# java - Time complexity of TreeMap<> operations: get() and subMap()

Based on this post,

Time complexity of TreeMap operations- subMap, headMap, tailMap

subMap() itself is O(1), and O(n) comes from iterating the sub map.

So, why use get(key) then?

We can use subMap(key, true, key, true) instead,

which is O(1) and iterating this sub map is also O(1).

Faster than get(key), which is O(log(n)). Something wrong here...

We can use subMap(key, true, key, true) instead, which is O(1)

This is correct

and iterating this sub map is also O(1).

O(n) comes from the question. The answer says nothing to imply this, which is good, because it's not true.

Time complexity of iterating a subtree is O(log n + k), where `n` is the number of elements in the whole map, and `k` is the number of elements in the sub-map. In other words, it still takes O(log n) to get to the first position when you start iterating. Look up `getFirstEntry()` implementation to see how it is done.

This brings the overall complexity of your approach to O(log n), but it is bound to be slower than a simple `get`, because an intermediate object is created and discarded in the process.

The answer is a bit confusing. Technically it's true that creating the submap is constant operation. But that's just because it actually does nothing apart from setting the low and high keys and still shares the tree structure with the original tree.

As a result any operation on the tree is actually postponed until the specific method is invoked. So then `get()` still goes through the whole original map and only checks whether it didn't cross the low and high boundaries. Simply saying the `get()` is still `O(n)` where the `n` comes from the original map, not from the submap.

The construction of subMap takes O(1) time, however all retrieval operations take the same O(log n) time as in the original map because SubMap just wraps this object and eventually complete a range check and delegate the invocation of get() method to the original source map object.