bianhuabianhua / omt

A cache-efficiency weight balanced binary tree

OMT is short for Order Maintenance Tree, which is dreamed up by Tokutek, and used in TokuDB.
It's a weight balanced binary tree, each node maintains the weights of its left and right subtrees.
OMT having better CPU cache efficiency than skiplist (it's very cool as you improve it to vEB layout).

For more details, please see Cartesian Tree: http://en.wikipedia.org/wiki/Cartesian_tree

Insertion as follows:

1) insert 'key-1'

    /*
     *            (key-1)
     */

2) insert 'key-4'

    /*
     *            (key-1)
     *                    \
     *                  (key-4)
     */

3) insert 'key-7'

    /*
     *            (key-1)
     *                    \
     *                  (key-4)
     *                          \
     *                        (key-7)
     */



4) insert 'key-5'

    /*
     *            (key-1)
     *                    \
     *                  (key-4)
     *                          \
     *                        (key-7)
     *                      /
     *                  (key-5)
     */

5) insert 'key-6', the tree need to be rebalanced:

    /*
     *            (key-1)
     *                    \
     *                  (key-4)
     *                          \
     *                        (key-7)
     *                      /
     *                  (key-5)
     *                        \
     *                        (key-6)
     */

After rebalance:
    /*
     *
     *               (key-5)
     *              /       \
     *         (key-4)      (key-7)
     *        /             /     \
     *    (key-1)       (key-6)   (key-71)
     *
     */

6) and we insert 'key-72', 'key-75', it cause a balance:

    /*
     *
     *               (key-5)
     *              /       \
     *         (key-4)      (key-7)
     *        /             /     \
     *    (key-1)       (key-6)   (key-71)
     *                                  \
     *                                  (key-72)
     *                                          \
     *                                          (key-75)
     *
     */

    /***************** after rebalance *********************/

    /*
     *
     *               (key-7)
     *              /       \
     *        (key-5)        (key-72)
     *        /   \          /       \
     *  (key-4)  (key-6)  (key-71)    (key-75)
     *   /
     *(key-1)
     *
     */


By BohuTANG @2013/9/19