{
  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;

var
  BinomialCoefficients: TBinomialCoefficientCache;

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;

initialization
  BinomialCoefficients := TBinomialCoefficientCache.Create;

finalization
  BinomialCoefficients.Free;

end.