How many rotations are needed to balance an AVL tree after a single insertion?

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Q: How many rotations are needed to balance an AVL tree after a single insertion?

Solution: Typically, only one rotation is needed to balance an AVL tree after a single insertion, unless it is a double rotation case.

Steps: 7

Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance by ensuring the heights of the two child subtrees of any node differ by no more than one.
Step 2: When you insert a new node into an AVL tree, it may cause the tree to become unbalanced.
Step 3: After the insertion, check the balance factor of the affected nodes. The balance factor is calculated as the height of the left subtree minus the height of the right subtree.
Step 4: If the balance factor of any node is -2 or +2, it indicates that the tree is unbalanced and needs to be fixed.
Step 5: Determine the type of imbalance: If the imbalance is on the left side (left-left case), a single right rotation is needed. If it is on the right side (right-right case), a single left rotation is needed.
Step 6: If the imbalance is a left-right case or a right-left case, a double rotation is needed. This involves performing one rotation followed by another rotation.
Step 7: In most cases, only one rotation (either left or right) is needed to restore balance, unless it is a double rotation case.