Merge branch 'day24-analytical'

tests/AdventOfCodeFPCUnit.lpi

@@ -40,10 +40,6 @@
         <Filename Value="UGearRatiosTestCases.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
-      <Unit>
-        <Filename Value="..\USolver.pas"/>
-        <IsPartOfProject Value="True"/>
-      </Unit>
       <Unit>
         <Filename Value="UBaseTestCases.pas"/>
         <IsPartOfProject Value="True"/>
@@ -140,6 +136,18 @@
         <Filename Value="UNeverTellMeTheOddsTestCases.pas"/>
         <IsPartOfProject Value="True"/>
       </Unit>
+      <Unit>
+        <Filename Value="UPolynomialTestCases.pas"/>
+        <IsPartOfProject Value="True"/>
+      </Unit>
+      <Unit>
+        <Filename Value="UPolynomialRootsTestCases.pas"/>
+        <IsPartOfProject Value="True"/>
+      </Unit>
+      <Unit>
+        <Filename Value="UBigIntTestCases.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, UBigIntTestCases, UPolynomialTestCases, UPolynomialRootsTestCases;
 
 {$R *.res}
 

tests/UNeverTellMeTheOddsTestCases.pas

@@ -33,6 +33,7 @@ type
     function CreateSolver: ISolver; override;
   published
     procedure TestPart1;
+    procedure TestPart2;
   end;
 
   { TNeverTellMeTheOddsExampleTestCase }
@@ -42,6 +43,7 @@ type
     function CreateSolver: ISolver; override;
   published
     procedure TestPart1;
+    procedure TestPart2;
   end;
 
   { TNeverTellMeTheOddsTestCase }
@@ -77,6 +79,11 @@ begin
   AssertEquals(15107, FSolver.GetResultPart1);
 end;
 
+procedure TNeverTellMeTheOddsFullDataTestCase.TestPart2;
+begin
+  AssertEquals(856642398547748, FSolver.GetResultPart2);
+end;
+
 { TNeverTellMeTheOddsExampleTestCase }
 
 function TNeverTellMeTheOddsExampleTestCase.CreateSolver: ISolver;
@@ -89,6 +96,11 @@ begin
   AssertEquals(2, FSolver.GetResultPart1);
 end;
 
+procedure TNeverTellMeTheOddsExampleTestCase.TestPart2;
+begin
+  AssertEquals(47, FSolver.GetResultPart2);
+end;
+
 { TNeverTellMeTheOddsTestCase }
 
 function TNeverTellMeTheOddsTestCase.CreateSolver: ISolver;

tests/UPolynomialRootsTestCases.pas

@@ -0,0 +1,138 @@
+{
+  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)
+  private
+    procedure AssertBisectIntervals(AIsolatingIntervals: TIsolatingIntervalArray; constref AExpectedRoots:
+      array of Cardinal);
+    procedure AssertBisectIntegers(ARoots: TBigIntArray; constref AExpectedRoots: array of Cardinal);
+  published
+    procedure TestBisectNoBound;
+    procedure TestBisectWithBound;
+    procedure TestBisectInteger;
+  end;
+
+implementation
+
+{ TPolynomialRootsTestCase }
+
+procedure TPolynomialRootsTestCase.AssertBisectIntervals(AIsolatingIntervals: TIsolatingIntervalArray;
+  constref AExpectedRoots: array of Cardinal);
+var
+  exp: Cardinal;
+  found: Boolean;
+  i, foundIndex: Integer;
+begin
+  AssertEquals('Unexpected number of isolating intervals.', Length(AExpectedRoots), Length(AIsolatingIntervals));
+  for exp in AExpectedRoots do
+  begin
+    found := False;
+    for i := 0 to Length(AIsolatingIntervals) - 1 do
+      if (AIsolatingIntervals[i].A <= exp) and (exp <= AIsolatingIntervals[i].B) then
+      begin
+        found := True;
+        foundIndex := i;
+        Break;
+      end;
+    AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
+    Delete(AIsolatingIntervals, foundIndex, 1);
+  end;
+end;
+
+procedure TPolynomialRootsTestCase.AssertBisectIntegers(ARoots: TBigIntArray; constref AExpectedRoots:
+  array of Cardinal);
+var
+  exp: Cardinal;
+  found: Boolean;
+  i, foundIndex: Integer;
+begin
+  AssertEquals('Unexpected number of integer roots.', Length(AExpectedRoots), Length(ARoots));
+  for exp in AExpectedRoots do
+  begin
+    found := False;
+    for i := 0 to Length(ARoots) - 1 do
+      if ARoots[i] = exp then
+      begin
+        found := True;
+        foundIndex := i;
+        Break;
+      end;
+    AssertTrue('Expected root ' + IntToStr(exp) + ' not found.', found);
+    Delete(ARoots, foundIndex, 1);
+  end;
+end;
+
+procedure TPolynomialRootsTestCase.TestBisectNoBound;
+const
+  expRoots: array of Cardinal = (34000, 23017, 5);
+var
+  a: TBigIntPolynomial;
+  r: TIsolatingIntervalArray;
+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 := TPolynomialRoots.BisectIsolation(a);
+  AssertBisectIntervals(r, expRoots);
+end;
+
+procedure TPolynomialRootsTestCase.TestBisectWithBound;
+const
+  expRoots: array of Cardinal = (23017, 5);
+var
+  a: TBigIntPolynomial;
+  r: TIsolatingIntervalArray;
+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 := TPolynomialRoots.BisectIsolation(a, 15);
+  AssertBisectIntervals(r, expRoots);
+end;
+
+procedure TPolynomialRootsTestCase.TestBisectInteger;
+const
+  expRoots: array of Cardinal = (23017, 5);
+var
+  a: TBigIntPolynomial;
+  r: TBigIntArray;
+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 := TPolynomialRoots.BisectInteger(a, 15);
+  AssertBisectIntegers(r, expRoots);
+end;
+
+initialization
+
+  RegisterTest(TPolynomialRootsTestCase);
+end.
+

tests/UPolynomialTestCases.pas

@@ -0,0 +1,187 @@
+{
+  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)
+  private
+    procedure TestCreateWithDegree(const ACoefficients: array of TBigInt; const ADegree: Integer);
+  published
+    procedure TestCreate;
+    procedure TestCreateDegreeZero;
+    procedure TestEqual;
+    procedure TestUnequalSameLength;
+    procedure TestUnequalDifferentLength;
+    procedure TestTrimLeadingZeros;
+    procedure TestCalcValueAt;
+    procedure TestSignVariations;
+    procedure TestScaleByPowerOfTwo;
+    procedure TestScaleVariable;
+    procedure TestScaleVariableByPowerOfTwo;
+    procedure TestTranslateVariableByOne;
+    procedure TestRevertOrderOfCoefficients;
+    procedure TestDivideByVariable;
+  end;
+
+implementation
+
+{ TBigIntPolynomialTestCase }
+
+procedure TBigIntPolynomialTestCase.TestCreateWithDegree(const ACoefficients: array of TBigInt; const ADegree: Integer);
+var
+  a: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create(ACoefficients);
+  AssertEquals('Degree of created polynomial incorrect.', ADegree, a.Degree);
+end;
+
+procedure TBigIntPolynomialTestCase.TestCreate;
+begin
+  TestCreateWithDegree([992123, 7, 20, 4550022], 3);
+end;
+
+procedure TBigIntPolynomialTestCase.TestCreateDegreeZero;
+begin
+  TestCreateWithDegree([4007], 0);
+  TestCreateWithDegree([], 0);
+  TestCreateWithDegree([0], 0);
+end;
+
+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.TestCalcValueAt;
+var
+  a: TBigIntPolynomial;
+  exp: TBigInt;
+begin
+  a := TBigIntPolynomial.Create([80, 892477222, 0, 921556, 7303]);
+  exp:= TBigInt.FromInt64(16867124285);
+  AssertTrue('Polynomial evaluation unexpected.', a.CalcValueAt(15) = exp);
+end;
+
+procedure TBigIntPolynomialTestCase.TestSignVariations;
+var
+  a: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([-10, 15, 0, 10, -20, -15, 0, 0, 5, 10, -10]);
+  AssertEquals(4, a.CalcSignVariations);
+end;
+
+procedure TBigIntPolynomialTestCase.TestScaleByPowerOfTwo;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]).ScaleByPowerOfTwo(7);
+  b := TBigIntPolynomial.Create([128 * 10, 128 * 7, 128 * 5, 128 * 1034]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestScaleVariable;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]).ScaleVariable(TBigInt.FromInt64(10));
+  b := TBigIntPolynomial.Create([10, 70, 500, 1034000]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestScaleVariableByPowerOfTwo;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]).ScaleVariableByPowerOfTwo(5);
+  b := TBigIntPolynomial.Create([10, 7 * 32, 5 * 32 * 32, 1034 * 32 * 32 * 32]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestTranslateVariableByOne;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]).TranslateVariableByOne;
+  b := TBigIntPolynomial.Create([1056, 3119, 3107, 1034]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestRevertOrderOfCoefficients;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([0, 10, 7, 5, 1034]).RevertOrderOfCoefficients;
+  b := TBigIntPolynomial.Create([1034, 5, 7, 10]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+procedure TBigIntPolynomialTestCase.TestDivideByVariable;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([0, 10, 7, 5, 1034]).DivideByVariable;
+  b := TBigIntPolynomial.Create([10, 7, 5, 1034]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
+initialization
+
+  RegisterTest(TBigIntPolynomialTestCase);
+end.
+