{
  Solutions to the Advent Of Code.
  Copyright (C) 2023  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 UMirageMaintenance;

{$mode ObjFPC}{$H+}

interface

uses
  Classes, SysUtils, Generics.Collections, USolver;

type

  { TMirageMaintenance }

  TMirageMaintenance = class(TSolver)
  private
    FN: Integer;
    FLagrangePolynomialsInN, FLagrangePolynomialsInMinusOne: specialize TList<Int64>;
    procedure CalcLagrangePolynomials;
  public
    constructor Create;
    destructor Destroy; override;
    procedure ProcessDataLine(const ALine: string); override;
    procedure Finish; override;
    function GetDataFileName: string; override;
    function GetPuzzleName: string; override;
  end;

implementation

{ TMirageMaintenance }

procedure TMirageMaintenance.CalcLagrangePolynomials;
var
  sign1, sign2, i, j: Integer;
begin
  FLagrangePolynomialsInN.Clear;
  FLagrangePolynomialsInMinusOne.Clear;
  if FN mod 2 = 0 then
    sign1 := -1
  else
    sign1 := 1;
  sign2 := 1;

  // Calculates the polynomials in N and -1.
  for i := 0 to FN - 1 do
  begin
    FLagrangePolynomialsInN.Add(sign1);
    sign1 := -sign1;
    FLagrangePolynomialsInMinusOne.Add(sign2);
    sign2 := -sign2;

    if i < FN - FN div 2 then
    begin
      // Multiplies by the non-cancelled numerator terms.
      for j := FN - i + 1 to FN do
        FLagrangePolynomialsInN[i] := FLagrangePolynomialsInN[i] * j;
      // Divides by the non-cancelled denominator terms.
      for j := 2 to i do
        FLagrangePolynomialsInN[i] := FLagrangePolynomialsInN[i] div j;
    end
    else begin
      // Multiplies by the non-cancelled numerator terms.
      for j := i + 1 to FN do
        FLagrangePolynomialsInN[i] := FLagrangePolynomialsInN[i] * j;
      // Divides by the non-cancelled over-counted numerator term.
      FLagrangePolynomialsInN[i] := FLagrangePolynomialsInN[i] div (FN - i);
      // Divides by the non-cancelled denominator terms.
      for j := 2 to FN - i - 1 do
        FLagrangePolynomialsInN[i] := FLagrangePolynomialsInN[i] div j;
    end;

    if i < FN div 2 then
    begin
      // Multiplies by the non-cancelled numerator terms.
      for j := FN - i to FN do
        FLagrangePolynomialsInMinusOne[i] := FLagrangePolynomialsInMinusOne[i] * j;
      // Divides by the non-cancelled denominator terms.
      for j := 2 to i + 1 do
        FLagrangePolynomialsInMinusOne[i] := FLagrangePolynomialsInMinusOne[i] div j;
    end
    else begin
      // Multiplies by the non-cancelled numerator terms.
      for j := i + 2 to FN do
        FLagrangePolynomialsInMinusOne[i] := FLagrangePolynomialsInMinusOne[i] * j;
      // Divides by the non-cancelled denominator terms.
      for j := 2 to FN - i - 1 do
        FLagrangePolynomialsInMinusOne[i] := FLagrangePolynomialsInMinusOne[i] div j;
    end;
  end;
end;

constructor TMirageMaintenance.Create;
begin
  FLagrangePolynomialsInN := specialize TList<Int64>.Create;
  FLagrangePolynomialsInMinusOne := specialize TList<Int64>.Create;
  FN := 0;
end;

destructor TMirageMaintenance.Destroy;
begin
  FLagrangePolynomialsInN.Free;
  FLagrangePolynomialsInMinusOne.Free;
  inherited Destroy;
end;

procedure TMirageMaintenance.ProcessDataLine(const ALine: string);
var
  split: TStringArray;
  i, y: Integer;
  p: Int64;
begin
  split := ALine.Split(' ');
  if Length(split) <> FN then
  begin
    FN := Length(split);
    CalcLagrangePolynomials;
  end;

  for i := 0 to FN - 1 do
  begin
    y := StrToInt(split[i]);
    p := y * FLagrangePolynomialsInN[i];
    Inc(FPart1, p);
    p := y * FLagrangePolynomialsInMinusOne[i];
    Inc(FPart2, p);
  end;
end;

procedure TMirageMaintenance.Finish;
begin

end;

function TMirageMaintenance.GetDataFileName: string;
begin
  Result := 'mirage_maintenance.txt';
end;

function TMirageMaintenance.GetPuzzleName: string;
begin
  Result := 'Day 9: Mirage Maintenance';
end;

end.