Zumkeller numbers: Difference between revisions

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Added AppleScript.
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557 edits
m →‎{{header|AppleScript}}: Pulled out the subtotal check to a separate handler. Slight speed improvement by only getting proper divisors and knowing the missing one.
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=={{header|AppleScript}}==
=={{header|AppleScript}}==
This takes about 0.38 seconds to execute the two main searches — then a further 115 for the stretch goal!
This takes about 0.38 seconds to execute the two main searches — then a further 109 for the stretch goal!


<lang applescript>on factors(n)
<lang applescript>on properDivisors(n)
set output to {}
set output to {}
set sqrt to n ^ 0.5
if (n > 1) then
set limit to sqrt div 1
set sqrt to n ^ 0.5
if (limit = sqrt) then
set limit to sqrt div 1
set end of output to limit
if (limit = sqrt) then
set limit to limit - 1
set end of output to limit
⚫
set limit to limit - 1
⚫
end if
⚫
repeat with i from limit to 2 by -1
⚫
if (n mod i is 0) then
⚫
set beginning of output to i
set end of output to n div i
end if
⚫
end repeat
set beginning of output to 1
end if
end if
⚫
repeat with i from limit to 1 by -1
⚫
if (n mod i is 0) then
⚫
set beginning of output to i
⚫
set end of output to n div i
⚫
end if
⚫
end repeat
return output
return output
end factors
end properDivisors


on containsSubtotal(lst, subtotal, i, j)
⚫
on isZumkeller(n)
script o
script o
property divisors : factors(n)
property l : lst
on semiperfect(n, i)
on cs(subtotal, j)
set d to item i of my divisors
set n to item j of my l
if (n = d) then return true
if (n = subtotal) then return true
if (i = 1) then return false
if (j = i) then return false
set i to i - 1
set j to j - 1
return (((n > d) and (semiperfect(n - d, i))) or (semiperfect(n, i)))
return (((subtotal > n) and (cs(subtotal - n, j))) or (cs(subtotal, j)))
end semiperfect
end cs
end script
end script
set sum to 0
return o's cs(subtotal, j)
end containsSubtotal

⚫
on isZumkeller(n)
script o
property divisors : properDivisors(n)
end script
set sum to n
repeat with thisDivisor in o's divisors
repeat with thisDivisor in o's divisors
set sum to sum + thisDivisor
set sum to sum + thisDivisor
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set halfSum to sum / 2
set halfSum to sum / 2
return ((halfSum ≥ n) and (halfSum as integer = halfSum) and (o's semiperfect(halfSum, (count o's divisors) - 1)))
return ((halfSum ≥ n) and (halfSum as integer = halfSum) and (containsSubtotal(o's divisors, halfSum, 1, (count o's divisors))))
end isZumkeller
end isZumkeller


⚫
-- Task code:
on zumkellerNumbers(target, n, interval, customiser)
on zumkellerNumbers(target, n, interval, filter)
-- Params: how many required, first number to test, interval between numbers tested,
-- Params: how many required, first number to test, interval between numbers tested,
-- script object imposing any further constraints on numbers tested.
-- script object imposing any further restrictions on the numbers.
script o
script o
property zumkellers : {}
property zumkellers : {}
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set counter to 0
set counter to 0
repeat until (counter = target)
repeat until (counter = target)
if ((customiser's OK(n)) and (isZumkeller(n))) then
if ((filter's OK(n)) and (isZumkeller(n))) then
set end of o's zumkellers to n
set end of o's zumkellers to n
set counter to counter + 1
set counter to counter + 1
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end zumkellerNumbers
end zumkellerNumbers


⚫
-- Task code:
on format(resultList, heading, resultsPerLine, separator)
on format(resultList, heading, resultsPerLine, separator)
script o
script o
Line 662: Line 673:


{{output}}
{{output}}
<lang applescript>Result:
<lang applescript>"1st 220 Zumkeller numbers:
"1st 220 Zumkeller numbers:
6 12 20 24 28 30 40 42 48 54 56 60 66 70 78 80 84 88 90 96
6 12 20 24 28 30 40 42 48 54 56 60 66 70 78 80 84 88 90 96
102 104 108 112 114 120 126 132 138 140 150 156 160 168 174 176 180 186 192 198
102 104 108 112 114 120 126 132 138 140 150 156 160 168 174 176 180 186 192 198
Retrieved from "https://rosettacode.org/wiki/Zumkeller_numbers"