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Analysis of Chaining

Let the load factor $\alpha$ be calculated as number of keys stored / number of slots = n/m. For our earlier example, \(\alpha \;=\; \frac{100}{10} \;=\; 10\).

$\alpha$ represents the of the chain.

The performance of Search is relative to the performance of the hash function computation and the length of the chain, or \(\Theta(1 + \alpha)\), both for successful and unsuccessful searches.

Thus, if m is proportional to n, then $\alpha$ is a constant, and all operations are $\Theta(1)$.

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