B+ tree height calculation of MySQL

problem

hypothesis B+ The height of the tree is 2, The record size of a row of data is 1K, Primary key ID yes int type .
ask ： The B+ The total number of records stored in the tree ？

Knowledge point

Mysql The default storage engine for is Innodb
Innodb The minimum storage unit of is page
One page is equal to 16K
B+ The leaf nodes of the tree are stored data , Internal node storage Key value and pointer

 At a height of 2 Of B+ Tree case ,
B+ The tree stores the total record = The number of record lines of a single leaf node  *  Number of root node pointers  

To solve the process

1） Calculate the number of record lines of a single leaf node
The size of a single page is 16K
The size of a row of data is 1K
So the number of lines =16K / 1K =16

2） Calculate the number of root node pointers
One int The character length of type is 4 byte
stay Innodb The length of a pointer in the setting is 4 byte
total 8 Bytes
So the number of root node pointers =16KB / 8B = 16 * 1024B / 8B = 2048
According to the formula ：B+ The tree stores the total record =2048 * 16 = 32768
in summary ： The height is 2 And meet the above conditions B+ Trees store records 32768 strip

Additional explanation ：
If B+ The height of the tree is 3,B+ The tree storage record is

2048 * 2048 * 16 = 67108864

thus it can be seen ,B+ The height of the tree exceeds 3 when , disk IO Rapid increase ,SQL Query pressure will also increase dramatically .