02 - Exercise About Tribonacci Sequence

Well met with Fibonacci bigger brother, AKA Tribonacci.

As the name may already reveal, it works basically like a Fibonacci, but summing the last 3 (instead of 2) numbers of the sequence to generate the next. And, worse part of it, regrettably I won‘t get to hear non-native Italian speakers trying to pronounce it :(

So, if we are to start our Tribonacci sequence with [1,1,1] as a starting input (AKA signature), we have this sequence:

[1,1,1,3,5,9,17,31,...]

But what if we started with [0,0,1] as a signature? As starting with [0,1] instead of [1,1] basically shifts the common Fibonacci sequence by once place, you may be tempted to think that we would get the same sequence shifted by 2 places, but that is not the case and we would get:

[0,0,1,1,2,4,7,13,24,...]

Well, you may have guessed it by now, but to be clear: you need to create a fibonacci function that given a signature array/list, returns the first n elements - signature included of the so seeded sequence.

Signature will always contain 3 numbers; n will always be a non-negative number; if n==0, then return an empty array and be ready for anything else which is not clearly specified ;)

If you enjoyed this kata more advanced and generalized version of it can be found in the Xbonacci kata

[Personal thanks to Professor Jim Fowler on Coursera for his awesome classes that I really recommend to any math enthusiast and for showing me this mathematical curiosity too with his usual contagious passion :)]

My Answer:

function tribonacci(signature,n){
  //your code here
  var result = signature;
  if(signature.length === 3 && n > 3){
    for(var i = 3; i < n; i ++){
      result[i] = result[i-1] + result[i-2] + result[i-3];
    }
  }
  result.length = n;
  return result;
}

Best Solution:

function tribonacci(signature,n){  
  for (var i = 0; i < n-3; i++) { // iterate n times
    signature.push(signature[i] + signature[i+1] + signature[i+2]); // add last 3 array items and push to trib
  }
  return signature.slice(0, n); //return trib - length of n
}