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

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
  6 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
  7 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 24  
 25 #define ms0(a) memset(a,0,sizeof(a))
 26 #define msI(a) memset(a,0x3f,sizeof(a))
 27 #define msM(a) memset(a,-1,sizeof(a))
 28 
 29 #define MP make_pair
 30 #define PB push_back
 31 #define ft first
 32 #define sd second
 33  
 34 template<typename T1, typename T2>
 35 istream &operator>>(istream &in, pair<T1, T2> &p) {
 36     in >> p.first >> p.second;
 37     return in;
 38 }
 39  
 40 template<typename T>
 41 istream &operator>>(istream &in, vector<T> &v) {
 42     for (auto &x: v)
 43         in >> x;
 44     return in;
 45 }
 46 
 47 template<typename T>
 48 ostream &operator<<(ostream &out, vector<T> &v) {
 49     Rep(i, v.size()) out << v[i] << " 
"[i == v.size() - 1];
 50     return out;
 51 }
 52  
 53 template<typename T1, typename T2>
 54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 55     out << "[" << p.first << ", " << p.second << "]" << "
";
 56     return out;
 57 }
 58 
 59 inline int gc(){
 60     static const int BUF = 1e7;
 61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 62     
 63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 64     return *bg++;
 65 } 
 66 
 67 inline int ri(){
 68     int x = 0, f = 1, c = gc();
 69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
 70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 71     return x*f;
 72 }
 73 
 74 template<class T>
 75 inline string toString(T x) {
 76     ostringstream sout;
 77     sout << x;
 78     return sout.str();
 79 }
 80 
 81 inline int toInt(string s) {
 82     int v;
 83     istringstream sin(s);
 84     sin >> v;
 85     return v;
 86 }
 87 
 88 //min <= aim <= max
 89 template<typename T>
 90 inline bool BETWEEN(const T aim, const T min, const T max) {
 91     return min <= aim && aim <= max;
 92 }
 93 
 94 typedef unsigned int uI;
 95 typedef long long LL;
 96 typedef unsigned long long uLL;
 97 typedef vector< int > VI;
 98 typedef vector< bool > VB;
 99 typedef vector< char > VC;
100 typedef vector< double > VD;
101 typedef vector< string > VS;
102 typedef vector< LL > VL;
103 typedef vector< VI > VVI;
104 typedef vector< VB > VVB;
105 typedef vector< VS > VVS;
106 typedef vector< VL > VVL;
107 typedef vector< VVI > VVVI;
108 typedef vector< VVL > VVVL;
109 typedef pair< int, int > PII;
110 typedef pair< LL, LL > PLL;
111 typedef pair< int, string > PIS;
112 typedef pair< string, int > PSI;
113 typedef pair< string, string > PSS;
114 typedef pair< double, double > PDD;
115 typedef vector< PII > VPII;
116 typedef vector< PLL > VPLL;
117 typedef vector< VPII > VVPII;
118 typedef vector< VPLL > VVPLL;
119 typedef vector< VS > VVS;
120 typedef map< int, int > MII;
121 typedef unordered_map< int, int > uMII;
122 typedef map< LL, LL > MLL;
123 typedef map< string, int > MSI;
124 typedef map< int, string > MIS;
125 typedef multiset< int > mSI;
126 typedef set< int > SI;
127 typedef stack< int > SKI;
128 typedef deque< int > DQI;
129 typedef queue< int > QI;
130 typedef priority_queue< int > PQIMax;
131 typedef priority_queue< int, VI, greater< int > > PQIMin;
132 const double EPS = 1e-8;
133 const LL inf = 0x7fffffff;
134 const LL infLL = 0x7fffffffffffffffLL;
135 const LL mod = 1e9 + 7;
136 const int maxN = 1e4 + 7;
137 const LL ONE = 1;
138 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
139 const LL oddBits = 0x5555555555555555;
140 
141 struct BigInteger{
142     static const LL BASE = 1000000000000000000;
143     static const LL WIDTH = 18;
144     LL num[maxN];
145     int len = 0;
146     
147     BigInteger operator= (const string& str){
148         assert(str != "");
149         LL x;
150         len = (str.length() - 1) / WIDTH + 1;
151         Rep(i, len){
152             LL end = str.length() - i * WIDTH;
153             LL start = max((LL)0, end - WIDTH);
154             sscanf(str.substr(start, end - start).c_str(), "%lld", &x);
155             num[i] = x;
156         }
157         return *this;
158     }
159     
160     bool operator< (const BigInteger& b) const {
161         if(len != b.len) return len < b.len;
162         rFor(i, len - 1, 0) if(num[i] != b.num[i]) return num[i] < b.num[i];
163         return false;
164     }
165     bool operator > (const BigInteger& b) const { return b < *this; }
166     bool operator <= (const BigInteger& b) const { return !(b < *this); }
167     bool operator >= (const BigInteger& b) const { return !(*this < b); }
168     bool operator != (const BigInteger& b) const { return b < *this || *this < b; }
169     bool operator == (const BigInteger& b) const { return !(b < *this) && !(*this < b); }
170     
171     BigInteger operator+ (const BigInteger& b) const {
172         BigInteger ret;
173         
174         for(LL i = 0, g = 0;; ++i){
175             if(g == 0 && i >= len && i >= b.len)break;
176             LL x = g;//进位
177             if(i < len) x += num[i];
178             if(i < b.len) x += b.num[i];
179             ret.num[ret.len++] = x % BASE;
180             g = x / BASE;
181         }
182         return ret;
183     }
184     BigInteger operator += (const BigInteger& b) { return *this = *this + b; }
185     
186     void clear() { len = 0; }
187     
188     void cutLower() { // 数组整体右移一位 
189         For(i, 1, len - 1) num[i - 1] = num[i];
190         num[len - 1] = 0;
191         --len;
192     }
193     
194     string getString() { // 返回字符串表示 
195         string ret; 
196         char buf[20];
197         
198         ret += toString(num[len - 1]);
199         
200         rFor(i, len - 2, 0) {
201             sprintf(buf, "%018lld", num[i]);
202             ret += buf;
203         }
204         return ret;
205     } 
206 };
207 
208 ostream& operator << (ostream& out, const BigInteger& x){
209     out << x.num[x.len - 1];
210     rFor(i, x.len - 2,0){
211         char buf[20];
212         sprintf(buf, "%018lld", x.num[i]);
213         out << buf;
214     }
215     return out;
216 }
217 
218 istream& operator >> (istream& in, BigInteger& x){
219     string s;
220     in >> s;
221     x = s;
222     return in;
223 }
224 
225 struct TrieNode {
226     int pass = 0;
227     int end = 0;
228     int firstIdx = inf;
229     TrieNode* nxt[10];
230 };
231 
232 int T;
233 string str;
234 BigInteger f[3]; 
235 TrieNode* root = new TrieNode();
236 
237 void add(TrieNode* rt, string s, int idx) {
238     TrieNode* p = rt;
239     ++p->pass;
240     
241     Rep(i, s.size()) {
242         if(p->nxt[s[i] - '0'] == NULL) p->nxt[s[i] - '0'] = new TrieNode();
243         p = p->nxt[s[i] - '0'];
244         ++p->pass;
245         p->firstIdx = min(p->firstIdx, idx);
246     }
247     ++p->end;
248 }
249 
250 int getAns(TrieNode* rt, string s) {
251     TrieNode* p = rt;
252     
253     Rep(i, s.size()) {
254         if(p->nxt[s[i] - '0'] == NULL) return -1;
255         p = p->nxt[s[i] - '0'];
256     }
257     return p->firstIdx;
258 }
259 
260 int main() {
261     //freopen("MyOutput.txt","w",stdout);
262     //freopen("input.txt","r",stdin);
263     INIT();
264     cin >> T;
265     f[0] = f[1] = "1";
266     add(root, "1", 0);
267     
268     For(i, 2, 99999) {
269         f[i % 3] = f[(i + 1) % 3] + f[(i + 2) % 3];
270         if(f[i % 3].len > 4) {
271             f[i % 3].cutLower();
272             f[(i + 1) % 3].cutLower();
273             f[(i + 2) % 3].cutLower();
274         }
275         str = f[i % 3].getString();
276         if(str.size() > 40) str = str.substr(0, 40);
277         
278         add(root, str, i);
279     }
280     
281     For(cs, 1, T) {
282         cin >> str;
283         cout << "Case #" << cs << ": " << getAns(root, str) << endl;
284     }
285     return 0;
286 }
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