TEZPUR 2025 — Computer PYQ

The correct answer is (b) To allow for efficient searching and insertion.

A hash table is a data structure that implements an associative array abstract data type, a structure that can map keys to values. Its primary advantage is its efficiency in performing data operations.

• Efficiency: Hash tables use a hash function to compute an index into an array of buckets or slots, from which the desired value can be found. On average, this allows for $O(1)$ time complexity for search, insertion, and deletion operations.

• Comparison: Unlike sorted arrays or balanced binary search trees, which typically offer $O(\log n)$ performance for searches, hash tables excel when the order of data is not required.

We can represent the average time complexity $T$ for common operations in a hash table as:

$$T_{search}\approx O(1)$$

$$T_{insert}\approx O(1)$$

In contrast, operations like sorting in a hash table do not hold constant time complexity, as sorting requires $O(n\log n)$ time, making options (a) and (d) incorrect.