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Unformatted text preview: f the ith insertion. ci = i
1 i 1 Starting from empty table, the cost of a sequence of n INSERT operations is:
n
n
i=1
i=1 ci
ci lg n
lg n n+
n+
<
<
=
= j =0
j =0 2j
2j n + 2n
n + 2n
3n
3n
▪ 40 Dynamic table: insert only 1 2 3 4 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 41 Dynamic table: insert only
Accounting. ・INSERT: charge 3 credits (use 1 credit to insert; save 2 with new item). Theorem. [via accounting method] Starting from an empty dynamic table,
any sequence of n INSERT operations takes O(n) time.
Pf. The algorithm maintains the invariant that there are 2 credits with each
item in right half of table. ・When table doubles, onehalf of the items in the table have 2 credits.
・This pays for the work needed to double the table. ▪ 42 Dynamic table: insert only
Theorem. [via potential method] Starting from an empty dynamic table,
any sequence of n INSERT operations takes O(n) time.
Pf. Let Φ(Di) = 2 size(Di) – capacity(Di).
number of
elements 1 2 3 capa...
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 Spring '14

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