Which data structure is efficient to use for searching, insertion, deletion operationSelect one:a. Linked listO b. Arrayc. Treed. Graph

To determine which data structure is efficient for searching, insertion, and deletion operations, let's analyze each option:

1. Linked List:

   • Searching: O(n) time complexity (you may need to traverse the entire list).
   • Insertion: O(1) time complexity when inserting at the head (but O(n) in general if it requires traversal).
   • Deletion: O(1) time complexity if you have a pointer to the node to delete, but O(n) if you need to search for it first.

2. Array:

   • Searching: O(n) time complexity for unsorted arrays (O(log n) for sorted arrays using binary search).
   • Insertion: O(n) time complexity in the average case due to shifting elements.
   • Deletion: O(n) time complexity due to shifting elements.

3. Tree (binary search tree):

   • Searching: O(log n) average time complexity with balanced trees.
   • Insertion: O(log n) average time complexity.
   • Deletion: O(log n) average time complexity.

4. Graph:

   • Searching, insertion, and deletion complexities depend on the representation (adjacency list/matrix) and are often more complex to analyze than the simpler structures.

Conclusion:

In general, a Tree (specifically, a balanced binary search tree) is the most efficient among the given options for searching, insertion, and deletion operations when considering average time complexities.

Final Answer

c. Tree