Tree Applications

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Section 9.2

• Tree Applications

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Binary Search Trees

• Goal is implementation of an efficient searching
  algorithm
• Binary Search Tree
• binary tree in which each vertex is labeled with
  a key value
• the key value of a vertex is larger than all key
  values in its left subtree, and smaller than all
  key values in its right subtree

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Recursive procedure for building a BST from list
of key values

• Start with tree containing one vertex (root) -
  first item in list is assigned as roots key
• To add a new item
• compare value to keys already in tree, starting
  at root
• if value is less than current key, move left if
  greater, move right
• when value is less than current key and current
  vertex is a leaf, then create new vertex with
  value as key and insert as current vertexs left
  child
• when value is greater, insert as current vertexs
  right child

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Example 1
Enter the following values into a binary search
tree 14, 9, 26, 7, 12, 34, 5, 2, 16
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Decision Trees

• Rooted trees can be used to model problems in
  which a series of decisions leads to a solution
• Each internal vertex is a decision point, and
  each leaf represents a possible outcome

6
Section 9.2

• Tree Applications