#include <vector> #include <iostream> #include <sstream> #include <math.h> #include <sys/time.h> #include <cstdlib> #include <algorithm> #include <cassert> #include <cstring> #include <fstream> #include <set> #define FOR(i,a,b) for(__typeof(b) i=(a);i<(b);++i) #define REP(i,a) FOR(i,0,a) #define FOREACH(x,c) for(__typeof(c.begin()) x=c.begin();x != c.end(); x++) #define ALL(c) c.begin(),c.end() #define CLEAR(c) memset(c,0,sizeof(c)) #define SIZE(c) (int) ((c).size()) #define PB push_back #define MP make_pair #define X first #define Y second #define ULL unsigned long long #define LL long long #define LD long double #define II pair<int, int> #define DD pair<double, double> #define VC vector #define VI VC<int> #define VVI VC<VI> #define VD VC<double> #define VS VC<string> #define VII VC<II> #define VDD VC<DD> #define DB(a) cerr << #a << ": " << a << endl; using namespace std; template<class T> void print(VC < T > v) {cerr << "[";if (SIZE(v) != 0) cerr << v[0]; FOR(i, 1, SIZE(v)) cerr << "," << v[i]; cerr << "]\n";} template<class T> string i2s(T &x) { ostringstream o; o << x; return o.str(); } VS split(string &s, char c = ' ') {VS all; int p = 0, np; while (np = s.find(c, p), np >= 0) {if (np != p) all.PB(s.substr(p, np - p)); p = np + 1;} if (p < SIZE(s)) all.PB(s.substr(p)); return all;} ULL target; int digits; #define MOD 1000000000000000000ULL ULL modMul(ULL a, ULL b){ VI ad(18,0); VI bd(18,0); VI cd(18,0); REP(i,18){ ad[i] = a%10; bd[i] = b%10; a /= 10; b /= 10; } REP(i,18) REP(j,18-i) cd[i+j] += ad[i]*bd[j]; int mod = 10; for(int i=17; i >= 0; i--){ cd[i] %= mod; mod *= 10; } ULL c = 0; for(int i=17; i >= 0; i--) c = (10*c + cd[i])%MOD; return c; } typedef tuple<ULL,ULL,ULL> Sol; struct Matrix{ ULL data[2][2]; Matrix(ULL a, ULL b, ULL c, ULL d){ data[0][0] = a; data[0][1] = b; data[1][0] = c; data[1][1] = d;} Matrix operator*(Matrix A){ Matrix ret(0,0,0,0); REP(i,2) REP(j,2){ REP(k,2) ret.data[i][j] += modMul(data[i][k], A.data[k][j]); ret.data[i][j] %= MOD; } return ret; } Sol operator*(Sol s){ Sol ret(get<0>(s),0ULL,0ULL); get<1>(ret) = (modMul(data[0][0],get<1>(s)) + modMul(data[0][1],get<2>(s)) ) % MOD; get<2>(ret) = (modMul(data[1][0],get<1>(s)) + modMul(data[1][1],get<2>(s)) ) % MOD; return ret; } Matrix pow(int k){ Matrix ret= *this; REP(i,k-1) ret = ret*(*this); return ret; } }; VC<Sol> baseCase(ULL target, int digits){ VC<Sol> ret; ULL mod = 1; REP(i,digits) mod *= 10; ULL a=0,b=1; ULL ind=0; REP(i,1500){ if (a%mod == target) ret.PB(make_tuple(ind,a,b)); ind++; ULL c = (a+b)%MOD; a = b; b = c; } return ret; } int main(int argc, char *argv[]){ //while(1){ string ns; cin >> ns; digits = SIZE(ns); target = stoull(ns); if (digits <= 3){ VC<Sol> answers = baseCase(target,digits); if (!answers.empty()) cout << get<0>(answers.back()) << endl; else cout << "NIE" << endl; } else{ VC<Sol> sols = baseCase(target%1000,3); ULL step = 1500; ULL mod = 10000; Matrix M(0,1,1,1); M = M.pow(step); int d = 4; while (d <= digits){ VC<Sol> newSols; for(auto s : sols){ REP(i,10){ if (get<1>(s)%mod == target%mod) newSols.PB(s); s = M*s; get<0>(s) += step; } } sols = newSols; step *= 10; mod *= 10; M = M.pow(10); d++; } sort(ALL(sols)); if (!sols.empty()) cout << get<0>(sols.back()) << endl; else cout << "NIE" << endl; } //} return 0; }
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 | #include <vector> #include <iostream> #include <sstream> #include <math.h> #include <sys/time.h> #include <cstdlib> #include <algorithm> #include <cassert> #include <cstring> #include <fstream> #include <set> #define FOR(i,a,b) for(__typeof(b) i=(a);i<(b);++i) #define REP(i,a) FOR(i,0,a) #define FOREACH(x,c) for(__typeof(c.begin()) x=c.begin();x != c.end(); x++) #define ALL(c) c.begin(),c.end() #define CLEAR(c) memset(c,0,sizeof(c)) #define SIZE(c) (int) ((c).size()) #define PB push_back #define MP make_pair #define X first #define Y second #define ULL unsigned long long #define LL long long #define LD long double #define II pair<int, int> #define DD pair<double, double> #define VC vector #define VI VC<int> #define VVI VC<VI> #define VD VC<double> #define VS VC<string> #define VII VC<II> #define VDD VC<DD> #define DB(a) cerr << #a << ": " << a << endl; using namespace std; template<class T> void print(VC < T > v) {cerr << "[";if (SIZE(v) != 0) cerr << v[0]; FOR(i, 1, SIZE(v)) cerr << "," << v[i]; cerr << "]\n";} template<class T> string i2s(T &x) { ostringstream o; o << x; return o.str(); } VS split(string &s, char c = ' ') {VS all; int p = 0, np; while (np = s.find(c, p), np >= 0) {if (np != p) all.PB(s.substr(p, np - p)); p = np + 1;} if (p < SIZE(s)) all.PB(s.substr(p)); return all;} ULL target; int digits; #define MOD 1000000000000000000ULL ULL modMul(ULL a, ULL b){ VI ad(18,0); VI bd(18,0); VI cd(18,0); REP(i,18){ ad[i] = a%10; bd[i] = b%10; a /= 10; b /= 10; } REP(i,18) REP(j,18-i) cd[i+j] += ad[i]*bd[j]; int mod = 10; for(int i=17; i >= 0; i--){ cd[i] %= mod; mod *= 10; } ULL c = 0; for(int i=17; i >= 0; i--) c = (10*c + cd[i])%MOD; return c; } typedef tuple<ULL,ULL,ULL> Sol; struct Matrix{ ULL data[2][2]; Matrix(ULL a, ULL b, ULL c, ULL d){ data[0][0] = a; data[0][1] = b; data[1][0] = c; data[1][1] = d;} Matrix operator*(Matrix A){ Matrix ret(0,0,0,0); REP(i,2) REP(j,2){ REP(k,2) ret.data[i][j] += modMul(data[i][k], A.data[k][j]); ret.data[i][j] %= MOD; } return ret; } Sol operator*(Sol s){ Sol ret(get<0>(s),0ULL,0ULL); get<1>(ret) = (modMul(data[0][0],get<1>(s)) + modMul(data[0][1],get<2>(s)) ) % MOD; get<2>(ret) = (modMul(data[1][0],get<1>(s)) + modMul(data[1][1],get<2>(s)) ) % MOD; return ret; } Matrix pow(int k){ Matrix ret= *this; REP(i,k-1) ret = ret*(*this); return ret; } }; VC<Sol> baseCase(ULL target, int digits){ VC<Sol> ret; ULL mod = 1; REP(i,digits) mod *= 10; ULL a=0,b=1; ULL ind=0; REP(i,1500){ if (a%mod == target) ret.PB(make_tuple(ind,a,b)); ind++; ULL c = (a+b)%MOD; a = b; b = c; } return ret; } int main(int argc, char *argv[]){ //while(1){ string ns; cin >> ns; digits = SIZE(ns); target = stoull(ns); if (digits <= 3){ VC<Sol> answers = baseCase(target,digits); if (!answers.empty()) cout << get<0>(answers.back()) << endl; else cout << "NIE" << endl; } else{ VC<Sol> sols = baseCase(target%1000,3); ULL step = 1500; ULL mod = 10000; Matrix M(0,1,1,1); M = M.pow(step); int d = 4; while (d <= digits){ VC<Sol> newSols; for(auto s : sols){ REP(i,10){ if (get<1>(s)%mod == target%mod) newSols.PB(s); s = M*s; get<0>(s) += step; } } sols = newSols; step *= 10; mod *= 10; M = M.pow(10); d++; } sort(ALL(sols)); if (!sols.empty()) cout << get<0>(sols.back()) << endl; else cout << "NIE" << endl; } //} return 0; } |