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。
一图看懂B树插入操作原理
B树插入算法
BreeInsertion(T, k)r root[T]if n[r] = 2t - 1
s = AllocateNode()
root[T] = s
leaf[s] = FALSE
n[s] <- 0
c1[s] <- r
BtreeSplitChild(s, 1, r)
BtreeInsertNonFull(s, k)else BtreeInsertNonFull(r, k)BtreeInsertNonFull(x, k)i = n[x]if leaf[x]
while i ≥ 1 and k < keyi[x]
keyi+1 [x] = keyi[x]
i = i - 1
keyi+1[x] = k
n[x] = n[x] + 1else while i ≥ 1 and k < keyi[x]
i = i - 1
i = i + 1
if n[ci[x]] == 2t - 1
BtreeSplitChild(x, i, ci[x])
if k &rt; keyi[x]
i = i + 1
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
keyj[z] = keyj+t[y]if not leaf [y]
for j = 1 to t
cj[z] = cj + t[y]n[y] = t - 1for j = n[x] + 1 to i + 1
cj+1[x] = cj[x]ci+1[x] = zfor j = n[x] to i
keyj+1[x] = keyj[x]keyi[x] = keyt[y]n[x] = n[x] + 1
用Python实现B树插入算法
class BTreeNode:
def __init__(self, leaf=False):
self.leaf = leaf
self.keys = []
self.child = []
class BTree:
def __init__(self, t):
self.root = BTreeNode(True)
self.t = t
def insert(self, k):
root = self.root
if len(root.keys) == (2 * self.t) - 1:
temp = BTreeNode()
self.root = temp
temp.child.insert(0, root)
self.split_child(temp, 0)
self.insert_non_full(temp, k)
else:
self.insert_non_full(root, k)
def insert_non_full(self, x, k):
i = len(x.keys) - 1
if x.leaf:
x.keys.append((None, None))
while i >= 0 and k[0] < x.keys[i][0]:
x.keys[i + 1] = x.keys[i]
i -= 1
x.keys[i + 1] = k
else:
while i >= 0 and k[0] < x.keys[i][0]:
i -= 1
i += 1
if len(x.child[i].keys) == (2 * self.t) - 1:
self.split_child(x, i)
if k[0] > x.keys[i][0]:
i += 1
self.insert_non_full(x.child[i], k)
def split_child(self, x, i):
t = self.t
y = x.child[i]
z = BTreeNode(y.leaf)
x.child.insert(i + 1, z)
x.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.child = y.child[t: 2 * t]
y.child = y.child[0: t - 1]
def print_tree(self, x, l=0):
print("Level ", l, " ", len(x.keys), end=":")
for i in x.keys:
print(i, end=" ")
print()
l += 1
if len(x.child) > 0:
for i in x.child:
self.print_tree(i, l)
def main():
B = BTree(3)
for i in range(10):
B.insert((i, 2 * i))
B.print_tree(B.root)
if __name__ == '__main__':
main()
