Database Design Principle [B tree, B-tree, B + tree]

Source: Internet
Author: User

B treeThat is, the binary search tree:

1. All non-leaf nodes have at most two sons (left and right );

2. All nodes store a keyword;

3. The left pointer of a non-leaf node points to the subtree smaller than its keyword, And the right Pointer Points to the subtree larger than its keyword;


B-tree search starts from the root node. If the query keyword is the same as the node keyword, it hits; otherwise, if the query keyword is smaller than the node keyword, it enters the left son; if it is larger than the node keyword, it enters the right son; If the left son or right son pointer is empty, the report cannot find the corresponding keyword;


B-treeIs a multi-path search tree (not binary ):

1. Define any non-leaf node with a maximum of M sons; and M> 2;

2. The number of sons at the root node is [2, m].

3. The number of non-leaf nodes except the root node is [m/2, m];

4. Each node holds at least m/2-1 (rounded up) and at most M-1 keywords; (at least 2 keywords)

5. Number of keywords for non-leaf nodes = number of pointers to Son-1;

6. Non-leaf node keywords: K [1], K [2],…, K [M-1]; and K [I] <K [I + 1];

7. Non-leaf node pointer: P [1], p [2],…, P [m]; where P [1] points to a subtree with a keyword less than K [1], p [m] points to a subtree with a keyword greater than K [M-1, other P [I] points to the subtree where the keyword belongs (K [I-1], K [I;

8. All leaf nodes are on the same layer;


B-tree search: starts from the root node and performs a binary search for the keyword (ordered) sequence in the node. If hit, the query ends. Otherwise, the son node in the search keyword range is entered; repeat until the corresponding son pointer is null or is already a leaf node;

B + treeThe B + tree is a variant of the B-tree and also a multi-path Search Tree:

1. Its definition is basically the same as that of B-tree,:

2. The number of subtree pointers and keywords for non-leaf nodes is the same;

3. the subtree pointer P [I] for non-leaf nodes, pointing to the subtree with the key value [K [I], K [I + 1]) (B-tree is an open interval );

5. Add a chain pointer to all leaf nodes;

6. All keywords appear at the leaf node;


The search for B + is basically the same as that for B-trees. The difference is that B + trees hit only when they reach the leaf node (B-trees can hit non-leaf nodes ), its performance is also equivalent to performing a binary search in the full set of keywords;





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