HMap_1
In the implementation discussed in our lectures, Hash Tables using Linear Probing to resolve collisions increase the likelihood of finding an empty slot if the load factor is less than or equal to:

Question

BlackTom AI · Accepted Answer

We begin by considering how linear probing behaves as the table fills up. 
Option A: 0.75. The statement claims that the likelihood of finding an empty slot remains favorable when the load factor α is ≤ 0.75. In many hash table analyses, a typical practical threshold is around 0.7–0.75, where there is still a reasonable chance to locate an empty slot during insertion before performance degrades sharply due to clustering. Therefore, this option aligns with common engineering guidelines and is plausible as the threshold being asked about.
Option B: 0.25. A load factor of 0.25 means the table is only 25% full, which certainly preserves a high probability of finding an empty slot, but the question asks for the point up to which the likelihood remains high. 0.25 is unnecessarily conservative and not the commonly cited threshold for maintaining “likelihood of finding an empty slot” during probing; the threshold is typically chosen higher, so this is not the stated bound.
Option C: 0.50. At α = 0.50, half the slots are occupied. While the chance of finding an empty slot is still good, many analyses and practical guidelines point to a higher upper limit before performance degrades notably. It’s reasonable but not the conventional threshold singled out for “increasing the likelihood” up to a specific limit; the phrasing usually targets a value around 0.75, making this a less precise match for the stated criterion.
Option D: 1.00. A load factor of 1.00 means the table is completely full, leaving no empty slots at all. In linear probing, this is the absolute boundary where insertion would fail (in a standard open-addressing scheme without resizing). Thus, saying the likelihood of finding an empty slot is favorable up to 1.00 is incorrect; in fact, beyond about α = 0.7–0.75 the chance drops quickly, and at 1.0 there is none.
In summary, the option stating 0.75 captures the commonly cited practical threshold at or below which the probability of locating an empty slot remains reasonably favorable during linear probing, whereas the other choices either underestimate the practical bound, or describe conditions where an empty slot is no longer available or becomes much less likely.

HMap_1 In the implementation discussed in our lectures, Hash Tables using Linear Probing to resolve collisions increase the likelihood of finding an empty slot if the load factor is less than or equal to:

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