Question

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nth fibonacci number in sublinear time

I was creating a program which is related to the stair problem, i.e you have n stairs and the player can climb on the stairs using them one by one or skipping one …

Now to solve this problem I needed nth (n+1)th term for the Fibonacci for n number of stairs, but the problem is my input range is 1 ≤ n ≤ 1000000.

And for that much greater value of n if I use the loop based method or recursion to calculate the Fibonacci the method takes very much time and space. That I do not have.

So please can you tell me some method in the Java or C to handle Fibonacci series up to that range with correct output?

Note: Please I do not need any solution which has recursion or loop.

Answer 1

Look at the following page, maybe it will help: https://www.nayuki.io/page/fast-fibonacci-algorithms

For me their Java example managed to calculate 1000000th Fibonacci number. It is 208988 digits long.