这是一个典型的非数值问题，如果使用非递归算法求解此问题，要设计复杂的算法，编写很长的程序。而使用递归算法可以使整个算法清晰，使程序简洁。本问题分析并建立递归算法的过程是典型的抽取问题本质、建立递归算法 并最终解决非数值问题递归实例。-This is a typical non_numerical value problem.you must design complicated arithmetic and long program if you use non_recursion arithmetic.But if you make use of recursion arithmetic,your arithmetic will be clear.The course of analysing and establish recursion arithmetic is a typical example to take out the principle ,establish recursion arithmetic and solve non_numerical value problem.