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// 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
}
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