Task: Closest-pair problem




Go: package main

import (
    "fmt"
    "math"
    "math/rand"
    "time"
)

type xy struct {
    x, y float64
}

const n = 1000
const scale = 100.

func d(p1, p2 xy) float64 {
    return math.Hypot(p2.x-p1.x, p2.y-p1.y)
}

func main() {
    rand.Seed(time.Now().Unix())
    points := make([]xy, n)
    for i := range points {
        points[i] = xy{rand.Float64() * scale, rand.Float64() * scale}
    }
    p1, p2 := closestPair(points)
    fmt.Println(p1, p2)
    fmt.Println("distance:", d(p1, p2))
}

func closestPair(points []xy) (p1, p2 xy) {
    if len(points) < 2 {
        panic("at least two points expected")
    }
    min := 2 * scale
    for i, q1 := range points[:len(points)-1] {
        for _, q2 := range points[i+1:] {
            if dq := d(q1, q2); dq < min {
                p1, p2 = q1, q2
                min = dq
            }
        }
    }
    return
}




Python: 

from random import randint, randrange
from operator import itemgetter, attrgetter

infinity = float('inf')



def bruteForceClosestPair(point):
    numPoints = len(point)
    if numPoints < 2:
        return infinity, (None, None)
    return min( ((abs(point[i] - point[j]), (point[i], point[j]))
                 for i in range(numPoints-1)
                 for j in range(i+1,numPoints)),
                key=itemgetter(0))

def closestPair(point):
    xP = sorted(point, key= attrgetter('real'))
    yP = sorted(point, key= attrgetter('imag'))
    return _closestPair(xP, yP)

def _closestPair(xP, yP):
    numPoints = len(xP)
    if numPoints <= 3:
        return bruteForceClosestPair(xP)
    Pl = xP[:numPoints/2]
    Pr = xP[numPoints/2:]
    Yl, Yr = [], []
    xDivider = Pl[-1].real
    for p in yP:
        if p.real <= xDivider:
            Yl.append(p)
        else:
            Yr.append(p)
    dl, pairl = _closestPair(Pl, Yl)
    dr, pairr = _closestPair(Pr, Yr)
    dm, pairm = (dl, pairl) if dl < dr else (dr, pairr)
    
    closeY = [p for p in yP  if abs(p.real - xDivider) < dm]
    numCloseY = len(closeY)
    if numCloseY > 1:
        
        closestY = min( ((abs(closeY[i] - closeY[j]), (closeY[i], closeY[j]))
                         for i in range(numCloseY-1)
                         for j in range(i+1,min(i+8, numCloseY))),
                        key=itemgetter(0))
        return (dm, pairm) if dm <= closestY[0] else closestY
    else:
        return dm, pairm
    
def times():
    
    import timeit

    functions = [bruteForceClosestPair, closestPair]
    for f in functions:
        print 'Time for', f.__name__, timeit.Timer(
            '%s(pointList)' % f.__name__,
            'from closestpair import %s, pointList' % f.__name__).timeit(number=1)
    


pointList = [randint(0,1000)+1j*randint(0,1000) for i in range(2000)]

if __name__ == '__main__':
    pointList = [(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
    print pointList
    print '  bruteForceClosestPair:', bruteForceClosestPair(pointList)
    print '            closestPair:', closestPair(pointList)
    for i in range(10):
        pointList = [randrange(11)+1j*randrange(11) for i in range(10)]
        print '\n', pointList
        print ' bruteForceClosestPair:', bruteForceClosestPair(pointList)
        print '           closestPair:', closestPair(pointList)
    print '\n'
    times()
    times()
    times()