算法：阶乘的五种算法

背景

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