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Aggregate Method

Let n = number of items in table.

The worst-case running time of this algorithm is O(n).

For n calls the worst-case running time is O(n²).

Double the table size when full. This expansion is performed once every power of 2 steps in 1...n.

Assuming $c_i \;=\; \left\{ \begin{array}{ll} i & {\rm if} \; i-1 \; {\rm is} \; {\rm power} \; {\rm of} \; 2 \\ 1 & {\rm otherwise} \end{array} \right.$ ,

$\sum_{i=1}^{n} c_i \;\leq n \;+\; \sum_{j=0}^{\lfloor lgn \rfloor} 2^j$

This is a geometric series $\sum_{k=0}^n x^k \;=\; \frac{x^{n+1} - 1}{x-1}$

$<\; n \;+\; 2n$

$=\; 3n$

The total amortized cost of a single call to TableInsert is 3.

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