#include #include #include using namespace std; typedef long long ll; typedef vector> matrix; typedef vector> d_matrix; const int maxn = 1e5 + 10; const int INF = 2e9; const ll MOD = 998244353; void print(matrix A) { int n = (int) A.size(), m = (int) A[0].size(); for(int i = 0; i < n; i++) { for(int j = 0; j < m; j++) { cout << A[i][j] << " "; } cout << endl; } cout << endl; } void print(d_matrix A) { int n = (int) A.size(), m = (int) A[0].size(); for(int i = 0; i < n; i++) { for(int j = 0; j < m; j++) { cout << A[i][j] << " "; } cout << endl; } cout << endl; } matrix multiply_by_k(matrix A, int k) { matrix res = A; int n = (int) A.size(), m = (int) A[0].size(); for(int i = 0; i < n; i++) { for(int j = 0; j < m; j++) { res[i][j] *= k; } } return res; } matrix add_two_matrices(matrix A, matrix B) { int n_a = (int) A.size(), m_a = (int) A[0].size(); int n_b = (int) B.size(), m_b = (int) B[0].size(); if(n_a == n_b and m_a == m_b) { matrix res = A; for(int i = 0; i < n_a; i++) { for(int j = 0; j < m_a; j++) { res[i][j] = A[i][j] + B[i][j]; } } return res; } cout << "Dimenziite na matricite treba da se isti za da mozhe da gi sobereme istite" << endl; return {{0}}; } matrix subtract_two_matrices(matrix A, matrix B) { int n_a = (int) A.size(), m_a = (int) A[0].size(); int n_b = (int) B.size(), m_b = (int) B[0].size(); if(n_a != n_b or m_a != m_b) { cout << "Dimenziite na matricite treba da se isti za da mozhe da gi sobereme istite" << endl; return {{0}}; } matrix res = A; for(int i = 0; i < n_a; i++) { for(int j = 0; j < m_a; j++) { res[i][j] = A[i][j] - B[i][j]; } } return res; } matrix multiply_two_matrices(matrix A, matrix B) { int n_a = (int) A.size(), m_a = (int) A[0].size(); int n_b = (int) B.size(), m_b = (int) B[0].size(); if(m_a != n_b) { cout << "Matricite ne mozhat da se mnozhat" << endl; return {{0}}; } matrix res(n_a, vector(m_b, 0)); for(int i = 0; i < n_a; i++) { for(int j = 0; j < m_b; j++) { int c = 0; for(int k = 0; k < n_a; k++) { c += (A[i][k] * B[k][j]) % MOD; c %= MOD; } res[i][j] = c % MOD; } } return res; } int determinant_of_matrix(matrix A) { int sz = (int) A.size(); if(sz == 2) { return (A[0][0] * A[1][1]) - (A[0][1] * A[1][0]); } int determinant = 0; int sign = 1; for(int i = 0; i < sz; i++) { int n = 0, m = 0; matrix tmp(sz - 1, vector(sz - 1, 0)); for(int j = 0; j < sz; j++) { for(int k = 0; k < sz; k++) { if(j != 0 and k != i) { tmp[n][m] = A[j][k]; if(m < sz - 2) { m++; } else { m = 0; n++; } } } } determinant = determinant + sign*(A[0][i]) * determinant_of_matrix(tmp); sign *= -1; } return determinant; } matrix transpose_matrix(matrix A) { int n = (int) A.size(); int m = (int) A[0].size(); matrix res(m, vector(n)); for(int j = 0; j < m; j++) { for(int i = 0; i < n; i++) { res[j][i] = A[i][j]; } } return res; } d_matrix inverse_of_matrix(matrix A) { int n = (int) A.size(); int m = (int) A[0].size(); d_matrix res(n, vector(m)); matrix adj_matrix(n, vector(m)); for(int i = 0; i < n; i++) { for(int j = 0; j < m; j++) { matrix minor(n - 1, vector(m - 1)); int r = 0, c = 0; for(int a = 0; a < n; a++) { if(a == i) continue; for(int b = 0; b < m; b++) { if(a == i or b == j) continue; minor[r][c] = A[a][b]; c++; } c = 0; r++; } adj_matrix[i][j] = determinant_of_matrix(minor); if((i + j) % 2 == 1) { adj_matrix[i][j] *= -1; } } } adj_matrix = transpose_matrix(adj_matrix); double det = determinant_of_matrix(A); cout << det << endl; for(int i = 0; i < n; i++) { for(int j = 0; j < m; j++) { res[i][j] = (1.0 / det) * adj_matrix[i][j]; } } return res; } ll power(ll a, ll b) { ll res = 1; while(b) { if(b % 2 == 1) { res *= a; } a *= a; b /= 2; } return res; } ll nth_fibbonaci_number(ll x) { matrix A = { {1, 1}, {1, 0} }; matrix B = A; // for(int i = 0; i < x; i++) { // A = multiply_two_matrices(A, B); // } matrix res = { {1, 0}, {0, 1} }; while(x) { if(x % 2 == 1) { res = multiply_two_matrices(res, A); } A = multiply_two_matrices(A, A); x /= 2; } return res[0][0]; } int main() { // nth_fibbonaci_number(8); // return 0; for(int i = 1; i <= 10; i++) { cout << nth_fibbonaci_number(i) << " "; } return 0; }