Hashing

Step 1: Analysis of Search Techniques.
- **Binary Search**: The search time in binary search is dependent on the number of elements, specifically ** **. It works on sorted arrays.
- **Hashing**: In hashing, the time for searching an element is independent of the number of elements, assuming a good hash function and proper collision resolution, giving ** ** average time complexity.
- **Linear Search**: The search time in linear search is ** **, dependent on the number of elements, as it checks each element one by one.
- **Jump Search**: Jump Search also depends on the number of elements but has a time complexity of ** **.

Step 2: Conclusion.
The correct answer is **(2) Hashing**, as search time is independent of the number of elements.

Step 1: Understanding the Concept:
Chaining is a collision resolution technique where each cell of the hash table points to a linked list of records that have the same hash value. The length of a chain is the number of elements in that specific bucket.
Step 2: Key Formula or Approach:
Calculate the remainder for each key using .
Step 3: Detailed Explanation:
Let's compute the hash values for all keys:
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Grouping keys by their hash values:
- Index 1: Length = 3
- Index 3: Length = 1
- Index 5: Length = 1
- Index 6: Length = 2
- Index 8: Length = 2
The maximum length observed is 3 at index 1.
Step 4: Final Answer:
The length of the longest chain is 3.