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| • |
The
worst-case time for a
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sorting
method must be ³ the
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height
of its comparison tree
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– |
The
height corresponds to
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the
worst-case number of
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comparisons
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– |
Each
comparison takes
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Q(1) time
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– |
The
algorithm is doing more
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than
just comparisons
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| • |
What
is the minimum
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possible
height for a binary
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tree
with n! leaves?
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Height ³
log(n!) = Q(n log n)
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This implies that
any
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comparison-based
sorting
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algorithm must
have a worst-
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case time of W(n log n)
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Note:
this is a lower bound;
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thus,
the use of big-Omega
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instead
of big-O
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