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| • |
We
know a node in rank-
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group
g pays less than
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tower(g)
credits
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– |
It
actually pays at most
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tower(g)-tower(g-1)
credits
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| • |
Further,
we know there are
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at
most n/tower(g) nodes in
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rank-group
g
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| • |
Thus,
each rank-group pays
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at
most n credits
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| • |
Note
that there are log*n
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different
rank groups
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| • |
Thus,
the nodes pay at most
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n
log* n credits
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| • |
We
now know that the
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number
of credits paid is
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|
less
than the number of
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|
credits
charged
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|
– |
The
proof is complete
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|
– |
Total
time for n Union/Find
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|
operations
starting from
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singletons
is O(n log*n)
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