Throne Inheritance

Throne Inheritance

What is this problem about?

Managing a royal succession can be complicated, especially with births and deaths. "Throne Inheritance" asks you to design a system that tracks a royal family tree. You need to support three operations: birth(parent, child), death(name), and getInheritanceOrder(). The order of inheritance is determined by a pre-order traversal of the family tree, excluding any members who are currently deceased.

Why is this asked in interviews?

This throne inheritance interview question is a design problem asked by Snowflake and Google. It tests your ability to model hierarchical relationships using appropriate data structures (like a hash map for the tree) and your proficiency with tree traversal algorithms (DFS). It also evaluates how you handle state changes (deaths) and whether you can produce the inheritance list efficiently.

Algorithmic pattern used

The problem utilizes the Hash Table, Design, Depth-First Search, Tree interview pattern.

1. Use a Hash Map to store the tree, where each key is a parent's name and the value is a list of their children in order of birth.
2. Maintain a Set to track the names of members who have died.
3. The getInheritanceOrder operation is a standard Depth-First Search (DFS) starting from the monarch:
   • Add the current member to the result list if they are not in the dead set.
   • Recursively call DFS for each of their children in order.
4. The birth and death operations are O(1), while getInheritanceOrder is O(N) where N is the number of people in the family.

Example explanation

1. Monarch: King.
2. birth("King", "Alice"), birth("King", "Bob").
3. birth("Alice", "Jack").
4. Inheritance: [King, Alice, Jack, Bob].
5. death("Alice").
6. Inheritance: [King, Jack, Bob] (Alice is skipped). Note: Jack is still in the line because he is Alice's descendant, even though Alice is dead.

Common mistakes candidates make

In "Throne Inheritance coding problem," a common mistake is removing a deceased person from the tree. This is incorrect because their descendants still remain in the line of succession. Another error is using an incorrect traversal (like BFS) which doesn't follow the rules of royal succession (which prioritize the eldest child's line).

Interview preparation tip

When designing a system, always consider the frequency of each operation. If getInheritanceOrder were called much more often than birth or death, you might consider maintaining the order in a linked list. However, given the standard constraints, a hash-map-based tree and DFS are the most balanced approach. Practice tree traversals until you can implement them flawlessly.