BASKETBALL FRVR?

Question

You might already be familiar with the game: Basketball FRVR in facebook. There are two types of score you can make:

• A virgin-shot:(we call it so in our country :D) When the ball enters the basket without touching the rim or
• A stale shot: When the ball enters the basket, but after touching the rim.

The game is over once you miss a shot. Stale shot always scores 2 points.The first in a run of consecutive virgin-shots scores 3 points, the second scores 6 points, and subsequent ones score 9 points each.

For example,

Hits             Total score 

S-V-V-V          2+3+6+9 = 20
S-V-V-V-V        2+3+6+9+9 = 29 (see how added score for consecutive virgin-
                                 shots                              
                                 saturates at the 5th hit)
S-V-S-V-V-S-V    2+3+2+3+6+2+3= 21

Using simple mathematics, it can easily be proven that any score greater than 1 n>1 can be scored in the game

The Challenge

For any given number 1<n<100, output all the possible ways to score n.

Rules:

• You can either write a complete program or function(s), snippets however are not acceptable.
• Hard-coding the output or loading from memory/other programs/website is strictly prohibited, you must compute the output in real-time.
• The output must be a well-separated collection of string of Ss and Vs. For eg: ['SVS','SSV','VSS'] or {'SVS','SSV','VSS'}.
• It is encouraged to, but the collection need not be sorted or contain only unique elements. Brownie points if you output sorted and unique collection of strings.

Winning condition:

• This is code-golf so the shortest code in bytes wins.

Input/Output (Test-cases)

2: {'S'}
3: {'V'}
4: {'SS'}
12: {'SSSSSS', 'VSSVS', 'VSVSS', 'VSSSV', 'SSVSV', 'SVSVS', 'SVSSV'}
16: {'SSSVSVS', 'SSSVSSV', 'VSSSSSV', 'SSVSSVS', 'SVVSV', 'VSSSSVS', 'SVSVV', 'SVSSSSV', 'VVSSV', 'VSVVS', 'SVSVSSS', 'SVSSSVS', 'VSSVSSS', 'SSVSSSV', 'SSSSSSSS', 'VVSVS', 'VSSSVSS', 'SVSSVSS', 'VSVSSSS', 'SSSSVSV', 'SSVSVSS', 'VSSVV'}

Thanks to Peter Taylor for improving this question

Answer 1

Jelly, 30 bytes

o2,5ṁo8‘
Hṗ@€⁾VSẎðOḂŒgÇ€FS=ðÐf

A monadic link returning a list of the strings (lists of characters).

Try it online! - The footer calls the link and separates the entries by newlines since a full program's implicit output would smash them together.

How?

o2,5ṁo8‘ - Link 1, helper to form shot scores: list of shots grouped by type (S=1 and V=0)
         -                                e.g. [[1,1],[0,0,0,0,0],[1,1],[0],[1,1]]
 2,5     - 2 paired with 5 = [2,5]
o        - logical or (vectorises)             [[1,1],[2,5,0,0,0],[1,1],[2,5],[1,1]]
    ṁ    - mould like the input                [[1,1],[2,5,0,0,0],[1,1],[2],[1,1]]
     o8  - logical or with 8                   [[1,1],[2,5,8,8,8],[1,1],[2],[1,1]]
       ‘ - increment                           [[2,2],[3,6,9,9,9],[2,2],[3],[2,2]]

Hṗ@€⁾VSẎðOḂŒgÇ€FS=ðÐf - Link: number, total score, n
H                     - halve n
    ⁾VS               - literal ['V','S']
 ṗ@€                  - Cartesian power with swapped @rguments for €ach
                      -   ...i.e. for each in [1,2,...,floor(half n)]
                      -   yielding all strings of Vs and Ss from length 1 to floor(half n)
       Ẏ              - tighten (from a list of lists of lists to a list of lists)
        ð         ðÐf - filter keep those entries for which this yields a truthy value:
         O            -   cast to ordinals (S->83, V->86)
          Ḃ           -   modulo 2         (S->1, V->0)
           Œg         -   group equal runs (e.g. [0,0,1,1,0] -> [[0,0],[1,1],[0]])
             Ç€       -   call the last link (1) as a monad for €ach (transform to scores)
               F      -   flatten (make one list of scores)
                S     -   sum (calculate the total score of the string)
                 =    -   equals right argument (n)?

The resulting order is actually lexicographical in reverse, to have it forward sorted just reverse it by appending Ṛ.

Answer 2

JavaScript (ES6), 73 72 bytes

Prints all unique, lexically sorted combinations.

f=(n,p=0,s='')=>n?n>1&&f(n-2,0,s+'S')&f(n-(p-9?p+=3:9),p,s+'V'):alert(s)

Test cases

In this snippet, alert() has been replaced by console.log() for user-friendliness.

f=(n,p=0,s='')=>n?n>1&&f(n-2,0,s+'S')&f(n-(p-9?p+=3:9),p,s+'V'):console.log(s)

;[2, 3, 4, 12, 16]
.forEach(n => { console.log('[' + n + ']'); f(n); })

Answer 3

PHP>=7.1, 158 bytes

function b($s="",$g=0){global$r,$i;$g-$i?$g>$i?:b($s."2",$g+2)&b($s.($n=$s[-1]>2?min(9,$s[-1]+3):3),$g+$n):$r[]=strtr($s,2369,SVVV);}$i=$argn;b();print_r($r);

PHP Sandbox Online

Expanded

function b($s="",$g=0){
  global$r,$i;
  $g-$i
    ?$g>$i
      ?
      :b($s."2",$g+2) # recursive call add a S
      &b($s.($n=$s[-1]>2?min(9,$s[-1]+3):3),$g+$n) # recursive call add a V
    :$r[]=strtr($s,2369,SVVV); # add to result array if reach score replace integers with S and V
} 
$i=$argn; #short input variable
b(); #call the function
print_r($r); #print results

Answer 4

Python 3, 96 95 85 77 73 bytes

-1 byte thanks to @notjagan
-4 bytes thanks to @xnor

f=lambda x,s='',i=3:f(x-2,s+'S')+f(x-i,s+'V',3*(i<9)+i)if x>0 else[s]*-~x

Try it online!

Answer 5

Mathematica, 95 102 105 112 bytes

If[#4==#2,Echo@#,If[#4>#2,#0[#<>"S",#2+2,0,#4];#0[#<>"V",#2+Min[3#3+3,9],#3+1,#4]]]&["",0,0,#]&

There should be a lot of golfing potential.

Bascially it is a recursive function that perform a DFS over all possible combinations.

Answer 6

Haskell, 75 bytes

n#v|n<1=[[]|n==0]|n>0=(('S':)<$>(n-2)#3)++(('V':)<$>(n-v)#min(v+3)9)
f=(#3)

Call f with the total score value. Uses a fairly straightforward depth-first search to find all the solutions. Sadly, Haskell's precedence rules seem to be out to get me today, so there are lots of parentheses here.