What is the time complexity of the lowerKey() operation in Java implementation of TreeMap ?
I think it is log(n) but I can't find it anywhere in the documentation.
The complexity of more basic operation is well documented:
This implementation provides guaranteed log(n) time cost for the containsKey, get, put and remove operations.
BTW: I'm also interested in the complexity of subMap(). I guess that a log(n) complexity of lowerKey() will allow log(n) time for constant size subMap().
lowerKey() is a search in a balanced binary search tree, so it's obviously O(log n). You might want to read the source code, e.g. from here, to see how the tree is traversed.
Similarly, each operation with a NavigableMap returned from subMap() also requires O(log n) because you will need to traverse the tree to find elements you want.