023_Tribonacci Sequence.py

"""
Codewars Coding Challenge

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 (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 :)]


https://www.codewars.com/kata/556deca17c58da83c00002db/train/python
"""



# My Solution
def tribonacci(signature, n):
    if n == 0:
        return []
    elif n <= 3:
        return signature[:n]
    result = signature[:]
    
    for i in range(3, n):
        next_term = sum(result[-3:])
        result.append(next_term)
    return result

# print(tribonacci([1,1,1], 10))
# print(tribonacci([0,0,1], 10))
# print(tribonacci([0,1,1], 10))
# print(tribonacci([1,0,0], 10))
# print(tribonacci([1,1,0], 10))
# print(tribonacci([0,0,0], 10))




"""
Sample Test:

import codewars_test as test
from solution import tribonacci

@test.describe("Basic Tests")
def basic_tests():
    
    @test.it("Basic Tests")
    def basic_tests():
        test.assert_equals(tribonacci([1, 1, 1], 10), [1, 1, 1, 3, 5, 9, 17, 31, 57, 105])
        test.assert_equals(tribonacci([0, 0, 1], 10), [0, 0, 1, 1, 2, 4, 7, 13, 24, 44])
        test.assert_equals(tribonacci([0, 1, 1], 10), [0, 1, 1, 2, 4, 7, 13, 24, 44, 81])
        test.assert_equals(tribonacci([1, 0, 0], 10), [1, 0, 0, 1, 1, 2, 4, 7, 13, 24])
        test.assert_equals(tribonacci([0, 0, 0], 10), [0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
        test.assert_equals(tribonacci([1, 2, 3], 10), [1, 2, 3, 6, 11, 20, 37, 68, 125, 230])
        test.assert_equals(tribonacci([3, 2, 1], 10), [3, 2, 1, 6, 9, 16, 31, 56, 103, 190])
        test.assert_equals(tribonacci([1, 1, 1], 1), [1])
        test.assert_equals(tribonacci([300, 200, 100], 0), [])
        test.assert_equals(tribonacci([0.5, 0.5, 0.5], 30), [0.5, 0.5, 0.5, 1.5, 2.5, 4.5, 8.5, 15.5, 28.5, 52.5, 96.5, 177.5, 326.5, 600.5, 1104.5, 2031.5, 3736.5, 6872.5, 12640.5, 23249.5, 42762.5, 78652.5, 144664.5, 266079.5, 489396.5, 900140.5, 1655616.5, 3045153.5, 5600910.5, 10301680.5])
"""



"""
Perfect Solution Form Codewars


=1=
def tribonancci(signature, n):
    result = signature[:n]
    for i in range(n - 3): result.append(sum(result[-3:]))
    return result


=2=
def tribonacci(signature,n):
    while len(signature) < n:
        signature.append(sum(signature[-3:]))
    
    return signature[:n]



=3=
def tribonacci(s, n):
    for i in range(3, n): s.append(s[i-1] + s[i-2] + s[i-3])
    return s[:n]



=4=
def tribonacci(signature,n):
    return signature[:n] if n<=len(signature) else tribonacci(signature + [sum(signature[-3:])],n)



=5=
def tribonacci(s, n):
    while n > len(s):
        s += [sum(s[-3:])]
    return s[:n]
"""