2 3 Trees Algorithm - Data Structure

2 3 Trees Algorithm - Data Structure

• 1.
  2-3 Trees Algorithm
• 2.
  Introduction  2-3 treeis a tree in which each internal node(non-leaf) has either 2 or 3 children, and all leaves are at the same level
• 3.
  Some Rules for2-3 Trees  A node may contain 1 or 2 keys  All leaf nodes are at the same depth  All non-leaf nodes (except the root) have either 1 key and two subtrees, or 2 keys and three subtrees  The only changes in depth are when the root splits or underflows
• 5.
  Another Example of2-3 Tree
• 6.
  The Advantages ofthe 2-3 Trees  Even though searching a 2-3 tree is not more efficient than searching a binary search tree, by allowing the node of a 2-3 tree to have three children, a 2-3 tree might be shorter than the shortest possible binary search tree.  Maintaining the balance of a 2-3 tree is relatively simple than maintaining the balance of a binary search tree .
• 7.
  Insertion Insert 39
• 8.
  Insert 38
• 9.
  Insert 37
• 10.
  Deletion  1.Locate noden, which contains item I  2.If node n is not a leaf swap I with inorder successor  deletion always begins at a leaf  3.If leaf node n contains another item, just delete item I
• 11.
  Delete 70
• 12.
  Deleting70: swap 70with inorder successor (80)
• 13.
  Deleting70: ... getrid of 70
• 14.
  Result… Now delete100
• 15.
  Deleting 100
• 16.
  Result… Now letsdelete 80
• 17.
  Deleting 80 ...
• 18.
  Deleting 80 ...
• 19.
  Deleting 80 ...
• 20.
  Result…