Create a class that allows you to build a directed graph of letters.

A directed graph contains Nodes, uniquely identified by a letter.
A directed graph contains Edges, which connect the Nodes as (from, to).

Your class should allow for the following operations:

1. Add a letter to the graph.
2. Is a letter in the graph?
3. Add an edge, specifying the letter "from" and "to".
4. For a given letter, get all the letters it leads to (by edges).
5. Remove an edge, specifying the letter "from" and "to".
6. Remove a letter, but not if it is involved in an edge.

Choose a language and begin:

创建一个类，允许你构建一个字母的有向图。

有向图包含节点，每个节点由一个字母唯一标识。
有向图包含边，连接节点的形式为 (from, to)。

你的类应该允许以下操作：

1. 向图中添加一个字母。
2. 检查一个字母是否在图中。
3. 添加一条边，指定字母“from”和“to”。
4. 对于给定的字母，获取所有它指向的字母（通过边）。
5. 删除一条边，指定字母“from”和“to”。
6. 删除一个字母，但如果它涉及到某条边则不能删除。

选择一种语言并开始：

This problem is a recent interview question from Amazon, focusing on Object-Oriented Design (OOD). It requires designing a class to represent a directed graph of letters with specific operations. This task tests the candidate's ability to apply OOD principles to create a flexible and efficient data structure. Key operations include adding and removing nodes and edges, checking for node existence, and retrieving adjacent nodes.

Solution Approach

1. Class Definition:
   • Define a class DirectedGraph.
   • Use a dictionary to store nodes and their corresponding edges for efficient lookups and updates.
2. Attributes:
   • Use a dictionary graph where keys are nodes and values are sets of adjacent nodes.
3. Methods:
   • add_node(letter): Add a node to the graph.
   • contains(letter): Check if a node exists in the graph.
   • add_edge(from_letter, to_letter): Add a directed edge from one node to another.
   • get_adjacent(letter): Get all nodes that a given node leads to.
   • remove_edge(from_letter, to_letter): Remove a directed edge between two nodes.
   • remove_node(letter): Remove a node if it has no incoming or outgoing edges.

Explanation

• Initialization: The DirectedGraph class is initialized with an empty dictionary.
• Add Node: The add_node method adds a new node if it doesn't already exist.
• Check Existence: The contains method checks if a node is in the graph.
• Add Edge: The add_edge method adds a directed edge from one node to another.
• Get Adjacent Nodes: The get_adjacent method retrieves all nodes that the given node points to.
• Remove Edge: The remove_edge method removes a directed edge between two nodes.
• Remove Node: The remove_node method removes a node only if it has no edges connected to or from it, ensuring no data integrity issues.

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