UVA 10334 Ray Through Glasses

自己手动画了第三项发现f[3]=5;就猜斐波那契了。实际上光线分为两种距离外界有2面玻璃，1面玻璃 其分别时n-1次反射，n-2次反射形成的

故推出斐波那契。 手动一些f1,f2,f3就OK

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <stack>
#include <queue>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define PI 3.1415926535897932626
using namespace std;
int gcd(int a, int b) {return a % b ==  ? b : gcd(b, a % b);}
const int numlen=;
struct bign {
    int len, s[numlen];
    bign() {
        memset(s, , sizeof(s));
        len = ;
    }
    bign(int num) { *this = num; }
    bign(const char *num) { *this = num; }
    bign operator = (const int num) {
        char s[numlen];
        sprintf(s, "%d", num);
        *this = s;
        return *this;
    }
    bign operator = (const char *num) {
        len = strlen(num);
        while(len >  && num[] == '') num++, len--;
        for(int i = ;i < len; i++) s[i] = num[len-i-] - '';
        return *this;
    }

    void deal() {
        while(len >  && !s[len-]) len--;
    }

    bign operator + (const bign &a) const {
        bign ret;
        ret.len = ;
        int top = max(len, a.len) , add = ;
        for(int i = ;add || i < top; i++) {
            int now = add;
            if(i < len) now += s[i];
            if(i < a.len)   now += a.s[i];
            ret.s[ret.len++] = now%;
            add = now/;
        }
        return ret;
    }
    bign operator - (const bign &a) const {
        bign ret;
        ret.len = ;
        int cal = ;
        for(int i = ;i < len; i++) {
            int now = s[i] - cal;
            if(i < a.len)   now -= a.s[i];
            if(now >= )    cal = ;
            else {
                cal = ; now += ;
            }
            ret.s[ret.len++] = now;
        }
        ret.deal();
        return ret;
    }
    bign operator * (const bign &a) const {
        bign ret;
        ret.len = len + a.len;
        for(int i = ;i < len; i++) {
            for(int j = ;j < a.len; j++)
                ret.s[i+j] += s[i]*a.s[j];
        }
        for(int i = ;i < ret.len; i++) {
            ret.s[i+] += ret.s[i]/;
            ret.s[i] %= ;
        }
        ret.deal();
        return ret;
    }

    bign operator * (const int num) {
//        printf("num = %d\n", num);
        bign ret;
        ret.len = ;
        int bb = ;
        for(int i = ;i < len; i++) {
            int now = bb + s[i]*num;
            ret.s[ret.len++] = now%;
            bb = now/;
        }
        while(bb) {
            ret.s[ret.len++] = bb % ;
            bb /= ;
        }
        ret.deal();
        return ret;
    }

    bign operator / (const bign &a) const {
        bign ret, cur = ;
        ret.len = len;
        for(int i = len-;i >= ; i--) {
            cur = cur*;
            cur.s[] = s[i];
            while(cur >= a) {
                cur -= a;
                ret.s[i]++;
            }
        }
        ret.deal();
        return ret;
    }

    bign operator % (const bign &a) const {
        bign b = *this / a;
        return *this - b*a;
    }

    bign operator += (const bign &a) { *this = *this + a; return *this; }
    bign operator -= (const bign &a) { *this = *this - a; return *this; }
    bign operator *= (const bign &a) { *this = *this * a; return *this; }
    bign operator /= (const bign &a) { *this = *this / a; return *this; }
    bign operator %= (const bign &a) { *this = *this % a; return *this; }

    bool operator < (const bign &a) const {
        if(len != a.len)    return len < a.len;
        for(int i = len-;i >= ; i--) if(s[i] != a.s[i])
            return s[i] < a.s[i];
        return false;
    }
    bool operator > (const bign &a) const  { return a < *this; }
    bool operator <= (const bign &a) const { return !(*this > a); }
    bool operator >= (const bign &a) const { return !(*this < a); }
    bool operator == (const bign &a) const { return !(*this > a || *this < a); }
    bool operator != (const bign &a) const { return *this > a || *this < a; }

    string str() const {
        string ret = "";
        for(int i = ;i < len; i++) ret = char(s[i] + '') + ret;
        return ret;
    }
};
istream& operator >> (istream &in, bign &x) {
    string s;
    in >> s;
    x = s.c_str();
    return in;
}
ostream& operator << (ostream &out, const bign &x) {
    out << x.str();
    return out;
}
bign res[];
void init()
{
    res[]=;res[]=;
    for (int i=;i<;i++)
        res[i]=res[i-]+res[i-];
}
int main()
{
    init();
    int N;
    while (scanf("%d",&N)!=EOF)
    cout<<res[N]<<endl;
    return ;
}