as follows F (n) =f (n-1) +f (n-2) +1 This is similar to a recursive sequence, can refer to the Fibonacci sequence, 1 is the root node, F (n-1) is the number of nodes of Zuozi, F (n-2) is the number of nodes of the right subtree.3. Red and black Trees3.1 Nature of red and black treesThe
: When a node is full, if its next sibling node is not full, move part of the data to the sibling node, and then insert a keyword into the original node, finally, modify the keywords of the sibling node in the parent node (because the keyword range of the sibling node has changed). If the sibling node is full, add a new node between the original and sibling nodes, copy 1/3 of the data each to the new node, and add a pointer to the new node at the parent node;
Therefore, the probability of B *
Use the red/black tree to find the minimum n numbers, suitable for big data processing and the number of red/Black
Use STL container multiset
Code:
# Include
Running result:
Minimum and maximum number of nodes in the Red
height of h , the maximum height difference of its inner subtree can be reached (result rounding, not rounded). For example, a balanced binary tree with a height of 8 , with a maximum height difference of 4for its inner subtree , and,Similarly, a balanced binary tree with a height of 9 , the maximum height difference of the inner subtree is 5, as shown below (Fig. 2):Figure 22.
Rotation
Shows how single rotation is performed for scenario 1. The left side is before rotation, and the right side is after rotation. In the tree on the left, a new node is inserted in subtree X so that node k2 no longer meets AVL's balanced nature, because its left subtree is two layers deeper than the right subtree (the dotted line in the middle of the graph represents the layers of the tree ).
Demons
suitable for Interval queries. Therefore, the B + tree is usually used for database indexing, while the B tree is often used for file indexing.
Red/black tree:
Reference: https://www.cnblogs.com/CarpenterLee/p/5503882.html
Summary:
The
If the balanced binary tree is a class, then the red-black tree is an example of the class.
Algorithm of the book I lost a long time, I can not find, I was based on memory said. The red-black
The dynamic look-up trees in our presentation are: Two fork search tree (BST), Balanced binary search tree (AVL), Red black Tree (RBT), b~/b+ tree (b-tree). These four kinds of trees ha
Red-black tree, is a special nature of the two-fork search tree, node, either red or blackThe root node is black.The leaf node is black.If a node is red, then its two sons are blackFor any node, each path of its leaf node
Red-black tree is a relatively common data structure in computer science, which makes the search, insertion and deletion of data can maintain the time complexity of O (LGN). However, compared to the general data structure, the implementation of red-black trees has increased
The previous blog mainly describes the basic concept of two-fork sorting tree and insert delete operation, it must be explained again: In a height of two-fork sorting tree, the implementation of dynamic collection operation query, insert and delete run time is O (h).The basic operational efficiency of the binary tree is determined by the shape of the
This blog mainly explains the B-tree and its insert delete operations, and gives the operation of the flowchart to achieve clear and understandable purpose, although the title is from the two-fork sorting tree to balance the binary tree and then to the Red Black
and black tree This data structure is widely used in many programming languages as a symbol table implementation, such as:
Java.util.treemap,java.util.treeset in Java
C + + STL: Map,multimap,multiset
. NET: Sorteddictionary,sortedset, etc.
Below with. NET as an example, through the reflector tool, we can see that the Add method of SortedDic
used in many programming languages as a symbol table implementation, such as:
Java.util.treemap,java.util.treeset in Java
C + + STL: Map,multimap,multiset
. NET: Sorteddictionary,sortedset, etc.
Below with. NET as an example, through the reflector tool, we can see that the Add method of SortedDictionary is as follows:public void Add (T item) {if (this.root = = null) {this.root = new nodeAs you can see, the internal implementatio
I. OverviewRed-black tree is a classic storage structure, in itself is a binary search tree, just on this basis, the tree node added a property to represent the color (red or black). By restricting the coloring of nodes from the r
trees respectively.Middle sequence traversal (left and right) binary sort tree can get an ordered sequence based on the keywordSearch, INSERT, delete time complexity is equal to tree height, expect O (Logn), the worst O (n) (sequence order, the tree degenerate into linear table, such as right oblique tree).Although th
http://cmsblogs.com/?p=1013 original source.TreeMap implementation is the implementation of red-black tree algorithm, so to understand the treemap must have a certain understanding of red and black trees, in fact, the name of this blog is called: According to the
Recently took some time to regain the basic knowledge of data structure, first tried the red and black trees, spent most of the month to study its principles and implementation, the following is learned knowledge and some notes sharing. I hope you will advise me. The implementation of this code please click: Red black
Defined:Tree:A tree is a finite set t of N (n≥0) nodes, and when n>0 meets the following conditions:(1) There is only one specific node called root (Root);(2) When n>1, the remaining nodes can be divided into m (m>0) disjoint finite set T1, T2 、...、 Tm, each set Ti (1≤i≤m) is a tree, and is called the subtree of the tree T (subtree).In particular, a
The previous article introduced the 2-3 lookup tree, you can see that the 2-3 find tree can ensure that after inserting elements can maintain the balance of the tree, the worst case is all the child nodes are 2-node, the height of the tree is lgn, thus guaranteeing the worst case of time Complexity. however, 2-3 trees
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