Expression Trees

1
Expression Trees

• Another way to process expressions is to build a
  parse tree during parsing
• Expression tree
• An expression tree is never empty
• An interior node represents a compound
  expression, consisting of an operator and its
  operands
• Each leaf node represents a numeric operand
• Operands of higher precedence usually appear near
  bottom of tree, unless overridden in source
  expression by parentheses

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Expression Trees (continued)
3
Binary Tree Traversals

• Four standard types of traversals for binary
  trees
• Preorder traversal Visits root node, and then
  traverses left subtree and right subtree in
  similar way
• Inorder traversal Traverses left subtree, visits
  root node, and traverses right subtree
• Appropriate for visiting items in a BST in sorted
  order
• Postorder traversal Traverses left subtree,
  traverses right subtree, and visits root node
• Level order traversal Beginning with level 0,
  visits the nodes at each level in left-to-right
  order

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Binary Tree Traversals (continued)
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Binary Tree Traversals (continued)
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Binary Tree Traversals (continued)
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Binary Tree Traversals (continued)
8
Write the order in which the nodes are visited in
the binary tree shown above using In-order
traversal Pre-order traversal
Post-order traversal Breadth-first
(level-order) traversal
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A Binary Tree ADT

• Provides many common operations required for
  building more specialized types of trees
• Should support basic operations for creating
  trees, determining if a tree is empty, and
  traversing a tree
• Remaining operations focus on accessing,
  replacing, or removing the component parts of a
  nonempty binary treeits root, left subtree, and
  right subtree

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The Interface for a Binary Tree ADT
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The Interface for a Binary Tree ADT (continued)
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Processing a Binary Tree

• Many algorithms for processing binary trees
  follow the trees recursive structure
• Programmers are occasionally interested in the
  frontier, or set of leaf nodes, of a tree
• Example Frontier of parse tree for English
  sentence contains the words in the sentence

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Processing a Binary Tree (continued)

• frontier expects a binary tree and returns a list
• Two base cases
• Tree is empty ? return an empty list
• Tree is a leaf node ? return a list containing
  root item

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Implementing a Binary Tree
15
Implementing a Binary Tree (continued)
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Implementing a Binary Tree (continued)
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The String Representation of a Tree

• __str__ can be implemented with any of the
  traversals