#include <cstdio> #include <queue> #include <string> #include <iostream> #include <set> typedef unsigned long long ULL; const ULL M = 1000000000000000000ULL; const ULL MSmall = 1000000000ULL; ULL mul(ULL a, ULL b) { a = a % M; b = b % M; ULL a1 = a / MSmall; ULL a2 = a % MSmall; ULL b1 = b / MSmall; ULL b2 = b % MSmall; ULL c3 = (b2 * a2) % MSmall; ULL c2 = ((b2 * a1) % MSmall + (b2 * a2) / MSmall + (b1 * a2) % MSmall) % MSmall; return (c2 * MSmall + c3) % M; } struct Matrix { ULL a1, a2, b1, b2; Matrix() : a1(1), a2(1), b1(1), b2(0) {} Matrix operator*(const Matrix &other) { Matrix m; m.a1 = mul(a1, other.a1) + mul(b1, other.a2); m.a2 = mul(a2, other.a1) + mul(b2, other.a2); m.b1 = mul(a1, other.b1) + mul(b1, other.b2); m.b2 = mul(a2, other.b1) + mul(b2, other.b2); return m; } ULL fib() { return b2; } }; Matrix matrixFib(ULL n) { if (n == 1) { return Matrix(); } Matrix m = matrixFib(n / 2); m = m * m; if (n & 1) { m = m * Matrix(); } return m; } ULL fib(ULL n) { if (n == 0) { return 0; } else if (n == 1) { return 1; } return matrixFib(n - 1).a1; } void verify(ULL power, ULL value, ULL fib) { if (value % power == ::fib(fib) % power) { // printf("TAK\n"); printf("%llu\n", fib); } else { // printf("WRONG!"); // printf(" (F_%llu = %llu)\n", fib, ::fib(fib)); } } struct Task { int digits; ULL fib; ULL value; Task(int digits, ULL fib, ULL value) : digits(digits), fib(fib), value(value) {} }; struct TaskComparer { bool operator()(const Task &a, const Task &b) { return a.digits > b.digits; } }; ULL cycle_size[19]; ULL ten_power[19]; int main() { cycle_size[1] = 60; cycle_size[2] = 300; cycle_size[3] = 1500; for (int i = 4; i <= 18; ++i) { cycle_size[i] = cycle_size[i - 1] * 10; } ten_power[0] = 1; for (int i = 1; i <= 18; ++i) { ten_power[i] = ten_power[i - 1] * 10; } std::string digits; std::cin >> digits; ULL value = 0; for (char c : digits) { value = value * 10 + c - '0'; } std::multiset<Task, TaskComparer> tasks; Matrix m; for (ULL i = 0; i < 1500; ++i) { int d = std::min((int)digits.size(), 3); if (m.fib() % ten_power[d] == value % ten_power[d]) { if (digits.size() <= 3) { verify(ten_power[digits.size()], value, i + 1500); return 0; } tasks.insert(Task(3, i, m.fib())); } m = m * Matrix(); } while (!tasks.empty()) { Task task = *tasks.begin(); tasks.erase(tasks.begin()); for (ULL i = 0; i < 10; ++i) { ULL f = fib(task.fib + i * cycle_size[task.digits]); ULL power = ten_power[task.digits + 1]; if (f % power == value % power) { // printf("FOUND %d/%d %llu\n", task.digits + 1, (int)digits.size(), f); if ((int)digits.size() == task.digits + 1) { ULL result = task.fib + i * cycle_size[task.digits] + cycle_size[digits.size()]; verify(ten_power[digits.size()], value, result); return 0; } tasks.insert(Task(task.digits + 1, task.fib + i * cycle_size[task.digits], f)); } } } printf("NIE\n"); 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 | #include <cstdio> #include <queue> #include <string> #include <iostream> #include <set> typedef unsigned long long ULL; const ULL M = 1000000000000000000ULL; const ULL MSmall = 1000000000ULL; ULL mul(ULL a, ULL b) { a = a % M; b = b % M; ULL a1 = a / MSmall; ULL a2 = a % MSmall; ULL b1 = b / MSmall; ULL b2 = b % MSmall; ULL c3 = (b2 * a2) % MSmall; ULL c2 = ((b2 * a1) % MSmall + (b2 * a2) / MSmall + (b1 * a2) % MSmall) % MSmall; return (c2 * MSmall + c3) % M; } struct Matrix { ULL a1, a2, b1, b2; Matrix() : a1(1), a2(1), b1(1), b2(0) {} Matrix operator*(const Matrix &other) { Matrix m; m.a1 = mul(a1, other.a1) + mul(b1, other.a2); m.a2 = mul(a2, other.a1) + mul(b2, other.a2); m.b1 = mul(a1, other.b1) + mul(b1, other.b2); m.b2 = mul(a2, other.b1) + mul(b2, other.b2); return m; } ULL fib() { return b2; } }; Matrix matrixFib(ULL n) { if (n == 1) { return Matrix(); } Matrix m = matrixFib(n / 2); m = m * m; if (n & 1) { m = m * Matrix(); } return m; } ULL fib(ULL n) { if (n == 0) { return 0; } else if (n == 1) { return 1; } return matrixFib(n - 1).a1; } void verify(ULL power, ULL value, ULL fib) { if (value % power == ::fib(fib) % power) { // printf("TAK\n"); printf("%llu\n", fib); } else { // printf("WRONG!"); // printf(" (F_%llu = %llu)\n", fib, ::fib(fib)); } } struct Task { int digits; ULL fib; ULL value; Task(int digits, ULL fib, ULL value) : digits(digits), fib(fib), value(value) {} }; struct TaskComparer { bool operator()(const Task &a, const Task &b) { return a.digits > b.digits; } }; ULL cycle_size[19]; ULL ten_power[19]; int main() { cycle_size[1] = 60; cycle_size[2] = 300; cycle_size[3] = 1500; for (int i = 4; i <= 18; ++i) { cycle_size[i] = cycle_size[i - 1] * 10; } ten_power[0] = 1; for (int i = 1; i <= 18; ++i) { ten_power[i] = ten_power[i - 1] * 10; } std::string digits; std::cin >> digits; ULL value = 0; for (char c : digits) { value = value * 10 + c - '0'; } std::multiset<Task, TaskComparer> tasks; Matrix m; for (ULL i = 0; i < 1500; ++i) { int d = std::min((int)digits.size(), 3); if (m.fib() % ten_power[d] == value % ten_power[d]) { if (digits.size() <= 3) { verify(ten_power[digits.size()], value, i + 1500); return 0; } tasks.insert(Task(3, i, m.fib())); } m = m * Matrix(); } while (!tasks.empty()) { Task task = *tasks.begin(); tasks.erase(tasks.begin()); for (ULL i = 0; i < 10; ++i) { ULL f = fib(task.fib + i * cycle_size[task.digits]); ULL power = ten_power[task.digits + 1]; if (f % power == value % power) { // printf("FOUND %d/%d %llu\n", task.digits + 1, (int)digits.size(), f); if ((int)digits.size() == task.digits + 1) { ULL result = task.fib + i * cycle_size[task.digits] + cycle_size[digits.size()]; verify(ten_power[digits.size()], value, result); return 0; } tasks.insert(Task(task.digits + 1, task.fib + i * cycle_size[task.digits], f)); } } } printf("NIE\n"); return 0; } |