June 2018 Update
This commit is contained in:
Ingy döt Net
parent
ba8067c3b7
commit
22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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@ -1,13 +1,13 @@
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use framework "Foundation"
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property ca : current application
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-- HERONIAN TRIANGLES --------------------------------------------------------
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-- heroniansOfSideUpTo :: Int -> [(Int, Int, Int)]
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on heroniansOfSideUpTo(n)
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script sideA
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on lambda(a)
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on |λ|(a)
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script sideB
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on lambda(b)
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on |λ|(b)
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script sideC
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-- primitiveHeronian :: Int -> Int -> Int -> Bool
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on primitiveHeronian(x, y, z)
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@ -16,55 +16,51 @@ on heroniansOfSideUpTo(n)
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isIntegerValue(hArea(x, y, z))
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end primitiveHeronian
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on lambda(c)
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on |λ|(c)
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if primitiveHeronian(a, b, c) then
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[[a, b, c]]
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{{a, b, c}}
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else
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[]
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{}
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end if
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end lambda
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end |λ|
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end script
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concatMap(sideC, range(b, n))
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end lambda
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concatMap(sideC, enumFromTo(b, n))
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end |λ|
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end script
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concatMap(sideB, range(a, n))
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end lambda
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concatMap(sideB, enumFromTo(a, n))
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end |λ|
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end script
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concatMap(sideA, range(1, n))
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concatMap(sideA, enumFromTo(1, n))
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end heroniansOfSideUpTo
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-- TEST
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-- TEST ----------------------------------------------------------------------
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on run
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set n to 200
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set lstHeron to sortByKeys(map(triangleDimensions, ¬
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heroniansOfSideUpTo(n)), ¬
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{"area", "perimeter", "maxSide"})
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set lstHeron to ¬
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sortByComparing({{"area", true}, {"perimeter", true}, {"maxSide", true}}, ¬
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map(triangleDimensions, heroniansOfSideUpTo(n)))
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set lstCols to {"sides", "perimeter", "area"}
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set lstColWidths to [20, 15, 0]
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set lstColWidths to {20, 15, 0}
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set area to 210
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script areaFilter
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-- Record -> [Record]
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on lambda(recTriangle)
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on |λ|(recTriangle)
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if area of recTriangle = area then
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[recTriangle]
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{recTriangle}
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else
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[]
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{}
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end if
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end lambda
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end |λ|
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end script
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intercalate("
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", {("Number of triangles found (with sides <= 200): " & ¬
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intercalate("\n \n", {("Number of triangles found (with sides <= 200): " & ¬
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length of lstHeron as string), ¬
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¬
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tabulation("First 10, ordered by area, perimeter, longest side", ¬
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@ -74,8 +70,6 @@ on run
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concatMap(areaFilter, lstHeron), lstCols, lstColWidths)})
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end run
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-- triangleDimensions :: (Int, Int, Int) ->
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-- {sides: (Int, Int, Int), area: Int, perimeter: Int, maxSize: Int}
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on triangleDimensions(lstSides)
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@ -105,23 +99,23 @@ on gcd(m, n)
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end gcd
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-- TABLE FORMATTING
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-- TABULATION ----------------------------------------------------------------
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-- tabulation :: [Record] -> [String] -> String -> [Integer] -> String
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on tabulation(strLegend, lstRecords, lstKeys, lstWidths)
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script heading
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on lambda(strTitle, iCol)
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set str to toCapitalized(strTitle)
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str & nreps(space, (item iCol of lstWidths) - (length of str))
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end lambda
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on |λ|(strTitle, iCol)
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set str to toTitle(strTitle)
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str & replicate((item iCol of lstWidths) - (length of str), space)
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end |λ|
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end script
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script lineString
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on lambda(rec)
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on |λ|(rec)
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script fieldString
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-- fieldString :: String -> Int -> String
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on lambda(strKey, i)
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set v to keyValue(rec, strKey)
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on |λ|(strKey, i)
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set v to keyValue(strKey, rec)
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if class of v is list then
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set strData to ("(" & intercalate(", ", v) & ")")
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@ -129,12 +123,12 @@ on tabulation(strLegend, lstRecords, lstKeys, lstWidths)
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set strData to v as string
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end if
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strData & nreps(space, (item i of (lstWidths)) - (length of strData))
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end lambda
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strData & replicate(space, (item i of (lstWidths)) - (length of strData))
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end |λ|
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end script
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tab & intercalate(tab, map(fieldString, lstKeys))
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end lambda
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end |λ|
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end script
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strLegend & ":" & linefeed & linefeed & ¬
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@ -143,81 +137,52 @@ on tabulation(strLegend, lstRecords, lstKeys, lstWidths)
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intercalate(linefeed, map(lineString, lstRecords))
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end tabulation
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-- isIntegerValue :: Num -> Bool
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on isIntegerValue(n)
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{real, integer} contains class of n and (n = (n as integer))
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end isIntegerValue
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-- GENERIC FUNCTIONS ---------------------------------------------------------
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-- sortByKeys :: [Record] -> [String] -> [Record]
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on sortByKeys(lstRecords, lstKeys)
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script keyDescriptor
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on lambda(strKey)
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ca's NSSortDescriptor's ¬
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sortDescriptorWithKey:(strKey) ascending:true
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end lambda
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end script
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((ca's NSArray's arrayWithArray:lstRecords)'s ¬
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sortedArrayUsingDescriptors:(map(keyDescriptor, lstKeys))) as list
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end sortByKeys
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-- keyValue :: Record -> String -> a
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on keyValue(rec, strKey)
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item 1 of ((ca's NSArray's ¬
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arrayWithObject:((ca's NSDictionary's dictionaryWithDictionary:rec)'s ¬
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objectForKey:strKey)) as list)
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end keyValue
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-- GENERIC FUNCTIONS
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-- concat :: [[a]] -> [a] | [String] -> String
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on concat(xs)
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if length of xs > 0 and class of (item 1 of xs) is string then
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set acc to ""
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else
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set acc to {}
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end if
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repeat with i from 1 to length of xs
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set acc to acc & item i of xs
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end repeat
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acc
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end concat
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-- concatMap :: (a -> [b]) -> [a] -> [b]
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on concatMap(f, xs)
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script append
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on lambda(a, b)
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a & b
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end lambda
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end script
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foldl(append, {}, map(f, xs))
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concat(map(f, xs))
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end concatMap
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-- enumFromTo :: Int -> Int -> [Int]
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on enumFromTo(m, n)
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if m > n then
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set d to -1
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else
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set d to 1
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end if
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set lst to {}
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repeat with i from m to n by d
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set end of lst to i
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end repeat
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return lst
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end enumFromTo
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-- foldl :: (a -> b -> a) -> a -> [b] -> a
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on foldl(f, startValue, xs)
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tell mReturn(f)
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set v to startValue
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set lng to length of xs
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repeat with i from 1 to lng
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set v to lambda(v, item i of xs, i, xs)
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set v to |λ|(v, item i of xs, i, xs)
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end repeat
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return v
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end tell
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end foldl
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-- map :: (a -> b) -> [a] -> [b]
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on map(f, xs)
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tell mReturn(f)
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set lng to length of xs
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set lst to {}
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repeat with i from 1 to lng
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set end of lst to lambda(item i of xs, i, xs)
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end repeat
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return lst
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end tell
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end map
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-- range :: Int -> Int -> [Int]
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on range(m, n)
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set d to 1
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if n < m then set d to -1
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set lst to {}
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repeat with i from m to n by d
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set end of lst to i
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end repeat
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return lst
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end range
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-- intercalate :: Text -> [Text] -> Text
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on intercalate(strText, lstText)
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set {dlm, my text item delimiters} to {my text item delimiters, strText}
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@ -226,24 +191,33 @@ on intercalate(strText, lstText)
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return strJoined
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end intercalate
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-- Text -> Text
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on toCapitalized(str)
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((ca's NSString's stringWithString:(str))'s ¬
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capitalizedStringWithLocale:(ca's NSLocale's currentLocale())) as text
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end toCapitalized
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-- isIntegerValue :: Num -> Bool
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on isIntegerValue(n)
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{real, integer} contains class of n and (n = (n as integer))
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end isIntegerValue
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-- String -> Int -> String
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on nreps(s, n)
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set o to ""
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if n < 1 then return o
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-- keyValue :: String -> Record -> Maybe String
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on keyValue(strKey, rec)
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set ca to current application
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set v to (ca's NSDictionary's dictionaryWithDictionary:rec)'s objectForKey:strKey
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if v is not missing value then
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item 1 of ((ca's NSArray's arrayWithObject:v) as list)
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else
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missing value
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end if
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end keyValue
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repeat while (n > 1)
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if (n mod 2) > 0 then set o to o & s
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set n to (n div 2)
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set s to (s & s)
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end repeat
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return o & s
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end nreps
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-- map :: (a -> b) -> [a] -> [b]
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on map(f, xs)
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tell mReturn(f)
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set lng to length of xs
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set lst to {}
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repeat with i from 1 to lng
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set end of lst to |λ|(item i of xs, i, xs)
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end repeat
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return lst
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end tell
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end map
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-- Lift 2nd class handler function into 1st class script wrapper
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-- mReturn :: Handler -> Script
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@ -252,7 +226,52 @@ on mReturn(f)
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f
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else
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script
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property lambda : f
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property |λ| : f
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end script
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end if
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end mReturn
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-- replicate :: Int -> String -> String
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on replicate(n, s)
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set out to ""
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if n < 1 then return out
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set dbl to s
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repeat while (n > 1)
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if (n mod 2) > 0 then set out to out & dbl
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set n to (n div 2)
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set dbl to (dbl & dbl)
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end repeat
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return out & dbl
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end replicate
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-- List of {strKey, blnAscending} pairs -> list of records -> sorted list of records
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-- sortByComparing :: [(String, Bool)] -> [Records] -> [Records]
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on sortByComparing(keyDirections, xs)
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set ca to current application
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script recDict
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on |λ|(x)
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ca's NSDictionary's dictionaryWithDictionary:x
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end |λ|
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end script
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set dcts to map(recDict, xs)
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script asDescriptor
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on |λ|(kd)
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set {k, d} to kd
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ca's NSSortDescriptor's sortDescriptorWithKey:k ascending:d selector:dcts
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end |λ|
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end script
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((ca's NSArray's arrayWithArray:dcts)'s ¬
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sortedArrayUsingDescriptors:map(asDescriptor, keyDirections)) as list
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end sortByComparing
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-- toTitle :: String -> String
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on toTitle(str)
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set ca to current application
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((ca's NSString's stringWithString:(str))'s ¬
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capitalizedStringWithLocale:(ca's NSLocale's currentLocale())) as text
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end toTitle
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122
Task/Heronian-triangles/C/heronian-triangles.c
Normal file
122
Task/Heronian-triangles/C/heronian-triangles.c
Normal file
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@ -0,0 +1,122 @@
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/*Abhishek Ghosh, 6th October 2017*/
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#include<stdlib.h>
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#include<stdio.h>
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#include<math.h>
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typedef struct{
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int a,b,c;
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int perimeter;
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double area;
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}triangle;
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typedef struct elem{
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triangle t;
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struct elem* next;
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}cell;
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typedef cell* list;
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void addAndOrderList(list *a,triangle t){
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list iter,temp;
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int flag = 0;
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if(*a==NULL){
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*a = (list)malloc(sizeof(cell));
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(*a)->t = t;
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(*a)->next = NULL;
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}
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else{
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temp = (list)malloc(sizeof(cell));
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iter = *a;
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while(iter->next!=NULL){
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if(((iter->t.area<t.area)||(iter->t.area==t.area && iter->t.perimeter<t.perimeter)||(iter->t.area==t.area && iter->t.perimeter==t.perimeter && iter->t.a<=t.a))
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&&
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(iter->next==NULL||(t.area<iter->next->t.area || t.perimeter<iter->next->t.perimeter || t.a<iter->next->t.a))){
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temp->t = t;
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temp->next = iter->next;
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iter->next = temp;
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flag = 1;
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break;
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}
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iter = iter->next;
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}
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if(flag!=1){
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temp->t = t;
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temp->next = NULL;
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iter->next = temp;
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}
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}
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}
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int gcd(int a,int b){
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if(b!=0)
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return gcd(b,a%b);
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return a;
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}
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void calculateArea(triangle *t){
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(*t).perimeter = (*t).a + (*t).b + (*t).c;
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(*t).area = sqrt(0.5*(*t).perimeter*(0.5*(*t).perimeter - (*t).a)*(0.5*(*t).perimeter - (*t).b)*(0.5*(*t).perimeter - (*t).c));
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}
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list generateTriangleList(int maxSide,int *count){
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int a,b,c;
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triangle t;
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list herons = NULL;
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*count = 0;
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for(a=1;a<=maxSide;a++){
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for(b=1;b<=a;b++){
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for(c=1;c<=b;c++){
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if(c+b > a && gcd(gcd(a,b),c)==1){
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t = (triangle){a,b,c};
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calculateArea(&t);
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if(t.area/(int)t.area == 1){
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addAndOrderList(&herons,t);
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(*count)++;
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}
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}
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}
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}
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}
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return herons;
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}
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void printList(list a,int limit,int area){
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list iter = a;
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int count = 1;
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printf("\nDimensions\tPerimeter\tArea");
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while(iter!=NULL && count!=limit+1){
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if(area==-1 ||(area==iter->t.area)){
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printf("\n%d x %d x %d\t%d\t\t%d",iter->t.a,iter->t.b,iter->t.c,iter->t.perimeter,(int)iter->t.area);
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count++;
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}
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iter = iter->next;
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}
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}
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int main(int argC,char* argV[])
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{
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int count;
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list herons = NULL;
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if(argC!=4)
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printf("Usage : %s <Max side, max triangles to print and area, -1 for area to ignore>",argV[0]);
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else{
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herons = generateTriangleList(atoi(argV[1]),&count);
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printf("Triangles found : %d",count);
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(atoi(argV[3])==-1)?printf("\nPrinting first %s triangles.",argV[2]):printf("\nPrinting triangles with area %s square units.",argV[3]);
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printList(herons,atoi(argV[2]),atoi(argV[3]));
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free(herons);
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}
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return 0;
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}
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@ -1,8 +1,8 @@
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/*REXX program generates & displays primitive Heronian triangles by side length and area*/
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parse arg N first area . /*obtain optional arguments from the CL*/
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if N=='' | N==',' then N=200 /*Not specified? Then use the default.*/
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if first=='' | first==',' then first= 10 /* " " " " " " */
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if area=='' | area==',' then area=210 /* " " " " " " */
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if N=='' | N=="," then N=200 /*Not specified? Then use the default.*/
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if first=='' | first=="," then first= 10 /* " " " " " " */
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if area=='' | area=="," then area=210 /* " " " " " " */
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numeric digits 99; numeric digits max(9, 1+length(N**5)) /*ensure 'nuff decimal digits.*/
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call Heron; HT= 'Heronian triangles' /*invoke the Heron subroutine. */
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say # ' primitive' HT "found with sides up to " N ' (inclusive).'
|
||||
|
|
|
|||
|
|
@ -1,32 +1,32 @@
|
|||
/*REXX program generates & displays primitive Heronian triangles by side length and area*/
|
||||
parse arg N first area . /*obtain optional arguments from the CL*/
|
||||
if N=='' | N==',' then N=200 /*Not specified? Then use the default.*/
|
||||
if first=='' | first==',' then first= 10 /* " " " " " " */
|
||||
if area=='' | area==',' then area=210 /* " " " " " " */
|
||||
if N=='' | N=="," then N=200 /*Not specified? Then use the default.*/
|
||||
if first=='' | first=="," then first= 10 /* " " " " " " */
|
||||
if area=='' | area=="," then area=210 /* " " " " " " */
|
||||
numeric digits 99; numeric digits max(9, 1+length(N**5)) /*ensure 'nuff decimal digits.*/
|
||||
call Heron; HT= 'Heronian triangles' /*invoke the Heron subroutine. */
|
||||
say # ' primitive' HT "found with sides up to " N ' (inclusive).'
|
||||
call show , 'Listing of the first ' first ' primitive' HT":"
|
||||
say # ' primitive' HT "found with sides up to " N ' (inclusive).'
|
||||
call show , 'Listing of the first ' first ' primitive' HT":"
|
||||
call show area, 'Listing of the (above) found primitive' HT "with an area of " area
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
Heron: @.=0; #=0; !.=.; minP=9e9; maxA=0; maxP=0; minA=9e9; Ln=length(N) /* __ */
|
||||
do i=5 to N**2%2; _=i*i; !._=i; end /*pre-calculate a fast √ */
|
||||
do i=5 to N**2%2; _=i*i; !._=i; end /*pre-calculate a fast √ */
|
||||
do a=3 to N /*start at a minimum side length of 3. */
|
||||
even= a//2==0 /*if A is even, B and C must be odd.*/
|
||||
do b=a+even to N by 1+even; ab=a+b /*AB: is a shortcut sum. */
|
||||
even= (a//2==0) /*if A is even, B and C must be odd.*/
|
||||
do b=a+even to N by 1+even; ab=a + b /*AB: is a shortcut sum. */
|
||||
if b//2==0 then bump=1 /*B is even? Then C is odd. */
|
||||
else if even then bump=0 /*A is even? " " " " */
|
||||
else bump=1 /*A & B odd, biz as usual. */
|
||||
do c=b+bump to N by 2; s=(ab+c)%2 /*calculate perimeter: S. */
|
||||
do c=b+bump to N by 2; s=(ab + c) % 2 /*calculate perimeter: S. */
|
||||
_=s*(s-a)*(s-b)*(s-c); if !._==. then iterate /*Is _ not a square? Skip.*/
|
||||
ar=!._; if ar*ar\==_ then iterate /*Area not an integer? Skip.*/
|
||||
if hGCD(a,b,c)\==1 then iterate /*GCD of sides not 1? Skip.*/
|
||||
#=#+1; p=ab+c /*primitive Heronian triangle*/
|
||||
minP=min( p,minP); maxP=max( p,maxP); Lp=length(maxP)
|
||||
minA=min(ar,minA); maxA=max(ar,maxA); La=length(maxA); @.ar=
|
||||
_=@.ar.p.0+1 /*bump the triangle counter.*/
|
||||
@.ar.p.0=_; @.ar.p._=right(a,Ln) right(b,Ln) right(c,Ln) /*unique.*/
|
||||
if hGCD(a,b,c) \== 1 then iterate /*GCD of sides not 1? Skip.*/
|
||||
#=# + 1; p=ab + c /*primitive Heronian triangle*/
|
||||
minP=min( p, minP); maxP=max( p, maxP); Lp=length(maxP)
|
||||
minA=min(ar, minA); maxA=max(ar, maxA); La=length(maxA); @.ar=
|
||||
_=@.ar.p.0 + 1 /*bump the triangle counter. */
|
||||
@.ar.p.0=_; @.ar.p._=right(a, Ln) right(b, Ln) right(c, Ln) /*unique.*/
|
||||
end /*c*/ /* [↑] keep each unique perimeter #. */
|
||||
end /*b*/
|
||||
end /*a*/
|
||||
|
|
@ -43,3 +43,4 @@ show: m=0; say; say; parse arg ae; say arg(2); if ae\=='' then
|
|||
end /*k*/
|
||||
end /*j*/ /* [↑] use the known perimeters. */
|
||||
end /*i*/ /* [↑] show any found triangles. */
|
||||
return
|
||||
|
|
|
|||
43
Task/Heronian-triangles/Ring/heronian-triangles.ring
Normal file
43
Task/Heronian-triangles/Ring/heronian-triangles.ring
Normal file
|
|
@ -0,0 +1,43 @@
|
|||
# Project : Heronian triangles
|
||||
# Date : 2017/11/04
|
||||
# Author : Gal Zsolt (~ CalmoSoft ~)
|
||||
# Email : <calmosoft@gmail.com>
|
||||
|
||||
see "Heronian triangles with sides up to 200" + nl
|
||||
see "Sides Perimeter Area" + nl
|
||||
for n = 1 to 200
|
||||
for m = n to 200
|
||||
for p = m to 200
|
||||
s = (n + m + p) / 2
|
||||
w = sqrt(s * (s - n) * (s - m) * (s - p))
|
||||
bool = (gcd(n, m) = 1 or gcd(n, m) = n) and (gcd(n, p) = 1 or gcd(n, p) = n) and (gcd(m, p) = 1 or gcd(m, p) = m)
|
||||
if w = floor(w) and w > 0 and bool
|
||||
see "{" + n + ", " + m + ", " + p + "}" + " " + s*2 + " " + w + nl
|
||||
ok
|
||||
next
|
||||
next
|
||||
next
|
||||
see nl
|
||||
|
||||
see "Heronian triangles with area 210:" + nl
|
||||
see "Sides Perimeter Area" + nl
|
||||
for n = 1 to 150
|
||||
for m = n to 150
|
||||
for p = m to 150
|
||||
s = (n + m + p) / 2
|
||||
w = sqrt(s * (s - n) * (s - m) * (s - p))
|
||||
bool = (gcd(n, m) = 1 or gcd(n, m) = n) and (gcd(n, p) = 1 or gcd(n, p) = n) and (gcd(m, p) = 1 or gcd(m, p) = m)
|
||||
if w = 210 and bool
|
||||
see "{" + n + ", " + m + ", " + p + "}" + " " + s*2 + " " + w + nl
|
||||
ok
|
||||
next
|
||||
next
|
||||
next
|
||||
|
||||
func gcd(gcd, b)
|
||||
while b
|
||||
c = gcd
|
||||
gcd = b
|
||||
b = c % b
|
||||
end
|
||||
return gcd
|
||||
Loading…
Add table
Add a link
Reference in a new issue