diff options
Diffstat (limited to 'other/nth_tribonacci_number.cpp')
-rw-r--r-- | other/nth_tribonacci_number.cpp | 61 |
1 files changed, 61 insertions, 0 deletions
diff --git a/other/nth_tribonacci_number.cpp b/other/nth_tribonacci_number.cpp new file mode 100644 index 0000000..cabdb39 --- /dev/null +++ b/other/nth_tribonacci_number.cpp @@ -0,0 +1,61 @@ +// 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 +} |