What is the worst-case complexity of get in separate chaining? (Make no assumption about the load factor or how good the hash function is.)

Question

BlackTom AI · Accepted Answer

In separate chaining the worst-case cost of a get operation is O(n) because all n keys might be stored in the same chain (bucket), forcing a linear scan.

1) Relevant knowledge points and concepts
- Separate chaining stores entries in buckets (typically linked lists or dynamic arrays) based on hash values.
- The get(key) operation computes the bucket index then searches that bucket for the key.
- Worst-case complexity assumes no favorable conditions: the hash function may be pathological and the load factor may be large.

2) Step-by-step reasoning
- Let n be the total number of items in the hash table.
- In the worst case the hash function maps every key to the same bucket, so that one bucket contains all n items.
- After computing the bucket index (O(1)), get must search through the entire bucket to find the key or determine it is absent.
- If the bucket is implemented as a singly linked list or array, searching requires comparing the target key with each stored key until match or end is reached.

3) Intermediate steps / simple calculation
- Comparisons required in worst case = number of elements in bucket = n.
- Time = O(1) (compute hash) + O(n) (scan bucket) = O(n).

4) Why the correct answer is correct
- Because the bucket can contain all n items, scanning that bucket is linear in n, so the asymptotic worst-case runtime for get is O(n).

5) Why other options are incorrect
- O(1): This is an average-case or expected performance with a good hash and bounded load factor, but not guaranteed in the worst case.
- O(log n): Achievable only if each bucket uses a balanced tree (not standard separate chaining) or other special structure; not guaranteed here.
- O(n2): This is asymptotically larger than needed for a single get; a single get cannot cost quadratic time in n.

6) Conclusion
The worst-case complexity of get in separate chaining (with no assumptions) is O(n), which matches the provided correct answer.

What is the worst-case complexity of get in separate chaining? (Make no assumption about the load factor or how good the hash function is.)单项选择题

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What is the worst-case complexity of get in separate chaining? (Make no assumption about the load factor or how good the hash function is.)单项选择题

类似问题

Open Addressing One of the advantages of chained hash table over the open addressing scheme is ______

Open Addressing One of the advantages of chained hash table over the open addressing scheme is ______

What is the worst-case complexity of insert in separate chaining? (Make no assumption about the load factor or how good the hash function is.)

In a separate chaining hashtable, what is the impact of increasing the load factor above 1?

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(4)?

Consider an implementation of a hash table with linear probing where the hash function runs in constant time and the cost of comparison is also constant. What is the best-case time complexity of the __getitem__ method? Consider n is the number of items in the hash table.

Which is TRUE?

What is the best case time complexity of deleting a key from a linear probe table?

更多留学生实用工具

希望你的学习变得更简单

Consider an implementation of a hash table with linear probing where the hash function runs in constant time and the cost of comparison is also constant. What is the best-case time complexity of the getitem method? Consider n is the number of items in the hash table.