UVa 12333 Revenge of Fibonacci (字典树+大数)

题意：给定一个长度小于40的序列，问你那是Fib数列的哪一项的前缀。

析：首先用大数把Fib数列的前100000-1项算出来，注意，一定不能是100000，要不然会WA的，然后每个数取前40位，不足40位的全取，然后插入到字典树上，

并用一个数组标记是哪一项，最后查询的时候，如果查不到就是无解，否则输出答案。

在我电脑上跑了10秒多，交上去才1秒多。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#define debug() puts("++++");
#define gcd(a, b) __gcd(a, b)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-5;
const int maxn = 40000 + 10;
const int mod = 1000000007;
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, 1, 0, -1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline bool is_in(int r, int c){
  return r >= 0 && r < n && c >= 0 && c < m;
}

struct BigInteger{
  static const int BASE = 100000000;
  static const int WIDTH = 8;
  vector<int> s;

  BigInteger(LL num = 0){ *this = num; }
  BigInteger operator = (LL num){
    s.clear();
    do{
      s.push_back(num % BASE);
      num /= BASE;
    } while(num);
    return *this;
  }
  BigInteger operator = (const string &str){
    s.clear();
    int x, len = (str.length() - 1) / WIDTH + 1;
    for(int i = 0; i < len; ++i){
      int end = str.length() - i * WIDTH;
      int start = max(0, end - WIDTH);
      sscanf(str.substr(start, end-start).c_str(), "%d", &x);
      s.push_back(x);
    }
    return *this;
  }
  friend istream &operator >> (istream &in, BigInteger &x){
    string s;
    if(!(in >> s))  return in;
    x = s;
    return in;
  }

  string getNum(){
    string ss;
    int t = s.back();
    while(t)  ss.push_back(t % 10 + '0'), t /= 10;
    reverse(ss.begin(), ss.end());
    for(int i = s.size()-2; i >= 0; --i){
      char buf[20];
      sprintf(buf, "%08d", s[i]);
      int len = strlen(buf);
      for(int j = 0; j < len; ++j)  ss.push_back(buf[j]);
      if(ss.size() >= 40)  return ss;
    }
    return ss;
  }

  friend ostream &operator << (ostream &out, const BigInteger &x){
    out << x.s.back();
    for(int i = x.s.size()-2; i >= 0; --i){
      char buf[20];
      sprintf(buf, "%08d", x.s[i]);
      int len = strlen(buf);
      for(int j = 0; j < len; ++j)  out << buf[j];
    }
    return out;
  }

  BigInteger operator + (const BigInteger &b) const{
    BigInteger c;
    c.s.clear();
    for(int i = 0, g = 0; ; ++i){
      if(!g && i >= s.size() && i >= b.s.size())  break;
      int x = g;
      if(i < s.size())  x += s[i];
      if(i < b.s.size()) x += b.s[i];
        c.s.push_back(x % BASE);
      g = x / BASE;
    }
    return c;
  }
};
const int maxnode = 40 * 100000 + 10;
const int sigam_size = 10;
struct Tire{
  int ch[maxnode][sigam_size];
  int val[maxnode];
  int sz;
  void init(){
    sz = 1;
    memset(ch, 0, sizeof ch);
    memset(val, 0, sizeof val);
  }
  int idx(char c){ return c - '0'; }

  void Insert(const string &s, int v){
    int u = 0;
    for(int i = 0; i < s.size(); ++i){
      int c = idx(s[i]);
      if(!val[u])  val[u] = v;
      if(!ch[u][c])  ch[u][c] = sz++;
      u = ch[u][c];
    }
    if(!val[u])  val[u] = v;
  }

  int query(const string &s){
    int u = 0;
    for(int i = 0; i < s.size(); ++i){
      int c = idx(s[i]);
      if(!ch[u][c])  return -1;
      u = ch[u][c];
    }
    return val[u] - 1;
  }
};

Tire fib;

void init(){
  fib.init();
  BigInteger a = 1;
  BigInteger b = 1;
  BigInteger c = 1;
  fib.Insert(a.getNum(), 1);
  fib.Insert(a.getNum(), 2);
  for(int i = 2; i < 100000; ++i){
    c = a + b;
    string s = c.getNum();
    if(s.size() > 40)  s = s.substr(0, 40);
    fib.Insert(s, i+1);
    a = b;  b = c;
  }
}

int main(){
  ios::sync_with_stdio(false);
  init();
  int T;  cin >> T;
  for(int kase = 1; kase <= T; ++kase){
    string s;
    cin >> s;
    int ans = fib.query(s);
    cout << "Case #" << kase << ": " << ans << endl;
  }
  return 0;
}