Sum and product puzzle: Difference between revisions

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=={{header|J}}==

'''Tacit Solution'''

<syntaxhighlight lang="j">o=. @:

<syntaxhighlight lang="j">(X=. 0&{"1) (Y=. 1&{"1)

and=. *.

X=. 0&{"1

Y=. 1&{"1

⚫

candidates=. ([ echo o (' candidates' ,~ ": o #))

⚫

constraints=. (X ~: Y) and (1 < X) and (1 < Y) and (~~100~~ >: S) ~~and~~ ~~(Y > X~~)

⚫

candidates=. ([ echo o (' candidates' ,~ ": (o=. @:) #))

⚫

constraints=. (([ >: S o ]) and ((1 < X) and (1 < Y) (and=. *.) (X < Y)) o ])

filter0=. candidates o (constraints # ])

S=. X + Y

(S=. X + Y) (P=. X * Y)

⚫

(sd=. S </. ]) (pd=. P </. ]) NB. sum and product decompositions

P=. X * Y

sd=. S </. ] NB. sum decompositions

⚫

pd=. P </. ] NB. product decompositions

patesd=. S (< o P)/. ] NB. products associated to each sum decomposition

pmtod=. P o ; o (pd #~ 1 < P #/. ]) NB. products with more than one decomposition

~~allhave~~=. ('' -: -.)&>"0 _

filter1=. candidates o ((patesd ('' -: -.)&>"0 _ < o pmtod) ; o # sd)

filter1=. candidates o ((patesd allhave < o pmtod) ; o # sd)

filter2=. candidates o ; o (pd #~ 1 = (#&>) o pd)

filter3=. candidates o ; o (sd #~ 1 = (#&>) o sd)

decompositions=. > o , o { o (;~) o i.

show=. 'X=' , ": o X ,' Y=' , ": o Y , ' X+Y=' , ": o (X + Y) , ' X*Y=' , ": o (X*Y)

show=. 'X=' , ": o X ,' Y=' , ": o Y , ' X+Y=' , ": o (X+Y) , ' X*Y=' , ": o (X*Y)

solve=. show o filter3 o filter2 o filter1 o ~~filter0~~ o decompositions f.</syntaxhighlight>

solve=. show o filter3 o filter2 o filter1 o (] filter0 decompositions) f.</syntaxhighlight>

Example use:

<syntaxhighlight lang="j"> solve ~~100~~

<syntaxhighlight lang="j"> solve 1684

706440 candidates

50485 candidates

17485 candidates

1 candidates

X=4 Y=13 X+Y=17 X*Y=52

solve 100

2352 candidates

145 candidates

86 candidates

1 candidates

X=4 Y=13 X+Y=17 X*Y=52~~</syntaxhighlight>~~

X=4 Y=13 X+Y=17 X*Y=52

solve 1684

706440 candidates

50485 candidates

17485 candidates

1 candidates

X=4 Y=13 X+Y=17 X*Y=52

solve 1685

707281 candidates

51011 candidates

17567 candidates

2 candidates

X=4 4 Y=13 61 X+Y=17 65 X*Y=52 244</syntaxhighlight>

The code is tacit and fixed (in other words, it is point-free):

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&{"1) </. ])))@:(([ 0 0&$@(1!:2&2)@:(' candidates' ,~ ":@:#))@:((((0&{"1 + 1&{"1

) <@:(0&{"1 * 1&{"1)/. ]) ('' -: -.)&>"0 _ <@:((0&{"1 * 1&{"1)@:;@:(((0&{"1 * 1&

{"1) </. ]) #~ 1 < (0&{"1 * 1&{"1) #/. ]))) ;@:# (0&{"1 + 1&{"1) </. ]))@:(([ 0

{"1) </. ]) #~ 1 < (0&{"1 * 1&{"1) #/. ]))) ;@:# (0&{"1 + 1&{"1) </. ]))@:(] ([

0&$@(1!:2&2)@:(' candidates' ,~ ":@:#))@:(((0&{"1 ~: 1&{"1) *. (1 < ~~0&{"1) *. (1~~

0 0&$@(1!:2&2)@:(' candidates' ,~ ":@:#))@:((([ >: (0&{"1 + 1&{"1)@:]) *. ((1 <

~~< 1~~&{"1) *. (~~100 >: 0&{"~~1 + 1&{"1) *. 1&{"1 > 0&{"1) # ])~~)@:(~~>@:,@:{@:(;~)@:i.)</syntaxhighlight>

0&{"1) *. (1 < 1&{"1) *. 0&{"1 < 1&{"1)@:]) # ]) >@:,@:{@:(;~)@:i.)</syntaxhighlight>

=={{header|Java}}==