/*
标题: 黄金连分数
黄金分割数0.61803... 是个无理数，这个常数十分重要，在许多工程问题中会出现。有时需要把这个数字求得很精确。
对于某些精密工程，常数的精度很重要。也许你听说过哈勃太空望远镜，它首次升空后就发现了一处人工加工错误，对那样一个庞然大物，其实只是镜面加工时有比头发丝还细许多倍的一处错误而已，却使它成了“近视眼”!!
言归正传，我们如何求得黄金分割数的尽可能精确的值呢？有许多方法。
比较简单的一种是用连分数：
1
黄金数 = ---------------------
1
1 + -----------------
1
1 + -------------
1
1 + ---------
1 + ...
这个连分数计算的“层数”越多，它的值越接近黄金分割数。
请你利用这一特性，求出黄金分割数的足够精确值，要求四舍五入到小数点后100位。
小数点后3位的值为：0.618
小数点后4位的值为：0.6180
小数点后5位的值为：0.61803
小数点后7位的值为：0.6180340
（注意尾部的0，不能忽略）
你的任务是：写出精确到小数点后100位精度的黄金分割值。
注意：尾数的四舍五入！ 尾数是0也要保留！
显然答案是一个小数，其小数点后有100位数字，请通过浏览器直接提交该数字。
注意：不要提交解答过程，或其它辅助说明类的内容。
*/
This question three points
- Think of Fibonacci number
- Expect large numbers, because enough layers, that is, sufficient number of Fibonacci and the next; the scene can knock out large numbers of addition and subtraction, and division can be accurate to 100 decimal places
- Not with the table to find that two adjacent Fibonacci number divided by deed, 100 decimal place can be, but to a certain extent N, and then further divided by two adjacent 100 after the decimal point is stable ; and according to the experiment, after item 243, and each post 100 is an exact division stable
the answer is
0.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911375
Code needs in a blog post
#include <iostream>
#include <string>
#include <sstream>
#include "../util/BigNumber.h"
using namespace std;
const int N=500;
string fib[N];
int main(int argc, const char *argv[]) {
fib[1] = "1";
fib[2] = "1";
for (int i = 3; i < N ; ++i) {
fib[i] = add(fib[i - 1], fib[i - 2]);
// cout << i << " " << fib[i] << endl;
}
int x=243;
const string &ans = divide(fib[x], fib[x+1], 101);
cout << ans << endl;
return 0;
}
This question is a pit spot to do it very time-consuming, even hundreds of times have to knock half a day.
