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9 changed files with 1178 additions and 96 deletions

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@ -157,6 +157,14 @@
<Filename Value="UCommon.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
<Unit>
<Filename Value="UMultiIndexEnumerator.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
<Unit>
<Filename Value="UBinomialCoefficients.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
</Units>
</ProjectOptions>
<CompilerOptions>

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UBinomialCoefficients.pas Normal file
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@ -0,0 +1,96 @@
{
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 UBinomialCoefficients;
{$mode ObjFPC}{$H+}
interface
uses
Classes, SysUtils, Generics.Collections;
type
TCardinalArray = array of Cardinal;
TCardinalArrays = specialize TList<TCardinalArray>;
{ TBinomialCoefficientCache }
TBinomialCoefficientCache = class
private
FCache: TCardinalArrays;
procedure AddRow;
public
constructor Create;
destructor Destroy; override;
// Returns N choose K, with N >= K >= 0.
function Get(const AN, AK: Cardinal): Cardinal;
// Returns the number of cached rows C = N + 1, where N is the highest from previously queried "N choose K". The
// actual number of cached binomial coefficient values is C * (C + 1) / 2.
function GetCachedRowsCount: Cardinal;
end;
implementation
{ TBinomialCoefficientCache }
procedure TBinomialCoefficientCache.AddRow;
var
row: TCardinalArray;
i: Cardinal;
begin
SetLength(row, FCache.Count + 1);
row[0] := 1;
if FCache.Count > 0 then
begin
row[FCache.Count] := 1;
for i := 1 to FCache.Count - 1 do
row[i] := FCache.Last[i - 1] + FCache.Last[i];
end;
FCache.Add(row);
end;
constructor TBinomialCoefficientCache.Create;
begin
FCache := TCardinalArrays.Create;
end;
destructor TBinomialCoefficientCache.Destroy;
begin
FCache.Free;
inherited Destroy;
end;
function TBinomialCoefficientCache.Get(const AN, AK: Cardinal): Cardinal;
var
i: Cardinal;
begin
if AN < AK then
raise ERangeError.Create('Cannot calculate binomial coefficient "n choose k" with k larger than n.');
for i := FCache.Count to AN do
AddRow;
Result := FCache[AN][AK];
end;
function TBinomialCoefficientCache.GetCachedRowsCount: Cardinal;
begin
Result := FCache.Count;
end;
end.

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@ -22,7 +22,7 @@ unit UCommon;
interface
uses
Classes, SysUtils;
Classes, SysUtils, Generics.Collections;
type
PPoint = ^TPoint;
@ -39,6 +39,9 @@ const
CDirectionLeftUp: TPoint = (X: -1; Y: -1);
CPCardinalDirections: array[0..3] of PPoint = (@CDirectionRight, @CDirectionDown, @CDirectionLeft, @CDirectionUp);
type
TIntegerList = specialize TList<Integer>;
implementation
end.

160
UMultiIndexEnumerator.pas Normal file
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@ -0,0 +1,160 @@
{
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 UMultiIndexEnumerator;
{$mode ObjFPC}{$H+}
interface
uses
Classes, SysUtils;
type
TIndexArray = array of Integer;
TIndexValidationResult = (ivrValid, ivrSkip, ivrBacktrack);
TEnumerableMultiIndexStrategy = class;
{ TMultiIndexEnumerator }
TMultiIndexEnumerator = class(TInterfacedObject, specialize IEnumerator<TIndexArray>)
private
FStrategy: TEnumerableMultiIndexStrategy;
FCurrent: TIndexArray;
FMustInit: Boolean;
function UpdateArray(const AInit: Boolean): Boolean;
public
constructor Create(const AStrategy: TEnumerableMultiIndexStrategy);
function GetCurrent: TIndexArray;
function MoveNext: Boolean;
procedure Reset;
property Current: TIndexArray read GetCurrent;
end;
{ TEnumerableMultiIndexStrategy }
TEnumerableMultiIndexStrategy = class(TInterfacedObject, specialize IEnumerable<TIndexArray>)
public
function GetEnumerator: specialize IEnumerator<TIndexArray>;
function GetCardinality: Integer; virtual; abstract;
function TryGetStartIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer;
out AStartIndexValue: Integer): Boolean; virtual; abstract;
function ValidateIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer):
TIndexValidationResult; virtual; abstract;
end;
implementation
{ TMultiIndexEnumerator }
function TMultiIndexEnumerator.UpdateArray(const AInit: Boolean): Boolean;
var
i, initialized: Integer;
r: TIndexValidationResult;
begin
if AInit then
begin
i := 0;
initialized := -1;
end
else begin
i := Length(FCurrent) - 1;
initialized := i;
end;
while i < Length(FCurrent) do
begin
if initialized < i then
begin
// Checks whether start index value can be set, and backtracks or aborts if not.
if not FStrategy.TryGetStartIndexValue(FCurrent, i, FCurrent[i]) then
if i > 0 then
begin
Dec(i);
Continue;
end
else begin
Result := False;
Exit;
end
end
else
// Sets next candidate for current index value.
Inc(FCurrent[i]);
// Checks if current index value is valid, and increases it until it is, or backtracks or aborts if so indicated.
while True do
begin
r := FStrategy.ValidateIndexValue(FCurrent, i);
case r of
ivrValid: begin
initialized := i;
Inc(i);
Break;
end;
ivrSkip:
Inc(FCurrent[i]);
ivrBacktrack:
if i > 0 then
begin
Dec(i);
Break;
end
else begin
Result := False;
Exit;
end;
end;
end;
end;
Result := True;
end;
constructor TMultiIndexEnumerator.Create(const AStrategy: TEnumerableMultiIndexStrategy);
begin
FStrategy := AStrategy;
SetLength(FCurrent, FStrategy.GetCardinality);
Reset;
end;
function TMultiIndexEnumerator.GetCurrent: TIndexArray;
begin
Result := FCurrent;
end;
function TMultiIndexEnumerator.MoveNext: Boolean;
begin
Result := UpdateArray(FMustInit);
FMustInit := False;
end;
procedure TMultiIndexEnumerator.Reset;
begin
FMustInit := True;
end;
{ TEnumerableMultiIndexStrategy }
function TEnumerableMultiIndexStrategy.GetEnumerator: specialize IEnumerator<TIndexArray>;
begin
Result := TMultiIndexEnumerator.Create(Self);
end;
end.

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@ -1,6 +1,6 @@
{
Solutions to the Advent Of Code.
Copyright (C) 2023 Stefan Müller
Copyright (C) 2023-2024 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
@ -21,28 +21,128 @@ unit UHotSprings;
interface
// TODO: Remove this and the ifdefs.
{$define debug}
uses
Classes, SysUtils, Generics.Collections, USolver;
Classes, SysUtils, Math, Generics.Collections, USolver, UCommon, UMultiIndexEnumerator, UBinomialCoefficients;
const
COperationalChar = '.';
CDamagedChar = '#';
CWildcardChar = '?';
COperationalPatternChars = [COperationalChar, CWildcardChar];
CDamagedPatternChars = [CDamagedChar, CWildcardChar];
CPart2Repetition = 5;
type
TValidationLengths = array of array of Integer;
// TODO: TIntegerArray probably not needed.
TIntegerArray = array of Integer;
{ TDamage }
TDamage = record
Start, Length, CharsRemaining: Integer;
end;
TDamages = specialize TList<TDamage>;
// TODO: Instead of using TDamagesBlocks, "block" should be a record of a string and its associated list TDamages.
TDamagesBlocks = specialize TObjectList<TDamages>;
{ TValidationToDamageAssignments }
TValidationToDamageAssignments = class(TEnumerableMultiIndexStrategy)
private
FValidation: TIntegerList;
FValidationLengths: TValidationLengths;
FDamages: TDamages;
FValidationStartIndex, FValidationStopIndex: Integer;
// Calculates "span", the length of all damages for this validation number combined.
function CalcValidationSpan(constref ACurrentIndexArray: TIndexArray; const ALastDamageIndex, AValidationNumber:
Integer): Integer;
public
constructor Create(constref AValidation: TIntegerList; constref AValidationLengths: TValidationLengths;
constref ADamages: TDamages; const AStartIndex, AStopIndex: Integer);
function GetCardinality: Integer; override;
function TryGetStartIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer;
out AStartIndexValue: Integer): Boolean; override;
function ValidateIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer):
TIndexValidationResult; override;
end;
{ TValidationPositionInfo }
TValidationPositionInfo = record
ValidationIndex, MinStart, MaxStart: Integer;
end;
TValidationPositionInfos = specialize TList<TValidationPositionInfo>;
{ TValidationPositionOffsets }
TValidationPositionOffsets = class(TEnumerableMultiIndexStrategy)
private
FValidation: TIntegerList;
FPositionInfos: TValidationPositionInfos;
public
constructor Create(constref AValidation: TIntegerList; constref APositionInfos: TValidationPositionInfos);
function GetCardinality: Integer; override;
function TryGetStartIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer;
out AStartIndexValue: Integer): Boolean; override;
function ValidateIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex: Integer):
TIndexValidationResult; override;
end;
{ TConditionRecord }
TConditionRecord = class
private
FBinomialCoefficients: TBinomialCoefficientCache;
FValidation: TIntegerList;
// List of non-empty, maximum-length parts of the pattern without operational springs ("blocks").
FBlocks: TStringList;
// Array 'a' of accumulated validation series lengths. 'a[i, j]' denotes the combined length of consecutive
// validation numbers from 'FValidation[i]' to 'FValidation[j - 1]' with a single space in between each pair of
// them.
FValidationLengths: TValidationLengths;
// Array 'a' of minimum indices 'a[i]', such that all remaining validation numbers starting at index 'a[i] - 1'
// cannot fit into the remaining blocks starting at 'FBlocks[i]'.
FMinIndices: TIntegerArray;
// List 'a' of lists of damages in a block. Each list of damages 'a[i]' contains exactly one entry for each block of
// consecutive damages characters in the i-th block.
// For example, if the pattern is '?#.??##?#?..??', then 'FDamagesBlocks' would have 3 entries, which are lists of
// 1, 2, and 0 damages, respectively.
FDamagesBlocks: TDamagesBlocks;
procedure InitValidationLengths;
procedure InitMinIndices;
function CalcCombinations(constref AIndices: TIntegerArray): Int64;
function CalcCombinationsBlock(const ABlock: string; constref ADamages: TDamages; const AStartIndex, AStopIndex:
Integer): Int64;
function CalcCombinationsBlockSingleValidation(const ABlockLength: Integer; constref ADamages: TDamages;
const AIndex: Integer): Int64;
function CalcCombinationsBlockMultiValidations(const ABlockLength: Integer; constref ADamages: TDamages;
constref AIndices: TIndexArray; const AStartIndex, AStopIndex: Integer): Int64;
function CalcCombinationsBlockAssignedValidations(const ABlockLength: Integer; constref APositionInfos:
TValidationPositionInfos; constref AOffsets: TIndexArray; const AStartIndex, AStopIndex: Integer): Int64;
function CalcCombinationsWildcardSequence(const ASequenceLength, AStartIndex, AStopIndex: Integer): Int64;
function ParseDamages(const ABlock: string): TDamages;
public
property Blocks: TStringList read FBlocks;
property Validation: TIntegerList read FValidation;
constructor Create(constref ABinomialCoefficients: TBinomialCoefficientCache);
destructor Destroy; override;
// Adds all non-empty, maximum-length parts of the pattern without operational springs ("blocks").
procedure AddBlocks(const APattern: string);
function GenerateBlockAssignments: Int64;
end;
{ THotSprings }
THotSprings = class(TSolver)
private
FValidation: specialize TList<Integer>;
FSpringPattern: string;
procedure ExtendArrangement(const AArrangement: string; const ARemainingFreeOperationalCount, ACurrentValidationIndex:
Integer);
function TryAppendOperationalChar(var AArrangement: string): Boolean;
function TryAppendValidationBlock(var AArrangement: string; const ALength: Integer): Boolean;
// Keeping the binomial coefficients calculator here so it can be shared for all lines.
FBinomialCoefficients: TBinomialCoefficientCache;
// TODO: Remove FDebugIndex.
FDebugIndex: Integer;
public
constructor Create;
destructor Destroy; override;
@ -54,99 +154,604 @@ type
implementation
{ THotSprings }
{ TValidationToDamageAssignments }
procedure THotSprings.ExtendArrangement(const AArrangement: string; const ARemainingFreeOperationalCount,
ACurrentValidationIndex: Integer);
function TValidationToDamageAssignments.CalcValidationSpan(constref ACurrentIndexArray: TIndexArray;
const ALastDamageIndex, AValidationNumber: Integer): Integer;
var
match: Boolean;
temp: string;
spanStart: Integer;
begin
if Length(AArrangement) = Length(FSpringPattern) then
Inc(FPart1)
else begin
temp := AArrangement;
// Tries to append a dot (operational) to the current arrangement.
if (ARemainingFreeOperationalCount > 0) and TryAppendOperationalChar(temp) then
begin
ExtendArrangement(temp, ARemainingFreeOperationalCount - 1, ACurrentValidationIndex);
spanStart := ALastDamageIndex;
while (spanStart > 0) and (ACurrentIndexArray[spanStart - 1] = AValidationNumber) do
Dec(spanStart);
Result := FDamages[ALastDamageIndex].Length;
if spanStart < ALastDamageIndex then
Inc(Result, FDamages[ALastDamageIndex].Start - FDamages[spanStart].Start);
end;
// Tries to append the current validation block (damaged) to the current arrangement.
if ACurrentValidationIndex < FValidation.Count then
constructor TValidationToDamageAssignments.Create(constref AValidation: TIntegerList; constref AValidationLengths:
TValidationLengths; constref ADamages: TDamages; const AStartIndex, AStopIndex: Integer);
begin
temp := AArrangement;
match := TryAppendValidationBlock(temp, FValidation[ACurrentValidationIndex]);
// ... and the mandatory dot after the block, if it is not the last block.
if match
and (ACurrentValidationIndex < FValidation.Count - 1)
and not TryAppendOperationalChar(temp) then
match := False;
if match then
ExtendArrangement(temp, ARemainingFreeOperationalCount, ACurrentValidationIndex + 1);
end;
end;
FValidation := AValidation;
FValidationLengths := AValidationLengths;
FDamages := ADamages;
FValidationStartIndex := AStartIndex;
FValidationStopIndex := AStopIndex;
end;
function THotSprings.TryAppendOperationalChar(var AArrangement: string): Boolean;
function TValidationToDamageAssignments.GetCardinality: Integer;
begin
if FSpringPattern[Length(AArrangement) + 1] in COperationalPatternChars then
Result := FDamages.Count;
end;
function TValidationToDamageAssignments.TryGetStartIndexValue(constref ACurrentIndexArray: TIndexArray;
const ACurrentIndex: Integer; out AStartIndexValue: Integer): Boolean;
begin
AArrangement := AArrangement + COperationalChar;
Result := True;
end
if ACurrentIndex > 0 then
AStartIndexValue := ACurrentIndexArray[ACurrentIndex - 1]
else
Result := False;
AStartIndexValue := FValidationStartIndex;
end;
function THotSprings.TryAppendValidationBlock(var AArrangement: string; const ALength: Integer): Boolean;
function TValidationToDamageAssignments.ValidateIndexValue(constref ACurrentIndexArray: TIndexArray;
const ACurrentIndex: Integer): TIndexValidationResult;
var
i, prev, firstSkip: Integer;
begin
i := ACurrentIndexArray[ACurrentIndex];
if i > FValidationStopIndex then
begin
Result := ivrBacktrack;
Exit;
end;
// Checks if there is enough space after this damage for remaining validation numbers.
if (i < FValidationStopIndex)
and (FValidationLengths[i + 1, FValidationStopIndex + 1] + 1 > FDamages[ACurrentIndex].CharsRemaining) then
begin
Result := ivrSkip;
Exit;
end;
// Checks if there is enough space before this damage for previous validation numbers.
if (FValidationStartIndex < i)
and (FValidationLengths[FValidationStartIndex, i] + 1 >= FDamages[ACurrentIndex].Start) then
begin
Result := ivrBacktrack;
Exit;
end;
// Checks if there is enough space between previous and this damage for skipped validation numbers.
if ACurrentIndex > 0 then
begin
prev := ACurrentIndex - 1;
firstSkip := ACurrentIndexArray[prev] + 1;
if (firstSkip < i) and (FValidationLengths[firstSkip, i] + 2 > FDamages[ACurrentIndex].Start - FDamages[prev].Start - FDamages[prev].Length) then
begin
Result := ivrBacktrack;
Exit;
end;
end;
// Checks if span is small enough to fit within this validation number.
if FValidation[i] < CalcValidationSpan(ACurrentIndexArray, ACurrentIndex, i) then
begin
Result := ivrSkip;
Exit;
end;
Result := ivrValid;
end;
{ TValidationPositionOffsets }
constructor TValidationPositionOffsets.Create(constref AValidation: TIntegerList; constref APositionInfos:
TValidationPositionInfos);
begin
FValidation := AValidation;
FPositionInfos := APositionInfos;
end;
function TValidationPositionOffsets.GetCardinality: Integer;
begin
Result := FPositionInfos.Count;
end;
function TValidationPositionOffsets.TryGetStartIndexValue(constref ACurrentIndexArray: TIndexArray;
const ACurrentIndex: Integer; out AStartIndexValue: Integer): Boolean;
var
info: TValidationPositionInfo;
begin
info := FPositionInfos[ACurrentIndex];
// Calculates start value such that the validation number just includes MinEnd.
//AStartIndexValue := info.MinEnd - FValidation[info.ValidationIndex] + 1;
AStartIndexValue := info.MinStart;
// Adjusts start value to avoid overlap of this validation number with the previous one (the one from previous
// position info).
if ACurrentIndex > 0 then
AStartIndexValue := Max(AStartIndexValue,
ACurrentIndexArray[ACurrentIndex - 1] + FValidation[FPositionInfos[ACurrentIndex - 1].ValidationIndex] + 1);
Result := True;
end;
function TValidationPositionOffsets.ValidateIndexValue(constref ACurrentIndexArray: TIndexArray; const ACurrentIndex:
Integer): TIndexValidationResult;
begin
if ACurrentIndexArray[ACurrentIndex] <= FPositionInfos[ACurrentIndex].MaxStart then
Result := ivrValid
else
Result := ivrBacktrack;
end;
{ TConditionRecord }
procedure TConditionRecord.InitValidationLengths;
var
i, j: Integer;
begin
SetLength(FValidationLengths, FValidation.Count + 1, FValidation.Count + 1);
for i := 0 to FValidation.Count do
begin
FValidationLengths[i, i] := 0;
for j := i + 1 to FValidation.Count do
if FValidationLengths[i, j - 1] <> 0 then
FValidationLengths[i, j] := FValidationLengths[i, j - 1] + FValidation[j - 1] + 1
else
FValidationLengths[i, j] := FValidationLengths[i, j - 1] + FValidation[j - 1]
end;
end;
procedure TConditionRecord.InitMinIndices;
var
i, j, patternsLength: Integer;
begin
SetLength(FMinIndices, FBlocks.Count - 1);
patternsLength := Length(FBlocks[FBlocks.Count - 1]);
j := FValidation.Count;
for i := FBlocks.Count - 2 downto 0 do
begin
while (j >= 0) and (FValidationLengths[j, FValidation.Count] <= patternsLength) do
Dec(j);
FMinIndices[i] := j + 1;
patternsLength := patternsLength + 1 + Length(FBlocks[i]);
end;
end;
function TConditionRecord.CalcCombinations(constref AIndices: TIntegerArray): Int64;
var
i, j: Integer;
// TODO: Remove r.
r: Int64;
begin
{$ifdef debug}
for i in AIndices do
Write(i, ' ');
WriteLn;
{$endif}
Result := 1;
i := 0;
while (Result > 0) and (i < FBlocks.Count) do
begin
if FDamagesBlocks[i].Count > 0 then
r := CalcCombinationsBlock(FBlocks[i], FDamagesBlocks[i], AIndices[i], AIndices[i + 1] - 1)
else begin
{$ifdef debug}
Write(' ', FBlocks[i], ' ');
for j := AIndices[i] to AIndices[i + 1] - 1 do
Write(FValidation[j], ' ');
WriteLn;
Write(' count/space/freedoms: ');
{$endif}
r := CalcCombinationsWildcardSequence(Length(FBlocks[i]), AIndices[i], AIndices[i + 1] - 1);
{$ifdef debug}
WriteLn(' result: ', r);
{$endif}
end;
{$ifdef debug}
WriteLn(' Result: ', r);
{$endif}
Result := Result * r;
Inc(i);
end;
end;
function TConditionRecord.CalcCombinationsBlock(const ABlock: string; constref ADamages: TDamages; const AStartIndex,
AStopIndex: Integer): Int64;
var
i, j, k: Integer;
indices: TIndexArray;
validationToDamageAssignments: TValidationToDamageAssignments;
begin
{$ifdef debug}
Write(' ', ABlock, ' ');
for i := AStartIndex to AStopIndex do
Write(FValidation[i], ' ');
WriteLn;
{$endif}
// No validation number assigned to this block.
if AStartIndex > AStopIndex then
begin
if ADamages.Count = 0 then
Result := 1
else
Result := 0;
end
// One validation number assigned to this block.
else if AStartIndex = AStopIndex then
Result := CalcCombinationsBlockSingleValidation(Length(ABlock), ADamages, AStartIndex)
// Multiple validation numbers assigned to this block.
else begin
{$ifdef debug}
Write(' min before: ');
for i := AStartIndex to AStopIndex do
Write(FValidationLengths[AStartIndex, i + 1] - FValidation[i], ' ');
WriteLn;
Write(' min after: ');
for i := AStartIndex to AStopIndex do
Write(FValidationLengths[i, AStopIndex + 1] - FValidation[i], ' ');
WriteLn;
for i := 0 to ADamages.Count - 1 do
begin
WriteLn(' damage: start ',ADamages[i].Start, ', length ', ADamages[i].Length, ', remain ', ADamages[i].CharsRemaining);
Write(' ');
for j := AStartIndex to AStopIndex do
// Enough space before damage for the other validation numbers?
if (FValidationLengths[AStartIndex, j + 1] - FValidation[j] < ADamages[i].Start)
// Enough space after damage for the other validation numbers?
and (FValidationLengths[j, AStopIndex + 1] - FValidation[j] <= ADamages[i].CharsRemaining)
// Damage itself small enough for this validation number?
and (FValidation[j] >= ADamages[i].Length) then
Write(j - AStartIndex, ' ');
WriteLn;
end;
{$endif}
Result := 0;
// Assigns validation numbers to specific damages.
validationToDamageAssignments := TValidationToDamageAssignments.Create(FValidation, FValidationLengths, ADamages,
AStartIndex, AStopIndex);
{$ifdef debug}
WriteLn(' validation numbers (indices) per damages:');
{$endif}
for indices in validationToDamageAssignments do
begin
{$ifdef debug}
Write(' ');
for i := 0 to ADamages.Count - 1 do
Write(FValidation[indices[i]], ' ');
Write('( ');
for i := 0 to ADamages.Count - 1 do
Write(indices[i] - AStartIndex, ' ');
WriteLn(')');
{$endif}
Result := Result + CalcCombinationsBlockMultiValidations(Length(ABlock), ADamages, indices, AStartIndex, AStopIndex);
end;
validationToDamageAssignments.Free;
end;
end;
function TConditionRecord.CalcCombinationsBlockSingleValidation(const ABlockLength: Integer; constref ADamages:
TDamages; const AIndex: Integer): Int64;
var
combinedDamagesLength: Integer;
begin
if ABlockLength < FValidation[AIndex] then
Result := 0
else if ADamages.Count = 0 then
Result := ABlockLength - FValidation[AIndex] + 1
else begin
combinedDamagesLength := ADamages.Last.Start + ADamages.Last.Length - ADamages.First.Start;
if FValidation[AIndex] < combinedDamagesLength then
Result := 0
else begin
Result := Min(Min(Min(
ADamages.First.Start,
FValidation[AIndex] - combinedDamagesLength + 1),
ABlockLength - FValidation[AIndex] + 1),
ADamages.Last.CharsRemaining + 1);
end;
end;
end;
function TConditionRecord.CalcCombinationsBlockMultiValidations(const ABlockLength: Integer; constref ADamages:
TDamages; constref AIndices: TIndexArray; const AStartIndex, AStopIndex: Integer): Int64;
var
i, high: Integer;
position: TValidationPositionInfo;
positions: TValidationPositionInfos;
validationPositionOffsets: TValidationPositionOffsets;
offsets: TIndexArray;
begin
positions := TValidationPositionInfos.Create;
high := Length(AIndices) - 1;
// Initializes first info record.
position.ValidationIndex := AIndices[0];
position.MaxStart := ADamages[0].Start;
position.MinStart := 1;
for i := 1 to high do
if AIndices[i] <> position.ValidationIndex then
begin
// Finalizes current info record.
position.MaxStart := Min(position.MaxStart, ADamages[i].Start - 1 - FValidation[position.ValidationIndex]);
position.MinStart := Max(position.MinStart,
ADamages[i - 1].Start + ADamages[i - 1].Length - FValidation[position.ValidationIndex]);
positions.Add(position);
// Initializes next info record.
position.ValidationIndex := AIndices[i];
position.MaxStart := ADamages[i].Start;
position.MinStart := position.MinStart + FValidationLengths[AIndices[i - 1], AIndices[i]] + 1; //FValidation[position.ValidationIndex - 1] + 1;
end;
// Finalizes last info record.
position.MaxStart := Min(position.MaxStart, ABlockLength + 1 - FValidation[position.ValidationIndex]);
position.MinStart := Max(position.MinStart,
ADamages[high].Start + ADamages[high].Length - FValidation[position.ValidationIndex]);
positions.Add(position);
{$ifdef debug}
WriteLn(' validation position infos');
for position in positions do
WriteLn(' ', position.ValidationIndex, ' ', position.MinStart, ' ', position.MaxStart);
WriteLn(' offsets');
{$endif}
Result := 0;
validationPositionOffsets := TValidationPositionOffsets.Create(FValidation, positions);
for offsets in validationPositionOffsets do
Result := Result + CalcCombinationsBlockAssignedValidations(ABlockLength, positions, offsets, AStartIndex, AStopIndex);
validationPositionOffsets.Free;
positions.Free;
end;
function TConditionRecord.CalcCombinationsBlockAssignedValidations(const ABlockLength: Integer; constref APositionInfos:
TValidationPositionInfos; constref AOffsets: TIndexArray; const AStartIndex, AStopIndex: Integer): Int64;
var
i, space: Integer;
begin
{$ifdef debug}
Write(' ');
for i in AOffsets do
Write(i, ' ');
Write(' count/space/freedoms: ');
{$endif}
space := AOffsets[0] - 2;
Result := CalcCombinationsWildcardSequence(space, AStartIndex, APositionInfos[0].ValidationIndex - 1);
if Result = 0 then begin
{$ifdef debug}
WriteLn(' result: ', Result);
{$endif}
Exit;
end;
for i := 0 to APositionInfos.Count - 2 do begin
space := AOffsets[i + 1] - AOffsets[i] - FValidation[APositionInfos[i].ValidationIndex] - 2;
Result := Result * CalcCombinationsWildcardSequence(space, APositionInfos[i].ValidationIndex + 1, APositionInfos[i + 1].ValidationIndex - 1);
if Result = 0 then begin
{$ifdef debug}
WriteLn(' result: ', Result);
{$endif}
Exit;
end;
end;
space := ABlockLength - AOffsets[APositionInfos.Count - 1] - FValidation[APositionInfos.Last.ValidationIndex];
Result := Result * CalcCombinationsWildcardSequence(space, APositionInfos.Last.ValidationIndex + 1, AStopIndex);
{$ifdef debug}
WriteLn(' result: ', Result);
{$endif}
end;
function TConditionRecord.CalcCombinationsWildcardSequence(const ASequenceLength, AStartIndex, AStopIndex: Integer):
Int64;
var
count, freedoms: Integer;
begin
if AStartIndex < AStopIndex + 1 then
begin
count := AStopIndex + 1 - AStartIndex;
freedoms := ASequenceLength - FValidationLengths[AStartIndex, AStopIndex + 1];
{$ifdef debug}
Write(count, '/', ASequenceLength, '/', freedoms, ' ');
{$endif}
if freedoms >= 0 then
Result := FBinomialCoefficients.Get(count + freedoms, freedoms)
else
Result := 0;
end
else begin
Result := 1;
{$ifdef debug}
Write('X ');
{$endif}
end;
end;
function TConditionRecord.ParseDamages(const ABlock: string): TDamages;
var
i, len: Integer;
damage: TDamage;
begin
Result := True;
len := Length(AArrangement);
for i := 1 to ALength do
Result := TDamages.Create;
damage.Length := 0;
len := Length(ABlock);
for i := 1 to len do
// The pattern must only contain damage and wildcard characters here.
if ABlock[i] = CDamagedChar then
begin
if FSpringPattern[len + i] in CDamagedPatternChars then
AArrangement := AArrangement + CDamagedChar
else begin
Result := False;
Break;
if damage.Length = 0 then
damage.Start := i;
Inc(damage.Length);
end
else if damage.Length > 0 then
begin
damage.CharsRemaining := len - damage.Start - damage.Length + 1;
Result.Add(damage);
damage.Length := 0;
end;
if damage.Length > 0 then
begin
damage.CharsRemaining := 0;
Result.Add(damage);
end;
end;
constructor TConditionRecord.Create(constref ABinomialCoefficients: TBinomialCoefficientCache);
begin
FBinomialCoefficients := ABinomialCoefficients;
FBlocks := TStringList.Create;
FValidation := TIntegerList.Create;
FDamagesBlocks := TDamagesBlocks.Create;
end;
destructor TConditionRecord.Destroy;
begin
FBlocks.Free;
FValidation.Free;
FDamagesBlocks.Free;
inherited Destroy;
end;
procedure TConditionRecord.AddBlocks(const APattern: string);
var
split: TStringArray;
part: string;
begin
split := APattern.Split([COperationalChar]);
for part in split do
if Length(part) > 0 then
begin
FBlocks.Add(part);
FDamagesBlocks.Add(ParseDamages(part));
end;
end;
function TConditionRecord.GenerateBlockAssignments: Int64;
var
indices: array of Integer;
i, j, k, high: Integer;
// TODO: Remove r, count, misses.
r: Int64;
count, misses: Integer;
begin
count := 0;
misses := 0;
// Each loop (each call to 'CalcCombinations') represents an independent set of arrangements, defined by 'indices',
// where specific validation numbers are assigned to specific block patterns.
//
// Here, 'indices[i]' denotes the index + 1 of the last validation number assigned to 'FBlockPattern[i]', and the
// index of the first validation number in 'FValidation' assigned to 'FBlockPattern[i + 1]'. If two consecutive values
// in 'indices' are the same, then the block in between has no numbers assigned to it.
//
// Note that 'indices[0] = 0' and 'indices[FBlockPatterns.Count] = FValidation.Count' are constant. Having these two
// numbers in the array simplifies the code a bit.
InitValidationLengths;
//FPatternLengths := CalcPatternLengths;
InitMinIndices;
SetLength(indices, FBlocks.Count + 1);
high := Length(indices) - 2;
indices[0] := 0;
indices[high + 1] := FValidation.Count;
// TODO: Use TMultiIndexEnumerator for this.
Result := 0;
k := 0;
repeat
i := k + 1;
while i <= high do
begin
indices[i] := Max(indices[i - 1], FMinIndices[i - 1]);
while FValidationLengths[indices[i - 1], indices[i]] > Length(FBlocks[i - 1]) do
begin
Dec(i);
Inc(indices[i]);
end;
Inc(i);
end;
Inc(count);
r := CalcCombinations(indices);
if r = 0 then
Inc(misses);
Result := Result + r;
k := high;
while (k > 0)
and ((indices[k] = FValidation.Count)
or (FValidationLengths[indices[k - 1], indices[k] + 1] > Length(FBlocks[k - 1]))) do
Dec(k);
Inc(indices[k]);
until k = 0;
WriteLn(' missed: ', misses, '/', count);
end;
{ THotSprings }
constructor THotSprings.Create;
begin
FValidation := specialize TList<Integer>.Create;
FDebugIndex := 0;
FBinomialCoefficients := TBinomialCoefficientCache.Create;
end;
destructor THotSprings.Destroy;
begin
FValidation.Free;
FBinomialCoefficients.Free;
inherited Destroy;
end;
procedure THotSprings.ProcessDataLine(const ALine: string);
var
split: TStringArray;
i, val, maxFreeOperationalCount: Integer;
conditionRecord1, conditionRecord2: TConditionRecord;
mainSplit, split: TStringArray;
part, unfolded: string;
i: Integer;
begin
FValidation.Clear;
split := ALine.Split([' ', ',']);
FSpringPattern := split[0];
{$ifdef debug}
WriteLn(ALine);
WriteLn;
{$endif}
maxFreeOperationalCount := Length(FSpringPattern) - Length(split) + 2;
for i := 1 to Length(split) - 1 do
begin
val := StrToInt(split[i]);
FValidation.Add(val);
Dec(maxFreeOperationalCount, val);
end;
conditionRecord1 := TConditionRecord.Create(FBinomialCoefficients);
conditionRecord2 := TConditionRecord.Create(FBinomialCoefficients);
ExtendArrangement('', maxFreeOperationalCount, 0);
mainSplit := ALine.Split([' ']);
// Adds blocks for part 1.
conditionRecord1.AddBlocks(mainSplit[0]);
// Adds blocks for part 2.
unfolded := mainSplit[0];
for i := 2 to CPart2Repetition do
unfolded := unfolded + CWildcardChar + mainSplit[0];
conditionRecord2.AddBlocks(unfolded);
// Adds validation numbers.
split := mainSplit[1].Split([',']);
for part in split do
conditionRecord1.Validation.Add(StrToInt(part));
for i := 1 to CPart2Repetition do
conditionRecord2.Validation.AddRange(conditionRecord1.Validation);
WriteLn(FDebugIndex + 1);
Inc(FDebugIndex);
FPart1 := FPart1 + conditionRecord1.GenerateBlockAssignments;
FPart2 := FPart2 + conditionRecord2.GenerateBlockAssignments;
conditionRecord1.Free;
conditionRecord2.Free;
{$ifdef debug}
WriteLn('------------------------');
WriteLn;
{$endif}
end;
procedure THotSprings.Finish;

View File

@ -152,6 +152,10 @@
<Filename Value="USnowverloadTestCases.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
<Unit>
<Filename Value="UBinomialCoefficientsTestCases.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
</Units>
</ProjectOptions>
<CompilerOptions>

View File

@ -10,7 +10,7 @@ uses
UFloorWillBeLavaTestCases, UClumsyCrucibleTestCases, ULavaductLagoonTestCases, UAplentyTestCases,
UPulsePropagationTestCases, UStepCounterTestCases, USandSlabsTestCases, ULongWalkTestCases,
UNeverTellMeTheOddsTestCases, USnowverloadTestCases, UBigIntTestCases, UPolynomialTestCases,
UPolynomialRootsTestCases;
UPolynomialRootsTestCases, UBinomialCoefficientsTestCases;
{$R *.res}

View File

@ -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 UBinomialCoefficientsTestCases;
{$mode ObjFPC}{$H+}
interface
uses
Classes, SysUtils, fpcunit, testregistry, UBinomialCoefficients;
type
{ TBinomialCoefficientsTestCase }
TBinomialCoefficientsTestCase = class(TTestCase)
private
FBinomialCoefficientCache: TBinomialCoefficientCache;
procedure RunRangeError;
procedure AssertEqualsCalculation(const AN, AK, AExpected: Cardinal);
procedure AssertEqualsCachedRowsCount(const AExpected: Cardinal);
protected
procedure SetUp; override;
procedure TearDown; override;
published
procedure TestZeroChooseZero;
procedure TestNChooseZero;
procedure TestNChooseN;
procedure TestNChooseK;
procedure TestCombined;
procedure TestFullRow;
procedure TestRangeError;
end;
implementation
{ TBinomialCoefficientsTestCase }
procedure TBinomialCoefficientsTestCase.RunRangeError;
begin
FBinomialCoefficientCache.Get(1, 5);
end;
procedure TBinomialCoefficientsTestCase.AssertEqualsCalculation(const AN, AK, AExpected: Cardinal);
begin
AssertEquals('Unexpected calculation result', AExpected, FBinomialCoefficientCache.Get(AN, AK));
end;
procedure TBinomialCoefficientsTestCase.AssertEqualsCachedRowsCount(const AExpected: Cardinal);
begin
AssertEquals('Unexpected cached rows count', AExpected, FBinomialCoefficientCache.GetCachedRowsCount);
end;
procedure TBinomialCoefficientsTestCase.SetUp;
begin
FBinomialCoefficientCache := TBinomialCoefficientCache.Create;
end;
procedure TBinomialCoefficientsTestCase.TearDown;
begin
FBinomialCoefficientCache.Free;
end;
procedure TBinomialCoefficientsTestCase.TestZeroChooseZero;
begin
AssertEqualsCalculation(0, 0, 1);
AssertEqualsCachedRowsCount(1);
end;
procedure TBinomialCoefficientsTestCase.TestNChooseZero;
begin
AssertEqualsCalculation(15, 0, 1);
AssertEqualsCachedRowsCount(16);
end;
procedure TBinomialCoefficientsTestCase.TestNChooseN;
begin
AssertEqualsCalculation(11, 11, 1);
AssertEqualsCachedRowsCount(12);
end;
procedure TBinomialCoefficientsTestCase.TestNChooseK;
begin
AssertEqualsCalculation(8, 3, 56);
AssertEqualsCachedRowsCount(9);
end;
procedure TBinomialCoefficientsTestCase.TestCombined;
begin
AssertEqualsCalculation(5, 1, 5);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(8, 4, 70);
AssertEqualsCachedRowsCount(9);
AssertEqualsCalculation(3, 1, 3);
AssertEqualsCachedRowsCount(9);
end;
procedure TBinomialCoefficientsTestCase.TestFullRow;
begin
AssertEqualsCalculation(5, 0, 1);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(5, 1, 5);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(5, 2, 10);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(5, 3, 10);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(5, 4, 5);
AssertEqualsCachedRowsCount(6);
AssertEqualsCalculation(5, 5, 1);
AssertEqualsCachedRowsCount(6);
end;
procedure TBinomialCoefficientsTestCase.TestRangeError;
begin
AssertException(ERangeError, @RunRangeError);
end;
initialization
RegisterTest('Helper', TBinomialCoefficientsTestCase);
end.

View File

@ -26,6 +26,16 @@ uses
type
{ THotSpringsFullDataTestCase }
THotSpringsFullDataTestCase = class(TEngineBaseTest)
protected
function CreateSolver: ISolver; override;
published
procedure TestPart1;
procedure TestPart2;
end;
{ THotSpringsExampleTestCase }
THotSpringsExampleTestCase = class(TExampleEngineBaseTest)
@ -33,6 +43,7 @@ type
function CreateSolver: ISolver; override;
published
procedure TestPart1;
procedure TestPart2;
end;
{ THotSpringsTestCase }
@ -40,18 +51,29 @@ type
THotSpringsTestCase = class(TSolverTestCase)
protected
function CreateSolver: ISolver; override;
procedure TestSingleLine(const ALine: string; const AValue: Integer);
procedure TestSingleLine(const ALine: string);
published
procedure TestExampleLine1;
procedure TestExampleLine2;
procedure TestExampleLine3;
procedure TestExampleLine4;
procedure TestExampleLine5;
procedure TestExampleLine6;
procedure TestExampleLine1Part1;
procedure TestExampleLine2Part1;
procedure TestExampleLine3Part1;
procedure TestExampleLine4Part1;
procedure TestExampleLine5Part1;
procedure TestExampleLine6Part1;
procedure TestExampleLine1Part2;
procedure TestExampleLine2Part2;
procedure TestExampleLine3Part2;
procedure TestExampleLine4Part2;
procedure TestExampleLine5Part2;
procedure TestExampleLine6Part2;
end;
implementation
procedure THotSpringsFullDataTestCase.TestPart2;
begin
AssertEquals(-1, FSolver.GetResultPart2);
end;
{ THotSpringsExampleTestCase }
function THotSpringsExampleTestCase.CreateSolver: ISolver;
@ -64,6 +86,11 @@ begin
AssertEquals(21, FSolver.GetResultPart1);
end;
procedure THotSpringsExampleTestCase.TestPart2;
begin
AssertEquals(525152, FSolver.GetResultPart2);
end;
{ THotSpringsTestCase }
function THotSpringsTestCase.CreateSolver: ISolver;
@ -71,42 +98,83 @@ begin
Result := THotSprings.Create;
end;
procedure THotSpringsTestCase.TestSingleLine(const ALine: string; const AValue: Integer);
procedure THotSpringsTestCase.TestSingleLine(const ALine: string);
begin
FSolver.Init;
FSolver.ProcessDataLine(ALine);
FSolver.Finish;
AssertEquals(AValue, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine1;
procedure THotSpringsTestCase.TestExampleLine1Part1;
begin
TestSingleLine('???.### 1,1,3', 1);
TestSingleLine('???.### 1,1,3');
AssertEquals(1, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine2;
procedure THotSpringsTestCase.TestExampleLine2Part1;
begin
TestSingleLine('.??..??...?##. 1,1,3', 4);
TestSingleLine('.??..??...?##. 1,1,3');
AssertEquals(4, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine3;
procedure THotSpringsTestCase.TestExampleLine3Part1;
begin
TestSingleLine('?#?#?#?#?#?#?#? 1,3,1,6', 1);
TestSingleLine('?#?#?#?#?#?#?#? 1,3,1,6');
AssertEquals(1, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine4;
procedure THotSpringsTestCase.TestExampleLine4Part1;
begin
TestSingleLine('????.#...#... 4,1,1', 1);
TestSingleLine('????.#...#... 4,1,1');
AssertEquals(1, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine5;
procedure THotSpringsTestCase.TestExampleLine5Part1;
begin
TestSingleLine('????.######..#####. 1,6,5', 4);
TestSingleLine('????.######..#####. 1,6,5');
AssertEquals(4, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine6;
procedure THotSpringsTestCase.TestExampleLine6Part1;
begin
TestSingleLine('?###???????? 3,2,1', 10);
TestSingleLine('?###???????? 3,2,1');
AssertEquals(10, FSolver.GetResultPart1);
end;
procedure THotSpringsTestCase.TestExampleLine1Part2;
begin
TestSingleLine('???.### 1,1,3');
AssertEquals(1, FSolver.GetResultPart2);
end;
procedure THotSpringsTestCase.TestExampleLine2Part2;
begin
TestSingleLine('.??..??...?##. 1,1,3');
AssertEquals(16384, FSolver.GetResultPart2);
end;
procedure THotSpringsTestCase.TestExampleLine3Part2;
begin
TestSingleLine('?#?#?#?#?#?#?#? 1,3,1,6');
AssertEquals(1, FSolver.GetResultPart2);
end;
procedure THotSpringsTestCase.TestExampleLine4Part2;
begin
TestSingleLine('????.#...#... 4,1,1');
AssertEquals(16, FSolver.GetResultPart2);
end;
procedure THotSpringsTestCase.TestExampleLine5Part2;
begin
TestSingleLine('????.######..#####. 1,6,5');
AssertEquals(2500, FSolver.GetResultPart2);
end;
procedure THotSpringsTestCase.TestExampleLine6Part2;
begin
TestSingleLine('?###???????? 3,2,1');
AssertEquals(506250, FSolver.GetResultPart2);
end;
initialization