Project Euler：Problem 25 1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n?1 + F_n?2, 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 index of the first term in the Fibonacci sequence to contain 1000 digits?

找到第一个1000位的斐波那契数的下标。

涉及到大数的加法。

两个string类型的数做加法，把短的那个数前面补上一定数量的‘0’使得做加法的两个数长度一致，然后从低位开始做加法。

#include <iostream>
#include <string>
using namespace std;

string pl(string a, string b)
{
	string res = "";
	if (a.length() < b.length())
	{
		string t = a;
		a = b;
		b = t;
	}
	int lo = a.length();
	int sh = b.length();
	string s(lo - sh, '0');
	b = s + b;
	int flag = 0;
	for (int i = lo - 1; i >= 0; i--)
	{
		int tmp = a[i] + b[i] - '0' - '0' + flag;
		int low = tmp % 10;
		flag = tmp / 10;
		char a1 = low + '0';
		res = a1 + res;
	}

	if (flag != 0)
		res = "1" + res;
	return res;
}

int main()
{
	string s[10000];
	s[1] = "1";
	s[2] = "1";
	for (int i = 3; i <= 10000; i++)
	{
		s[i] = pl(s[i-1], s[i-2]);
		if (s[i].length() >= 1000)
		{
			cout << i << endl;
			break;
		}
	}

	system("pause");
	return 0;
}