使用c＃的二叉树字典 [英] binary tree dictionary using c #

问题描述

问候！我需要一个关于如何使用c＃中的二叉树创建字典的示例或指南，提前感谢。

Greetings!. I need an example or a guide on how to create a dictionary using binary trees in c #, thanks in advance.

推荐答案

这是二叉树的设计方式： http://en.wikipedia.org/wiki/Binary_tree [ ^ ]。



这是用于二进制文件的方式搜索： http://en.wikipedia.org/wiki/Binary_search_tree [ ^ ]。



如果看一下算法，您将看到密钥需要一个比较标准，但实际上只使用少于的关系。您需要使用允许订购的一组值： http://en.wikipedia.org/wiki/Total_order [ ^ ]。



您需要定义键值的顺序关系。要使make是通用的，您可以定义接口以进行排序（不需要定义''<''运算符，但如果方便的话，您可以这样做）。或者您可以使用已经可用的更复杂和通用的界面： System.IComparable ：

http://msdn.microsoft.com/en-us/library/system.icomparable.aspx [ ^ ]。



同样，如果你想要一个比较运算符，你可以从这个接口派生。您的密钥类型应该实现此接口，然后您可以定义一个通用的节点类型，假设密钥类型是 IComparable ，这是使用泛型类型约束完成的：

http://msdn.microsoft.com/en -us / library / bb384067.aspx [ ^ ]。



对于树节点，使用泛型类看起来像这样：

This is how the binary tree is designed: http://en.wikipedia.org/wiki/Binary_tree[^].

This is how it is used for binary search: http://en.wikipedia.org/wiki/Binary_search_tree[^].

If you look at the algorithms, you will see that keys need a comparison criterion, but only "less then" relationship is actually used. You need to use the set of values that allows for the ordering: http://en.wikipedia.org/wiki/Total_order[^].

You need to define the order relationship for the the key values. To make is generic, you can define the interface for ordering (there is no a big need to define the ''<'' operator, but you can do it if it is convenient for your). Or you can use the more complex and general interface which is already available: System.IComparable:
http://msdn.microsoft.com/en-us/library/system.icomparable.aspx[^].

Again, you can derive from this interface, if you want a comparison operator. Your key type should implement this interface, and then you can define a generic your node type assuming that the key type is IComparable, which is done using the generic type constraint:
http://msdn.microsoft.com/en-us/library/bb384067.aspx[^].

For a tree node, use generic class would look like this:

class Node<KEY_TYPE, VALUE_TYPE> : IComparable where KEY_TYPE : System.IComparable {

    KEY_TYPE key; //
    VALUE_TYPE data; // anything you need to put in data
    Node<KEY_TYPE, VALUE_TYPE> left, right;

    int IComparable.CompareTo(object @object) {
        Node<KEY_TYPE, VALUE_TYPE> nodeObject = @object as Node<KEY_TYPE, VALUE_TYPE>; // use it for comparison with "this"
        // implement comparison between @object and this
        // take into account that @object can be null
        // and that @object can be of different type
    }

    // implement constructors, operations with left, right, etc...

}

请注意，我建议为节点类型实现 IComparable 。这样，您就不需要比较键，就能立即比较节点。



这将为您提供一种实用树的文化和便捷方式构建算法和搜索。



字典的界面应与类 System.Collections.Generic.Dictionary<>类相同。 ：

http://msdn.microsoft.com/en-us/library/xfhwa508%28v=vs.110%29.aspx [ ^ ]。



没有什么可以发明的，一对一地使用它。算法在第二个链接中描述。祝你好运。







回应Matt T Heffron的好评：



渐近地，这种算法对于大量数据来说并不是最快的;它提供了O（ln N）的计算时间复杂度，而 System.Collections.Generic.Dictionary （以及另外两个基于的类bucket 存储和哈希函数）的时间复杂度为O（1）。



请参阅：

http://en.wikipedia.org/wiki/Big_O_notation [ ^ ]，

http://en.wikipedia.org/wiki/Time_complexity [ ^ ]，

http://en.wikipedia.org / wiki / Asymptotic_complexity [ ^ ]，
http://en.wikipedia.org/w iki / Asymptote [ ^ ]。

-SA

Note that I suggested to implement IComparable also for the Node type. This way, you won''t need to compare keys, will be able to compare nodes, immediately.

This will give you a cultured and convenient way to implement tree building algorithm and search.

The interface of your dictionary should identical to the one of the class System.Collections.Generic.Dictionary<>:
http://msdn.microsoft.com/en-us/library/xfhwa508%28v=vs.110%29.aspx[^].

There is nothing to invent, use it one-to-one. The algorithms are described in the second link. Good luck.



In response to a good note by Matt T Heffron:

Asymptotically, this algorithm is not the fastest for big volumes of data; it provides computational time complexity of O(ln N), while System.Collections.Generic.Dictionary (and two more classes based on bucket storage and hash function) has time complexity of O(1).

Please see:
http://en.wikipedia.org/wiki/Big_O_notation[^],
http://en.wikipedia.org/wiki/Time_complexity[^],
http://en.wikipedia.org/wiki/Asymptotic_complexity[^],
http://en.wikipedia.org/wiki/Asymptote[^].

—SA

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