#include <bits/stdc++.h> using namespace std; const int N = 18; typedef array<int, N> Num; const Num Zero = {0}; Num MakeOne() { Num a = Zero; a[0] = 1; return a; } const Num One = MakeOne(); void Normalize(Num& a) { for (int i = 0; i < N; ++i) { if (i + 1 < N) a[i + 1] += a[i] / 10; a[i] %= 10; } } Num Add(const Num& a, const Num &b) { Num c = Zero; for (int i = 0; i < N; ++i) c[i] = a[i] + b[i]; Normalize(c); return c; } Num Mul(const Num& a, const Num& b) { Num c = Zero; for (int i = 0; i < N; ++i) for (int j = 0; i + j < N; ++j) c[i + j] += a[i] * b[j]; Normalize(c); return c; } typedef array<array<Num, 2>, 2> Mat; Mat Mul(const Mat& a, const Mat& b) { Mat c = {Zero, Zero, Zero, Zero}; for (int i = 0; i < 2; ++i) for (int j = 0; j < 2; ++j) for (int k = 0; k < 2; ++k) c[i][j] = Add(c[i][j], Mul(a[i][k], b[k][j])); return c; } Mat Pow(Mat a, unsigned long long d) { Mat q = {One, Zero, Zero, One}; while (d) { if (d & 1) q = Mul(q, a); a = Mul(a, a); d >>= 1; } return q; } unsigned long long Fib(unsigned long long d) { Mat f = {One, One, One, Zero}; Num temp = Pow(f, d)[1][0]; unsigned long long result = 0; for (int i = N - 1; i >= 0; --i) result = result * 10 + temp[i]; return result; } unsigned long long PeriodForP10(unsigned long long p10) { if (p10 == 10) return 60; else if (p10 == 100) return 300; else return p10 + p10 / 2; } vector<unsigned long long> Brute(unsigned long long p10, unsigned long long residue) { vector<unsigned long long> solutions; unsigned long long period = PeriodForP10(p10); unsigned long long a = 1, b = 0; for (unsigned long long k = 0; k < period; ++k) { if (b == residue) solutions.push_back(k); b = (a + b) % p10; swap(a, b); } return solutions; } int main() { /* for (int i = 0; i < 150000; ++i) { if (Fib(i) % 100000 == 31888) cerr << i << " " << Fib(i) << endl; } */ /* for (int i = 0; i < 10; ++i) { int x = 65484 + i * 150000; cerr << x << " x " << Fib(x) << endl; int y = 140484 + i * 150000; cerr << y << " y " << Fib(y) << endl; } */ // return 0; string buf; cin >> buf; int n = buf.length(); unsigned long long residue = atoll(buf.c_str()); unsigned long long p10 = 1; for (int i = 0; i < n; ++i) p10 *= 10; if (n < 5) { vector<unsigned long long> solutions = Brute(p10, residue); if (solutions.empty()) { cout << "NIE" << endl; } else { unsigned long long result = solutions[0]; if (result < 100) result += PeriodForP10(p10); cout << result << endl; } } else { unsigned long long q10 = 100000; vector<unsigned long long> solutions = Brute(q10, residue % q10); assert((!solutions.empty()) == (residue % 2 == 1 or residue % 8 == 0 or residue % 32 == 2)); if (solutions.empty()) { cout << "NIE" << endl; } else { while (q10 < p10) { /* cerr << q10 << endl; for (unsigned long long solution : solutions) cerr << solution << " " << Fib(solution) << endl; */ unsigned long long period = PeriodForP10(q10); q10 *= 10; vector<unsigned long long> new_solutions; for (unsigned long long solution : solutions) for (int i = 0; i < 10; ++i) if (Fib(solution + i * period) % q10 == residue % q10) new_solutions.push_back(solution + i * period); assert(new_solutions.size() == solutions.size()); solutions = new_solutions; } unsigned long long result = solutions[0]; if (result < 100) result += PeriodForP10(p10); assert(Fib(result) % p10 == residue); cout << result << endl; } } }
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 | #include <bits/stdc++.h> using namespace std; const int N = 18; typedef array<int, N> Num; const Num Zero = {0}; Num MakeOne() { Num a = Zero; a[0] = 1; return a; } const Num One = MakeOne(); void Normalize(Num& a) { for (int i = 0; i < N; ++i) { if (i + 1 < N) a[i + 1] += a[i] / 10; a[i] %= 10; } } Num Add(const Num& a, const Num &b) { Num c = Zero; for (int i = 0; i < N; ++i) c[i] = a[i] + b[i]; Normalize(c); return c; } Num Mul(const Num& a, const Num& b) { Num c = Zero; for (int i = 0; i < N; ++i) for (int j = 0; i + j < N; ++j) c[i + j] += a[i] * b[j]; Normalize(c); return c; } typedef array<array<Num, 2>, 2> Mat; Mat Mul(const Mat& a, const Mat& b) { Mat c = {Zero, Zero, Zero, Zero}; for (int i = 0; i < 2; ++i) for (int j = 0; j < 2; ++j) for (int k = 0; k < 2; ++k) c[i][j] = Add(c[i][j], Mul(a[i][k], b[k][j])); return c; } Mat Pow(Mat a, unsigned long long d) { Mat q = {One, Zero, Zero, One}; while (d) { if (d & 1) q = Mul(q, a); a = Mul(a, a); d >>= 1; } return q; } unsigned long long Fib(unsigned long long d) { Mat f = {One, One, One, Zero}; Num temp = Pow(f, d)[1][0]; unsigned long long result = 0; for (int i = N - 1; i >= 0; --i) result = result * 10 + temp[i]; return result; } unsigned long long PeriodForP10(unsigned long long p10) { if (p10 == 10) return 60; else if (p10 == 100) return 300; else return p10 + p10 / 2; } vector<unsigned long long> Brute(unsigned long long p10, unsigned long long residue) { vector<unsigned long long> solutions; unsigned long long period = PeriodForP10(p10); unsigned long long a = 1, b = 0; for (unsigned long long k = 0; k < period; ++k) { if (b == residue) solutions.push_back(k); b = (a + b) % p10; swap(a, b); } return solutions; } int main() { /* for (int i = 0; i < 150000; ++i) { if (Fib(i) % 100000 == 31888) cerr << i << " " << Fib(i) << endl; } */ /* for (int i = 0; i < 10; ++i) { int x = 65484 + i * 150000; cerr << x << " x " << Fib(x) << endl; int y = 140484 + i * 150000; cerr << y << " y " << Fib(y) << endl; } */ // return 0; string buf; cin >> buf; int n = buf.length(); unsigned long long residue = atoll(buf.c_str()); unsigned long long p10 = 1; for (int i = 0; i < n; ++i) p10 *= 10; if (n < 5) { vector<unsigned long long> solutions = Brute(p10, residue); if (solutions.empty()) { cout << "NIE" << endl; } else { unsigned long long result = solutions[0]; if (result < 100) result += PeriodForP10(p10); cout << result << endl; } } else { unsigned long long q10 = 100000; vector<unsigned long long> solutions = Brute(q10, residue % q10); assert((!solutions.empty()) == (residue % 2 == 1 or residue % 8 == 0 or residue % 32 == 2)); if (solutions.empty()) { cout << "NIE" << endl; } else { while (q10 < p10) { /* cerr << q10 << endl; for (unsigned long long solution : solutions) cerr << solution << " " << Fib(solution) << endl; */ unsigned long long period = PeriodForP10(q10); q10 *= 10; vector<unsigned long long> new_solutions; for (unsigned long long solution : solutions) for (int i = 0; i < 10; ++i) if (Fib(solution + i * period) % q10 == residue % q10) new_solutions.push_back(solution + i * period); assert(new_solutions.size() == solutions.size()); solutions = new_solutions; } unsigned long long result = solutions[0]; if (result < 100) result += PeriodForP10(p10); assert(Fib(result) % p10 == residue); cout << result << endl; } } } |