Introduction

In this blog post, we will explore how to solve the LeetCode problem "1600" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

A kingdom consists of a king, his children, his grandchildren, and so on. Every once in a while, someone in the family dies or a child is born. The kingdom has a well-defined order of inheritance that consists of the king as the first member. Let's define the recursive function Successor(x, curOrder), which given a person x and the inheritance order so far, returns who should be the next person after x in the order of inheritance. Successor(x, curOrder): if x has no children or all of x's children are in curOrder: if x is the king return null else return Successor(x's parent, curOrder) else return x's oldest child who's not in curOrder For example, assume we have a kingdom that consists of the king, his children Alice and Bob (Alice is older than Bob), and finally Alice's son Jack. In the beginning, curOrder will be ["king"]. Calling Successor(king, curOrder) will return Alice, so we append to curOrder to get ["king", "Alice"]. Calling Successor(Alice, curOrder) will return Jack, so we append to curOrder to get ["king", "Alice", "Jack"]. Calling Successor(Jack, curOrder) will return Bob, so we append to curOrder to get ["king", "Alice", "Jack", "Bob"]. Calling Successor(Bob, curOrder) will return null. Thus the order of inheritance will be ["king", "Alice", "Jack", "Bob"]. Using the above function, we can always obtain a unique order of inheritance. Implement the ThroneInheritance class: ThroneInheritance(string kingName) Initializes an object of the ThroneInheritance class. The name of the king is given as part of the constructor. void birth(string parentName, string childName) Indicates that parentName gave birth to childName. void death(string name) Indicates the death of name. The death of the person doesn't affect the Successor function nor the current inheritance order. You can treat it as just marking the person as dead. string[] getInheritanceOrder() Returns a list representing the current order of inheritance excluding dead people. Example 1: Input ["ThroneInheritance", "birth", "birth", "birth", "birth", "birth", "birth", "getInheritanceOrder", "death", "getInheritanceOrder"] [["king"], ["king", "andy"], ["king", "bob"], ["king", "catherine"], ["andy", "matthew"], ["bob", "alex"], ["bob", "asha"], [null], ["bob"], [null]] Output [null, null, null, null, null, null, null, ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"], null, ["king", "andy", "matthew", "alex", "asha", "catherine"]] Explanation ThroneInheritance t= new ThroneInheritance("king"); // order: king t.birth("king", "andy"); // order: king > andy t.birth("king", "bob"); // order: king > andy > bob t.birth("king", "catherine"); // order: king > andy > bob > catherine t.birth("andy", "matthew"); // order: king > andy > matthew > bob > catherine t.birth("bob", "alex"); // order: king > andy > matthew > bob > alex > catherine t.birth("bob", "asha"); // order: king > andy > matthew > bob > alex > asha > catherine t.getInheritanceOrder(); // return ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"] t.death("bob"); // order: king > andy > matthew > bob > alex > asha > catherine t.getInheritanceOrder(); // return ["king", "andy", "matthew", "alex", "asha", "catherine"] Constraints: 1 <= kingName.length, parentName.length, childName.length, name.length <= 15 kingName, parentName, childName, and name consist of lowercase English letters only. All arguments childName and kingName are distinct. All name arguments of death will be passed to either the constructor or as childName to birth first. For each call to birth(parentName, childName), it is guaranteed that parentName is alive. At most 105 calls will be made to birth and death. At most 10 calls will be made to getInheritanceOrder.

Explanation

• Data Structures: Use a dictionary (hash map) to store the family tree, where each person's name maps to a list of their children. Also, store a set of dead people for efficient death checks.
  • Depth-First Search (DFS): Implement getInheritanceOrder using DFS to traverse the family tree, following the order of children from oldest to youngest. Skip dead people during traversal.
  • Birth and Death Operations: Implement birth by simply adding the child to the parent's list of children. Implement death by adding the deceased person to the set of dead people.

• Runtime Complexity: birth: O(1), death: O(1), getInheritanceOrder: O(N), where N is the total number of people in the kingdom. Storage Complexity: O(N) to store the family tree and the set of dead people.

Code

    class ThroneInheritance:

    def __init__(self, kingName: str):
        self.king = kingName
        self.family = {kingName: []}
        self.dead = set()

    def birth(self, parentName: str, childName: str) -> None:
        self.family[parentName].append(childName)
        self.family[childName] = []  # Initialize children list for the new child

    def death(self, name: str) -> None:
        self.dead.add(name)

    def getInheritanceOrder(self) -> list[str]:
        inheritance_order = []

        def dfs(person):
            if person not in self.dead:
                inheritance_order.append(person)

            for child in self.family[person]:
                dfs(child)

        dfs(self.king)
        return inheritance_order