UVA 12333 Revenge of Fibonacci

题目链接：https://vjudge.net/problem/UVA-12333

题意摘自《算法禁赛入门经典》

题目大意

　　有一天晚上，你梦到了 Fibonacci，它告诉你一个有趣的 Fibonacci 数。醒来以后，你只记得了它的开头几个数字。你的任务是找出以它开头的最小 Fibonacci 数的序号。例如以 12 开头的最小 Fibonacci 数是 F(25)。输入不超过 40 个数字，输出满足条件的序号。 如果序号小于 100000 的 Fibonacci 数均不满足条件，输出 -1。

分析

　　大整数模拟 + 字典树。

代码如下

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
#define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
#define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
#define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
#define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
#define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
#define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,0x3f,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}

template<typename T>
ostream &operator<<(ostream &out, vector<T> &v) {
    Rep(i, v.size()) out << v[i] << " 
"[i == v.size() - 1];
    return out;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}

template<class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}

inline int toInt(string s) {
    int v;
    istringstream sin(s);
    sin >> v;
    return v;
}

//min <= aim <= max
template<typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
    return min <= aim && aim <= max;
}

typedef unsigned int uI;
typedef long long LL;
typedef unsigned long long uLL;
typedef vector< int > VI;
typedef vector< bool > VB;
typedef vector< char > VC;
typedef vector< double > VD;
typedef vector< string > VS;
typedef vector< LL > VL;
typedef vector< VI > VVI;
typedef vector< VB > VVB;
typedef vector< VS > VVS;
typedef vector< VL > VVL;
typedef vector< VVI > VVVI;
typedef vector< VVL > VVVL;
typedef pair< int, int > PII;
typedef pair< LL, LL > PLL;
typedef pair< int, string > PIS;
typedef pair< string, int > PSI;
typedef pair< string, string > PSS;
typedef pair< double, double > PDD;
typedef vector< PII > VPII;
typedef vector< PLL > VPLL;
typedef vector< VPII > VVPII;
typedef vector< VPLL > VVPLL;
typedef vector< VS > VVS;
typedef map< int, int > MII;
typedef unordered_map< int, int > uMII;
typedef map< LL, LL > MLL;
typedef map< string, int > MSI;
typedef map< int, string > MIS;
typedef multiset< int > mSI;
typedef set< int > SI;
typedef stack< int > SKI;
typedef deque< int > DQI;
typedef queue< int > QI;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-8;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e4 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

struct BigInteger{
    static const LL BASE = 1000000000000000000;
    static const LL WIDTH = 18;
    LL num[maxN];
    int len = 0;
    
    BigInteger operator= (const string& str){
        assert(str != "");
        LL x;
        len = (str.length() - 1) / WIDTH + 1;
        Rep(i, len){
            LL end = str.length() - i * WIDTH;
            LL start = max((LL)0, end - WIDTH);
            sscanf(str.substr(start, end - start).c_str(), "%lld", &x);
            num[i] = x;
        }
        return *this;
    }
    
    bool operator< (const BigInteger& b) const {
        if(len != b.len) return len < b.len;
        rFor(i, len - 1, 0) if(num[i] != b.num[i]) return num[i] < b.num[i];
        return false;
    }
    bool operator > (const BigInteger& b) const { return b < *this; }
    bool operator <= (const BigInteger& b) const { return !(b < *this); }
    bool operator >= (const BigInteger& b) const { return !(*this < b); }
    bool operator != (const BigInteger& b) const { return b < *this || *this < b; }
    bool operator == (const BigInteger& b) const { return !(b < *this) && !(*this < b); }
    
    BigInteger operator+ (const BigInteger& b) const {
        BigInteger ret;
        
        for(LL i = 0, g = 0;; ++i){
            if(g == 0 && i >= len && i >= b.len)break;
            LL x = g;//进位
            if(i < len) x += num[i];
            if(i < b.len) x += b.num[i];
            ret.num[ret.len++] = x % BASE;
            g = x / BASE;
        }
        return ret;
    }
    BigInteger operator += (const BigInteger& b) { return *this = *this + b; }
    
    void clear() { len = 0; }
    
    void cutLower() { // 数组整体右移一位 
        For(i, 1, len - 1) num[i - 1] = num[i];
        num[len - 1] = 0;
        --len;
    }
    
    string getString() { // 返回字符串表示 
        string ret; 
        char buf[20];
        
        ret += toString(num[len - 1]);
        
        rFor(i, len - 2, 0) {
            sprintf(buf, "%018lld", num[i]);
            ret += buf;
        }
        return ret;
    } 
};

ostream& operator << (ostream& out, const BigInteger& x){
    out << x.num[x.len - 1];
    rFor(i, x.len - 2,0){
        char buf[20];
        sprintf(buf, "%018lld", x.num[i]);
        out << buf;
    }
    return out;
}

istream& operator >> (istream& in, BigInteger& x){
    string s;
    in >> s;
    x = s;
    return in;
}

struct TrieNode {
    int pass = 0;
    int end = 0;
    int firstIdx = inf;
    TrieNode* nxt[10];
};

int T;
string str;
BigInteger f[3]; 
TrieNode* root = new TrieNode();

void add(TrieNode* rt, string s, int idx) {
    TrieNode* p = rt;
    ++p->pass;
    
    Rep(i, s.size()) {
        if(p->nxt[s[i] - '0'] == NULL) p->nxt[s[i] - '0'] = new TrieNode();
        p = p->nxt[s[i] - '0'];
        ++p->pass;
        p->firstIdx = min(p->firstIdx, idx);
    }
    ++p->end;
}

int getAns(TrieNode* rt, string s) {
    TrieNode* p = rt;
    
    Rep(i, s.size()) {
        if(p->nxt[s[i] - '0'] == NULL) return -1;
        p = p->nxt[s[i] - '0'];
    }
    return p->firstIdx;
}

int main() {
    //freopen("MyOutput.txt","w",stdout);
    //freopen("input.txt","r",stdin);
    INIT();
    cin >> T;
    f[0] = f[1] = "1";
    add(root, "1", 0);
    
    For(i, 2, 99999) {
        f[i % 3] = f[(i + 1) % 3] + f[(i + 2) % 3];
        if(f[i % 3].len > 4) {
            f[i % 3].cutLower();
            f[(i + 1) % 3].cutLower();
            f[(i + 2) % 3].cutLower();
        }
        str = f[i % 3].getString();
        if(str.size() > 40) str = str.substr(0, 40);
        
        add(root, str, i);
    }
    
    For(cs, 1, T) {
        cin >> str;
        cout << "Case #" << cs << ": " << getAns(root, str) << endl;
    }
    return 0;
}