Consider the formula below for evaluating the number of hash table comparisons:

where:

c = the number of comparisons

L = the load factor of the hash table

Given that a hash table of size 66,319 contains 34,754 items, how many comparisons are expected in a linear probe for an item? Use up to 2 decimal places of the load factor when computing c. Your final answer could include up to 2 decimal places, no spaces.

Question

Consider the formula below for evaluating the number of hash table comparisons:

where:

c = the number of comparisons

L = the load factor of the hash table

Given that a hash table of size 66,319 contains 34,754 items, how many comparisons are expected in a linear probe for an item?  Use up to 2 decimal places of the load factor when computing c. Your final answer could include up to 2 decimal places, no spaces.

BlackTom AI · Accepted Answer

To approach this problem, I first determine the load factor L by dividing the number of items by the hash table size. Here, L = 34,754 / 66,319, which computes to approximately 0.5180 (more precisely about 0.5180–0.5181 when using additional decimal places). Next, I recall the standard formulas for probe counts in linear probing:
- For an unsuccessful search, the expected number of probes (comparisons) is 1 / (1 − L).
- For a successful search (finding an item), the commonly cited average is (1/2) * (1 + 1 / (1 − L)).
These reflect the two main scenarios in linear probing: not finding the item, and finding the item, respectively.

Since the prompt asks for the number of comparisons for an item using linear probing, we interpret this as the typical case of locating an item (a successful search). Therefore, we use the successful-search formula: c = (1/2) * (1 + 1 / (1 − L)).

Plugging in L ≈ 0.5180:
1 − L ≈ 0.4820
1 / (1 − L) ≈ 1 / 0.4820 ≈ 2.074
Then c ≈ (1/2) * (1 + 2.074) ≈ (1/2) * 3.074 ≈ 1.537.
Rounding to two decimal places as requested, c ≈ 1.54.

If instead one were calculating the cost of an unsuccessful search, the result would be 1 / (1 − L) ≈ 2.07, which is notably higher than the approximately 1.54 for a successful search. The key conceptual distinction is between searching for an item that is present versus querying for an absent item.

Summary of steps:
- Compute L = 34,754 / 66,319 ≈ 0.5180.
- Compute 1 − L ≈ 0.4820.
- Compute 1 / (1 − L) ≈ 2.074.
- For a successful search (finding an item), use c = (1/2) * (1 + 1 / (1 − L)) ≈ 1.537 → 1.54.

Note: If the problem intended the cost of an unsuccessful search, the value would be about 2.07, but the interpretation here assumes a successful item lookup in a linear probe.

类似问题

Linear Probing Consider a hash table named idTable that uses linear probing and a hash function of key % 10. Which bucket will 97 be inserted to? HashInsert(idTable, item 97) 0 1 2 3 4 5 6 7 8 9 ??? ??? 92 ??? ??? 45 76 67 78 79

HT-Linear Probing (Search) Given the following hash table and a hash function of key % 10, HashSearch(hashTable, 53) probes A buckets. HashSearch(hashTable, 63) probes B buckets. Note that # probes means the #slots that were visited. 1: A 2: B

Consider the hash table of size 11 that uses linear probing shown below, where the hash function is h(k) = (k mod 11). Thus h(14)=3, h(25)=3. What indices are examined if we now perform get(3)?

A project has a required return of 12.6 percent, an initial cash outflow of $42,100, and cash inflows of $16,500 in Year 1, $11,700 in Year 2, and $10,400 in Year 4. What is the net present value?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单