </ProjectOptions>
   <CompilerOptions>

UPolynomial.pas

@@ -0,0 +1,106 @@
+{
+  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 UPolynomial;
+
+{$mode ObjFPC}{$H+}
+
+interface
+
+uses
+  Classes, SysUtils, UBigInt;
+
+type
+  TInt64Array = array of Int64;
+
+  { TBigIntPolynomial }
+
+  TBigIntPolynomial = object
+  private
+    FCoefficients: array of TBigInt;
+  public
+    function CalcValueAt(const AX: Int64): TBigInt;
+    function IsEqualTo(const AOther: TBigIntPolynomial): Boolean;
+    class function Create(const ACoefficients: array of TBigInt): TBigIntPolynomial; static;
+  end;
+
+  { Operators }
+
+  operator = (const A, B: TBigIntPolynomial): Boolean;
+  operator <> (const A, B: TBigIntPolynomial): Boolean;
+
+implementation
+
+{ TBigIntPolynomial }
+
+function TBigIntPolynomial.CalcValueAt(const AX: Int64): TBigInt;
+var
+  i: Integer;
+begin
+  Result := TBigInt.Zero;
+  for i := High(FCoefficients) downto 0 do
+    Result := Result * AX + FCoefficients[i];
+end;
+
+function TBigIntPolynomial.IsEqualTo(const AOther: TBigIntPolynomial): Boolean;
+var
+  i: Integer;
+begin
+  if Length(FCoefficients) = Length(AOther.FCoefficients) then
+  begin
+    Result := True;
+    for i := 0 to Length(FCoefficients) - 1 do
+      if FCoefficients[i] <> AOther.FCoefficients[i] then
+      begin
+        Result := False;
+        Break;
+      end;
+  end
+  else
+    Result := False;
+end;
+
+class function TBigIntPolynomial.Create(const ACoefficients: array of TBigInt): TBigIntPolynomial;
+var
+  high, i: integer;
+begin
+  high := 1;
+  for i := Length(ACoefficients) - 1 downto 1 do
+    if ACoefficients[i] <> 0 then
+    begin
+      high := i;
+      Break;
+    end;
+  SetLength(Result.FCoefficients, high + 1);
+  for i := 0 to high do
+    Result.FCoefficients[i] := ACoefficients[i];
+end;
+
+{ Operators }
+
+operator = (const A, B: TBigIntPolynomial): Boolean;
+begin
+  Result := A.IsEqualTo(B);
+end;
+
+operator <> (const A, B: TBigIntPolynomial): Boolean;
+begin
+  Result := not A.IsEqualTo(B);
+end;
+
+end.
+

tests/AdventOfCodeFPCUnit.lpi

@@ -140,6 +140,10 @@
         <Filename Value="UNeverTellMeTheOddsTestCases.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
+      <Unit>
+        <Filename Value="UPolynomialTestCases.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;
+  UNeverTellMeTheOddsTestCases, UPolynomialTestCases;
 
 {$R *.res}
 

tests/UPolynomialTestCases.pas

@@ -0,0 +1,94 @@
+{
+  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 UPolynomialTestCases;
+
+{$mode ObjFPC}{$H+}
+
+interface
+
+uses
+  Classes, SysUtils, fpcunit, testregistry, UPolynomial, UBigInt;
+
+type
+
+  { TBigIntPolynomialTestCase }
+
+  TBigIntPolynomialTestCase = class(TTestCase)
+  published
+    procedure TestEqual;
+    procedure TestUnequalSameLength;
+    procedure TestUnequalDifferentLength;
+    procedure TestTrimLeadingZeros;
+    procedure TestBisectionRootIsolation;
+  end;
+
+implementation
+
+{ TBigIntPolynomialTestCase }
+
+procedure TBigIntPolynomialTestCase.TestEqual;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]);
+  b := TBigIntPolynomial.Create([10, 7, 5, 1034]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestUnequalSameLength;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([103, 7, 5, 10]);
+  b := TBigIntPolynomial.Create([1034, 7, 5, 10]);
+  AssertTrue('Polynomials are equal.', a <> b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestUnequalDifferentLength;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([40000, 10, 7, 5, 1034]);
+  b := TBigIntPolynomial.Create([10, 7, 5, 1034]);
+  AssertTrue('Polynomials are equal.', a <> b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestTrimLeadingZeros;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034, 0, 0]);
+  b := TBigIntPolynomial.Create([10, 7, 5, 1034]);
+  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);
+end.
+