What algorithm is used for searching an element in TreeMap, and how effective is it?

TreeMap in Java is implemented based on a red-black tree — a type of balanced binary search tree. It uses a binary search algorithm on the tree, which, due to balancing, maintains the height of the tree approximately at (O(\log n)).

This ensures efficient search, insertion, and deletion of elements in (O(\log n)) time, which is significantly faster than linear search in an unsorted structure.

Example of using TreeMap:

TreeMap<Integer, String> map = new TreeMap<>();
map.put(10, "ten");
map.put(5, "five");
map.put(20, "twenty");

String value = map.get(10); // search by key 10 in O(log n)