A computer science tree
Second, the definition of a binary tree
A tree, each node can have it at most two child nodes, this time is called a binary tree. (We usually see in the book questions the tree is a binary tree, but it does not mean that all trees are binary if more than two nodes, we also call multiple trees)
can be seen: full binary tree certain It is a complete binary tree; not necessarily a complete binary tree is a full binary tree.
If we give a binary tree add additional conditions, you can get a special method called binary tree binary search tree (binary search tree) is.
Binary search tree requirements: if its left subtree is not empty, then the value of the left sub-tree, all the nodes are less than the value of the root node; if its right subtree is not empty, then all the right subtree nodes which are greater than the value of the root; its left and right sub-trees are binary sort tree. [ Small left bottom, right side of the big top ]
Daily operations Third, a binary search tree
PS: binary tree lot, but for us, in practical application, the application binary sort tree more.
1. Insert a new node
Suppose we want to array a [] = {10, 5, 15, 6, 4, 16} build a binary sort tree, we insert elements sequentially one by one.
The insertion process is as follows:
If the tree is empty, create a new node, the new node as the root, so a binary search tree to the root node element 10 constructed for that.
- 5,5 insertion smaller than 10, the left child node 10 are compared, left child node 10 is empty, for insertion.
- Insert 15, 15 is greater than 10, were compared, 10 right child node is empty and the right child node 10, for insertion.
- 6,6 insertion than 10 hours, compared with the left child node 510; 6 is larger than 5, compared with the right child node 5, 5 right child is empty, for insertion.
- 4,4 insertion than 10 hours, compared with the left child node 510; less than 45, compared with the left child node 5, left child 5 is empty, insert.
- Insert 10 is greater than 16, 16, 10 compared to the right child of node 15; 16 larger than 15, compared with the right child nodes 15, 15 of the right child is empty insertion.
From this we can conclude that the process steps to insert a new element:
- Suitable elements to find the insertion position: the new element with the current node comparison, if the value is greater than the current node, then find the right subtree; otherwise subtrees left to find.
- After finding the insertion position, the value of the element in the construction of new node is inserted into binary sort tree.
2. balanced binary tree traversal
] [Baidu Encyclopedia balanced binary search tree, also known as AVL trees, and having the following properties: it is the absolute value of the difference between the height of the empty tree or a subtree left and right does not exceed 1, and the left and right subtrees It is a balanced binary tree. 
Balanced binary tree traversal is that in some way one by one "visit" each node binary tree. for example:
Preorder traversal
- Data Access root node in
- Preorder traversal left subtree
- Preorder traversal right subtree
preorder traversal results:
1, 2, 4, 8, 9, 5, 10, 3, 6, 7
Preorder
- Preorder left subtree
- Data Access root node in
- Right subtree preorder
traversal sequence results:
8, 4, 9, 2, 10, 5, 1, 6, 3, 7
Postorder
- Postorder left subtree
- Postorder right subtree
- The root node to access data in
postorder traversal results:
8, 9, 4, 10, 5, 2, 6, 7, 3, 1
Traverse the level
- Data Access root node in
- Data of the second layer to access all the nodes
- All data in the third layer of the access node
- ......
levels through the results:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
3. Delete Node
Delete binary sort tree is a node in three ways:
- Nodes have been removed while the left subtree and the right subtree. The predecessor node value stored in the current node, then remove the precursor node.
- Node is deleted only the left subtree or only a right subtree. Direct replacement with truncated point subtree.
- No sub-tree nodes are removed. You can delete a node directly.
4. Find the value of the element
Minimum binary sort tree is located on its left-most node; maximum is at its rightmost node
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Fourth, references
https://blog.csdn.net/wannuoge4766/article/details/83998377
https://www.cnblogs.com/shixiangwan/p/7530015.html
https://www.cnblogs.com/ysocean/p/8032642.html
https://blog.csdn.net/u014634338/article/details/42465089
http://www.it610.com/article/3607922.htm