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ClosestPair
(pointSet):
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Split pointSet in
half with a
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vertical line so
that half are
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on left and half
are on right;
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Recursively
determine closest
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pair in each
half;
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Let d be
smallest of these two
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distances;
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Search along the
boundary
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between the two
halves to
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see if there are
any pairs
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closer than d;
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| • |
Analysis
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– |
The
last step appears to
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require
time O(n2)
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– |
Recurrence
for total time is
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T(n) =
2T(n/2) + n2
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and
T(1) = 1
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– |
Solution: T(n) = O(n2)
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| • |
The
algorithm’s last step is
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the
problem
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How
can we do the last step
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in
linear time?
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