
class BTreeNode:
    def __init__(self, leaf=False):
        self.leaf = leaf
        self.keys = []
        self.children = []
 
class BTree:
    def __init__(self, t):
        self.root = BTreeNode(True)
        self.t = t  # 最小度数
 
    def insert(self, key):
        root = self.root
        if len(root.keys) == 2 * self.t - 1:
            temp = BTreeNode()
            self.root = temp
            temp.children.insert(0, root)
            self._split_child(temp, 0)
            self._insert_non_full(temp, key)
        else:
            self._insert_non_full(root, key)
 
    def _split_child(self, node, i):
        t = self.t
        y = node.children[i]
        z = BTreeNode(y.leaf)
        node.children.insert(i + 1, z)
        node.keys.insert(i, y.keys[t - 1])
        z.keys = y.keys[t: (2 * t - 1)]
        y.keys = y.keys[0: (t - 1)]
        if not y.leaf:
            z.children = y.children[t: (2 * t)]
            y.children = y.children[0: (t - 1)]
 
    def _insert_non_full(self, node, key):
        i = len(node.keys) - 1
        if node.leaf:
            node.keys.append(0)
            while i >= 0 and key < node.keys[i]:
                node.keys[i + 1] = node.keys[i]
                i -= 1
            node.keys[i + 1] = key
        else:
            while i >= 0 and key < node.keys[i]:
                i -= 1
            i += 1
            if len(node.children[i].keys) == 2 * self.t - 1:
                self._split_child(node, i)
                if key > node.keys[i]:
                    i += 1
            self._insert_non_full(node.children[i], key)

6.2 B树的搜索操作示例

以下是一个B树搜索操作的示例，演示了在B树中查找关键字的过程：


def search(self, node, key):
    i = 0
    while i < len(node.keys) and key > node.keys[i]:
        i += 1
    if i < len(node.keys) and key == node.keys[i]:
        return (node, i)
    elif node.leaf:
        return None
    else:
        return self.search(node.children[i], key)

6.3 B树的删除操作示例

以下是一个B树删除操作的示例，演示了在B树中删除关键字的过程：


def delete(self, key):
    self._delete(self.root, key)
    if len(self.root.keys) == 0:
        if not self.root.leaf:
            self.root = self.root.children[0]
        else:
            self.root = BTreeNode(True)
 
def _delete(self, node, key):
    t = self.t
    i = 0
    while i < len(node.keys) and key > node.keys[i]:
        i += 1
    if i < len(node.keys) and key == node.keys[i]:
        if node.leaf:
            node.keys.pop(i)
        else:
            self._delete_internal_node(node, key, i)
    elif node.leaf:
        return
    else:
        self._delete(node.children[i], key)
        if len(node.children[i].keys) < t - 1:
            self._fix(node, i)
 
def _delete_internal_node(self, node, key, i):
    t = self.t
    if len(node.children[i].keys) >= t:
        pred = self._get_predecessor(node.children[i])
        node.keys[i] = pred
        self._delete(node.children[i], pred)
    elif len(node.children[i + 1].keys) >= t:
        succ = self._get_successor(node.children[i + 1])
        node.keys[i] = succ
        self._delete(node.children[i + 1], succ)
    else:
        self._merge(node, i)
        self._delete(node.children[i], key)
 
def _get_predecessor(self, node):
    if node.leaf:
        return node.keys[-1]
    else:
        return self._get_predecessor(node.children[-1])
 
def _get_successor(self, node):
    if node.leaf:
        return node.keys[0]
    else:
        return self._get_successor(node.children[0])
 
def _merge(self, node, i):
    child = node.children[i]
    sibling = node.children[i + 1]
    child.keys.append(node.keys.pop(i))
    child.keys.extend(sibling.keys)
    if not child.leaf:
        child.children.extend(sibling.children)
    node.children.pop(i + 1)
 
def _fix(self, node, i):
    t = self.t
    if i != 0 and len(node.children[i - 1].keys) >= t:
        self._borrow_from_prev(node, i)
    elif i != len(node.children) - 1 and len(node.children[i + 1].keys) >= t:
        self._borrow_from_next(node, i)
    else:
        if i != len(node.children) - 1:
            self._merge(node, i)
        else:
            self._merge(node, i - 1)
 
def _borrow_from_prev(self, node, i):
    child = node.children[i]
    sibling = node.children[i - 1]
    child.keys.insert(0, node.keys[i - 1])
    if not child.leaf:
        child.children.insert(0, sibling.children.pop())
    node.keys[i - 1] = sibling.keys.pop()
 
def _borrow_from_next(self, node, i):
    child = node.children[i]
    sibling = node.children[i + 1]
    child.keys.append(node.keys[i])
    if not child.leaf:
        child.children.append(sibling.children.pop(0))
    node.keys[i] = sibling.keys.pop(0)

7. 结论

B树作为一种高效的多路查找树，广泛应用于数据库、文件系统和内存管理等领域。通过深入理解B树的结构和操作，读者可以更好地应用B树来优化数据管理和查询性能。本文详细介绍了B树的基本概念、结构、操作及其应用，并提供了具体的实现示例，帮助读者全面掌握B树的理论和实践。

声明：本文内容由网友自发贡献，不代表【wpsshop博客】立场，版权归原作者所有，本站不承担相应法律责任。如您发现有侵权的内容，请联系我们。转载请注明出处：https://www.wpsshop.cn/w/小惠珠哦/article/detail/770436