// Czy to wejdzie, czy to nie wejdzie? ;d // Ciekawostka: pod oitimetool x=(x*2)%Mod jest 2x wolniejsze niz // x*=2; if(x>=Mod) x -= Mod; #include <bits/stdc++.h> using namespace std; typedef long long LL; template<typename TH> void debug_vars(const char* data, TH head){ cerr << data << "=" << head << "\n"; } template<typename TH, typename... TA> void debug_vars(const char* data, TH head, TA... tail){ while(*data != ',') cerr << *data++; cerr << "=" << head << ","; debug_vars(data+1, tail...); } #ifdef LOCAL #define debug(...) debug_vars(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (__VA_ARGS__) #endif ///////////////////////////////////////////////////////// const int Base = 1000000000; // dziala tylko dla poteg 10 do 10^18 LL mul_mod(LL a, LL b, LL mod){ LL ah = a/Base, al = a%Base, bh = b/Base, bl = b%Base, mh = mod/Base; if(mod < Base){ return (al*bl) % mod; } else { return ((al*bh + ah*bl)%mh*Base + al*bl) % mod; } /*a %= mod; LL res = 0; while(b){ if(b & 1) res = (res+a) % mod; b >>= 1; a <<= 1; if(a>=mod) a -= mod; } return res;*/ } template<LL N> struct Matrix { array<array<LL, N>,N> data; LL Mod; Matrix(LL mod) : Mod(mod) { for(int i = 0; i < N; i++){ for(int j = 0; j < N; j++){ data[i][j] = 0; } } } Matrix(LL mod, vector<vector<LL>> mat) : Mod(mod) { for(int i = 0; i < N; i++){ for(int j = 0; j < N; j++){ data[i][j] = mat[i][j]; } } } Matrix mul(const Matrix other) const { assert(Mod == other.Mod); Matrix result(Mod); for(int j = 0; j < N; j++){ for(int i = 0; i < N; i++){ LL res = 0; for(int k = 0; k < N; k++){ res += mul_mod(data[i][k], other.data[k][j], Mod); if(res >= Mod) res -= Mod; } result.data[i][j] = res; } } return result; } Matrix pow(LL pwr) const { Matrix result(Mod), cur(*this); for(int i = 0; i < N; i++) result.data[i][i] = (1%Mod); while(pwr){ if(pwr & 1) result = result.mul(cur); pwr >>= 1; cur = cur.mul(cur); } return result; } }; LL fib_mod(LL n, LL mod){ if(n <= 1){ return n%mod; } Matrix<2> fibMat = Matrix<2>(mod, {{0,1},{1,1}}).pow(n); return fibMat.data[0][1]; } // okres liczb fibonacciego modulo mod (mod - potega 10) LL get_period(LL mod){ switch(mod){ case 1: return 1; case 10: return 60; case 100: return 300; default: return mod*3/2; } } LL N, K; void input(){ string s; cin >> s; N = (int)s.size(); K = stoll(s); debug(N, K); } int main(){ input(); LL curMod = 1; vector<LL> possibilities{0}; for(int digits = 1; digits <= N; digits++){ curMod *= 10; LL prevPeriod = get_period(curMod/10), thisPeriod = get_period(curMod); vector<LL> nextPoss; for(LL v : possibilities){ for(LL nxt = v; nxt < thisPeriod; nxt += prevPeriod){ LL f = fib_mod(nxt, curMod); if(f == K%curMod){ nextPoss.push_back(nxt); } } } possibilities = nextPoss; debug(curMod, possibilities.size()); if(possibilities.size() == 0){ printf("NIE\n"); return 0; } } printf("%lld\n", possibilities[0] + get_period(curMod)); }
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 | // Czy to wejdzie, czy to nie wejdzie? ;d // Ciekawostka: pod oitimetool x=(x*2)%Mod jest 2x wolniejsze niz // x*=2; if(x>=Mod) x -= Mod; #include <bits/stdc++.h> using namespace std; typedef long long LL; template<typename TH> void debug_vars(const char* data, TH head){ cerr << data << "=" << head << "\n"; } template<typename TH, typename... TA> void debug_vars(const char* data, TH head, TA... tail){ while(*data != ',') cerr << *data++; cerr << "=" << head << ","; debug_vars(data+1, tail...); } #ifdef LOCAL #define debug(...) debug_vars(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (__VA_ARGS__) #endif ///////////////////////////////////////////////////////// const int Base = 1000000000; // dziala tylko dla poteg 10 do 10^18 LL mul_mod(LL a, LL b, LL mod){ LL ah = a/Base, al = a%Base, bh = b/Base, bl = b%Base, mh = mod/Base; if(mod < Base){ return (al*bl) % mod; } else { return ((al*bh + ah*bl)%mh*Base + al*bl) % mod; } /*a %= mod; LL res = 0; while(b){ if(b & 1) res = (res+a) % mod; b >>= 1; a <<= 1; if(a>=mod) a -= mod; } return res;*/ } template<LL N> struct Matrix { array<array<LL, N>,N> data; LL Mod; Matrix(LL mod) : Mod(mod) { for(int i = 0; i < N; i++){ for(int j = 0; j < N; j++){ data[i][j] = 0; } } } Matrix(LL mod, vector<vector<LL>> mat) : Mod(mod) { for(int i = 0; i < N; i++){ for(int j = 0; j < N; j++){ data[i][j] = mat[i][j]; } } } Matrix mul(const Matrix other) const { assert(Mod == other.Mod); Matrix result(Mod); for(int j = 0; j < N; j++){ for(int i = 0; i < N; i++){ LL res = 0; for(int k = 0; k < N; k++){ res += mul_mod(data[i][k], other.data[k][j], Mod); if(res >= Mod) res -= Mod; } result.data[i][j] = res; } } return result; } Matrix pow(LL pwr) const { Matrix result(Mod), cur(*this); for(int i = 0; i < N; i++) result.data[i][i] = (1%Mod); while(pwr){ if(pwr & 1) result = result.mul(cur); pwr >>= 1; cur = cur.mul(cur); } return result; } }; LL fib_mod(LL n, LL mod){ if(n <= 1){ return n%mod; } Matrix<2> fibMat = Matrix<2>(mod, {{0,1},{1,1}}).pow(n); return fibMat.data[0][1]; } // okres liczb fibonacciego modulo mod (mod - potega 10) LL get_period(LL mod){ switch(mod){ case 1: return 1; case 10: return 60; case 100: return 300; default: return mod*3/2; } } LL N, K; void input(){ string s; cin >> s; N = (int)s.size(); K = stoll(s); debug(N, K); } int main(){ input(); LL curMod = 1; vector<LL> possibilities{0}; for(int digits = 1; digits <= N; digits++){ curMod *= 10; LL prevPeriod = get_period(curMod/10), thisPeriod = get_period(curMod); vector<LL> nextPoss; for(LL v : possibilities){ for(LL nxt = v; nxt < thisPeriod; nxt += prevPeriod){ LL f = fib_mod(nxt, curMod); if(f == K%curMod){ nextPoss.push_back(nxt); } } } possibilities = nextPoss; debug(curMod, possibilities.size()); if(possibilities.size() == 0){ printf("NIE\n"); return 0; } } printf("%lld\n", possibilities[0] + get_period(curMod)); } |