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)?

Question

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)?

BlackTom AI · Accepted Answer

h(4) = 4, so linear probing begins at index 4.

1) Relevant knowledge points and concepts
- Hash function: h(k) = k mod 11. For key 4, h(4) = 4.
- Linear probing probe sequence: indices examined are (h(k) + i) mod m for i = 0,1,2,...
- In open addressing with deletions, a "defunct" (deleted) slot does not terminate the search — you must continue probing. Only a truly empty (never-occupied) slot guarantees the key is not present.

2) Step-by-step reasoning
- Compute initial index: h(4) = 4 mod 11 = 4. Start at index 4 (i = 0).
- Inspect index 4: the slot is marked defunct (deleted). Because it is not an empty/never-used slot, the search cannot stop; continue with i = 1.
- Next index: (4 + 1) mod 11 = 5. Inspect index 5: it contains key 25, which is not key 4. Continue probing (i = 2).
- Next index: (4 + 2) mod 11 = 6. Inspect index 6: it contains key 4 → found. Stop.

3) Calculations / intermediate steps
- h(4) = 4
- Probe 0: index = (4 + 0) mod 11 = 4 → defunct (not match)
- Probe 1: index = (4 + 1) mod 11 = 5 → contains 25 (not match)
- Probe 2: index = (4 + 2) mod 11 = 6 → contains 4 (match) → stop

4) Why the correct answer is correct
Because linear probing requires checking index 4 first (h(4)), then continuing past a deleted slot at 4 to 5, and then reaching index 6 where key 4 is stored. The search terminates when the key is found at index 6.

5) Why the other options are incorrect
- "4,5" is incorrect: after checking 5 the key has not been found; index 6 must be examined and contains the key.
- "4,5,6,7" is incorrect: probing stops at index 6 once the key is found; index 7 is never examined.
- "4" is incorrect: index 4 is defunct and does not contain key 4, so further probing is required.

6) Conclusion / final confirmation
The indices examined are 4, 5, and 6. This matches the provided correct answer: 4,5,6.

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)?单项选择题

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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)?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.)

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 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.