Day 20 k-d tree
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2 changed files with 132 additions and 22 deletions
141
days/day20.st
141
days/day20.st
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@ -1,11 +1,12 @@
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Object subclass: Racetrack [
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| grid distToEnd start end trackLen allCheats |
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| grid distToEnd start end trackLen allCheats tree |
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rows: r
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[ grid := Grid new rows: r.
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self initTrack ]
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initTrack
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[ | pos dir step |
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[ | pos dir step posnList |
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"Find the start, end, and count the path tiles..."
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trackLen := 1.
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grid allPosnsDo: [
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:p | | c | c := grid at: p.
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@ -19,6 +20,7 @@ Object subclass: Racetrack [
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height: grid height
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initWith: [:p | nil].
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"Trace the path, obtaining the distances to the end..."
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pos := start.
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dir := {Posn up. Posn down. Posn left. Posn right} findFirstElt: [
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:dir | self isEmpty: start + dir ].
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@ -31,34 +33,43 @@ Object subclass: Racetrack [
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step := step + 1.
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].
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distToEnd at: end put: 0.
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]
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"Build a k-d tree to answer range queries
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over the {distToEnd . x . y} dimensions."
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posnList := OrderedCollection new.
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distToEnd allPosnsDo: [
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:p | (distToEnd at: p) ifNotNil: [
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:dist | posnList add: {dist. p x. p y}]].
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tree := KDTree fromPoints: posnList. ]
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isEmpty: pos [ ^(grid at: pos) = $. ]
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countCheatsWithTime: time
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[ | total |
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total := 0.
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"allCheats := Bag new."
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grid allPosnsDo: [
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:pos | total := total + (self countCheatsFrom: pos withTime: time) ].
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"allCheats printNl."
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^total ]
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countCheatsFrom: pos withTime: time
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[ | dist |
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[ | dist count |
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dist := distToEnd at: pos.
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dist ifNil: [^0].
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"dist < 100 ifTrue: [^0]."
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^self rangeCount: [
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dist < 102 ifTrue: [^0].
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count := 0.
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self rangeDo: [
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:dpos :ddist |
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self validCheatFrom: pos dist: dist
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to: dpos dist: ddist
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withTime: time
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]
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inManhDistance: time
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from: pos
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maxDist: dist - 100. ]
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(self validCheatFrom: pos dist: dist
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to: dpos dist: ddist
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withTime: time) ifTrue: [
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count := count + 1 ]]
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inManhDistance: time
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from: pos
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maxDist: dist - 102.
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^count ]
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"Answers whether POS -> DPOS is a cheat that indeed only takes
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TIME ps, and saves more than 100 ps."
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validCheatFrom: pos dist: dist
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to: dpos dist: ddist
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withTime: time
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@ -67,15 +78,16 @@ Object subclass: Racetrack [
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(dpos y - pos y) abs.
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ctime > time ifTrue: [^false].
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saved := dist - ddist - ctime.
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"saved > 0 ifTrue: [allCheats add: saved]."
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^saved >= 100 ]
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rangeCount: block
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"Call BLOCK with DPOS and DDIST for each position within
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DISTMH of POS, which is at most MSCORE away from the end.
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BLOCK may be called with other positions."
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OLDrangeDo: block
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inManhDistance: distmh
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from: pos
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maxDist: mscore
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[ | ddist dpos count px py doit |
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count := 0.
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[ | ddist dpos px py |
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dpos := Posn new.
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px := pos x. py := pos y.
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distmh negated to: distmh do: [
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@ -85,9 +97,94 @@ Object subclass: Racetrack [
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dpos x: px + dx; y: py + dy.
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ddist := distToEnd at: dpos.
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ddist ifNotNil: [
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(block value: dpos value: ddist)
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ifTrue: [ count := count + 1 ]]]]].
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^count ]
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block value: dpos value: ddist ]]]] ]
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"Optimisation of the above that uses the k-d tree to answer range queries."
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rangeDo: block
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inManhDistance: distmh
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from: pos
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maxDist: mscore
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[ | min max dpos |
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min := {0. pos x - distmh. pos y - distmh}.
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max := {mscore. pos x + distmh. pos y + distmh}.
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dpos := Posn new.
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tree from: min to: max do: [
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:ddist :dstx :dsty |
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dpos x: dstx y: dsty.
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block value: dpos value: ddist ] asSpreader ]
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]
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Object subclass: KDTree [
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from: min to: max do: block
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[ self subclassResponsibility ]
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]
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KDTree class extend [
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fromPoints: points
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[ ^self fromShuffledPoints: (Random new shuffle: points asArray) ]
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fromShuffledPoints: points
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[ ^self fromShuffledPoints: points axis: 1 ]
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leafMaxSize [ ^5 ]
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fromShuffledPoints: points axis: ax
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[ | med splits dims nextAx value |
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points size <= self leafMaxSize ifTrue: [^KDLeaf new points: points asArray].
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med := self guessMedian: points axis: ax.
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dims := med size.
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nextAx := ax \\ dims + 1.
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value := med at: ax.
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splits := self splitPoints: points axis: ax on: value.
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^KDInner new
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left: (self fromShuffledPoints: (splits at: 1) axis: nextAx)
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right: (self fromShuffledPoints: (splits at: 2) axis: nextAx)
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axis: ax
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value: value ]
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splitPoints: points axis: ax on: val
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[ | l r fairLeft |
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l := OrderedCollection new.
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r := OrderedCollection new.
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fairLeft := true.
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points do: [
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:point | | v onLeft |
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v := point at: ax.
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onLeft := (v < val) or: [
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v = val and: [fairLeft := fairLeft not. fairLeft]].
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(onLeft ifTrue: [l] ifFalse: [r]) add: point ].
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^{l . r} ]
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medianGuessSize [ ^5 ]
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guessMedian: points axis: ax
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[ | arr |
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arr := 1 to: (points size min: self medianGuessSize)
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collect: [:i | points at: i].
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arr sort: [:l :r | (l at: ax) <= (r at: ax)].
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^arr at: arr size // 2 + 1 ]
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]
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KDTree subclass: KDLeaf [
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| points |
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points: n [points := n. "self class leafSize: points size"]
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from: min to: max do: block [ points do: block ]
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printOn: st [ st << 'lf' << points ]
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]
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KDLeaf class extend [
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| leafSizes |
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leafSizes [ ^leafSizes ifNil: [leafSizes := Bag new] ]
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leafSize: sz [ self leafSizes add: sz ]
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]
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KDTree subclass: KDInner [
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| left right axis value |
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left: l right: r axis: ax value: v
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[left:=l. right:=r. axis:=ax. value:=v]
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from: min to: max do: block
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[ (min at: axis) <= value ifTrue: [ left from: min to: max do: block ].
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(max at: axis) >= value ifTrue: [ right from: min to: max do: block ] ]
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printOn: st [ st << '{' << left << ' <= [' << axis << '] '
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<< value << ' <= ' << right << '}' ]
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]
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AOC input: [ Racetrack new rows: stdin toLines asArray ];
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@ -218,6 +218,7 @@ Object extend [ chain [ ^MessageChain new pipelineValue: self ] ]
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Object subclass: Posn [
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| x y | x [^x] y [^y] x: n [x:=n] y: n [y:=n]
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x: nx y: ny [x := nx. y := ny]
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+ o [ ^Posn x: x + o x y: y + o y ]
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+= o [ self x: x + o x; y: y + o y. ]
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@ -384,3 +385,15 @@ Integer extend [
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^{s0 . t0}
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]
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]
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Random extend [
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shuffle: coll
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[ 1 to: coll size do: [
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:i | | j tmp |
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j := self between: 1 and: coll size.
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tmp := coll at: i.
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coll at: i put: (coll at: j).
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coll at: j put: tmp.
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].
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^coll ]
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]
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