This is the documentation for HashMap.containsKey(). As you can see, it uses getNode(). I could be wrong, but it looks like the the hash map is still being iterated through, which would be linear time.
/**
* Implements Map.get and related methods.
*
* @param key the key
* @return the node, or null if none
*/
final Node<K,V> getNode(Object key) {
Node<K,V>[] tab; Node<K,V> first, e; int n, hash; K k;
if ((tab = table) != null && (n = tab.length) > 0 &&
(first = tab[(n - 1) & (hash = hash(key))]) != null) {
if (first.hash == hash && // always check first node
((k = first.key) == key || (key != null && key.equals(k))))
return first;
if ((e = first.next) != null) {
if (first instanceof TreeNode)
return ((TreeNode<K,V>)first).getTreeNode(hash, key);
do {
if (e.hash == hash &&
((k = e.key) == key || (key != null && key.equals(k))))
return e;
} while ((e = e.next) != null);
}
}
return null;
}
/**
* Returns {@code true} if this map contains a mapping for the
* specified key.
*
* @param key The key whose presence in this map is to be tested
* @return {@code true} if this map contains a mapping for the specified
* key.
*/
public boolean containsKey(Object key) {
return getNode(key) != null;
}