算法：阶乘的五种算法

背景

周末温习了一下递归相关的一些概念，本文先给出阶乘的五种算法。

第一种实现：递归

        private static long RecursiveFac(long n)
        {
            if (n == 0)
            {
                return 1;
            }
            else
            {
                return n * RecursiveFac(n - 1);
            }
        }

第二种实现：递推

        private static long Fac(long n)
        {
            var result = 1;

            for (var i = 1; i <= n; i++)
            {
                result = result * i;
            }

            return result;
        }

第三种实现：尾递归

        private static int TailRecursiveFac(int n, int accumulator)
        {
            if (n == 0)
            {
                return accumulator;
            }

            return Fac(n - 1, n * accumulator);
        }

第四种实现：消除尾递归

        private static int Fac(int n, int accumulator)
        {
            while (true)
            {
                var tempN = n;
                var tempAccumulator = accumulator;

                if (tempN == 0)
                {
                    return tempAccumulator;
                }

                n = tempN - 1;
                accumulator = tempN * tempAccumulator;
            }
        }

第五种实现：堆栈（堆中分配的栈）替换函数栈

        private enum CodeAddress
        {
            Start,
            AfterFirstRecursiveCall
        }

        private class StackFrame
        {
            public long N { get; set; }

            public long FirstRecursiveCallResult { get; set; }

            public CodeAddress CodeAddress { get; set; }
        }

        private static long StackFac(long n)
        {
            var stack = new Stack<StackFrame>();
            stack.Push(new StackFrame
            {
                N = n,
                CodeAddress = CodeAddress.Start
            });

            long result = 0;

            while (stack.Count > 0)
            {
                var current = stack.Peek();

                switch (current.CodeAddress)
                {
                    case CodeAddress.Start:
                        if (current.N == 0)
                        {
                            result = 1;
                            stack.Pop();
                        }
                        else
                        {
                            current.CodeAddress = CodeAddress.AfterFirstRecursiveCall;
                            stack.Push(new StackFrame
                            {
                                N = current.N - 1,
                                CodeAddress = CodeAddress.Start
                            });
                        }
                        break;
                    case CodeAddress.AfterFirstRecursiveCall:
                        current.FirstRecursiveCallResult = result;

                        result = current.N * current.FirstRecursiveCallResult;
                        stack.Pop();
                        break;
                }
            }

            return result;
        }

备注

这里比较有意思的实现是：尾递归和基于堆中的栈的递归，本文先不详细介绍了，后面再细说，有兴趣的朋友先看如下资源：

• Replacing Recursion With a Stack。
• How to replace recursive functions using stack and while-loop to avoid the stack-overflow。
• HOW TO CONVERT A RECURSIVE ALGORITHM TO A NON-RECURSIVE ONE。
• Replace Recursion with Iteration。
• Provide an explanation of recursion, including an example。
• Tail Recursion。
• Understanding Tail Recursion。