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2-node at bottom: convert to 3-node. Locate the node v, which should be the parent of x 2. If v has two children, make x another child of v and place it in the proper order adjust k 1 and k 2 at node v to reflect the new situation 3. Ex. Figure 4 shows an insert operation to add the number 151 to the tree. If v has three children, split v into two nodes v and v'. 2-3-4 Tree Insert Operation Example. Click the Insert button to insert the key into the tree. Ex. Click the Remove button to remove the key from the tree. For the best display, use integers between 0 and 99. Insert B F G J S V K R C E M O W D L N Q Y Z smaller than K B fits here smaller than C A B Insert.! Figure 5.24: Insertion in 2-3 trees: An example Figure 5.25: Deletion in 2-3 trees: An Example; Insert (x) 1. Enter an integer key and click the Search button to search the key in the tree. Search to bottom for key.! Insertion in a 2-3-4 Tree Insert.! In the following insert example, a search and insert will take place. Unlike a BST, a 2-3 Tree remains balanced even if clients insert data in pre-sorted order. Search to bottom for key. Before reading the code for the 2-3 Insertion Algorithm, review some key concepts about… 2-4 Tree Animation by Y. Daniel Liang. Time Complexity of Insertion in 2-3-4 Trees Time complexity: • A search visits O(log N) nodes • An insertion requires O(log N) node splits • Each node split takes constant time • Hence, operationsSearch and Insert each take time O(log N) Notes: • Instead of doing splits top-down, we can perform them bottom-up starting at the in-sertion node, and only when needed. Preemtive Split / Merge (Even max degree only) Animation Speed: w: h: A 2-3 Tree provides the near logarithmic search efficiency of a complete Binary Search Tree (BST) by guaranteeing that the tree will always remain balanced. Insert X 10 Insertion in a 2-3-4 Tree F G J S V K R C E M O W A D L N Q Y Z X not found larger than R larger than W 11 Insertion in a 2-3-4 Tree Insert.!

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