unit Unit1;

interface

uses
   Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants,
   System.Classes, Vcl.Graphics,
   Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.Menus, Vcl.StdCtrls, Vcl.Grids;

type
   TArray = array of Integer;

   TForm1 = class(TForm)
      mnPanel: TMainMenu;
      File1: TMenuItem;
      Help1: TMenuItem;
      Open1: TMenuItem;
      Save1: TMenuItem;
      N1: TMenuItem;
      Exit1: TMenuItem;
      Aboutprogram1: TMenuItem;
      Aboutthedeveloper1: TMenuItem;
      lbDescription: TLabel;
      lbCoordinates: TLabel;
      lbAnswer: TLabel;
      PopupMenu1: TPopupMenu;
      SaveFileDialog: TSaveDialog;
      edInputN: TEdit;
      lbN: TLabel;
      OpenFileDialog: TOpenDialog;
      bAnswer: TButton;
      sgFillMatrix: TStringGrid;
      procedure edInputAKeyPress(Sender: TObject; var Key: Char);
      procedure Aboutprogram1Click(Sender: TObject);
      procedure Aboutthedeveloper1Click(Sender: TObject);
      procedure Exit1Click(Sender: TObject);
      procedure FormCloseQuery(Sender: TObject; var CanClose: Boolean);
      procedure Save1Click(Sender: TObject);
      procedure Open1Click(Sender: TObject);
      function FillArrCoords(CoordsArr: TArray; ArrLength: Integer): Boolean;
      procedure bAnswerClick(Sender: TObject);
      procedure sgFillMatrixDblClvarick(Sender: TObject);
      function CheckN(TextN: String): Boolean;
    procedure FormCreate(Sender: TObject);
   private
      { Private declarations }
   public
      { Public declarations }
   end;

var
   Form1: TForm1;

implementation

{$R *.dfm}

procedure TForm1.Aboutprogram1Click(Sender: TObject);
begin
   ShowMessage
     ('This program will caluclate the smallest side of a N gone, where N entered from the keyboard');
end;

procedure TForm1.Aboutthedeveloper1Click(Sender: TObject);
begin
   ShowMessage
     ('This program was developed by a student of the group 951007 Alexander Voroshilov');
end;

function TForm1.CheckN(TextN: String): Boolean;
var
   N: Integer;
   IsCorrect: Boolean;
begin
   IsCorrect := True;
   try
      N := StrToInt(TextN);
      if (N < 3) or (N > 9) then
      begin
         ShowMessage('Incorrect value of N. N should be from 3 to 9');
         IsCorrect := False;
      end;
   except
      ShowMessage('Empty field or not integer value of N.');
      IsCorrect := False;
   end;
   if not IsCorrect then
      edInputN.Text := '';
   CheckN := IsCorrect;
end;

function CheckPoint(CoordsArr: TArray; i: Integer): Boolean;
const
   ErrorMessage = 'Error. Some points are on one point. Try again ';
var
   j: Integer;
   IsCorrect: Boolean;
begin
   IsCorrect := True;
   j := 0;
   while (j <= i - 2) do
   begin
      if (CoordsArr[j] = CoordsArr[i]) and (CoordsArr[j + 1] = CoordsArr[i + 1])
      then
      begin
         IsCorrect := False;
         ShowMessage(ErrorMessage);
      end;
      j := j + 2;
   end;
   Result := IsCorrect;
end;

function CheckLine(CoordsArr: TArray; i: Integer): Boolean;
const
   ErrorMessage =
     'Error. Some points are on one line, that is not correct for polygon. Try again ';
var
   IsCorrect: Boolean;
begin
   IsCorrect := True;
   // ((y1-y2)*x3+(x2-x1)*y3+(x1*y2-x2*y1)==0) - one line
   if ((CoordsArr[i - 3] - CoordsArr[i - 1]) * CoordsArr[i] +
     (CoordsArr[i - 2] - CoordsArr[i - 4]) * CoordsArr[i + 1] +
     (CoordsArr[i - 4] * CoordsArr[i - 1] - CoordsArr[i - 2] * CoordsArr[i - 3]
     ) = 0) then
   begin
      IsCorrect := False;
      ShowMessage(ErrorMessage);
   end;
   Result := IsCorrect;
end;

function TForm1.FillArrCoords(CoordsArr: TArray; ArrLength: Integer): Boolean;
var
   IsCorrect1: Boolean;
   IsCorrect2: Boolean;
   i: Integer;
   j: Integer;
begin
   i := 0;
   j := 1;
   IsCorrect1 := True;
   IsCorrect2 := True;
   while (i < ArrLength * 2 - 1) do
   begin
      if IsCorrect1 and IsCorrect2 then
      begin
         try
            CoordsArr[i] := StrToInt(sgFillMatrix.Cells[j, (i div 2) + 1]);
            CoordsArr[i + 1] :=
              StrToInt(sgFillMatrix.Cells[(j + 1), (i div 2) + 1]);
            if i >= 2 then
            begin
               IsCorrect1 := CheckPoint(CoordsArr, i);
               if i >= 4 then
                  IsCorrect2 := CheckLine(CoordsArr, i);
            end;
         except
            ShowMessage('Empty fields or not integer coordinates');
            IsCorrect1 := False;
         end;
      end;
      i := i + 2;
   end;
   if IsCorrect1 and IsCorrect2 then
      FillArrCoords := True
   else
      FillArrCoords := False;
end;

function CalculateSize(CoordsFirst: Integer; CoordsSecond: Integer;
  CoordsArr: TArray): Double;
begin
   // side^2 = (х2 — х1)^2 + (y2 — y1)^2
   Result := Sqrt((CoordsArr[CoordsSecond] * CoordsArr[CoordsSecond] +
     CoordsArr[CoordsFirst] * CoordsArr[CoordsFirst] - 2 * CoordsArr
     [CoordsSecond] * CoordsArr[CoordsFirst]) + (CoordsArr[CoordsSecond + 1] *
     CoordsArr[CoordsSecond + 1] + CoordsArr[CoordsFirst + 1] *
     CoordsArr[CoordsFirst + 1] - 2 * CoordsArr[CoordsFirst + 1] *
     CoordsArr[CoordsSecond + 1]));
end;

function FindSide(ArrLength: Integer; CoordsArr: TArray): String;
var
   Size: Double;
   NumberOfXandY: Integer;
   EqualSides: Integer;
   TempSide: Double;
   LastSide: Double;
   FirstPoint: Integer;
   SecondPoint: Integer;
   i: Integer;
   Answer: String;

begin
   EqualSides := 0;
   FirstPoint := 0;
   SecondPoint := ArrLength * 2 - 2;
   // LastSide = side between (x1,y1) and (xLast,yLast)
   LastSide := CalculateSize(FirstPoint, SecondPoint, CoordsArr);
   Size := LastSide;
   NumberOfXandY := ArrLength;
   i := 0;
   while i < ArrLength * 2 - 3 do
   begin
      FirstPoint := i;
      SecondPoint := i + 2;
      TempSide := CalculateSize(FirstPoint, SecondPoint, CoordsArr);
      if (TempSide < Size) then
      begin
         Size := TempSide;
         NumberOfXandY := (i + 2) div 2;
         EqualSides := 0;
      end
      else if (TempSide = Size) then
         EqualSides := EqualSides + 1;
      i := i + 2;
   end;
   Answer := 'The smallest side is ';
   if NumberOfXandY = ArrLength then
      Answer := Answer + '(x' + IntToStr(NumberOfXandY) + ', y' +
        IntToStr(NumberOfXandY) + ') and (x1, y1)'
   else
      Answer := Answer + '(x' + IntToStr(NumberOfXandY) + ', y' +
        IntToStr(NumberOfXandY) + ') and (x' + IntToStr(NumberOfXandY + 1) +
        ', y' + IntToStr(NumberOfXandY + 1) + ')';
   Answer := Answer + ' and equal ' + FloatToStr(Size);
   Answer := Answer + #13#10 + IntToStr(EqualSides) +
     ' other sides also have this length';
   FindSide := Answer;
end;

procedure TForm1.bAnswerClick(Sender: TObject);
var
   N: Integer;
   IsCorrect: Boolean;
   CoordsArr: TArray;
begin
   N := StrToInt(edInputN.Text);
   SetLength(CoordsArr, N * 2);
   IsCorrect := FillArrCoords(CoordsArr, N);
   if IsCorrect then
      lbAnswer.Caption := FindSide(N, CoordsArr);
end;

function FileExtensionCheck(var NameOfFile: string): Boolean;
var
   Extension: string;
   i, j: Integer;
begin
   if (pos('.', NameOfFile) = 0) then
   begin
      ShowMessage
        ('Since the extension does not appear in the entered file name, the extension ".txt" is automatically assigned.');
      NameOfFile := NameOfFile + '.txt';
      FileExtensionCheck := True;
   end
   else
   begin
      Extension := '';
      j := length(NameOfFile);
      for i := pos('.', NameOfFile) to j do
         Extension := Extension + NameOfFile[i];
      if (Extension <> '.txt') and (Extension <> '.doc') and
        (Extension <> '.text') then
      begin
         ShowMessage
           ('Attention, an error has occurred! A file with this extension cannot be used. The program supports the extensions: ".txt", ".doc", ".text".');
         FileExtensionCheck := False;
      end
      else
         FileExtensionCheck := True;
   end;
end;

procedure TForm1.edInputAKeyPress(Sender: TObject; var Key: Char);
begin
   if not(Key in [#8, #13, ',', '-', '0' .. '9']) then
   begin
      ShowMessage('Enter numbers!');
      Key := #0;
   end;
end;

procedure TForm1.Exit1Click(Sender: TObject);
begin
   Close;
end;

procedure TForm1.FormCloseQuery(Sender: TObject; var CanClose: Boolean);
begin
   case Application.MessageBox('Are you sure you want to exit the program?',
     'Exit', MB_YESNO) of
      ID_YES:
         ;
   else
      CanClose := False;
   end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin

end;

procedure TForm1.Open1Click(Sender: TObject);
var
   SourceFile: TextFile;
   FileData, FileName: String;
   IsInvalidInput: Boolean;
   i: Integer;
   N: Integer;
   NRow, NCol: Integer;

begin
   if OpenFileDialog.Execute then
   begin
      FileName := OpenFileDialog.FileName;
      IsInvalidInput := FileExtensionCheck(FileName);
      if FileExists(FileName) and IsInvalidInput then
      begin
         try
            AssignFile(SourceFile, FileName);
            Reset(SourceFile);
         except
            ShowMessage
              ('Error! Impossible to open the file. Please, check the file.');
         end;
         if EoF(SourceFile) then
            ShowMessage('Error! The file is empty')
         else
         begin
            ReadLn(SourceFile, FileData);
            edInputN.Text := FileData;
            try
               sgFillMatrixDblClvarick(Sender);
               if (sgFillMatrix.EditorMode) then
               begin
                  N := StrToInt(FileData);
                  edInputN.Text := IntToStr(N);
                  for NRow := 1 to sgFillMatrix.RowCount do
                  begin
                     i := 1;
                     ReadLn(SourceFile, FileData);
                     for NCol := 1 to N - 1 do
                     begin
                        while (FileData[i] in [',', '0' .. '9']) do
                        begin
                           sgFillMatrix.Cells[NCol, NRow] :=
                             sgFillMatrix.Cells[NCol, NRow] + FileData[i];
                           Inc(i);
                        end;
                        Inc(i);
                     end;
                  end
               end;
            except
               ShowMessage('Error! Invalid N');
            end
         end;
         CloseFile(SourceFile);
      end
      else if IsInvalidInput then
         ShowMessage('Error! The file is not found.');
   end;
end;

procedure TForm1.Save1Click(Sender: TObject);
var
   AnswerFile: TextFile;
   FileName: string;
   IsInvalidInput: Boolean;

begin
   if SaveFileDialog.Execute then
   begin
      FileName := SaveFileDialog.FileName;
      IsInvalidInput := FileExtensionCheck(FileName);
      if FileExists(FileName) and IsInvalidInput then
      begin
         AssignFile(AnswerFile, SaveFileDialog.FileName);
         Rewrite(AnswerFile);
         Write(AnswerFile, lbAnswer.Caption);
         CloseFile(AnswerFile);
      end
      else if IsInvalidInput then
         ShowMessage('Error! The file is not found.');
   end;
end;

procedure TForm1.sgFillMatrixDblClvarick(Sender: TObject);
var
   NRow: Integer;
begin
   if (CheckN(edInputN.Text)) then
   begin
      sgFillMatrix.RowCount := StrToInt(edInputN.Text) + 1;
      sgFillMatrix.EditorMode := True;
      sgFillMatrix.Options := sgFillMatrix.Options + [goEditing] + [goTabs];
      sgFillMatrix.Cells[0, 0] := '=)';
      sgFillMatrix.Cells[1, 0] := 'x';
      sgFillMatrix.Cells[2, 0] := 'y';
      for NRow := 1 to sgFillMatrix.RowCount - 1 do
         sgFillMatrix.Cells[0, NRow] := IntToStr(NRow) + ' coord';
      bAnswer.Visible := True;
   end
end;

end.