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15-5 Trees

15-5 Trees. Trees are used extensively in computer science to represent algebraic formulas; as an efficient method for searching large, dynamic lists; and for such diverse applications as artificial intelligence systems and encoding algorithms. Topics discussed in this section:.

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15-5 Trees

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  1. 15-5 Trees Trees are used extensively in computer science to represent algebraic formulas; as an efficient method for searching large, dynamic lists; and for such diverse applications as artificial intelligence systems and encoding algorithms. Topics discussed in this section: Basic Tree Concepts Terminology Binary Trees Binary Search TreesBinary Tree Example Computer Science: A Structured Programming Approach Using C

  2. Note A tree consists of a finite set of elements, called nodes, and a finite set of directed lines, called branches, that connect the nodes. Computer Science: A Structured Programming Approach Using C

  3. FIGURE 15-30 Tree Computer Science: A Structured Programming Approach Using C

  4. FIGURE 15-31 Tree Nomenclature Computer Science: A Structured Programming Approach Using C

  5. Note The level of a node is its distance from the root. The height of a tree is the level of the leaf in the longest path from the root plus 1. Computer Science: A Structured Programming Approach Using C

  6. FIGURE 15-32 Subtrees Computer Science: A Structured Programming Approach Using C

  7. Note A tree is a set of nodes that either: 1. Is empty, or 2. Has a designated node, called the root, from which hierarchically descend zero or more subtrees, which are also trees Computer Science: A Structured Programming Approach Using C

  8. FIGURE 15-33 Collection of Binary Trees Computer Science: A Structured Programming Approach Using C

  9. FIGURE 15-34 Binary Tree Data Structure Computer Science: A Structured Programming Approach Using C

  10. FIGURE 15-35 Binary Tree Traversals Computer Science: A Structured Programming Approach Using C

  11. FIGURE 15-36 Binary Tree for Traversals Computer Science: A Structured Programming Approach Using C

  12. Note In the preorder traversal, the root is processed first,before its subtrees. Computer Science: A Structured Programming Approach Using C

  13. PROGRAM 15-19 Preorder Traversal of a Binary Tree Computer Science: A Structured Programming Approach Using C

  14. FIGURE 15-37Preorder Traversal—A B C D E F Computer Science: A Structured Programming Approach Using C

  15. FIGURE 15-38 Algorithmic Traversal of Binary Tree Computer Science: A Structured Programming Approach Using C

  16. PROGRAM 15-20 Inorder Traversal of a Binary Tree Computer Science: A Structured Programming Approach Using C

  17. FIGURE 15-39 Inorder Traversal—C B D A E F Computer Science: A Structured Programming Approach Using C

  18. Note In the inorder traversal, the root is processedbetween its subtrees. Computer Science: A Structured Programming Approach Using C

  19. Note In a binary search tree, the left subtree contains key values less than the root, and the right subtree containskey values greater than or equal to the root. Computer Science: A Structured Programming Approach Using C

  20. FIGURE 15-40 Binary Search Tree Computer Science: A Structured Programming Approach Using C

  21. FIGURE 15-41 Valid Binary Search Trees Computer Science: A Structured Programming Approach Using C

  22. FIGURE 15-42 Invalid Binary Search Trees Computer Science: A Structured Programming Approach Using C

  23. Note All BST insertions take place at a leaf or a leaflike node. Computer Science: A Structured Programming Approach Using C

  24. FIGURE 15-43 BST Insertion Computer Science: A Structured Programming Approach Using C

  25. PROGRAM 15-21 Binary Tree Insert Function Computer Science: A Structured Programming Approach Using C

  26. PROGRAM 15-21 Binary Tree Insert Function Computer Science: A Structured Programming Approach Using C

  27. FIGURE 15-44 Binary Tree Example Computer Science: A Structured Programming Approach Using C

  28. PROGRAM 15-22 Binary Tree Example Computer Science: A Structured Programming Approach Using C

  29. PROGRAM 15-22 Binary Tree Example Computer Science: A Structured Programming Approach Using C

  30. PROGRAM 15-22 Binary Tree Example Computer Science: A Structured Programming Approach Using C

  31. PROGRAM 15-22 Binary Tree Example Computer Science: A Structured Programming Approach Using C

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