Description:
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
}