[hdu5351]找规律,大整数模板
题意:f(1)="a",f(2)="b",f(i)=f(i-1)+f(i-2),"+"表示连接符。给定n,m,求f(n)的前m个字符的“next值”。
思路:并不知道如何一步步推出结论,只能打个表找找规律了:找到最小的i使得f(i)>m+1,则答案就是m-f(i-2)。然后就是大整数模板了
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 | #include <map> #include <set> #include <cmath> #include <ctime> #include <deque> #include <queue> #include <vector> #include <cstdio> #include <string> #include <cstdlib> #include <cstring> #include <iostream> #include <algorithm> using namespace std; #define X first #define Y second #define pb push_back #define mp make_pair #define all(a) (a).begin(), (a).end() #define fillchar(a, x) memset(a, x, sizeof(a)) typedef long long ll; typedef pair< int , int > pii; typedef unsigned long long ull; #ifndef ONLINE_JUDGE void RI(vector< int >&a, int n){a.resize(n); for ( int i=0;i<n;i++) scanf ( "%d" ,&a[i]);} void RI(){} void RI( int &X){ scanf ( "%d" ,&X);} template < typename ...R> void RI( int &f,R&...r){RI(f);RI(r...);} void RI( int *p, int *q){ int d=p<q?1:-1; while (p!=q){ scanf ( "%d" ,p);p+=d;}} void print(){cout<<endl;} template < typename T> void print( const T t){cout<<t<<endl;} template < typename F, typename ...R> void print( const F f, const R...r){cout<<f<< ", " ;print(r...);} template < typename T> void print(T*p, T*q){ int d=p<q?1:-1; while (p!=q){cout<<*p<< ", " ;p+=d;}cout<<endl;} #endif template < typename T> bool umax(T&a, const T&b){ return b<=a? false :(a=b, true );} template < typename T> bool umin(T&a, const T&b){ return b>=a? false :(a=b, true );} template < typename T> void V2A(T a[], const vector<T>&b){ for ( int i=0;i<b.size();i++)a[i]=b[i];} template < typename T> void A2V(vector<T>&a, const T b[]){ for ( int i=0;i<a.size();i++)a[i]=b[i];} const double PI = acos (-1.0); const int INF = 1e9 + 7; /* -------------------------------------------------------------------------------- */ struct BigInt { const static int maxI = 1e8; const static int Len = 8; typedef vector< int > vi; typedef long long LL; vi num; bool symbol; BigInt() { num.clear(); symbol = 0; } BigInt( int x) { symbol = 0; if (x < 0) { symbol = 1; x = -x; } num.push_back(x % maxI); if (x >= maxI) num.push_back(x / maxI); } BigInt( bool s, vi x) { symbol = s; num = x; } BigInt( char s[]) { int len = strlen (s), x = 1, sum = 0, p = s[0] == '-' ; symbol = p; for ( int i = len - 1; i >= p; i--) { sum += (s[i] - '0' ) * x; x *= 10; if (x == 1e8 || i == p) { num.push_back(sum); sum = 0; x = 1; } } while (num.back() == 0 && num.size() > 1) num.pop_back(); } void push( int x) { num.push_back(x); } BigInt abs () const { return BigInt( false , num); } bool smaller( const vi &a, const vi &b) const { if (a.size() != b.size()) return a.size() < b.size(); for ( int i = a.size() - 1; i >= 0; i--) { if (a[i] != b[i]) return a[i] < b[i]; } return 0; } bool operator < ( const BigInt &p) const { if (symbol && !p.symbol) return true ; if (!symbol && p.symbol) return false ; if (symbol && p.symbol) return smaller(p.num, num); return smaller(num, p.num); } bool operator > ( const BigInt &p) const { return p < * this ; } bool operator == ( const BigInt &p) const { return !(p < * this ) && !(* this < p); } bool operator >= ( const BigInt &p) const { return !(* this < p); } bool operator <= ( const BigInt &p) const { return !(p < * this ); } vi add( const vi &a, const vi &b) const { vi c; c.clear(); int x = 0; for ( int i = 0; i < a.size(); i++) { x += a[i]; if (i < b.size()) x += b[i]; c.push_back(x % maxI); x /= maxI; } for ( int i = a.size(); i < b.size(); i++) { x += b[i]; c.push_back(x % maxI); x /= maxI; } if (x) c.push_back(x); while (c.back() == 0 && c.size() > 1) c.pop_back(); return c; } vi sub( const vi &a, const vi &b) const { vi c; c.clear(); int x = 1; for ( int i = 0; i < b.size(); i++) { x += maxI + a[i] - b[i] - 1; c.push_back(x % maxI); x /= maxI; } for ( int i = b.size(); i < a.size(); i++) { x += maxI + a[i] - 1; c.push_back(x % maxI); x /= maxI; } while (c.back() == 0 && c.size() > 1) c.pop_back(); return c; } vi mul( const vi &a, const vi &b) const { vi c; c.resize(a.size() + b.size()); for ( int i = 0; i < a.size(); i++) { for ( int j = 0; j < b.size(); j++) { LL tmp = (LL)a[i] * b[j] + c[i + j]; c[i + j + 1] += tmp / maxI; c[i + j] = tmp % maxI; } } while (c.back() == 0 && c.size() > 1) c.pop_back(); return c; } vi div ( const vi &a, const vi &b) const { vi c(a.size()), x(1, 0), y(1, 0), z(1, 0), t(1, 0); y.push_back(1); for ( int i = a.size() - 1; i >= 0; i--) { z[0] = a[i]; x = add(mul(x, y), z); if (smaller(x, b)) continue ; int l = 1, r = maxI - 1; while (l < r) { int m = (l + r + 1) >> 1; t[0] = m; if (smaller(x, mul(b, t))) r = m - 1; else l = m; } c[i] = l; t[0] = l; x = sub(x, mul(b, t)); } while (c.back() == 0 && c.size() > 1) c.pop_back(); return c; } BigInt operator + ( const BigInt &p) const { if (!symbol && !p.symbol) return BigInt( false , add(num, p.num)); if (!symbol && p.symbol) { return * this >= p. abs () ? BigInt( false , sub(num, p.num)) : BigInt( true , sub(p.num, num)); } if (symbol && !p.symbol) { return (* this ). abs () > p ? BigInt( true , sub(num, p.num)) : BigInt( false , sub(p.num, num)); } return BigInt( true , add(num, p.num)); } BigInt operator - ( const BigInt &p) const { return * this + BigInt(!p.symbol, p.num); } BigInt operator * ( const BigInt &p) const { BigInt res(symbol ^ p.symbol, mul(num, p.num)); if (res.symbol && res.num.size() == 1 && res.num[0] == 0) res.symbol = false ; return res; } BigInt operator / ( const BigInt &p) const { if (p == BigInt(0)) return p; BigInt res(symbol ^ p.symbol, div (num, p.num)); if (res.symbol && res.num.size() == 1 && res.num[0] == 0) res.symbol = false ; return res; } BigInt operator % ( const BigInt &p) const { return * this - * this / p * p; } void show() const { if (symbol) putchar ( '-' ); printf ( "%d" , num[num.size() - 1]); for ( int i = num.size() - 2; i >= 0; i--) { printf ( "%08d" , num[i]); } putchar ( '\n' ); } int TotalDigit() const { int x = num[num.size() - 1] / 10, t = 1; while (x) { x /= 10; t++; } return t + (num.size() - 1) * Len; } }; const int md = 258280327; BigInt f[1234]; char s[1000]; void pre_init() { f[0] = 0; f[1] = f[2] = 1; for ( int i = 3; i <= 1111; i ++) { f[i] = f[i - 1] + f[i - 2]; } } int main() { #ifndef ONLINE_JUDGE freopen ( "in.txt" , "r" , stdin); //freopen("out.txt", "w", stdout); #endif // ONLINE_JUDGE pre_init(); int T; cin >> T; while (T --) { int n; cin >> n; scanf ( "%s" , s); BigInt buf(s); int L = 1, R = 1111; while (L < R) { int M = (L + R) >> 1; if (f[M] > buf + 1) R = M; else L = M + 1; } ((buf - f[L - 2]) % md).show(); } return 0; } |