# A problem of rarity [closed]

Given a positive input $$\n > 0\$$, output the amout of two types based on their rarity. The two types are called $$\A\$$ and $$\B\$$, we know the followings:

• $$\n\$$ is a limited input and the maximum is $$\nmax\$$
• At the start $$\B\$$ is twice as rare as $$\A\$$
• As the presence of $$\A\$$ increade the rarity of $$\B\$$ decreases
• When $$\n\$$ = $$\nmax\$$, $$\A\$$ will be equal to $$\B\$$
• When $$\n\$$ is not $$\nmax\$$, $$\A\$$ cannot be equal to $$\B\$$
• The value of $$\A\$$ and $$\B\$$ cannot be decimal.

## Example

nmax = 10

n = 1, output = [1A, 0B]
n = 2, output = [2A, 0B]
n = 3, output = [2A, 1B]
n = 4, output = [3A, 1B]
n = 5, output = [3A, 2B]
n = 6, output = [4A, 2B]
n = 7, output = [4A, 3B]
n = 8, output = [5A, 3B]
n = 9, output = [5A, 4B]
n = 10, output = [5A, 5B]



Shortest code win.

• So we have $n = A+B$ for any $n$ and $nmax = 2A = 2B$. Is that correct? If so, is $nmax$ guaranteed to be even? Apr 12 at 9:37
• Is $nmax$ another output? Or is it a constant which will always be $10$? May I output some values different to current one while it meets all requirements here? Or should I output exactly the same values as the example shown?
– tsh
Apr 12 at 9:51
• Say may I implement $A_{nmax}(n)=\min\left\{n, nmax\right\}$, $B_{nmax}(n)=\max\left\{n - nmax, 0\right\}$?
– tsh
Apr 12 at 9:53
• Sorry it's my first question in this stack, i'll try to edit and be more clear. Apr 12 at 10:20
• Welcome to Code Golf and nice first question! For future reference, we recommend using the Sandbox to get feedback on challenge ideas before posting them to main Apr 12 at 12:25

# JavaScript (Node.js), 25 bytes

m=>n=>[a=n/2+(n<m)|0,n-a]


Try it online!

# JavaScript (Node.js), 24 bytes

m=>n=>[b=n-(n<m)>>1,n-b]


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# JavaScript (ES6), 28 bytes

Expects (nmax)(n). Returns [B,A].

(This is based on my current understanding of the task.)

m=>n=>[b=n/2-(n<m&~n)|0,n-b]


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# Python, 266 63 bytes

And we're down to less than half one-third one-quarter two-sevenths one-quarter of my original, so a lot less scuffed than anything I've put out, but it's a first answer:

def a(b,c):
m=(b<c)*(1-.5*(b%2))
return int(b/2+m),int(b/2-m)


Takes advantage of the fact that $$\\frac {a+1} {b+1} < \frac a b\$$, if $$\a > b\$$: after that, it's just handling evens and a few exception cases.

-58 due to Wasif and a lambda of str(int(n)), plus dropping of whitespace.

-24 due to Wasif and the lambda function 2.

-14 by Wasif again and more cleaner conditionals.

-5 due to Wasif again by dropping the last else.

-15/-1 to Dominic van Essen and Lyxal respectively.

-3 from Wasif (making a return) and -6 from Dominic Van Essen again.

-39 from pxeger due to input semantics, taking us under halfway.

-9 from pxeger and -7 from Lyxal, taking us under 100, by returning a tuple instead of a list.

-2 from Dominic Van Essen, also managing to fix an error in the process

-14 from Dominic Van Essen again, with a nice simplification.

So far, total bytes saved:

• Wasif: 104
• pxeger: 48
• Dominic Van Essen: 47
• Lyxal: 8
• This comment chain's gotten a bit long, but it's still a relevant discussion, so to reduce clutter on this post, I've moved this conversation to chat. Apr 12 at 15:11

# Husk, 11 10 bytes

Se≠¹÷2+¹←=


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Se≠¹÷2+¹←=      # full program:
Se≠⁰÷2+⁰←=²⁰    # here with implicit final arguments added for clarity;