33.Tribonacci Sequence

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 (except in C return NULL) 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 :)]

 

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function tribonacci(signature, n) {
  let numArr = signature;
  
  if (n < 4) {
    return signature.slice(0, n);
  } else {
    for (i=0; i < n-3; i++) {
      numArr.push((numArr[i] + numArr[i+1] + numArr[i+2]));
    }
    return numArr;
  }
}

먼저 배열인 signature를 numArr로 선언해주었다.

let numArr = signature;

만약에 n이 4 미만인 경우에 signature 배열을 배열의 0번째 자리부터 n번째 자리까지 slice한 것을 리턴해주기로 했다. 

if (n < 4) {

return signature.slice(0, n);

그렇지 않은 경우에는 i를 n-3번까지 반복을 시키면서 numArr의 0번째 1번째 2번째 수를 더하고 1번째 2번째 3번째 수를 더하는 형식으로 코드를 작성하였다. 

else {

for (i=0; i < n-3; i++) {

numArr.push((numArr[i] + numArr[i+1] + numArr[i+2]));

}

이를 push()를 사용해서 새로운 배열이 되게끔 해주었으니 numArr를 리턴해주면 된다.