Re: [Bug-apl] Best way to solve my daughter's maths problem

[Jay Foad]

Simpler f and g:

e←{⍵,⊂f ⍵}
f←{↑,/⍵ g¨⌽⍵}
g←{↑,/,⍺∘.h ⍵}
h←{(⊂'(',⍺),¨'+-×÷',¨⊂(⍵,')')}

Jay.

On 25 January 2017 at 10:59, Jay Foad <address@hidden> wrote:
> How about this, based on enumerating binary trees:
>
>       e←{⍵,⊂f ⍵}
>       f←{↑,/(⊂⍵)g¨⍳≢⍵}
>       g←{↑,/,(⍵⊃⍺)∘.h ⍵⊃⌽⍺}
>       h←{(⊂'(',⍺),¨'+-×÷',¨⊂(⍵,')')}
>       t1←,⊂,'4' ⍝ vec of charvecs representing trees of size 1
>       t←,⊂t1 ⋄ t←e⍣4⊢t
>       (t1 t2 t3 t4 t5)←t
>
> Now t5 is a list of parenthesised expressions of "size" 5, i.e.
> containing 5 4s. At this point in Dyalog APL I would do:
>
>       ⊃t5/⍨7={11::0 ⋄ ⍎⍵}¨t5 ⍝ 11::0 means return 0 if ⍎ signalled DOMAIN 
> ERROR
> (4+((4+(4+4))÷4))
> (4-((4-(4×4))÷4))
> (4+(((4+4)+4)÷4))
> (4+(((4×4)-4)÷4))
> (((4+(4+4))÷4)+4)
> (((4×(4+4))-4)÷4)
> ((((4+4)+4)÷4)+4)
> ((((4+4)×4)-4)÷4)
> ((((4×4)-4)÷4)+4)
>
> I am sure there is a simple equivalent in GNU APL.
>
> For bonus marks I guess you might want to remove from this list any
> expressions that are equivalent due to + and × being commutative and
> associative.
>
> Jay.
>
> On 24 January 2017 at 15:47, Elias Mårtenson <address@hidden> wrote:
>> My daughter had this maths problem, and quote it from memory:
>>
>> Given five 4's, separated by the mathematical functions +, -, × and ÷ form
>> the number 7. The problem also allowed her to use parentheses.
>>
>> I decided to write an APL expression to solve this, and this is what I came
>> up with:
>>
>>     d ← {⍵÷⍺}
>>     (↑¨ 7 = ⍎¨ v) / v ← {"4 " , ↑,/ {{⍵," 4 "}¨⍵} ⍵}¨ ,↑∘.,/4 ⍴ ⊂'+-×d'
>>
>> Now, this program finds two solutions, which is good enough for me. However,
>> my program doesn't find solutions that require parentheses.
>>
>> Problem 1: Can anyone simplify my program?
>> Problem 2: Can anyone come up with a solution that also checks for
>> parentheses?
>>
>> Regards,
>> Elias