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13.6: Self-balancing trees

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  • There are two possible solutions to this problem:

    • You could avoid adding keys to the Map in order. But this is not always possible.
    • You could make a tree that does a better job of handling keys if they happen to be in order.

    The second solution is better, and there are several ways to do it. The most common is to modify put so that it detects when the tree is starting to become unbalanced and, if so, rearranges the nodes. Trees with this capability are called “self-balancing”. Common self-balancing trees include the AVL tree (“AVL” are the initials of the inventors), and the red-black tree, which is what the Java TreeMap uses.

    In our example code, if we replace MyTreeMap with the Java TreeMap, the run times are about the same for the random strings and the timestamps. In fact, the timestamps run faster, even though they are in order, probably because they take less time to hash.

    In summary, a binary search tree can implement get and put in logarithmic time, but only if the keys are added in an order that keeps the tree sufficiently balanced. Self-balancing trees avoid this problem by doing some additional work each time a new key is added.

    You can read more about self-balancing trees at

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