Choose what to practice. In Quick rotation practice, the tree is already built: your task is to balance it. In the Complete exercise, open Configure or restart, select a mode and 6 to 20 values (the default is 8), then choose Start exercise. Mixed includes at least two case types; LL, RR, LR and RL modes guarantee the chosen case and may include others.

In the complete exercise, read the current value and use Insert at root for the first node. For later values, walk down the tree comparing with every ancestor. Select the parent by clicking a node or using the Select node list, then choose Insert on the left or Insert on the right. The position must be empty and respect every bound along the path. An incorrect attempt preserves the tree and current value while explaining the mistake.

After each valid insertion, check whether rebalancing is required. Help and hints lets you display balance factors and reveal progressive clues. Start at the newly inserted value, follow its parents upward, and stop at the first ancestor with factor +2 or −2. The path from that ancestor identifies LL, RR, LR or RL; the case name is not the direction of the rotation button.

Select the node for the next operation and choose Rotate left or Rotate right. Each click performs just one simple rotation. For LR and RL, first rotate the corresponding child, then the original ancestor: the still-unbalanced intermediate state is part of the solution. The next value is unlocked only when BST order, heights and balance are correct. The student's tree never repairs itself automatically.

Use zoom, panning and Fit to view to inspect nodes; the list lets you select a node even when it is outside the frame. Footer indicators track correct actions, errors, rotations and hints without a collapsed panel. When finished, review your score and retry or generate a new exercise. In quick practice, the corrected tree stays visible until you choose Next exercise; doing so does not restart the complete exercise.

A binary search tree (BST) does not compare a node only with its parent. Every value in an ancestor's left subtree must be smaller than that ancestor; every value in its right subtree must be larger. As you move down the tree, those comparisons accumulate an allowed interval for the new position.

Consider 30 at the root and 20 to its left. To insert 25 to the right of 20, it must be larger than 20 and smaller than 30: both conditions hold. Although 35 is also larger than 20, it cannot occupy that position because it would still be inside 30's left subtree. The correct path for 35 starts to the right of 30.

In the tool, selecting 20 and choosing Insert on the right is valid only when the current value lies in 20 < value < 30. If an attempt violates a bound, feedback identifies the responsible ancestor and preserves the tree. Trace the path from the root again before choosing another parent or side; a later rotation must not be used to try to repair an invalid BST insertion.

A leaf has height 0; an empty subtree has height −1. The factor is height(left) − height(right). A valid AVL tree has factors −1, 0 or +1 at every node. After insertion, move up to the first unbalanced ancestor. The student's tree never fixes itself automatically.

For example, a node with a left leaf and no right child has height 1 and balance factor 0 − (−1) = +1. If its left subtree grows to height 1 while the right side stays empty, the factor becomes 1 − (−1) = +2: rebalancing is needed.

L means left and R means right. Starting at the first unbalanced ancestor, the first letter identifies the taller child's side; the second identifies the side that grew within that child. The name describes the imbalance path, not the direction of the corrective rotation. LL is fixed by rotating right, RR by rotating left; LR and RL require two operations. In the diagrams, a dashed ring identifies the node for the next rotation, also named in the caption.