What is the time complexity of Throne Inheritance?

The optimal solution has a time complexity of O(N).

What data structures are used to solve Throne Inheritance?

This problem uses Hash Table, Tree, Depth-First Search, Design. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Throne Inheritance?

Insight 1: The core of the problem is to efficiently maintain and traverse a tree structure representing the family relationships, combined with a mechanism to track dead individuals. Insight 2: Depth-First Search (DFS) is a natural choice for traversing the family tree to determine the inheritance order.

Which companies ask LeetCode 1600. Throne Inheritance in interviews?

This problem is frequently asked at Snowflake.

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Throne Inheritance - LeetCode 1600 Solution

Throne Inheritance - Complete Solution Guide

Throne Inheritance is LeetCode problem 1600, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

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 child

Detailed Explanation

The problem asks us to implement a `ThroneInheritance` class that simulates the inheritance order of a kingdom. The class needs to handle births, deaths, and return the current inheritance order, excluding dead people. The inheritance order is determined by a specific recursive function `Successor(x, curOrder)` which dictates who comes after person `x` in the order. The class has four methods: `ThroneInheritance(kingName)` to initialize the kingdom, `birth(parentName, childName)` to add a child to a parent, `death(name)` to mark a person as dead, and `getInheritanceOrder()` to return the current inheritance order.

Solution Approach

The provided code uses a tree structure implemented with a hash map to represent the family relationships. Each person's name is a node in the tree, and the keys in the hash map represent parents, with the values being lists of their children. A hash set stores the names of dead people. The `getInheritanceOrder()` method performs a Depth-First Search (DFS) traversal of the tree, adding living people to the result list. Specifically, it uses a stack to simulate the recursive calls in a non-recursive manner.

Step-by-Step Algorithm

Step 1: Initialize the `ThroneInheritance` object with the king's name, an empty hash map to store the family tree, and an empty hash set to store the dead people.
Step 2: Implement the `birth(parentName, childName)` method by adding the `childName` to the list of children associated with the `parentName` in the family tree hash map. If `parentName` doesn't already exist as a key, create a new list for them.
Step 3: Implement the `death(name)` method by adding the `name` to the set of dead people.
Step 4: Implement the `getInheritanceOrder()` method as follows:
Step 5: Create an empty list `result` to store the inheritance order and initialize a stack with the king's name.
Step 6: While the stack is not empty, pop the top name `personName` from the stack.
Step 7: If `personName` is not in the set of dead people, add it to the `result` list.
Step 8: Get the children of `personName` from the family tree hash map.
Step 9: Iterate through the children in reverse order (from the last child to the first) and push them onto the stack. Iterating in reverse order is important to keep the correct succession order as the stack reverses the order that it retrieves the elements.
Step 10: Repeat steps 6-9 until the stack is empty.
Step 11: Return the `result` list, which contains the inheritance order of living people.

Key Insights

Insight 1: The core of the problem is to efficiently maintain and traverse a tree structure representing the family relationships, combined with a mechanism to track dead individuals.
Insight 2: Depth-First Search (DFS) is a natural choice for traversing the family tree to determine the inheritance order.
Insight 3: Using a set to store the dead people allows for quick lookups (O(1) on average) to determine whether a person should be included in the inheritance order.

Complexity Analysis

Time Complexity: O(N)

Space Complexity: O(N)

Topics

This problem involves: Hash Table, Tree, Depth-First Search, Design.

Companies

Asked at: Snowflake.

Throne Inheritance | LeetCode 1600

Medium

Hash Table Tree Depth-First Search Design

Time: O(N)Space: O(N)

Solution Code

Available in:

import java.util.*;

class ThroneInheritance {

    private String king;
    private Map<String, List<String>> tree;
    private Set<String> dead;

    public ThroneInheritance(String kingName) {
        this.king = kingName;
        this.tree = new HashMap<>();
        this.dead = new HashSet<>();
    }
    
    public void birth(String parentName, String childName) {
        this.tree.computeIfAbsent(parentName, k -> new ArrayList<>()).add(childName);
    }
    
    public void death(String name) {
        this.dead.add(name);
    }
    
    public List<String> getInheritanceOrder() {
        List<String> result = new ArrayList<>();
        Stack<String> stack = new Stack<>();
        stack.push(this.king);

        while (!stack.isEmpty()) {
            String personName = stack.pop();

            if (!this.dead.contains(personName)) {
                result.add(personName);
            }

            List<String> children = this.tree.getOrDefault(personName, new ArrayList<>());

            for (int i = children.size() - 1; i >= 0; i--) {
                stack.push(children.get(i));
            }
        }

        return result;
    }
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * ThroneInheritance obj = new ThroneInheritance(kingName);
 * obj.birth(parentName,childName);
 * obj.death(name);
 * List<String> param_3 = obj.getInheritanceOrder();
 */

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Problem Info

Description

Problem 1600: Throne Inheritance - Detailed explanation and solution approaches.

Topics

Hash Table Tree Depth-First Search Design

Companies

Snowflake

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1600

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

11 steps

1
Step 1: Initialize the `ThroneInheritance` object with the king's name, an empty hash map to store the family tree, and an empty hash set to store the dead people.
2
Step 2: Implement the `birth(parentName, childName)` method by adding the `childName` to the list of children associated with the `parentName` in the family tree hash map. If `parentName` doesn't already exist as a key, create a new list for them.
3
Step 3: Implement the `death(name)` method by adding the `name` to the set of dead people.
4
Step 4: Implement the `getInheritanceOrder()` method as follows:
5
Step 5: Create an empty list `result` to store the inheritance order and initialize a stack with the king's name.
6
Step 6: While the stack is not empty, pop the top name `personName` from the stack.
7
Step 7: If `personName` is not in the set of dead people, add it to the `result` list.
8
Step 8: Get the children of `personName` from the family tree hash map.
9
Step 9: Iterate through the children in reverse order (from the last child to the first) and push them onto the stack. Iterating in reverse order is important to keep the correct succession order as the stack reverses the order that it retrieves the elements.
10
Step 10: Repeat steps 6-9 until the stack is empty.
11
Step 11: Return the `result` list, which contains the inheritance order of living people.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(N)

💾

Space Complexity

O(N)

📝

Why?

The time complexity is dominated by the `getInheritanceOrder()` method, which performs a DFS traversal of the family tree. In the worst case, it visits every person in the kingdom. The space complexity arises from storing the tree, the dead set, and the stack and result list used during the traversal, all of which can grow linearly with the number of people.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Recursive DFS

Instead of using a stack to implement DFS, a recursive function can be used. This would directly mirror the recursive definition of the Successor function in the problem description.

Time: O(N)Space: O(N) in the worst case due to the call stack depth potentially reaching N for a skewed tree.

Trade-offs: The recursive approach can be more concise and easier to read. However, it can be less efficient due to function call overhead and may lead to stack overflow issues for very large family trees. The iterative approach using a stack avoids stack overflow issues.

Using a doubly linked list

Maintaining an explicit doubly linked list to represent the current inheritance order. Births would involve inserting new nodes into the list and deaths would remove nodes from the list.

Time: birth() would be O(1) for insertion, death() would be O(1) for removal if you had a map from name to list node. getInheritanceOrder() would be O(N).Space: O(N)

Trade-offs: While potentially offering faster `birth` and `death` operations, `getInheritanceOrder` would still be O(N) and the linked list structure is more complex to manage. This alternative is generally not preferred due to the increased complexity without significant performance benefits.

✨

Key Insights

1Insight 1: The core of the problem is to efficiently maintain and traverse a tree structure representing the family relationships, combined with a mechanism to track dead individuals.
2Insight 2: Depth-First Search (DFS) is a natural choice for traversing the family tree to determine the inheritance order.
3Insight 3: Using a set to store the dead people allows for quick lookups (O(1) on average) to determine whether a person should be included in the inheritance order.

📚

Key Terms Explained

For Students

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: The king has no children. In this case, the `getInheritanceOrder()` method will simply return a list containing only the king's name if they are not dead.
Edge case 2: A parent is dead. The algorithm correctly skips dead people when generating the inheritance order, so a deceased parent doesn't affect the children's order relative to each other.
Edge case 3: Multiple levels of inheritance. The DFS approach correctly handles multiple generations in the family tree, ensuring the correct inheritance order.
Edge case 4: When a name is passed to the death function that does not exist as a person. The implementation simply adds the name to the dead set. This can be regarded as not a bug since it does not cause the application to crash and it doesn't break the main functionality. This could however be addressed by checking whether the name passed to the function exists within the inheritance tree.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to consider the death of individuals when generating the inheritance order. This can be avoided by always checking the 'dead' set before adding a person to the result list.

✗Common mistake 2: Incorrectly implementing the DFS traversal, leading to an incorrect inheritance order. Specifically, pushing the children onto the stack in the wrong order.

✗Common mistake 3: Using recursion without considering the potential for stack overflow errors for large family trees. Iterative DFS avoids this issue.

✗Common mistake 4: Assuming a certain fixed number of children per person, which is not specified in the problem description. Use dynamic data structures like lists to handle variable numbers of children.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Organizational charts and reporting structures. Tracking who reports to whom and generating the reporting hierarchy. The 'death' analogy could represent an employee leaving the company.

🏦Real-world scenario 2: Genealogy tracking and family tree management. Representing family relationships and inheritance laws (not necessarily monetary, but e.g., succession to a title or role).

🎮Real-world scenario 3: Social networks and influence mapping. Determining the hierarchy of influence and reach based on connections and relationships between users.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 8, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 14

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 7

❓

Frequently Asked Questions

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

How do I choose between recursive and iterative tree traversal?

Use recursive traversal for cleaner code when stack depth isn't a concern (tree height < ~1000). Use iterative with explicit stack for very deep trees to avoid stack overflow. Iterative is also preferred when you need fine-grained control over the traversal process.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Throne Inheritance"?

For this medium-level Hash Table problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether tree techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?