Consider an unrolled linked list with n elements. This list stores multiple elements in each node. What is the worst case time complexity to find the kthelement if the number of nodes and the number of elements in each node are equal?a)O(n)b)O(√n)c)O(nlogn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?

Question

Consider an unrolled linked list with n elements. This list stores multiple elements in each node. What is the worst case time complexity to find the kthelement if the number of nodes and the number of elements in each node are equal?a)O(n)b)O(&radic;n)c)O(nlogn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?

Answer

Explanation:

Unrolled Linked List:
An unrolled linked list is a variant of the traditional linked list data structure where each node stores multiple elements instead of just one. This helps in reducing the memory overhead associated with storing individual elements in separate nodes.

Time Complexity to Find kth Element:
In the worst-case scenario, if the number of nodes and the number of elements in each node are equal, the time complexity to find the kth element in the unrolled linked list is O(√n). This is because each node contains √n elements, and we need to traverse through √n elements in each node to find the kth element.

Explanation:
- In an unrolled linked list with n elements, if each node contains √n elements, the total number of nodes will be n/√n = √n.
- To find the kth element, we need to traverse through each node until we reach the corresponding node containing the kth element.
- Since there are √n nodes in total, the worst-case time complexity to find the kth element would be O(√n).
Therefore, the correct answer is option B - O(√n).

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