專欄 | 九章演算法
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樹的很多概念非常confusing，讓主頁群帶大家來過一遍五花八門的樹的概念吧！
（一）
About the Tree: full binary tree: A binary tree in which each node has exactly zero or two children.
Perfect binary tree: A binary tree with all leaf nodes at the same depth. All internal nodes have degree 2 [1]
滿二叉樹：每個節點都有0或是2個孩子。
完美二叉樹：所有的葉子都擁有同的深度，所有的內部節點擁有 2個孩子
（二）
The difference between Full Binary Tree & Complete Binary Tree:
(1). a binary tree T is full if each node is either a leaf or possesses exactly two child nodes.
(2). a binary tree T with n levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side. [2]
滿二叉樹和完全二叉樹的區別：
滿二叉樹：是每個節點要不是葉子要不擁有 2個孩子
完全二叉樹：每一層都是完全的，除了最後一層，而最後一層所有的節點都在左邊。
（三）
AVL Trees: AVL trees are self-balancing binary search trees. These trees are named after their two inventors G.M. Adel’son-Vel’skii and E.M. Landis. [3]
The height/depth of a tree:
The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree.
The depth of a node is the length of the path to its root (i.e., its root path).
（四）
This is commonly needed in the manipulation of the various self-balancing trees, AVL Trees in particular. The root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has depth and height −1.[4]
根的深度為0，葉子高度為0.只有一個節點的樹的depth height 都為0.
按照慣例，一個空樹的depth, height 都是-1
參考資料：
- xlinux.nist.gov/dads//HTML/…
- courses.cs.vt.edu/~cs3114/Fal…
- courses.csail.mit.edu/6.006/fall0…
- www.cs.cmu.edu/~adamchik/1…
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