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數列定義為：
        ///             無窮數列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">第幾個斐波那契數</param>
        /// <returns></returns>
        public int Fibonacci(int number)
        {
            if (number <= 1)
            {
                return 1;
            }
            else
            {
                return Fibonacci(number - 1) + Fibonacci(number - 2);
            }
        }

        /// <summary>
        /// 動態規劃思想：
        ///     1.自底向上非遞歸算法
        /// </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.自頂向下遞歸算法
        /// </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
            {
                //遞歸只是一個“牽引線”，目的是為了讓數組儲存值。
                TopDownRecursion(number - 1);
                array[number] = array[number - 1] + array[number - 2];
            }
            return array[number];
        }
    }
}