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Challenges

Comments on Length of a Sumac Sequence

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Length of a Sumac Sequence

+9
−0

Heavily based on this closed challenge from SE.

Description

A Sumac sequence starts with two non-zero integers $t_1$ and $t_2.$

The next term, $t_3 = t_1 - t_2$

More generally, $t_n = t_{n-2} - t_{n-1}$

The sequence ends when $t_n ≤ 0$. All values in the sequence must be positive.

Challenge

Given two integers $t_1$ and $t_2$, compute the Sumac sequence, and output it's length.

If there is a negative number in the input, remove everything after it, and compute the length.

You may take the input in any way (Array, two numbers, etc.)

Test Cases

(Sequence is included for clarification)

[t1,t2]   Sequence          n
------------------------------
[120,71]  [120,71,49,22,27] 5
[101,42]  [101,42,59]       3
[500,499] [500,499,1,498]   4
[387,1]   [387,1,386]       3
[3,-128]  [3]               1
[-2,3]    []                0
[3,2]     [3,2,1,1]         4

Scoring

This is code-golf. Shortest answer in each language wins.

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General comments (4 comments)
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+4
−0

Python 3, 49 47 44 35 bytes

a=lambda x,y:+(x>=0)and(1+a(y,x-y))

Try it online!

-3 bytes thanks to @Hakerh400‭

-9 bytes thanks to @Jo King‭

Python 2, 50 bytes

x,y=input()
a=0
while x>0:x,y,a=y,x-y,a+1
print(a)

An alternate solution I also came up with that I swear I should be able to make shorter, but can't think of it currently.

Try it online!

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1 comment thread

General comments (3 comments)
General comments
Hakerh400‭ wrote over 3 years ago

44 bytes: a=lambda x,y:(x>=0)*(1if y<0else 1+a(y,x-y))

Jo King‭ wrote over 3 years ago

32 bytes if you don't mind 0 being False else 35

Quintec‭ wrote over 3 years ago

y'all are too good at this