二叉树平衡二叉树_二叉树简介

二叉树平衡二叉树

二叉树简介 (Introduction To Binary Trees)

A binary tree is a hierarchical data structure in which each node has at most two children generally referred as left child and right child.

二叉树是一种分层数据结构，其中每个节点最多具有两个子节点，通常称为左子节点和右子节点。

Each node contains three components:

每个节点包含三个组件：

Pointer to left subtree
指向左子树的指针
Pointer to right subtree
指向右子树的指针
Data element
数据元素

The topmost node in the tree is called the root. An empty tree is represented by NULL pointer.

树中最顶层的节点称为根。空树由NULL指针表示。

A representation of binary tree is shown:

显示了二叉树的表示形式：

二叉树：通用术语 (Binary Tree: Common Terminologies)

Root: Topmost node in a tree.根：树中的最高节点。
Parent: Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. This node is called a parent.父级：树中的每个节点（不包括根节点）都通过有向边与正好一个其他节点相连。该节点称为父节点。
Child: A node directly connected to another node when moving away from the root.
子节点：远离根节点时直接连接到另一个节点的节点。
Leaf/External node: Node with no children.
叶子/外部节点：没有子节点的节点。
Internal node: Node with atleast one children.内部节点：至少有一个孩子的节点。
Depth of a node: Number of edges from root to the node.节点深度：从根到节点的边数。
Height of a node: Number of edges from the node to the deepest leaf. Height of the tree is the height of the root.节点的高度：从节点到最深的叶子的边数。树的高度是根的高度。

In the above binary tree we see that root node is A. The tree has 10 nodes with 5 internal nodes, i.e, A,B,C,E,G and 5 external nodes, i.e, D,F,H,I,J. The height of the tree is 3. B is the parent of D and E while D and E are children of B.

在上面的二叉树中，我们看到根节点是A。该树有10个节点，其中5个内部节点即A，B，C，E，G和5个外部节点即D，F，H，I，J 。树的高度是3 B是d和E的母公司，而d和E是B的孩子。

树木的优势 (Advantages of Trees)

Trees are so useful and frequently used, because they have some very serious advantages:

树是如此有用且经常使用，因为它们具有一些非常重要的优点：

Trees reflect structural relationships in the data.
树反映了数据中的结构关系。
Trees are used to represent hierarchies.
树用于表示层次结构。
Trees provide an efficient insertion and searching.
树提供了有效的插入和搜索。
Trees are very flexible data, allowing to move subtrees around with minumum effort.
树是非常灵活的数据，允许以最小的努力来移动子树。

二叉树的类型（基于结构） (Types of Binary Trees (Based on Structure))

Rooted binary tree: It has a root node and every node has atmost two children.根二叉树：它有一个根节点，每个节点最多有两个子节点。
Full binary tree: It is a tree in which every node in the tree has either 0 or 2 children. 完整的二叉树：这是一棵树，其中树中的每个节点都有0或2个子节点。
- n, in a full binary tree is atleast n = 2h – 1, and atmost n至少为n = 2h – 1，最大为^h+1 – 1^{h + 1} – 1h is the height of the tree. h是树的高度。
- l, in a full binary tree is number, l是内部节点的数量L of internal nodes + 1, i.e, L + 1，即l = L+1.l = L + 1 。
Perfect binary tree: It is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level. 完美的二叉树：这是一棵二叉树，其中所有内部节点都有两个子节点，所有叶子的深度或级别相同。
- l leaves has l个叶子的理想二叉树具有n = 2l-1 nodes.n = 2l-1个节点。
- l = 2h and l = 2h且n = 2h+1 - 1 where, n = 2h + 1-1，其中， n is number of nodes, n是节点数， h is height of tree and h是树的高度， l is number of leaf nodesl是叶节点的数目
Complete binary tree: It is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. 完整的二叉树：它是一棵二叉树，其中除最后一个级别外，每个级别都已完全填充，并且所有节点都尽可能地靠左。
- floor(n/2).floor（n / 2）。
Balanced binary tree: A binary tree is height balanced if it satisfies the following constraints: 平衡二叉树：如果满足以下约束，则二叉树是高度平衡的：
1. The left and right subtrees' heights differ by at most one, AND
  左右子树的高度最多相差一，并且
2. The left subtree is balanced, AND
  左子树是平衡的，并且
3. The right subtree is balanced
  正确的子树是平衡的
An empty tree is height balanced.

空树是高度平衡的。
- Log n) where Log n ），其中n is number of nodes.n是节点数。
Degenarate tree: It is a tree is where each parent node has only one child node. It behaves like a linked list. 退化树：每个父节点只有一个子节点的树。它的行为就像一个链表。

翻译自: https://www.studytonight.com/data-structures/introduction-to-binary-trees

二叉树平衡二叉树