This seems to be an interesting thread so let's talk about Ken Iverson and
notation as a tool for thought.
In j notation (projecteuler jumps to mind) brute force solutions may be
easily expressed. How many? Prefix the sentence with a tally verb. How
many are there on [0, 10^18) ? Change 100+i.900 to i.1e18 . Problem
solved, on paper. Rethinking the problem as combinations of ways the
digits add to 5 there are 15 solutions. Brutishness can generate test
cases.
2 (1: + -&! + -&! + %&! + %&!)~ 3
15
Explanation
005 1: 500 is it.
014 3 -&! 2 permutations of 3 items less the ways in which 0 is 1st
023 3 -&! 2
113 3 %&! 2 permutations of 3 items divided by the tally of ways to
form the set
122 3 %&! 2
Relax the constraint, the solution interval is now [0,n), and we want the
solutions tally.
!3 for 014 and 023
3%&!2 for 005 113 221
2 ((2 * !@:]) + (3 * %&!)~) 3
21
side track to implement my brutish solution
NB. "The fluid that passes through is called the filtrate"--wikipedia
NB. mark the filtrate with ones in the logical verb u to adverb Filter
Filter=:(#~`)(`:6)
odometer =: (4 $. $.)@:($&1)
NB. original problem
(10 #. [: (0 ~: {."1)Filter (5 = +/"1)Filter)@:odometer 6 5 5
104 113 122 131 140 203 212 221 230 302 311 320 401 410 500
NB. new challenge, solutions tally. 21 agrees with permutations above
brute =: #@:(10 #. (5 = +/"1)Filter)@:odometer
brute 6 6 6
21
NB. f is the tally of unique arrangements of items
NB. and I've re-derived a formula taught
NB. in probability & statistics 101
f =: !@:# % ([: */@:! #/.~)
brute 6#6 NB. interval [0,1e6)
252
NB. After finally remembering other combinations having digits adding to
5,
+/ f&> ('ooo'&,L:_1;:'ooF oBE oCD BBD BCC'),'ooBBBC';'oBBBBB'
252
NB. care to check? The tally of numbers on [0,1e18) having
NB. digits summing to 5 when expressed in base 10 is... 26334
>WORDS =: (12#'o')&,L:_1('ooo'&,L:_1 ;:'ooF oBE oCD BBD
BCC'),'ooBBBC';'oBBBBB'
oooooooooooooooooF
ooooooooooooooooBE
ooooooooooooooooCD
oooooooooooooooBBD
oooooooooooooooBCC
ooooooooooooooBBBC
oooooooooooooBBBBB
+/ f&> WORDS
26334
>Date: Wed, 16 Jan 2019 01:12:56 -0600
>From: "'Skip Cave' via Programming" <[email protected]>
>To: "[email protected]" <[email protected]>
>Subject: [Jprogramming] Implicit Coding
>Message-ID:
> <caj8lg_cfpxy-s67sp9gdcfwchan5sdzw1sv7fpaha19zmdh...@mail.gmail.com
>
>Content-Type: text/plain; charset="UTF-8"
>
>A Quora question asks "List all the three-digit numbers which have the
>property that the sum of their digits is equal to 5"
>
>I got the answer explicitly, by a straightforward brute force approach::
>a#~5=+/"1]10#.^:_1 a=:100+i.900
>104 113 122 131 140 203 212 221 230 302 311 320 401 410 500
>How can this be written implicitly?
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
