B树是高度平衡的二叉搜索树，进行插入操作，要先获取插入节点的位置，遵循节点比左子树大，比右子树小，在需要时拆分节点。
<code>BreeInsertion(T, k)r root[T]if n[r] = 2t - 1<br/> s = AllocateNode()<br/> root[T] = s<br/> leaf[s] = FALSE<br/> n[s] <- 0<br/> c1[s] <- r<br/> BtreeSplitChild(s, 1, r)<br/> BtreeInsertNonFull(s, k)else BtreeInsertNonFull(r, k)BtreeInsertNonFull(x, k)i = n[x]if leaf[x]<br/> while i ≥ 1 and k < keyi[x]<br/> keyi+1 [x] = keyi[x]<br/> i = i - 1<br/> keyi+1[x] = k<br/> n[x] = n[x] + 1else while i ≥ 1 and k < keyi[x]<br/> i = i - 1<br/> i = i + 1<br/> if n[ci[x]] == 2t - 1<br/> BtreeSplitChild(x, i, ci[x])<br/> if k &rt; keyi[x]<br/> i = i + 1<br/> BtreeInsertNonFull(ci[x], k)BtreeSplitChild(x, i)BtreeSplitChild(x, i, y)z = AllocateNode()leaf[z] = leaf[y]n[z] = t - 1for j = 1 to t - 1<br/> keyj[z] = keyj+t[y]if not leaf [y]<br/> for j = 1 to t<br/> cj[z] = cj + t[y]n[y] = t - 1for j = n[x] + 1 to i + 1<br/> cj+1[x] = cj[x]ci+1[x] = zfor j = n[x] to i<br/> keyj+1[x] = keyj[x]keyi[x] = keyt[y]n[x] = n[x] + 1</code>
<code>class BTreeNode:<br/> def __init__(self, leaf=False):<br/> self.leaf = leaf<br/> self.keys = []<br/> self.child = []<br/> <br/>class BTree:<br/> def __init__(self, t):<br/> self.root = BTreeNode(True)<br/> self.t = t<br/> <br/> def insert(self, k):<br/> root = self.root<br/> if len(root.keys) == (2 * self.t) - 1:<br/> temp = BTreeNode()<br/> self.root = temp<br/> temp.child.insert(0, root)<br/> self.split_child(temp, 0)<br/> self.insert_non_full(temp, k)<br/> else:<br/> self.insert_non_full(root, k)<br/> <br/> def insert_non_full(self, x, k):<br/> i = len(x.keys) - 1<br/> if x.leaf:<br/> x.keys.append((None, None))<br/> while i >= 0 and k[0] < x.keys[i][0]:<br/> x.keys[i + 1] = x.keys[i]<br/> i -= 1<br/> x.keys[i + 1] = k<br/> else:<br/> while i >= 0 and k[0] < x.keys[i][0]:<br/> i -= 1<br/> i += 1<br/> if len(x.child[i].keys) == (2 * self.t) - 1:<br/> self.split_child(x, i)<br/> if k[0] > x.keys[i][0]:<br/> i += 1<br/> self.insert_non_full(x.child[i], k)<br/> <br/> def split_child(self, x, i):<br/> t = self.t<br/> y = x.child[i]<br/> z = BTreeNode(y.leaf)<br/> x.child.insert(i + 1, z)<br/> x.keys.insert(i, y.keys[t - 1])<br/> z.keys = y.keys[t: (2 * t) - 1]<br/> y.keys = y.keys[0: t - 1]<br/> if not y.leaf:<br/> z.child = y.child[t: 2 * t]<br/> y.child = y.child[0: t - 1]<br/> <br/> def print_tree(self, x, l=0):<br/> print("Level ", l, " ", len(x.keys), end=":")<br/> for i in x.keys:<br/> print(i, end=" ")<br/> print()<br/> l += 1<br/> if len(x.child) > 0:<br/> for i in x.child:<br/> self.print_tree(i, l)<br/> <br/>def main():<br/> B = BTree(3)<br/> <br/> for i in range(10):<br/> B.insert((i, 2 * i))<br/> <br/> B.print_tree(B.root)<br/> <br/>if __name__ == '__main__':<br/> main()</code>以上是Python实现B树插入算法的原理图解的详细内容。更多信息请关注PHP中文网其他相关文章！
