Solution: The 2-3 trees is a balanced tree. It is a specific form the B – tree. It is B – tree of order 3, where every node can have two child subtrees and one key or 3 child subtrees and two keys.

Solution: The number of elements in a 2-3 tree with height h is between 2h – 1 and 3h – 1. Therefore, the 2-3 tree with n elements will have the height between log3(n + 1) and log2(n + 1).

Solution: AA tree is isometric of the 2-3 trees. In an AA tree, we store each node a level, which is the height of the corresponding 2-3 tree node. So, we can convert a 2-3 tree to an AA tree.

Solution: The average case time for lookup in a binary search tree, treap and 2-3 tree is O(log n) and in unordered lists it is O(n). But in the worst case, only the 2-3 trees perform lookup efficiently as it takes O(log n), while others take O(n).

Solution: LLRB (Left Leaning Red Black tree)is the data structure which is used to implement the 2-3 tree with very basic code. The LLRB is like the 2-3 tree where each node has one key and two links. In LLRB the 3-node is implemented as two 2-nodes connected by the red link that leans left. Thus, LLRB maintains 1-1 correspondence with 2–3 tree.data-structures-questions-answers-2-3-tree-q7

Solution: In a 2-3 tree, leaves are at the same level. And 2-3 trees are perfectly balanced as every path from root node to the null link is of equal length. In 2-3 tree in-order traversal yields elements in sorted order.

Solution: Insertion in AVL tree and 2-3 tree requires searching for proper position for insertion and transformations for balancing the tree. In both, the trees searching takes O(log n) time, but rebalancing in AVL tree takes O(log n), while the 2-3 tree takes O(1). So, 2-3 tree provides better insertions.

Solution: Search is more efficient in the 2-3 tree than in BST. 2-3 tree is a balanced tree and performs efficient insertion and deletion and it is shallower than BST. But, 2-3 tree requires more storage than the BST.