POJ 2084 (Catalan数)

卡特兰数三大公式

C(n)=C(n-1)*(4*n-2)/(n+1)

C(n)=C(2n-1,n+1)-C(2n-1,n-1)

C(n)=C(2n,n)/(n+1)

Program p2084;
Const
   F=10000;
Type
   arr=record
       a:array[1..10000] of longint;
       len:longint;
       end;
var
   n,i,j:longint;
   c:array[1..101] of arr;
Procedure Mulpily(a:arr;b:longint;var c:arr);
var
   i,j:longint;
begin
   fillchar(c,sizeof(c),0);
   for i:=1 to a.len do
   begin
      inc(c.a[i],a.a[i]*b);
      inc(c.a[i+1],c.a[i] div F);
      c.a[i]:=c.a[i] mod F;
   end;
   c.len:=a.len;
   while c.a[c.len+1]>0 do
   begin
      inc(c.len);
      inc(c.a[c.len+1],c.a[c.len] div F);
      c.a[c.len]:=c.a[c.len] mod F;
   end;
   while (c.len>1) and (c.a[c.len]=0) do dec(c.len);

end;
Procedure Divede(a:arr;b:longint;var c:arr);
var
   i,j,d:longint;
begin
   fillchar(c,sizeof(c),0);
   d:=0;
   for i:=a.len downto 1 do
   begin
      d:=d*F+a.a[i];
      c.a[i]:=d div b;
      d:=d mod b;
   end;
   c.len:=a.len;
   while (c.len>1) and (c.a[c.len]=0) do dec(c.len);

end;
Procedure prin(a:arr);
var
   i,j:longint;
begin
   write(a.a[a.len]);
   for i:=a.len-1 downto 1 do
   begin
      if a.a[i]<1000 then write('0');
      if a.a[i]<100 then write('0');
      if a.a[i]<10 then write('0');
      write(a.a[i]);
   end;
   writeln;
end;
begin
   fillchar(c,sizeof(c),0);
   c[1].len:=1;
   c[1].a[1]:=1;
   c[2].len:=1;
   c[2].a[1]:=1;
   for i:=3 to 101 do
   begin
      Mulpily(c[i-1],4*i-2,c[i]);
      divede(c[i],i+1,c[i]);
   end;
   read(n);
   while (n<>-1) do
   begin
      prin(c[n+1]);
      read(n);
   end;

end.