How is the effectiveness of element search in the TreeMap data structure evaluated?

TreeMap in Java is implemented based on a red-black tree — a balanced binary search tree. The efficiency of searching for an element in TreeMap is estimated as O(log n), where n is the number of elements in the map.

This means that the search time grows logarithmically with the size of the structure, which is significantly faster than linear search.

Working principle:

• When searching for a key, TreeMap traverses the tree, comparing keys.
• Thanks to tree balancing, the depth is limited, ensuring logarithmic access time.

Example:

TreeMap<Integer, String> map = new TreeMap<>();
map.put(10, "ten");
map.put(20, "twenty");
map.put(15, "fifteen");

String value = map.get(15);  // Search in O(log n)
System.out.println(value);  // Will output "fifteen"

Thus, TreeMap provides efficient search, insertion, and deletion of elements.