【ProjectEuler】ProjectEuler_025

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本文介绍了一个算法挑战，即找出斐波那契数列中第一个拥有1000位数字的项。通过使用C#编程语言，实现了一个递归函数来计算斐波那契数，并成功找到了该数位于数列中的位置。

// Problem 25
// 30 August 2002
// 
// The Fibonacci sequence is defined by the recurrence relation:
// 
// Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.
// Hence the first 12 terms will be:
// 
// F1 = 1
// F2 = 1
// F3 = 2
// F4 = 3
// F5 = 5
// F6 = 8
// F7 = 13
// F8 = 21
// F9 = 34
// F10 = 55
// F11 = 89
// F12 = 144
// The 12th term, F12, is the first term to contain three digits.
// 
// What is the first term in the Fibonacci sequence to contain 1000 digits?

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

namespace projecteuler025
{
    class Program
    {
        static string[] data = new string[1000000];

        static void Main(string[] args)
        {
            F1();
        }

        private static void F1()
        {
            Console.WriteLine(new System.Diagnostics.StackTrace().GetFrame(0).GetMethod());
            DateTime timeStart = DateTime.Now;

            int i = 1;
            while (Fibonacci(i).Length < 1000)
            {
                i++;
            }
            Console.WriteLine("Fibonacci(" + i + ") = " + data[i]);

            Console.WriteLine("Total Milliseconds is " + DateTime.Now.Subtract(timeStart).TotalMilliseconds + "\n\n");
        }

        private static string Fibonacci(int n)
        {
            if (n<=2)
            {
                data[n] = "1";
            }
            else
            {
                data[n] = longAdd(data[n - 1], data[n - 2], 0);
            }
            return data[n];
        }

        /// <summary>
        /// 超大数字表达式加法
        /// </summary>
        /// <param name="s1">数1</param>
        /// <param name="s2">数2</param>
        /// <param name="c">后面的数的进位，范围0~2</param>
        /// <returns></returns>
        private static string longAdd(string s1, string s2, int c)
        {
            //s1,s2的末位Index
            int l1 = s1.Length - 1;
            int l2 = s2.Length - 1;
            int x;

            //如果2个数都不为空
            if (l1 >= 0 && l2 >= 0)
            {
                x = s1[l1] - '0' + s2[l2] - '0' + c;
                return longAdd(s1.Substring(0, l1), s2.Substring(0, l2), x / 10) + (x % 10).ToString();
            }


            //下面的情况，s1和s2中至少有一个为空，我们要做的是找到那个不为空的进行下一步操作
            //把不为空的值放到s1里
            if (l2 >= 0)
            {
                s1 = s2;
                l1 = l2;
            }
            else if (l1 == -1)   //表示全为空，判断最后的进位，如果没进位，返回空白，结束递归
            {
                if (c != 0)
                {
                    return c.ToString();
                }
                return "";
            }

            x = s1[l1] - '0' + c;

            //如果s1只有1位
            if (l1 == 0)
            {
                return x.ToString();
            }

            //如果s1有不止一位
            return longAdd(s1.Substring(0, l1), "", x / 10) + (x % 10).ToString();
        }

    }
}


/*
Void F1()
Fibonacci(4782) = 10700662663827589367649805844573968850836838966321516650132352
03375314520604694040621889147582489792657804694888177591957484336466672569959512
99603046126274809248218614406943305123477444275027378175308757939166619214925918
67595539664228371489431130746995034395470019854326097230672901928705264472437261
17715821825548491120525013201478612965931381792235559657452039506137551467837543
22911960212993404826070617539770684706820289548690266618543512452190036948064135
74474709117076197669456910700980243934396174741037369125032313655321647736970231
67755051595173518460579954919410967778373229665796581646513903488154256310184224
19025984608800011018625555024549393711365165703944762958471454852342595042858242
53060835444354282126110089928637950480068943303097732178348645431132057656598684
56288616808718693835297350643986297640660000723562917905207051164077614812491885
83094594056668833910935094445657635766615161931775379289166158132715961687748798
3821820492520348473874384736771934512787029218636250627816
Total Milliseconds is 7583.463

By GodMoon
*/