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  1. """
  2.   Compute nearest pair of points using two algorithms
  3.  
  4.   First algorithm is 'brute force' comparison of every possible pair.
  5.   Second, 'divide and conquer', is based on:
  6.     www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt 
  7. """
  8.  
  9. from random import randint, randrange
  10. from operator import itemgetter, attrgetter
  11.  
  12. infinity = float('inf')
  13.  
  14. # Note the use of complex numbers to represent 2D points making distance == abs(P1-P2)
  15.  
  16. def bruteForceClosestPair(point):
  17.     numPoints = len(point)
  18.  
  19.  
  20.     if numPoints < 2:
  21.         return infinity, (None, None)
  22.     return min( ((abs(point[i] - point[j]), (point[i], point[j]))
  23.                  for i in range(numPoints-1)
  24.                  for j in range(i+1,numPoints)),
  25.                 key=itemgetter(0))
  26.  
  27. def closestPair(point):
  28.     xP = sorted(point, key= attrgetter('real'))
  29.     yP = sorted(point, key= attrgetter('imag'))
  30.     return _closestPair(xP, yP)
  31.  
  32. def _closestPair(xP, yP):
  33.     numPoints = len(xP)
  34.     if numPoints <= 3:
  35.         return bruteForceClosestPair(xP)
  36.     Pl = xP[:numPoints/2]
  37.     Pr = xP[numPoints/2:]
  38.     Yl, Yr = [], []
  39.     xDivider = Pl[-1].real
  40.     for p in yP:
  41.         if p.real <= xDivider:
  42.             Yl.append(p)
  43.         else:
  44.             Yr.append(p)
  45.     dl, pairl = _closestPair(Pl, Yl)
  46.     dr, pairr = _closestPair(Pr, Yr)
  47.     dm, pairm = (dl, pairl) if dl < dr else (dr, pairr)
  48.     # Points within dm of xDivider sorted by Y coord
  49.     closeY = [p for p in yP  if abs(p.real - xDivider) < dm]
  50.     numCloseY = len(closeY)
  51.     if numCloseY > 1:
  52.         # There is a proof that you only need compare a max of 7 next points
  53.         closestY = min( ((abs(closeY[i] - closeY[j]), (closeY[i], closeY[j]))
  54.                          for i in range(numCloseY-1)
  55.                          for j in range(i+1,min(i+8, numCloseY))),
  56.                         key=itemgetter(0))
  57.         return (dm, pairm) if dm <= closestY[0] else closestY
  58.     else:
  59.         return dm, pairm
  60.  
  61. def times():
  62.     ''' Time the different functions
  63.     '''
  64.     import timeit
  65.  
  66.     functions = [bruteForceClosestPair, closestPair]
  67.     for f in functions:
  68.         print 'Time for', f.__name__, timeit.Timer(
  69.             '%s(pointList)' % f.__name__,
  70.             'from closestpair import %s, pointList' % f.__name__).timeit(number=1)
  71.  
  72.  
  73.  
  74. pointList = [randint(0,1000)+1j*randint(0,1000) for i in range(2000)]
  75.  
  76. if __name__ == '__main__':
  77.     pointList = [(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
  78.     print pointList
  79.     print '  bruteForceClosestPair:', bruteForceClosestPair(pointList)
  80.     print '            closestPair:', closestPair(pointList)
  81.     for i in range(3):
  82.         pointList = [randrange(11)+1j*randrange(11) for i in range(10)]
  83.         print '\n', pointList 
  84.         print ' bruteForceClosestPair:', bruteForceClosestPair(pointList)
  85.         print '           closestPair:', closestPair(pointList)
  86.     print '\n'
  87.     times()
  88.     times()
  89.     times()
  90.  
  91. #testPl = [(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
  92. #print(closestPair(testPl))
  93.  
  94.  
Runtime error #stdin #stdout #stderr 0.03s 10464KB
comments (?)
stdin
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Standard input is empty
stdout
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[(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
  bruteForceClosestPair: (1.0, ((8+4j), (7+4j)))
            closestPair: (1.0, ((8+4j), (7+4j)))

[(7+7j), (7+1j), 2j, (7+0j), (2+3j), (2+3j), (10+3j), (3+8j), (9+5j), (3+2j)]
 bruteForceClosestPair: (0.0, ((2+3j), (2+3j)))
           closestPair: (0.0, ((2+3j), (2+3j)))

[(6+0j), (1+4j), (8+8j), (7+2j), (6+9j), (7+8j), (4+10j), 1j, (8+1j), (1+2j)]
 bruteForceClosestPair: (1.0, ((8+8j), (7+8j)))
           closestPair: (1.0, ((7+8j), (8+8j)))

[(6+1j), (9+9j), (9+5j), 10j, (6+1j), (2+8j), (2+10j), 9j, 7j, (3+8j)]
 bruteForceClosestPair: (0.0, ((6+1j), (6+1j)))
           closestPair: (0.0, ((6+1j), (6+1j)))


Time for bruteForceClosestPair
stderr
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Traceback (most recent call last):
  File "prog.py", line 87, in <module>
  File "prog.py", line 70, in times
  File "/usr/lib/python2.7/timeit.py", line 195, in timeit
    timing = self.inner(it, self.timer)
  File "<timeit-src>", line 3, in inner
ImportError: No module named closestpair
https://ideone.com/1u27f9
Closest pair
language:
Python (cpython 2.7.16)
created:
11 years ago
visibility:
public

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