斐波那契数列(Fibonacci)（递归，非递归）（动态规划，自顶向下，自底向上）

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Fibonacci
{
class Program
{
static void Main(string[] args)
{
Console.WriteLine("Would you like to know which Fibonacci Numbers：");
int number = Convert.ToInt32(Console.ReadLine());
//
Function obj = new Function();
Console.WriteLine();
Console.Write("The {0} Fibonacci number is：{1}", number, obj.Fibonacci(number));
//
Console.WriteLine();
Function obj2 = new Function(number);
Console.Write("The {0} Fibonacci number is：{1}", number, obj2.BottomUpNotRecursion(number));
//
Console.WriteLine();
Console.Write("The {0} Fibonacci number is：{1}", number, obj2.TopDownRecursion(number));
Console.ReadKey();

}
}
}

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Fibonacci
{
class Function
{
private int[] array;

public Function()
{

}

/// <summary>
/// Function
/// </summary>
/// <param name="length"></param>
public Function(int length)
{
if (length > 0)
{
array = new int[length + 1];
array[0] = 1;
array[1] = 1;
}
if (length == 0)
{
array = new int[1];
array[0] = 1;
}
}

/// <summary>
/// Fibonacci数列定义为：
///             无穷数列1，1，2，3，5，8，13，21，34，55，……
///        ┌ 1             n=0
///   F(n)=│ 1             n=1
///        └ F(n-1)+F(n-2) n>1
/// </summary>
/// <param name="number">第几个斐波那契数</param>
/// <returns></returns>
public int Fibonacci(int number)
{
if (number <= 1)
{
return 1;
}
else
{
return Fibonacci(number - 1) + Fibonacci(number - 2);
}
}

/// <summary>
/// 动态规划思想：
///     1.自底向上非递归算法
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public int BottomUpNotRecursion(int number)
{
int copynumber = 0;
if (number < 2)
{
copynumber = 1;
}
else
{
int one = array[0];
int two = array[1];

for (int i = 2; i < array.Length; i++)
{
array[i] = one + two;
one = two;
two = array[i];
copynumber = array[i];
}
}

return copynumber;
}

/// <summary>
///     2.自顶向下递归算法
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public int TopDownRecursion(int number)
{
if (number <= 2)
{
if (number == 0)
return array[0];
if (number == 1)
return array[1];
if (number == 2)
return array[2] = array[0] + array[1];
}
else
{
//递归只是一个“牵引线”，目的是为了让数组储存值。
TopDownRecursion(number - 1);
array[number] = array[number - 1] + array[number - 2];
}
return array[number];
}
}
}