Minimum time complexity in linked list deletion

O(1) refers to the performance cost scaling linearly with complexity. The only way to reduce that is to use a collection with efficient searching capability. A linked list is not efficient at searching. An unordered_map[^] from the Standard Template Library is an example of a collection with VERY efficient searching. A hash table[^] is a generic example of a high performance collection. The hash table is probably a good example to pursue if you have to implement it yourself since it is fairly simple.

You cannot achieve a better performance of O(1) on a arbitrary linked list.
In order to obtain a better time complexity, you have to use a ordered list (pardon the pun). Then you may perform a binary search.

Quote:

Please help me for logic.

I fear there is no such logic, or it is not linked list anymore.
Linked list is a data structure, and each data structure have its own set of advantages and disadvantages, you choose the data structure depending on your usage of the data.

If you have copy the list to another data structure to perform heap search the cost of building that structure us usually more than the gain of using that structure.