Consider performing uniform hashing on an open address hash table with load factor $\alpha=\frac{n}{m}<1$, where $n$ elements are stored in the table with $m$ slots. The expected number of probes in an unsuccessful search is at most $\frac{1}{1-\alpha}$.
Inserting an element in this hash table requires at most probes,$\_\_\_\_\_\_\_$ on average.
- $\ln \left(\frac{1}{1-\alpha}\right)$
- $\frac{1}{1-\alpha}$
- $1+\frac{\alpha}{2}$
- $\frac{1}{1+\alpha}$
