我们将表格的格式从未排序的行组转变成了B树。这个变化非常大，需要很多篇文章才能完成。在本篇的末尾，我们将定义叶子节点的布局，并且实现在单节点树中插入键值对。但首先让我们回顾一下为什么将数据结构改为树。
以目前的格式，每页只存储行（不包括元数据）所以空间很充足。插入操作的执行会很快，因为我们只在行末追加。然而，要找到特定行需要扫描整个表。当我们删除某行的时候，我们需要把该行后面的所有行向前移动来填补该行的空缺。
如果我们用树结构，每个节点都包含可变的行数，我们需要在每个节点中存储一些信息来追踪每个节点存了多少行。另外所有不存储任何行的内部节点也存储开销。在大数据库文件操作的时候我们插入，删除，查找更快速。
每个节点将对应一个页面。内部节点将通过存储子节点的页码来找到其子代。 B树向pager询问特定的页码，然后指向该页缓存的指针。页面按页面编号排序，一个一个的存储在数据库文件中。
在页面起点，节点会在头信息里存储元数据。每个节点都会存储自己的节点类型，不论自己是不是根节点（为了能找到同级节点），也同时存储指向父节点的指针信息。下面为每个头字段的大小和偏移量定义常量：
现在在数据库存储页数比行数更有意义了。页数应与pager对象关联而不是与表相关联，因为它是被数据库所使用的页数，而不是表。B树由其根节点页号标识，因此表对象需要对其进行跟踪。（Now it makes more sense to store the number of pages in our database rather than the number of rows. The number of pages should be associated with the pager object, not the table, since it’s the number of pages used by the database, not a particular table. A btree is identified by its root node page number, so the table object needs to keep track of that.）
pages[i] = NULL;
对cursor对象的更改
Cursor表示表中的位置。当我们的表是一个简单的由行组成的数组时，我们通过行号访问行。现在已经是树结构了，我们通过节点的页码以及该节点内的单元格编号来确定位置。
typedef struct {
Table* table;
- uint32_t row_num;
+ uint32_t page_num;
+ uint32_t cell_num;
bool end_of_table; // Indicates a position one past the last element
} Cursor;
Cursor* table_start(Table* table) {
Cursor* cursor = malloc(sizeof(Cursor));
cursor->table = table;
- cursor->row_num = 0;
- cursor->end_of_table = (table->num_rows == 0);
+ cursor->page_num = table->root_page_num;
+ cursor->cell_num = 0;
+
+ void* root_node = get_page(table->pager, table->root_page_num);
+ uint32_t num_cells = *leaf_node_num_cells(root_node);
+ cursor->end_of_table = (num_cells == 0);
return cursor;
}
Cursor* table_end(Table* table) {
Cursor* cursor = malloc(sizeof(Cursor));
cursor->table = table;
- cursor->row_num = table->num_rows;
+ cursor->page_num = table->root_page_num;
+
+ void* root_node = get_page(table->pager, table->root_page_num);
+ uint32_t num_cells = *leaf_node_num_cells(root_node);
+ cursor->cell_num = num_cells;
cursor->end_of_table = true;
return cursor;
}
void* cursor_value(Cursor* cursor) {
- uint32_t row_num = cursor->row_num;
- uint32_t page_num = row_num / ROWS_PER_PAGE;
+ uint32_t page_num = cursor->page_num;
void* page = get_page(cursor->table->pager, page_num);
- uint32_t row_offset = row_num % ROWS_PER_PAGE;
- uint32_t byte_offset = row_offset * ROW_SIZE;
- return page + byte_offset;
+ return leaf_node_value(page, cursor->cell_num);
}
void cursor_advance(Cursor* cursor) {
- cursor->row_num += 1;
- if (cursor->row_num >= cursor->table->num_rows) {
+ uint32_t page_num = cursor->page_num;
+ void* node = get_page(cursor->table->pager, page_num);
+
+ cursor->cell_num += 1;
+ if (cursor->cell_num >= (*leaf_node_num_cells(node))) {
cursor->end_of_table = true;
}
}
在叶子节点中做插入
在本篇中，我们仅实现足以获得单节点树的方法。回想一下上一篇文章，树开始时是一个空的叶子节点：
空树
可以一直添加键值对直到叶子节点填满：
单节点B树
当我们第一次打开数据库文件，文件是空的，所以我们把页面0作为空的叶子节点（也是根节点）：
Table* db_open(const char* filename) {
Pager* pager = pager_open(filename);
- uint32_t num_rows = pager->file_length / ROW_SIZE;
Table* table = malloc(sizeof(Table));
table->pager = pager;
- table->num_rows = num_rows;
+ table->root_page_num = 0;
+
+ if (pager->num_pages == 0) {
+ // New database file. Initialize page 0 as leaf node.
+ void* root_node = get_page(pager, 0);
+ initialize_leaf_node(root_node);
+ }
return table;
}
接下来我们写个函数来向叶子节点插入键值对，它以光标为输入，作为插入的位置。
+void leaf_node_insert(Cursor* cursor, uint32_t key, Row* value) {
+ void* node = get_page(cursor->table->pager, cursor->page_num);
+
+ uint32_t num_cells = *leaf_node_num_cells(node);
+ if (num_cells >= LEAF_NODE_MAX_CELLS) {
+ // Node full
+ printf("Need to implement splitting a leaf node.\n");
+ exit(EXIT_FAILURE);
+ }
+
+ if (cursor->cell_num cursor->cell_num; i--) {
+ memcpy(leaf_node_cell(node, i), leaf_node_cell(node, i - 1),
+ LEAF_NODE_CELL_SIZE);
+ }
+ }
+
+ *(leaf_node_num_cells(node)) += 1;
+ *(leaf_node_key(node, cursor->cell_num)) = key;
+ serialize_row(value, leaf_node_value(node, cursor->cell_num));
+}
+
我们还没实现拆分，因此如果节点满了就会出错。接下来，我们将单元格向右移动一个空间，为新单元格腾出空间。然后，我们将新的键/值写入空白处。
由于我们假设树只有一个节点，因此execute_insert（）函数只需要调用此辅助方法：
ExecuteResult execute_insert(Statement* statement, Table* table) {
- if (table->num_rows >= TABLE_MAX_ROWS) {
+ void* node = get_page(table->pager, table->root_page_num);
+ if ((*leaf_node_num_cells(node) >= LEAF_NODE_MAX_CELLS)) {
return EXECUTE_TABLE_FULL;
}
Row* row_to_insert = &(statement->row_to_insert);
Cursor* cursor = table_end(table);
- serialize_row(row_to_insert, cursor_value(cursor));
- table->num_rows += 1;
- leaf_node_insert(cursor, row_to_insert->id, row_to_insert);
free(cursor);
有了这些更改，我们的数据库就能像之前一样共工作了。但是现在返回了“table full”的报错，因为目前我们不能拆分节点。
那么一个叶子节点可以承载多少行?
打印常量的命令
我现在添加一个新的元命令，用它可以打印出一些您感兴趣的常数
+void print_constants() {
+ printf("ROW_SIZE: %d\n", ROW_SIZE);
+ printf("COMMON_NODE_HEADER_SIZE: %d\n", COMMON_NODE_HEADER_SIZE);
+ printf("LEAF_NODE_HEADER_SIZE: %d\n", LEAF_NODE_HEADER_SIZE);
+ printf("LEAF_NODE_CELL_SIZE: %d\n", LEAF_NODE_CELL_SIZE);
+ printf("LEAF_NODE_SPACE_FOR_CELLS: %d\n", LEAF_NODE_SPACE_FOR_CELLS);
+ printf("LEAF_NODE_MAX_CELLS: %d\n", LEAF_NODE_MAX_CELLS);
+}
+
@@ -294,6 +376,14 @@ MetaCommandResult do_meta_command(InputBuffer* input_buffer, Table* table) {
if (strcmp(input_buffer->buffer, ".exit") == 0) {
db_close(table);
exit(EXIT_SUCCESS);
+ } else if (strcmp(input_buffer->buffer, ".constants") == 0) {
+ printf("Constants:\n");
+ print_constants();
+ return META_COMMAND_SUCCESS;
} else {
return META_COMMAND_UNRECOGNIZED_COMMAND;
}
我再添加一段测试代码，这样常量有变化时我们可以被通知到
+ it 'prints constants' do
+ script = [
+ ".constants",
+ ".exit",
+ ]
+ result = run_script(script)
+
+ expect(result).to match_array([
+ "db > Constants:",
+ "ROW_SIZE: 293",
+ "COMMON_NODE_HEADER_SIZE: 6",
+ "LEAF_NODE_HEADER_SIZE: 10",
+ "LEAF_NODE_CELL_SIZE: 297",
+ "LEAF_NODE_SPACE_FOR_CELLS: 4086",
+ "LEAF_NODE_MAX_CELLS: 13",
+ "db > ",
+ ])
+ end
现在我们的表可以承载最多13行了
树的可视化
为了帮助代码调试和可视化，我再添加元命令来打印出B树
+void print_leaf_node(void* node) {
+ uint32_t num_cells = *leaf_node_num_cells(node);
+ printf("leaf (size %d)\n", num_cells);
+ for (uint32_t i = 0; i buffer, ".exit") == 0) {
db_close(table);
exit(EXIT_SUCCESS);
+ } else if (strcmp(input_buffer->buffer, ".btree") == 0) {
+ printf("Tree:\n");
+ print_leaf_node(get_page(table->pager, 0));
+ return META_COMMAND_SUCCESS;
} else if (strcmp(input_buffer->buffer, ".constants") == 0) {
printf("Constants:\n");
print_constants();
return META_COMMAND_SUCCESS;
} else {
return META_COMMAND_UNRECOGNIZED_COMMAND;
}
测试：
+ it 'allows printing out the structure of a one-node btree' do
+ script = [3, 1, 2].map do |i|
+ "insert #{i} user#{i} person#{i}@example.com"
+ end
+ script << ".btree"
+ script < Executed.",
+ "db > Executed.",
+ "db > Executed.",
+ "db > Tree:",
+ "leaf (size 3)",
+ " - 0 : 3",
+ " - 1 : 1",
+ " - 2 : 2",
+ "db > "
+ ])
+ end
目前我们还是没法实现按顺序存储行。您会注意到，execute_insert（）以table_end（）的返回值为位置插入数据到叶节点中。因此像以前一样，行按插入顺序存储。
下一篇
这一切似乎都倒退了。现在，我们的数据库存储的行比以前少了，而且我们仍按未排序的顺序存储行。但就像我刚开始所说的那样，这是一个很大的变化，将其分解为可管理的步骤非常重要。
下次，我们将实现通过主键查找数据，并开始按排序顺序存储行。
代码如下：
@@ -62,29 +62,101 @@ const uint32_t ROW_SIZE = ID_SIZE + USERNAME_SIZE + EMAIL_SIZE;
const uint32_t PAGE_SIZE = 4096;
#define TABLE_MAX_PAGES 100
-const uint32_t ROWS_PER_PAGE = PAGE_SIZE / ROW_SIZE;
-const uint32_t TABLE_MAX_ROWS = ROWS_PER_PAGE * TABLE_MAX_PAGES;
typedef struct {
int file_descriptor;
uint32_t file_length;
+ uint32_t num_pages;
void* pages[TABLE_MAX_PAGES];
} Pager;
typedef struct {
Pager* pager;
- uint32_t num_rows;
+ uint32_t root_page_num;
} Table;
typedef struct {
Table* table;
- uint32_t row_num;
+ uint32_t page_num;
+ uint32_t cell_num;
bool end_of_table; // Indicates a position one past the last element
} Cursor;
+typedef enum { NODE_INTERNAL, NODE_LEAF } NodeType;
+
+/*
+ * Common Node Header Layout
+ */
+const uint32_t NODE_TYPE_SIZE = sizeof(uint8_t);
+const uint32_t NODE_TYPE_OFFSET = 0;
+const uint32_t IS_ROOT_SIZE = sizeof(uint8_t);
+const uint32_t IS_ROOT_OFFSET = NODE_TYPE_SIZE;
+const uint32_t PARENT_POINTER_SIZE = sizeof(uint32_t);
+const uint32_t PARENT_POINTER_OFFSET = IS_ROOT_OFFSET + IS_ROOT_SIZE;
+const uint8_t COMMON_NODE_HEADER_SIZE =
+ NODE_TYPE_SIZE + IS_ROOT_SIZE + PARENT_POINTER_SIZE;
+
+/*
+ * Leaf Node Header Layout
+ */
+const uint32_t LEAF_NODE_NUM_CELLS_SIZE = sizeof(uint32_t);
+const uint32_t LEAF_NODE_NUM_CELLS_OFFSET = COMMON_NODE_HEADER_SIZE;
+const uint32_t LEAF_NODE_HEADER_SIZE =
+ COMMON_NODE_HEADER_SIZE + LEAF_NODE_NUM_CELLS_SIZE;
+
+/*
+ * Leaf Node Body Layout
+ */
+const uint32_t LEAF_NODE_KEY_SIZE = sizeof(uint32_t);
+const uint32_t LEAF_NODE_KEY_OFFSET = 0;
+const uint32_t LEAF_NODE_VALUE_SIZE = ROW_SIZE;
+const uint32_t LEAF_NODE_VALUE_OFFSET =
+ LEAF_NODE_KEY_OFFSET + LEAF_NODE_KEY_SIZE;
+const uint32_t LEAF_NODE_CELL_SIZE = LEAF_NODE_KEY_SIZE + LEAF_NODE_VALUE_SIZE;
+const uint32_t LEAF_NODE_SPACE_FOR_CELLS = PAGE_SIZE - LEAF_NODE_HEADER_SIZE;
+const uint32_t LEAF_NODE_MAX_CELLS =
+ LEAF_NODE_SPACE_FOR_CELLS / LEAF_NODE_CELL_SIZE;
+
+uint32_t* leaf_node_num_cells(void* node) {
+ return node + LEAF_NODE_NUM_CELLS_OFFSET;
+}
+
+void* leaf_node_cell(void* node, uint32_t cell_num) {
+ return node + LEAF_NODE_HEADER_SIZE + cell_num * LEAF_NODE_CELL_SIZE;
+}
+
+uint32_t* leaf_node_key(void* node, uint32_t cell_num) {
+ return leaf_node_cell(node, cell_num);
+}
+
+void* leaf_node_value(void* node, uint32_t cell_num) {
+ return leaf_node_cell(node, cell_num) + LEAF_NODE_KEY_SIZE;
+}
+
+void print_constants() {
+ printf("ROW_SIZE: %d\n", ROW_SIZE);
+ printf("COMMON_NODE_HEADER_SIZE: %d\n", COMMON_NODE_HEADER_SIZE);
+ printf("LEAF_NODE_HEADER_SIZE: %d\n", LEAF_NODE_HEADER_SIZE);
+ printf("LEAF_NODE_CELL_SIZE: %d\n", LEAF_NODE_CELL_SIZE);
+ printf("LEAF_NODE_SPACE_FOR_CELLS: %d\n", LEAF_NODE_SPACE_FOR_CELLS);
+ printf("LEAF_NODE_MAX_CELLS: %d\n", LEAF_NODE_MAX_CELLS);
+}
+
+void print_leaf_node(void* node) {
+ uint32_t num_cells = *leaf_node_num_cells(node);
+ printf("leaf (size %d)\n", num_cells);
+ for (uint32_t i = 0; i id, row->username, row->email);
}
@@ -101,6 +173,8 @@ void deserialize_row(void *source, Row* destination) {
memcpy(&(destination->email), source + EMAIL_OFFSET, EMAIL_SIZE);
}
+void initialize_leaf_node(void* node) { *leaf_node_num_cells(node) = 0; }
+
void* get_page(Pager* pager, uint32_t page_num) {
if (page_num > TABLE_MAX_PAGES) {
printf("Tried to fetch page number out of bounds. %d > %d\n", page_num,
@@ -128,6 +202,10 @@ void* get_page(Pager* pager, uint32_t page_num) {
}
pager->pages[page_num] = page;
+
+ if (page_num >= pager->num_pages) {
+ pager->num_pages = page_num + 1;
+ }
}
return pager->pages[page_num];
@@ -136,8 +214,12 @@ void* get_page(Pager* pager, uint32_t page_num) {
Cursor* table_start(Table* table) {
Cursor* cursor = malloc(sizeof(Cursor));
cursor->table = table;
- cursor->row_num = 0;
- cursor->end_of_table = (table->num_rows == 0);
+ cursor->page_num = table->root_page_num;
+ cursor->cell_num = 0;
+
+ void* root_node = get_page(table->pager, table->root_page_num);
+ uint32_t num_cells = *leaf_node_num_cells(root_node);
+ cursor->end_of_table = (num_cells == 0);
return cursor;
}
@@ -145,24 +227,28 @@ Cursor* table_start(Table* table) {
Cursor* table_end(Table* table) {
Cursor* cursor = malloc(sizeof(Cursor));
cursor->table = table;
- cursor->row_num = table->num_rows;
+ cursor->page_num = table->root_page_num;
+
+ void* root_node = get_page(table->pager, table->root_page_num);
+ uint32_t num_cells = *leaf_node_num_cells(root_node);
+ cursor->cell_num = num_cells;
cursor->end_of_table = true;
return cursor;
}
void* cursor_value(Cursor* cursor) {
- uint32_t row_num = cursor->row_num;
- uint32_t page_num = row_num / ROWS_PER_PAGE;
+ uint32_t page_num = cursor->page_num;
void* page = get_page(cursor->table->pager, page_num);
- uint32_t row_offset = row_num % ROWS_PER_PAGE;
- uint32_t byte_offset = row_offset * ROW_SIZE;
- return page + byte_offset;
+ return leaf_node_value(page, cursor->cell_num);
}
void cursor_advance(Cursor* cursor) {
- cursor->row_num += 1;
- if (cursor->row_num >= cursor->table->num_rows) {
+ uint32_t page_num = cursor->page_num;
+ void* node = get_page(cursor->table->pager, page_num);
+
+ cursor->cell_num += 1;
+ if (cursor->cell_num >= (*leaf_node_num_cells(node))) {
cursor->end_of_table = true;
}
}
@@ -185,6 +271,12 @@ Pager* pager_open(const char* filename) {
Pager* pager = malloc(sizeof(Pager));
pager->file_descriptor = fd;
pager->file_length = file_length;
+ pager->num_pages = (file_length / PAGE_SIZE);
+
+ if (file_length % PAGE_SIZE != 0) {
+ printf("Db file is not a whole number of pages. Corrupt file.\n");
+ exit(EXIT_FAILURE);
+ }
for (uint32_t i = 0; i pages[i] = NULL;
@@ -194,11 +285,15 @@ Pager* pager_open(const char* filename) {
@@ -195,11 +287,16 @@ Pager* pager_open(const char* filename) {
Table* db_open(const char* filename) {
Pager* pager = pager_open(filename);
- uint32_t num_rows = pager->file_length / ROW_SIZE;
Table* table = malloc(sizeof(Table));
table->pager = pager;
- table->num_rows = num_rows;
+ table->root_page_num = 0;
+
+ if (pager->num_pages == 0) {
+ // New database file. Initialize page 0 as leaf node.
+ void* root_node = get_page(pager, 0);
+ initialize_leaf_node(root_node);
+ }
return table;
}
@@ -234,7 +331,7 @@ void close_input_buffer(InputBuffer* input_buffer) {
free(input_buffer);
}
-void pager_flush(Pager* pager, uint32_t page_num, uint32_t size) {
+void pager_flush(Pager* pager, uint32_t page_num) {
if (pager->pages[page_num] == NULL) {
printf("Tried to flush null page\n");
exit(EXIT_FAILURE);
@@ -242,7 +337,7 @@ void pager_flush(Pager* pager, uint32_t page_num, uint32_t size) {
@@ -249,7 +346,7 @@ void pager_flush(Pager* pager, uint32_t page_num, uint32_t size) {
}
ssize_t bytes_written =
- write(pager->file_descriptor, pager->pages[page_num], size);
+ write(pager->file_descriptor, pager->pages[page_num], PAGE_SIZE);
if (bytes_written == -1) {
printf("Error writing: %d\n", errno);
@@ -252,29 +347,16 @@ void pager_flush(Pager* pager, uint32_t page_num, uint32_t size) {
@@ -260,29 +357,16 @@ void pager_flush(Pager* pager, uint32_t page_num, uint32_t size) {
void db_close(Table* table) {
Pager* pager = table->pager;
- uint32_t num_full_pages = table->num_rows / ROWS_PER_PAGE;
- for (uint32_t i = 0; i < num_full_pages; i++) {
- for (uint32_t i = 0; i num_pages; i++) {
if (pager->pages[i] == NULL) {
continue;
}
- pager_flush(pager, i, PAGE_SIZE);
- pager_flush(pager, i);
free(pager->pages[i]);
pager->pages[i] = NULL;
}
- // There may be a partial page to write to the end of the file
- // This should not be needed after we switch to a B-tree
- uint32_t num_additional_rows = table->num_rows % ROWS_PER_PAGE;
- if (num_additional_rows > 0) {
- uint32_t page_num = num_full_pages;
- if (pager->pages[page_num] != NULL) {
- pager_flush(pager, page_num, num_additional_rows * ROW_SIZE);
- free(pager->pages[page_num]);
- pager->pages[page_num] = NULL;
- int result = close(pager->file_descriptor);
if (result == -1) {
printf(“Error closing db file.\n”);
@@ -305,6 +389,14 @@ MetaCommandResult do_meta_command(InputBuffer* input_buffer, Table *table) {
if (strcmp(input_buffer->buffer, “.exit”) == 0) {
db_close(table);
exit(EXIT_SUCCESS);
- } else if (strcmp(input_buffer->buffer, “.btree”) == 0) {
- printf(“Tree:\n”);
- print_leaf_node(get_page(table->pager, 0));
- return META_COMMAND_SUCCESS;
- } else if (strcmp(input_buffer->buffer, “.constants”) == 0) {
- printf(“Constants:\n”);
- print_constants();
- return META_COMMAND_SUCCESS;
} else {
return META_COMMAND_UNRECOGNIZED_COMMAND;
}
@@ -354,16 +446,39 @@ PrepareResult prepare_statement(InputBuffer* input_buffer,
return PREPARE_UNRECOGNIZED_STATEMENT;
}
+void leaf_node_insert(Cursor* cursor, uint32_t key, Row* value) {
+ void* node = get_page(cursor->table->pager, cursor->page_num);
+
+ uint32_t num_cells = *leaf_node_num_cells(node);
+ if (num_cells >= LEAF_NODE_MAX_CELLS) {
+ // Node full
+ printf(“Need to implement splitting a leaf node.\n”);
+ exit(EXIT_FAILURE);
+ }
+
+ if (cursor->cell_num < num_cells) {
+ // Make room for new cell
+ for (uint32_t i = num_cells; i > cursor->cell_num; i–) {
+ memcpy(leaf_node_cell(node, i), leaf_node_cell(node, i – 1),
+ LEAF_NODE_CELL_SIZE);
+ }
+ }
+
+ *(leaf_node_num_cells(node)) += 1;
+ *(leaf_node_key(node, cursor->cell_num)) = key;
+ serialize_row(value, leaf_node_value(node, cursor->cell_num));
+}
+
ExecuteResult execute_insert(Statement* statement, Table* table) {
– if (table->num_rows >= TABLE_MAX_ROWS) {
+ void* node = get_page(table->pager, table->root_page_num);
+ if ((*leaf_node_num_cells(node) >= LEAF_NODE_MAX_CELLS)) {
return EXECUTE_TABLE_FULL;
}
Row* row_to_insert = &(statement->row_to_insert);
Cursor* cursor = table_end(table);
- serialize_row(row_to_insert, cursor_value(cursor));
- table->num_rows += 1;
- leaf_node_insert(cursor, row_to_insert->id, row_to_insert);
free(cursor);
And the specs:
- it ‘allows printing out the structure of a one-node btree’ do
- script = [3, 1, 2].map do |i|
- “insert #{i} user#{i} person#{i}@example.com”
- end
- script << ".btree"
- script << ".exit"
- result = run_script(script)
- expect(result).to match_array([
- “db > Executed.”,
- “db > Executed.”,
- “db > Executed.”,
- “db > Tree:”,
- “leaf (size 3)”,
- ” – 0 : 3″,
- ” – 1 : 1″,
- ” – 2 : 2″,
- “db > “
- ])
- end
- it ‘prints constants’ do
- script = [
- “.constants”,
- “.exit”,
- result = run_script(script)
- expect(result).to match_array([
- “db > Constants:”,
- “ROW_SIZE: 293”,
- “COMMON_NODE_HEADER_SIZE: 6”,
- “LEAF_NODE_HEADER_SIZE: 10”,
- “LEAF_NODE_CELL_SIZE: 297”,
- “LEAF_NODE_SPACE_FOR_CELLS: 4086”,
- “LEAF_NODE_MAX_CELLS: 13”,
- “db > “,
- ])
- end
end
原文链接： Part 8 – B-Tree Leaf Node Format （翻译：吴世曦）
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