Given a hash table T with 25 slots that stores 3000 elements, the load factor α for T is a. 0.0083 b. 0.83 c. 75000 d. 120

1. Break Down the Problem

To find the load factor $\alpha$ of a hash table, we use the formula:

$\alpha = \frac{n}{m}$

where $n$ is the number of elements stored and $m$ is the number of slots in the hash table.

2. Relevant Concepts

In this case:

• $n = 3000$ (the number of elements)
• $m = 25$ (the number of slots)

3. Analysis and Detail

Substituting the given values into the formula:

$\alpha = \frac{3000}{25}$

Performing the calculation:

1. Divide 3000 by 25: $\alpha = 120$

4. Verify and Summarize

The calculation shows that the load factor of the hash table is $120$. Since a load factor above 1 means more elements than slots, this indicates significant overcrowding.

Final Answer

The load factor $\alpha$ for the hash table $T$ is:

d. 120