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What is the perfect balance property for 2-3 trees?
Properties of 2–3 Trees Perfect Balance: Every path from the root to the null link has the same length. Symmetric Order: Every node is larger than all the nodes on the left subtree, smaller than the keys on the right subtree, and in case of 3-node, all nodes in the middle are between the two keys of the 3-node.
What is the height of a 2-3 tree?
The height of a 2-3 tree with n nodes cannot exceed log2(n + 1). Together, the tree balance and the ordered nature of the nodes means that testing membership in, inserting an element into, and deleting an element from a 2-3 tree takes logarithmic time.
Why is it called a 2-3 tree?
The 2-3 tree is not a binary tree, but instead its shape obeys the following definition: A node contains one or two keys. Every internal node has either two children (if it contains one key) or three children (if it contains two keys). Hence the name.
Is 2/3 tree a B+ tree?
A 2–3 tree is a B-tree of order 3. Nodes on the outside of the tree (leaf nodes) have no children and one or two data elements. 2–3 trees are required to be balanced, meaning that each leaf is at the same level.
Are 2/3 trees binary trees?
The 2-3 tree is not a binary tree, but instead its shape obeys the following definition: A node contains one or two keys. Every internal node has either two children (if it contains one key) or three children (if it contains two keys).
What is a perfect tree?
A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level. An example of a perfect binary tree is the (non-incestuous) ancestry chart of a person to a given depth, as each person has exactly two biological parents (one mother and one father).
How do you make a 2-3 tree?
In a two-three tree, the algorithm will be as follows:
- If the tree is empty, create a node and put value into the node.
- Otherwise find the leaf node where the value belongs.
- If the leaf node has only one value, put the new value into the node.
How does the height of a 2-3 tree increase?
The kicking-up process continues until either the kicked-up value is absorbed or the root of the tree is reached. In the latter case, the kicked-up value becomes the value of a new 2-node that 5 Page 6 increases the height of the tree by one. This is the only way that the height of a 2-3 tree can increase.