PL/SQL :: Oracle 10g Express - Mutating Table Error

Oracle version: 10g express.

case study: one class has many students, only one student has reward.

original design:
drop table student;
drop table class;

[Code]...

questions:

1. If I want insert into student values('stu2','cls1','yes'); I can put a trigger on student to check whether it has only one student in class has reward. This trigger should tell me error: I can not let 'stu2' has 'yes' on reward column. But it will lead Oracle error: ora-04091: mutating table. It seems use "after" or "instead of" trigger can solve this problem, so how to do it?

2. Another way to make sure only one student in a class has reward is change design as:

drop table student;
drop table class;
create table class(
clsid varchar2(9) primary key,
reward_stuid varchar2(9));
create table student(
stuid varchar2(9) primary key,
clsid varchar2(9)

not null references class(cid) on delete cascade);But the question is these two tables has foreign key from each other, is it a good design?.