September 2017 Update
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129
Task/Closest-pair-problem/360-Assembly/closest-pair-problem.360
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129
Task/Closest-pair-problem/360-Assembly/closest-pair-problem.360
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* Closest Pair Problem 10/03/2017
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CLOSEST CSECT
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USING CLOSEST,R13 base register
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B 72(R15) skip savearea
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DC 17F'0' savearea
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STM R14,R12,12(R13) save previous context
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ST R13,4(R15) link backward
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ST R15,8(R13) link forward
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LR R13,R15 set addressability
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LA R6,1 i=1
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LA R7,2 j=2
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BAL R14,DDCALC dd=(px(i)-px(j))^2+(py(i)-py(j))^2
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BAL R14,DDSTORE ddmin=dd; ii=i; jj=j
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LA R6,1 i=1
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DO WHILE=(C,R6,LE,N) do i=1 to n
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LA R7,1 j=1
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DO WHILE=(C,R7,LE,N) do j=1 to n
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BAL R14,DDCALC dd=(px(i)-px(j))^2+(py(i)-py(j))^2
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IF CP,DD,GT,=P'0' THEN if dd>0 then
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IF CP,DD,LT,DDMIN THEN if dd<ddmin then
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BAL R14,DDSTORE ddmin=dd; ii=i; jj=j
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ENDIF , endif
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ENDIF , endif
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LA R7,1(R7) j++
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ENDDO , enddo j
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LA R6,1(R6) i++
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ENDDO , enddo i
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ZAP WPD,DDMIN ddmin
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DP WPD,=PL8'2' ddmin/2
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ZAP SQRT2,WPD(8) sqrt2=ddmin/2
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ZAP SQRT1,DDMIN sqrt1=ddmin
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DO WHILE=(CP,SQRT1,NE,SQRT2) do while sqrt1<>sqrt2
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ZAP SQRT1,SQRT2 sqrt1=sqrt2
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ZAP WPD,DDMIN ddmin
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DP WPD,SQRT1 /sqrt1
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ZAP WP1,WPD(8) ddmin/sqrt1
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AP WP1,SQRT1 +sqrt1
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ZAP WPD,WP1 ~
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DP WPD,=PL8'2' /2
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ZAP SQRT2,WPD(8) sqrt2=(sqrt1+(ddmin/sqrt1))/2
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ENDDO , enddo while
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MVC PG,=CL80'the minimum distance '
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ZAP WP1,SQRT2 sqrt2
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BAL R14,EDITPK edit
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MVC PG+21(L'WC),WC output
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XPRNT PG,L'PG print buffer
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XPRNT =CL22'is between the points:',22
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MVC PG,PGP init buffer
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L R1,II ii
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SLA R1,4 *16
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LA R4,PXY-16(R1) @px(ii)
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MVC WP1,0(R4) px(ii)
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BAL R14,EDITPK edit
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MVC PG+3(L'WC),WC output
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MVC WP1,8(R4) py(ii)
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BAL R14,EDITPK edit
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MVC PG+21(L'WC),WC output
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XPRNT PG,L'PG print buffer
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MVC PG,PGP init buffer
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L R1,JJ jj
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SLA R1,4 *16
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LA R4,PXY-16(R1) @px(jj)
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MVC WP1,0(R4) px(jj)
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BAL R14,EDITPK edit
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MVC PG+3(L'WC),WC output
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MVC WP1,8(R4) py(jj)
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BAL R14,EDITPK edit
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MVC PG+21(L'WC),WC output
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XPRNT PG,L'PG print buffer
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L R13,4(0,R13) restore previous savearea pointer
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LM R14,R12,12(R13) restore previous context
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XR R15,R15 rc=0
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BR R14 exit
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DDCALC EQU * ---- dd=(px(i)-px(j))^2+(py(i)-py(j))^2
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LR R1,R6 i
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SLA R1,4 *16
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LA R4,PXY-16(R1) @px(i)
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LR R1,R7 j
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SLA R1,4 *16
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LA R5,PXY-16(R1) @px(j)
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ZAP WP1,0(8,R4) px(i)
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ZAP WP2,0(8,R5) px(j)
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SP WP1,WP2 px(i)-px(j)
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ZAP WPS,WP1 =
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MP WP1,WPS (px(i)-px(j))*(px(i)-px(j))
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ZAP WP2,8(8,R4) py(i)
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ZAP WP3,8(8,R5) py(j)
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SP WP2,WP3 py(i)-py(j)
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ZAP WPS,WP2 =
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MP WP2,WPS (py(i)-py(j))*(py(i)-py(j))
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AP WP1,WP2 (px(i)-px(j))^2+(py(i)-py(j))^2
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ZAP DD,WP1 dd=(px(i)-px(j))^2+(py(i)-py(j))^2
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BR R14 ---- return
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DDSTORE EQU * ---- ddmin=dd; ii=i; jj=j
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ZAP DDMIN,DD ddmin=dd
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ST R6,II ii=i
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ST R7,JJ jj=j
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BR R14 ---- return
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EDITPK EQU * ----
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MVC WM,MASK set mask
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EDMK WM,WP1 edit and mark
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BCTR R1,0 -1
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MVC 0(1,R1),WM+17 set sign
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MVC WC,WM len17<-len18
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BR R14 ---- return
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N DC A((PGP-PXY)/16)
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PXY DC PL8'0.654682',PL8'0.925557',PL8'0.409382',PL8'0.619391'
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DC PL8'0.891663',PL8'0.888594',PL8'0.716629',PL8'0.996200'
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DC PL8'0.477721',PL8'0.946355',PL8'0.925092',PL8'0.818220'
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DC PL8'0.624291',PL8'0.142924',PL8'0.211332',PL8'0.221507'
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DC PL8'0.293786',PL8'0.691701',PL8'0.839186',PL8'0.728260'
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PGP DC CL80' [+xxxxxxxxx.xxxxxx,+xxxxxxxxx.xxxxxx]'
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MASK DC C' ',7X'20',X'21',X'20',C'.',6X'20',C'-' CL18 15num
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II DS F
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JJ DS F
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DD DS PL8
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DDMIN DS PL8
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SQRT1 DS PL8
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SQRT2 DS PL8
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WP1 DS PL8
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WP2 DS PL8
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WP3 DS PL8
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WPS DS PL8
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WPD DS PL16
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WM DS CL18
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WC DS CL17
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PG DS CL80
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YREGS
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END CLOSEST
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@ -1,16 +1,23 @@
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import Data.List
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import System.Random
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import Control.Monad
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import Control.Arrow
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import Data.Ord
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import Data.List (minimumBy, tails, unfoldr, foldl1') --'
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vecLeng [[a,b],[p,q]] = sqrt $ (a-p)^2+(b-q)^2
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import System.Random (newStdGen, randomRs)
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findClosestPair = foldl1' ((minimumBy (comparing vecLeng). ). (. return). (:)) .
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concatMap (\(x:xs) -> map ((x:).return) xs) . init . tails
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import Control.Arrow ((&&&))
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import Data.Ord (comparing)
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vecLeng [[a, b], [p, q]] = sqrt $ (a - p) ^ 2 + (b - q) ^ 2
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findClosestPair =
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foldl1'' ((minimumBy (comparing vecLeng) .) . (. return) . (:)) .
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concatMap (\(x:xs) -> map ((x :) . return) xs) . init . tails
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testCP = do
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g <- newStdGen
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let pts :: [[Double]]
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pts = take 1000. unfoldr (Just. splitAt 2) $ randomRs(-1,1) g
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print . (id &&& vecLeng ) . findClosestPair $ pts
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g <- newStdGen
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let pts :: [[Double]]
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pts = take 1000 . unfoldr (Just . splitAt 2) $ randomRs (-1, 1) g
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print . (id &&& vecLeng) . findClosestPair $ pts
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main = testCP
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foldl1'' = foldl1'
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16
Task/Closest-pair-problem/Julia/closest-pair-problem.julia
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Task/Closest-pair-problem/Julia/closest-pair-problem.julia
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function closestpair(P::Vector{Vector{T}}) where T <: Number
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N = length(P)
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if N < 2 return (Inf, ()) end
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mindst = norm(P[1] - P[2])
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minpts = (P[1], P[2])
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for i in 1:N-1, j in i+1:N
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tmpdst = norm(P[i] - P[j])
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if tmpdst < mindst
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mindst = tmpdst
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minpts = (P[i], P[j])
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end
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end
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return mindst, minpts
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end
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closestpair([[0, -0.3], [1., 1.], [1.5, 2], [2, 2], [3, 3]])
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79
Task/Closest-pair-problem/Kotlin/closest-pair-problem.kotlin
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Task/Closest-pair-problem/Kotlin/closest-pair-problem.kotlin
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// version 1.1.2
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typealias Point = Pair<Double, Double>
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fun distance(p1: Point, p2: Point) = Math.hypot(p1.first- p2.first, p1.second - p2.second)
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fun bruteForceClosestPair(p: List<Point>): Pair<Double, Pair<Point, Point>> {
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val n = p.size
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if (n < 2) throw IllegalArgumentException("Must be at least two points")
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var minPoints = p[0] to p[1]
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var minDistance = distance(p[0], p[1])
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for (i in 0 until n - 1)
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for (j in i + 1 until n) {
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val dist = distance(p[i], p[j])
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if (dist < minDistance) {
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minDistance = dist
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minPoints = p[i] to p[j]
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}
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}
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return minDistance to Pair(minPoints.first, minPoints.second)
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}
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fun optimizedClosestPair(xP: List<Point>, yP: List<Point>): Pair<Double, Pair<Point, Point>> {
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val n = xP.size
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if (n <= 3) return bruteForceClosestPair(xP)
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val xL = xP.take(n / 2)
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val xR = xP.drop(n / 2)
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val xm = xP[n / 2 - 1].first
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val yL = yP.filter { it.first <= xm }
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val yR = yP.filter { it.first > xm }
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val (dL, pairL) = optimizedClosestPair(xL, yL)
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val (dR, pairR) = optimizedClosestPair(xR, yR)
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var dmin = dR
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var pairMin = pairR
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if (dL < dR) {
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dmin = dL
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pairMin = pairL
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}
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val yS = yP.filter { Math.abs(xm - it.first) < dmin }
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val nS = yS.size
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var closest = dmin
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var closestPair = pairMin
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for (i in 0 until nS - 1) {
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var k = i + 1
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while (k < nS && (yS[k].second - yS[i].second < dmin)) {
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val dist = distance(yS[k], yS[i])
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if (dist < closest) {
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closest = dist
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closestPair = Pair(yS[k], yS[i])
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}
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k++
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}
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}
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return closest to closestPair
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}
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fun main(args: Array<String>) {
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val points = listOf(
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listOf(
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5.0 to 9.0, 9.0 to 3.0, 2.0 to 0.0, 8.0 to 4.0, 7.0 to 4.0,
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9.0 to 10.0, 1.0 to 9.0, 8.0 to 2.0, 0.0 to 10.0, 9.0 to 6.0
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),
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listOf(
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0.654682 to 0.925557, 0.409382 to 0.619391, 0.891663 to 0.888594,
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0.716629 to 0.996200, 0.477721 to 0.946355, 0.925092 to 0.818220,
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0.624291 to 0.142924, 0.211332 to 0.221507, 0.293786 to 0.691701,
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0.839186 to 0.728260
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)
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)
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for (p in points) {
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val (dist, pair) = bruteForceClosestPair(p)
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println("Closest pair (brute force) is ${pair.first} and ${pair.second}, distance $dist")
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val xP = p.sortedBy { it.first }
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val yP = p.sortedBy { it.second }
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val (dist2, pair2) = optimizedClosestPair(xP, yP)
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println("Closest pair (optimized) is ${pair2.first} and ${pair2.second}, distance $dist2\n")
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}
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}
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15
Task/Closest-pair-problem/Zkl/closest-pair-problem-1.zkl
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15
Task/Closest-pair-problem/Zkl/closest-pair-problem-1.zkl
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@ -0,0 +1,15 @@
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class Point{
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fcn init(_x,_y){ var[const] x=_x, y=_y; }
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fcn distance(p){ (p.x-x).hypot(p.y-y) }
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fcn toString { String("Point(",x,",",y,")") }
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}
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// find closest two points using brute ugly force:
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// find all combinations of two points, measure distance, pick smallest
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fcn closestPoints(points){
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pairs:=Utils.Helpers.pickNFrom(2,points);
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triples:=pairs.apply(fcn([(p1,p2)]){ T(p1,p2,p1.distance(p2)) });
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triples.reduce(fcn([(_,_,d1)]p1,[(_,_,d2)]p2){
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if(d1 < d2) p1 else p2
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});
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}
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15
Task/Closest-pair-problem/Zkl/closest-pair-problem-2.zkl
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15
Task/Closest-pair-problem/Zkl/closest-pair-problem-2.zkl
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@ -0,0 +1,15 @@
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points:=T( 5.0, 9.0, 9.0, 3.0,
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2.0, 0.0, 8.0, 4.0,
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7.0, 4.0, 9.0, 10.0,
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1.0, 9.0, 8.0, 2.0,
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0.0, 10.0, 9.0, 6.0 ).pump(List,Void.Read,Point);
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closestPoints(points).println(); //-->L(Point(8,4),Point(7,4),1)
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points:=T( 0.654682, 0.925557, 0.409382, 0.619391,
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0.891663, 0.888594, 0.716629, 0.9962,
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0.477721, 0.946355, 0.925092, 0.81822,
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0.624291, 0.142924, 0.211332, 0.221507,
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0.293786, 0.691701, 0.839186, 0.72826)
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.pump(List,Void.Read,Point);
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closestPoints(points).println();
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