Fibonacci sequence in Ruby (recursion)

Question

I\'m trying to implement the following function, but it keeps giving me the stack level too deep (SystemStackError) error.

Any ideas what the problem mi

Answer 1

Recursion's very slow, here's a faster way

a = []; a[0] = 1; a[1] = 1
i = 1
while i < 1000000
    a[i+1] = (a[i] + a[i-1])%1000000007
    i += 1
end

puts a[n]    

It's O(1), however you could use matrix exponentiation, here's one of mine's implementation, but it's in java => http://pastebin.com/DgbekCJM, but matrix exp.'s O(8logn) .Here's a much faster algorithm, called fast doubling. Here's a java implementation of fast doubling.

class FD {

    static int mod = 1000000007;

    static long fastDoubling(int n) {
        if(n <= 2) return 1;
        int k = n/2;
        long a = fastDoubling(k+1);
        long b = fastDoubling(k);
        if(n%2 == 1) return (a*a + b*b)%mod;
        else return (b*(2*a - b))%mod;
}

Yet, using karatsuba multiplication, both matrix exp. and fast doubling becomes much faster, yet fast doubling beats matrix exp. by a constant factor, well i didn't want to be very thorough here. But i recently did a lot of research on fibonacci numbers and i want my research to be of use to anyone willing to learn, ;).