Problem Description The well-known Fibonacci sequence is defined as following:

  Here we regard n as the index of the Fibonacci number F(n).

  This sequence has been studied since the publication of Fibonacci’s book Liber Abaci. So far, many properties of this sequence have been introduced.

  You had been interested in this sequence, while after reading lots of papers about it. You think there’s no need to research in it anymore because of the lack of its unrevealed properties. Yesterday, you decided to study some other sequences like Lucas sequence instead.

  Fibonacci came into your dream last night. “Stupid human beings. Lots of important properties of Fibonacci sequence have not been studied by anyone, for example, from the Fibonacci number 347746739…”

  You woke up and couldn’t remember the whole number except the first few digits Fibonacci told you. You decided to write a program to find this number out in order to continue your research on Fibonacci sequence.  

Input   There are multiple test cases. The first line of input contains a single integer T denoting the number of test cases (T<=50000).

  For each test case, there is a single line containing one non-empty string made up of at most 40 digits. And there won’t be any unnecessary leading zeroes.  

Output   For each test case, output the smallest index of the smallest Fibonacci number whose decimal notation begins with the given digits. If no Fibonacci number with index smaller than 100000 satisfy that condition, output -1 instead – you think what Fibonacci wants to told you beyonds your ability.  

Sample Input

15 1 12 123 1234 12345 9 98 987 9876 98765 89 32 51075176167176176176 347746739 5610  

Sample Output

Case #1: 0 Case #2: 25 Case #3: 226 Case #4: 1628 Case #5: 49516 Case #6: 15 Case #7: 15 Case #8: 15 Case #9: 43764 Case #10: 49750 Case #11: 10 Case #12: 51 Case #13: -1 Case #14: 1233 Case #15: 22374  

Source
2011 Asia Shanghai Regional Contest

题目要求斐波那契数列前100000项的所有数，之后输入一个数对比看其是否为斐波那契数列的某一项的前缀，如果是那就输出对应的第几项，如果不是那就输出-1.（输入最多40个字符）

首先求斐波那契我们应该都会吧！由于输入最多40个字符也就是说最多查询斐波那契数列前40位数，所以我们计算斐波那契数列前40位就ok！不过怎么计算呢？

如果位数超过40位就将位数降1？然后依次循环？

仔细想想！我举个例子：

假若保留3位数字！435+699=1134，699+1134=1833，1134+1833=2976，1833+2976=4800,2976+4800=7767！假若我们超过了第3位，那么从第一个式子开始，我们退一位！结果会是怎样？：69+113=182（才第一步就错了） 113+182=295（继续错）182+295=477（更加错！）；也许有人会说是第一步没进位造成的，那么我们进一个位：69+113+1=183（前三位对了！） 113+183=296（又对了！有希望！）183+296=479（唉，最终还是wa！！哪怕进位了还是只到了第三步就错！！！）

如果我们进位不这样写难道还有更好的办法吗？？？

当然不是！刚才虽然确实是有错误，可是这只是对于第2位造成的误差，等位数多了也一定会造成误差，只不过！！误差只是该位的前几位！当然算的越多可能误差的位数越多，但是误差的位数增长速度并不大！所以我们要算前40位，那么可以到55位再开始保留位数，一定确保前40位肯定没有一丁点误差！！（就是因为这个原因刚开始总是保留40,41,42,43，，45位数，都试过了，但就是w！a！，当我看了题解才发现其实方法完全一样！只是保留的位数不同，这样就导致的精度有了很大区别，因此！！我们发现大数其实也是有精度的。。。还有一点感悟就是精度啥的一定越精越好吧！就好比数组开的越大越好吧，前提是不mle，哈哈）

解决完斐波那契的精度，再来看查询！

由于有查询，而且斐波那契数列的位数很多，我们要想办法去存呀！比对前缀不是trie树吗？，所以把斐波那契数列都存到trie树里面不就得了！

至于trie树没啥好说的了，时间长了会觉得trie树越来越简单的！

ac代码：

#include <iostream>
#include <stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;


struct TrieNode{
	int id;
	TrieNode *next[10];
	TrieNode(){
		id=-1;
		memset(next,0,sizeof next);
	}
}root;

void InsertNode(char *s,int id){
	int k=0;
	TrieNode *p=&root;
	while(s[k]!='\0')
    {
		if(!p->next[s[k]-'0'])p->next[s[k]-'0']=new TrieNode;
		p=p->next[s[k++]-'0'];
		if(p->id == -1)p->id=id;
	}
}

int SearchTrie(char *s){
	int k=0;
	TrieNode *p=&root;
	while(s[k]!='\0' && p->next[s[k]-'0'])p=p->next[s[k++]-'0'];
	if(s[k]!='\0')return -1;
	return p->id;
}

char a[65],b[65],c[65];
void init()
{
    memset(a,'0',sizeof(a));
    memset(b,'0',sizeof(b));
    memset(c,'0',sizeof(c));
    int t=0,num=2;
    a[0]='1',a[1]='\0';b[0]='1',b[1]='\0';
    InsertNode(a,t++);
    InsertNode(b,t++);
    a[1]='0';b[1]='0';
    while(num<100000)
    {
        for(int i=0;i<64;i++)
    {
        if(a[i]+b[i]+c[i]-'0'-'0'-'0'>9)
            c[i+1]+=1,c[i]+=a[i]+b[i]-10-'0'-'0';
        else c[i]+=a[i]+b[i]-'0'-'0';
    }//cout<<"c             "<<c<<endl;
    int bj;
    for(int i=64;i>=0;i--)
    if(c[i]!='0')
    {
        bj=i;break;
    }
    if(bj>55)
    {
        for(int i=0;i<63;i++)
        b[i]=b[i+1],c[i]=c[i+1];
        bj--;
    }
    char jl[65];
    int i;
        for(i=0;i<65;i++)
    {
        jl[i]=c[bj--];
        if(i==39)break;
        if(bj==-1)break;
    }
    jl[i+1]='\0';
    //cout<<jl<<endl;
    InsertNode(jl,t++);
    strcpy(a,b);//cout<<"a      "<<a<<endl;
    strcpy(b,c);//cout<<"b      "<<b<<endl;
    memset(c,'0',sizeof(c));
    num++;
    }
}

int main()
{
    init();
    char x[60];int o=1,t;
   cin>>t;
    while(t--)
    {
        cin>>x;
        printf("Case #%d: %d\n",o++,SearchTrie(x));
    }

    return 0;
}