UVA 12333 Revenge of Fibonacci

川长思鸟来 2023-06-04 14:54 27阅读 0赞

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

![ContractedBlock.gif][] ![ExpandedBlockStart.gif][]

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] << " \n"[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 << "]" << "\n";
     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 }

转载于:https://www.cnblogs.com/zaq19970105/p/11386408.html

[https_vjudge.net_problem_UVA-12333]: https://vjudge.net/problem/UVA-12333
[ContractedBlock.gif]: https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif
[ExpandedBlockStart.gif]: /images/20230601/268a169f44194dc78cb5b557df8a7c04.png