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How
many credits are paid from
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a
Find?
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We
pay from the Find when
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we
(1) change rank groups
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as
we move up the path or
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(2)
reach the root
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How
many rank groups are
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there?
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There
are at most log*n - 1
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rank-groups
(not counting
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group
0, the singletons)
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Thus
Find pays at most
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log*n
credits
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How
many credits are paid from
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nodes?
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If
node v pays then we know
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v is
not a root (thus its rank
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will no
longer change)
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vs
parent is in the same
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rank-group
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v is
going to have a new
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parent
(with a higher rank)
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due to
path compression
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Thus
v pays at most a
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number
of credits equal to
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the
number of different ranks
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in
its rank group
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