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.)

Question

BlackTom AI · Accepted Answer

If the hash function maps every key to the same bucket (or the load factor is unconstrained), a single chain can contain all n items, so insertion can require time proportional to n.

1. Relevant knowledge points and concepts
- Separate chaining stores items in buckets; each bucket holds a collection (commonly a linked list) of all keys hashing to that bucket.
- Time to insert consists of computing the hash (usually O(1)) plus the time to handle the chain for that bucket.
- Worst-case complexity assumes no guarantees about the hash function or load factor, so collisions can be extreme (all keys in one chain).

2. Step-by-step reasoning
- Suppose there are n keys already in the table and the hash function sends every key to bucket b.
- To insert a new key, you compute its hash (O(1)) and then must process bucket b’s chain.
- Typical implementations either (a) check the chain to avoid duplicates or (b) maintain some ordering; both require scanning the chain in the worst case.
- The chain length is n, so scanning it takes Θ(n) time.

3. Intermediate steps / small calculation
- Hash computation: O(1)
- Chain traversal: Θ(n) (because chain length = n)
- Total = O(1) + Θ(n) = Θ(n) → O(n)

4. Why the correct answer is correct
Because with no assumptions about hash quality or load factor, all elements can collide into a single bucket. Any necessary traversal or duplicate check of that chain costs linear time in n, producing a worst-case O(n) insert.

5. Why other plausible answers are incorrect
- O(1): true on average with good hashing and bounded load factor, but not in the unconstrained worst case.
- O(log n): would require a balanced-tree bucket implementation; typical chaining uses lists, so log n is not guaranteed.
- O(n^2): overly large; insertion at worst is linear, not quadratic.

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

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.)单项选择题

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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.)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 get 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.