What is a non recursive solution for Fibonacci-like sequence in Java?

Question

Given this pseudo code of a function

f(0) = 1; 
f(1) = 3; 
f(n) = 3 * f(n - 1) - f(n - 2); // for n >= 2.

Is there a non recursive way o

Answer 1

Answers here are correct, but they work in O(n), while you can do it in O(log n), exponentially faster. Observe that

[f(n)  ] = [3 -1] [f(n-1)]
[f(n-1)]   [1  0] [f(n-2)]

Let v_n be the vector [f(n), f(n-1)] and A the matrix as above, so you get v_n = A v_n-1, therefore v_n = A^n-1 v₁. Compute (n-1)-th power of matrix A using binary exponentiation and multiply it by v₁. For more on linear recurrences see here.