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B+ 1 & 2 的树顺序

[英]B+ Tree order of 1 & 2

原文 2020-04-22 07:28:43 5 1 algorithm/ data-structures/ b-tree

I am confused regarding the maximum and minimum number of keys to be inserted in a B+ Tree having an order of 1 and order of 2.我对要在顺序为 1 和顺序为 2 的 B+ 树中插入的最大和最小键数感到困惑。

In the videos I watch, it is said that the maximum number of keys to be inserted in a node (except the root) is at least m and at most 2m (assuming m is the order).在我看的视频中，据说一个节点（根除外）中插入的最大键数至少为m ，最多为2m （假设m为顺序）。

According to these 2 statements, what is the minimum & maximum number of keys to be inserted in a B+ Tree, having an order of 1 and order of 2?根据这两条语句，在 B+ 树中插入的最小和最大键数是多少，顺序为 1，顺序为 2？ I am not sure if the 2 statements above conflict, or I misunderstood something.我不确定上面的两个陈述是否冲突，或者我误解了一些东西。 Any idea?任何想法？

1 个解决方案

Without having the reference to the video, it looks like they use a non-standard definition of the term order , which is the cause of the confusion.在没有参考视频的情况下，看起来他们使用了术语order的非标准定义，这是造成混淆的原因。

The standard definition of order for a tree would be the maximum branching factor, ie the maximum number of children that a node may have.树的顺序的标准定义是最大分支因子，即一个节点可能拥有的最大子节点数。 So, in that definition it is not the minimum , but the maximum , and it is not about the number of keys , but about the number of children .因此，在该定义中，它不是最小值，而是最大值，并且与键的数量无关，而是与子项的数量有关。

The video's definition would mean that the maximum number of keys would always be an even number, while in reality there is no such requirement.视频的定义意味着最大键数始终为偶数，而实际上并没有这样的要求。 B+ trees may well have a maximum branching factor that is even, making the maximum number of keys odd. B+ 树的最大分支因子很可能是偶数，从而使最大键数为奇数。

Using standard definition of the term order , we specifically have for B+ trees these constraints:使用术语order的标准定义，我们专门针对 B+ 树具有以下约束：

Its internal nodes have at the most m children.它的内部节点最多有m个子节点。 This means that they have at the most m - 1 keys.这意味着它们最多有m - 1 个键。
Its internal nodes have at least m/2 (rounded upwards) children, except for the root:它的内部节点至少有m/2 （向上舍入）子节点，根除外：
If its root is not a leaf, it may have as few as 2 children.如果它的根不是叶子，它可能只有 2 个孩子。
Its leaves contain the actual data values.它的叶子包含实际的数据值。

Here is an example B+ tree with order 4 (standard definition), which corresponds to a B+ tree where the number of keys must be between 1 and 3 -- something that does not fit with the video's definition:下面是一个具有 4 阶（标准定义）的示例 B+ 树，它对应于一个 B+ 树，其中键的数量必须在 1 到 3 之间——这不符合视频的定义：

As you can see, a node can here at most have 4 children, and at most 3 keys.如您所见，一个节点在这里最多可以有 4 个孩子，最多可以有 3 个键。 In your definition where 2m represents the maximum number of keys, the order is actually 2m+1 .在您的定义中， 2m表示最大键数，顺序实际上是2m+1 。 So you are asking for examples of B+ trees of order 3 and 5, using the standard definition of order .因此，您要求使用 order 的标准定义来提供 3 和 5阶B+ 树的示例。

Here is an example of order 3 -- the lowest possible order for B+ trees -- which means the number of keys must be either 1 or 2 in each node:下面是 3 阶的示例——B+ 树的最低阶——这意味着每个节点中的键数必须是 1 或 2：