new tasks

Task/Closest-pair_problem/Python/closest_pair_problem.py

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+"""
+  Compute nearest pair of points using two algorithms
+
+  First algorithm is 'brute force' comparison of every possible pair.
+  Second, 'divide and conquer', is based on:
+    www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt
+"""
+
+from random import randint, randrange
+from operator import itemgetter, attrgetter
+
+infinity = float('inf')
+
+# Note the use of complex numbers to represent 2D points making distance == abs(P1-P2)
+
+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)
+    # Points within dm of xDivider sorted by Y coord
+    closeY = [p for p in yP  if abs(p.real - xDivider) < dm]
+    numCloseY = len(closeY)
+    if numCloseY > 1:
+        # There is a proof that you only need compare a max of 7 next points
+        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():
+    ''' Time the different functions
+    '''
+    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()