// 1137. N-th Tribonacci Number #include "leetcode.h" /* * the tribonacci sequence t^n is defined as follows * t0 = 0, t1 = 1, t2 = 1, & tn+3 = tn + tn+1 + tn+2 for n >= 0 * given n, return value of tn * eg. * n = 4, output: 4 * t3 = 0 + 1 + 1 = 2 * t4 = 1 + 1 + 2 = 4 */ typedef long long ll; struct Matrix { vvd(ll) a; int rows, cols; Matrix(int rows = 0, int cols = 0) : rows(rows), cols(cols) { a.resize(rows); for (int i = 0; i < rows; ++i) a[i].assign(cols, 0); } Matrix(const vvd(ll) & matrix) : a(matrix), rows(matrix.size()), cols(matrix[0].size()) {} }; Matrix operator*(const Matrix &a, const Matrix &b) { Matrix res(a.rows, b.cols); for (int i = 0; i < a.rows; ++i) for (int j = 0; j < b.cols; ++j) for (int k = 0; k < a.cols; ++k) res.a[i][j] += a.a[i][k] * b.a[k][j]; return res; } Matrix fastPow(const Matrix &matrix, int pow) { if (pow == 1) return matrix; Matrix half = fastPow(matrix, pow / 2); if (pow & 1) return half * half * matrix; return half * half; } class Solution { public: int tribonacci(int n) { if (n == 0) return 0; Matrix m({{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}); Matrix m0({{0}, {1}, {1}}); Matrix mn = fastPow(m, n) * m0; return mn.a[0][0]; } }; int main() { Solution obj; cout << obj.tribonacci(4) << endl; // expect: 4 cout << obj.tribonacci(25) << endl; // expect: 1389537 }