How do you solve Throne Inheritance on LeetCode?

Throne Inheritance (LeetCode #1600) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The order of inheritance is a pre-order traversal of the family tree.

What is the brute force solution for Throne Inheritance?

The brute force approach for Throne Inheritance is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves recursively checking each person in the inheritance order to find the next successor. This method is straightforward but inefficient as it may require multiple traversals of the family tree. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Throne Inheritance?

Throne Inheritance uses the following concepts: Hash Table, Tree, Depth-First Search, Design. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Throne Inheritance?

Think about how to represent the family tree effectively. Consider edge cases like deaths and multiple births. Practice depth-first search as it's a common pattern in tree problems.

What are common mistakes when solving Throne Inheritance?

Not correctly managing the alive status of family members. Failing to account for the order of children when determining successors.

#1600

Throne Inheritance

Medium

Hash TableTreeDepth-First SearchDesignHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a depth-first search (DFS) to traverse the family tree in a pre-order manner, ensuring we build the inheritance order efficiently without redundant checks.

⚙️

Algorithm

3 steps

1Step 1: Create a tree structure to represent the family.
2Step 2: Use a DFS function to traverse the tree and add each alive person to the inheritance order.
3Step 3: Return the complete inheritance order.

solution.py30 lines

1class Person:
2    def __init__(self, name):
3        self.name = name
4        self.children = []
5        self.is_alive = True
6
7class ThroneInheritance:
8    def __init__(self, kingName):
9        self.king = Person(kingName)
10        self.people = {kingName: self.king}
11
12    def birth(self, parentName, childName):
13        parent = self.people[parentName]
14        child = Person(childName)
15        child.parent = parent
16        parent.children.append(child)
17        self.people[childName] = child
18
19    def death(self, name):
20        self.people[name].is_alive = False
21
22    def getInheritanceOrder(self):
23        order = []
24        def dfs(person):
25            if person.is_alive:
26                order.append(person.name)
27            for child in person.children:
28                dfs(child)
29        dfs(self.king)
30        return order

ℹ

Complexity note: The time complexity is O(n) because we visit each person exactly once during the DFS traversal. The space complexity is O(n) due to the storage of the order list and the recursion stack.

1The order of inheritance is a pre-order traversal of the family tree.
2Handling births and deaths dynamically requires careful management of the tree structure.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.