Java Program Fibonacci Sequence

Question

I am writing a \"simple\" program to determine the Nth number in the Fibonacci sequence. Ex: the 7th number in the sequence is: 13. I have finished writing the program, it

Answer 1

Naive implementation is natural and elegant but during execution recursive calls are creating binary tree. Beside already mentioned memoization, cashing of previous F(n) results and avoiding of unnecessary tree traversal, you can go for tail call optimization, already mentioned iterative or matrix multiplication. For example, Java 8 memoization:

private static final Map memo = new HashMap<>();
static {
  memo.put(0L, 0L);
  memo.put(1L, 1L);
}
public static void main(String[] args) {
  System.out.println(fibonacci(0));
  System.out.println(fibonacci(43));
  System.out.println(fibonacci(92));
}
public static long fibonacci(long n) {
  return memo.computeIfAbsent(n, m -> fibonacci(m - 1) + fibonacci(m - 2));
}

Or maybe tail call optimized version:

interface FewArgs {
  public R apply(T t, U u, V v);
}

static FewArgs tailRecursive;

static {
  tailRecursive = (a, b, n) -> {
    if (n > 0)
      return tailRecursive.apply(b, a + b, n - 1);
    return a;
  };
}

You call it with a = 0, b = 1, n is required nth Fibonacci number but must be smaller than 93. More efficient ways to calculate Fibonacci numbers are matrix squaring, you will find example on my blog, and Binet formula