Abstract
Writing a program with the recursive method is a simple and effective way of program design, making the logic of the program concise and clear. This paper will focus on the analytical program, writing method of the recursive algorithm, as well as the optimization of recursive program. Formula method or mathematical induction can be applied for writing of the recursive algorithm more simply. Meanwhile, either of them could provide the method of tail recursive to deal with the problem lies in recursive algorithm that massive time and space of the system are occupied.
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