An unrolled linked list contains more than 1 element in each node.
The question asks to find some kth element, and if the no. of nodes and the no. of elements in each node are equal then n should be a perfect square. If in each node there are m elements then there has to be m nodes each of containing m elements, this implies total elements will be m^{2}.
So in the given question if there are n elements then each node must be having $\sqrt{n}$ elements. if each node is having $\sqrt{n}$ elements then there has to be such $\sqrt{n}$ nodes. so the complexity to reach last node becomes O($\sqrt{n}$) as we need to search to max $\sqrt{n}$ nodes to find desire element.
1. How to find node in which kth element is present?
-> $\lceil$$K/$$\sqrt{n}$ $\rceil$
2. How much time it will take to reach that node ( there are max $\sqrt{n}$ nodes)
-> $\sqrt{n}$
3. Once the node is reach how much time it will take search that element in that node
-> $\sqrt{n}$ = as there are total $\sqrt{n}$ elements in each node
So Overall time complexity becomes
= Time to reach that node + Time to search that element
= O($\sqrt{n}$+$\sqrt{n}$) = O($\sqrt{n}$) .