petak

MODULE petak;
FROM InOut IMPORT WriteString, WriteLn, WriteInt, ReadInt;
CONST maxR=20;
      maxN=30;
TYPE niz=ARRAY [0..maxN] OF INTEGER;

PROCEDURE grec(n,r: INTEGER): INTEGER; FORWARD;
PROCEDURE frec(n,r:INTEGER):INTEGER;
BEGIN
  IF n<r THEN
    RETURN 2
  ELSE
    IF ODD(n) THEN
      RETURN frec(n-2,r)-grec(n-1,r)+frec(n-r+1,r)-grec(n-r,r)
    ELSE
      RETURN -frec(n-1,r)+grec(n-1,r)-grec(n-2,r)-frec(n-r,r)+grec(n-r,r);
    END;
  END;
END frec;
PROCEDURE grec(n,r:INTEGER):INTEGER;
BEGIN
  IF n<r THEN
    RETURN -1
  ELSE
    RETURN 2*grec(n-1,r)-2*frec(n-r,r)+grec(n-r+1,r)
  END;
END grec;

PROCEDURE frec2(n,r: INTEGER): INTEGER;
  PROCEDURE F(f,g: niz; i:INTEGER): INTEGER;
  VAR j: INTEGER;
  BEGIN
  IF i>n THEN
    RETURN f[r]
  ELSE
    IF ODD(i) THEN
      f[r]:=f[r-2]-g[r-1]+f[1]-g[0];
    ELSE
      f[r]:=-f[r-1]+g[r-1]-g[r-2]-f[0]+g[0];
    END;
      g[r]:=2*g[r-1]-2*f[0]+g[1];
      FOR j:=0 TO r-1 DO
        f[j]:=f[j+1];
        g[j]:=g[j+1];
      END;
      RETURN F(f,g,i+1);
    END;
  END F;
VAR f,g:niz;
    j: INTEGER;
BEGIN
  IF n<r THEN
    RETURN 2
  ELSE
    FOR j:=0 TO r-1 DO
      f[j]:=2;
      g[j]:=-1;
    END;
    RETURN F(f,g,r);
  END;
END frec2;

PROCEDURE fiter(n,r: INTEGER):INTEGER;
VAR f,g:niz;
    i,j: INTEGER;
BEGIN
  FOR i:=0 TO r-1 DO
    f[i]:=2;
    g[i]:=-1;
  END;
  IF n<r THEN
    RETURN f[n]
  ELSE
    FOR i:=r TO n DO
      IF ODD(i) THEN
        f[r]:=f[r-2]-g[r-1]+f[1]-g[0];
      ELSE
        f[r]:=-f[r-1]+g[r-1]-g[r-2]-f[0]+g[0];
      END;
      g[r]:=2*g[r-1]-2*f[0]+g[1];
      FOR j:=0 TO r-1 DO
        f[j]:=f[j+1];
        g[j]:=g[j+1];
      END;
     END;
     RETURN f[r];
  END;
END fiter;

VAR n,r: INTEGER;
BEGIN
  REPEAT
    WriteString('Unesite n (0<=n<= ');
    WriteInt(maxN,1);
    WriteString('): ');
    ReadInt(n);
    WriteLn;
  UNTIL (0<=n) AND (n<=maxN);
  REPEAT
    WriteString('Unesite r (5<=r<= ');
    WriteInt(maxR,1);
    WriteString('): ');
    ReadInt(r);
    WriteLn;
  UNTIL (0<=r) AND (r<=maxR);
  WriteString('frec1(n,r) = ');
  WriteInt(frec(n,r),0);
  WriteLn;
  WriteString('frec2(n,r) = ');
  WriteInt(frec2(n,r),0);
  WriteLn;
  WriteString('fiter(n,r) = ');
  WriteInt(fiter(n,r),0);
  WriteLn;
END petak.