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;
}