用Python实现的B树插入算法解析及图示

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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

<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>

用Python实现B树插入算法

<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>

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