The goal of hashing is to produce a search that takesAO(1) timeBO(n2) timeCO(log n ) timeDO(n log n ) timePrevious

Break Down the Problem

1. Understanding the Question: The question asks about the goal of hashing in terms of search time complexity.
2. Identifying Options: The options provided are:
   • A) $O(1)$
   • B) $O(n^2)$
   • C) $O(\log n)$
   • D) $O(n \log n)$

Relevant Concepts

3. Hashing: Hashing is a technique used in data structures (like hash tables) that allows for fast data retrieval. The ideal scenario for a hashing structure is that it will allow searching for an element in constant time, i.e., $O(1)$, under ideal conditions with no collisions.

Analysis and Detail

4. Examine Each Option:
   • A) $O(1)$: If there are no collisions in the hash table, the average time complexity for search operations can be $O(1)$.
   • B) $O(n^2)$: This represents a worst-case time complexity for certain algorithms but is not relevant to hashing.
   • C) $O(\log n)$: This is more suited for data structures like balanced binary search trees.
   • D) $O(n \log n)$: This is typically related to sorting algorithms, not search operations in hashing.

Verify and Summarize

5. Summarization of the Options: Based on the analysis, the most accurate and beneficial time complexity for search operations when using a good hashing technique is $O(1)$.

Final Answer

The goal of hashing is to produce a search that takes $O(1)$ time. Therefore, the correct answer is A) $O(1)$.