1. Chapter 9
Binary Trees

2. Chap.9 Contents 9.1 Definition of Binary Tree
9.2 Properties of Binary Trees
9.3 The Binary Tree Theorem
9.4 External Path Length
9.5 Traversals of a Binary Tree

4. 9.1 Definition of Binary Tree
binary tree t
可為 empty tree 或 包含:
一個 root element, 與兩個不同的 binary trees,
分別叫 t 的 left sub-tree 及
right sub-tree

11. Binary trees (elements 大小無規定)

12. Binary search tree (elements 左小右大)2

13. Tri-nary (3-nary) search tree
2 4
What about N-nary search tree(n-元搜尋樹)?
It is called B tree.

15. This is NOT a binary search tree5
Because 4 is NOT less than 3

18. 9.2 Properties of Binary Trees

35. level (x), the level of x,
is the same as the depth (x).
Is height (t) the same as depth(x)?
ANS: No. See next page,
height(50) is 3. depth(62) is 2.

48. 這暗示我們:
Complete binary tree
可用 array來實作. A B C D E R S F G L

55. 9.3 The Binary Tree Theorem

65. 9.4 External Path Length

69. 9.5 Traversals of a Binary Tree

84. ANS:
inOrder FDGBLEARCS
postOrder FGDLEBRSCA
preOrder ABDFGELCRS
breathFirst ABCDERSFGL