C++ :

#include <cstdio>
#include <cstring>

using namespace std ;

char data[1026<<1] ;

char change( char a , char b ) {
    if( a != b )return 'F' ;
    if( a == '0' ) return 'B' ;
    if( a == '1' ) return 'I' ;
    return a ;
}

char dfs( int deep , int idx ) {
    char c ;
    if( deep == 0 ) c = change(data[idx],data[idx]) ;
    else c = change( dfs(deep-1 , idx*2+1) , dfs( deep-1 , idx*2) ) ;//参数从右边往左边传
    printf("%c" , c ) ;
    return c ;
}

int main() {
    int deep ; scanf("%d" , &deep ) ;
    scanf("%s" , data + (1<<deep) ) ;
    dfs( deep , 1 ) ;
}

Pascal :

var f:array[1..1024] of char;
  i,k,n:integer;
  c:char;
  function lastorder(i,j,n:integer):char;
    var lc,rc:char;
    begin
      if n=0 then lastorder:=f[ i ]
      else begin
      lc:=lastorder(i,(i+j) div 2,n-1);
      write(lc);
      rc:=lastorder((i+j) div 2+1,j,n-1);
      write(rc);
      if lc=rc then lastorder:=lc else lastorder:='F';
      end;
    end;
begin
  { assign(input,'fbi.in');
   reset(input);}
   readln(n);
   k:=1;
   for i:=1 to n do k:=k*2;
   for i:=1 to k do
   begin
     read(c);
     if c='0' then f[ i ]:='B' else f[ i ]:='I'
     end;
  readln;
  //close(input);
  //assign(output,'fbi.out');
  //rewrite(output);
  writeln(lastorder(1,k,n));
  //close(output);
end.

Java :

import java.util.Scanner;
public class Main {
	/**
	 * @param args
	 * @throws IOException 
	 * @throws NumberFormatException 
	 */
	static int s,t,A,B;
	public static void main(String[] args){
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int N=in.nextInt();
		String s=in.next();
		fbi(s);
	}
	public static char fbi(String s){
        if (s.length()==1){
            if (s.charAt(0)=='0'){
                System.out.print('B');
                return 'B';
            }else {
                System.out.print('I');
                return 'I';
            }
        }else {
            char left=fbi(s.substring(0,s.length()/2));
            char right=fbi(s.substring(s.length()/2));
            if (left=='B'&&right=='B'){
                System.out.print('B');
                return 'B';
            }else if (left=='I'&&right=='I'){
                System.out.print('I');
                return 'I';
            }else {
                System.out.print('F');
                return 'F';
            }
        }
    }
}