Design Linked List

Here’s a simple implementation of a singly linked list in Python. We create a Node class to hold the value and the reference to the next node, then a MyLinkedList class to hold operations like get, add, and delete.

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class Node:
    def __init__(self, x):
        self.val = x
        self.next = None


class MyLinkedList:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.size = 0
        self.head = Node(0)  # sentinel node as pseudo-head

    def get(self, index: int) -> int:
        """
        Get the value of the index-th node in the linked list. If the index is invalid, return -1.
        """
        # if index is invalid
        if index < 0 or index >= self.size:
            return -1
        
        node = self.head
        # index steps needed 
        # to move from sentinel node to wanted index
        for _ in range(index + 1):
            node = node.next
        return node.val

    def addAtHead(self, val: int) -> None:
        """
        Add a node of value val before the first element of the linked list. After the insertion, the new node will be the first node of the linked list.
        """
        self.addAtIndex(0, val)

    def addAtTail(self, val: int) -> None:
        """
        Append a node of value val to the last element of the linked list.
        """
        self.addAtIndex(self.size, val)

    def addAtIndex(self, index: int, val: int) -> None:
        """
        Add a node of value val before the index-th node in the linked list. If index equals to the length of linked list, the node will be appended to the end of linked list. If index is greater than the length, the node will not be inserted.
        """
        # If index is greater than the length, 
        # the node will not be inserted.
        if index > self.size:
            return
        
        # [so weird] If index is negative, 
        # the node will be inserted at the head of the list.
        if index < 0:
            index = 0
        
        self.size += 1
        # find predecessor of the node to be added
        pred = self.head
        for _ in range(index):
            pred = pred.next
            
        # node to be added
        to_add = Node(val)
        # insertion itself
        to_add.next = pred.next
        pred.next = to_add

    def deleteAtIndex(self, index: int) -> None:
        """
        Delete the index-th node in the linked list, if the index is valid.
        """
        # if the index is invalid, do nothing
        if index < 0 or index >= self.size:
            return
        
        self.size -= 1
        # find predecessor of the node to be deleted
        pred = self.head
        for _ in range(index):
            pred = pred.next
            
        # delete pred.next 
        pred.next = pred.next.next

This code uses a sentinel node, which is a dummy node at the head and tail of the linked list. It simplifies the operations and we don’t need to handle many edge cases, such as an empty list, or inserting/deleting at the head or the tail.

“LRU Cache” iss a more complex variant of “Design Linked List”. In both problems, you’re essentially tasked with implementing certain operations of a data structure, with linked list being the common fundamental structure involved.

“Design Linked List” problem is about designing your own linked list and implementing functions like addAtHead, addAtTail, addAtIndex, deleteAtIndex. It is a great problem for understanding the basic operations of a linked list.

“LRU Cache” requires the design of a data structure that performs get and put operations with the constraint of maintaining the total size under a certain limit. The least recently used items are removed when the size limit is exceeded. To efficiently implement this, a combination of a doubly linked list and a hash map is used. The linked list is used to track the usage of items and the hash map provides quick access to any item.

“Design Linked List” is simpler as it focuses on basic linked list operations, while “LRU Cache” involves more advanced use of linked lists along with hash maps, also introducing the concept of cache eviction strategies. Therefore, if you’re comfortable with “Design Linked List”, you’ll likely find “LRU Cache” to be a good next step.

10 Prerequisite LeetCode Problems

For this, the following are a good preparation:

“206. Reverse Linked List” - This problem is fundamental to understand how to traverse and manipulate a singly linked list.
“203. Remove Linked List Elements” - This problem helps understand how to handle and remove nodes in a linked list.
“21. Merge Two Sorted Lists” - This problem involves working with two linked lists simultaneously, and it gives a sense of how to manipulate multiple pointers.
“141. Linked List Cycle” - This problem introduces the concept of detecting a cycle in a linked list, which is essential for understanding linked list traversal and potential issues that can arise.
“160. Intersection of Two Linked Lists” - This problem deals with finding the intersection point of two linked lists and is useful for understanding more complex linked list manipulation.
“234. Palindrome Linked List” - This problem requires understanding how to traverse a linked list both forward and backward, which can be helpful for implementing a doubly linked list.
“83. Remove Duplicates from Sorted List” - This problem requires understanding how to remove duplicate nodes in a linked list, which is a key aspect of linked list manipulation.
“19. Remove Nth Node From End of List” - This problem helps to understand how to traverse the linked list from the end, which is necessary for adding or deleting a node at a specific position.
“148. Sort List” - This problem involves sorting a linked list and helps to understand more complex manipulation of linked lists.
“138. Copy List with Random Pointer” - This problem involves creating a deep copy of a linked list, including a random pointer, and can provide a deeper understanding of the structure and manipulation of linked lists.

These cover linked list manipulation, which is necessary for the “707. Design Linked List” problem. They cover basic operations such as adding, deleting, and retrieving nodes, as well as more complex operations such as reversing, sorting, and finding intersections or cycles.

Problem Classification

Problem Statement:Design your implementation of the linked list. You can choose to use a singly or doubly linked list. A node in a singly linked list should have two attributes: val and next. val is the value of the current node, and next is a pointer/reference to the next node. If you want to use the doubly linked list, you will need one more attribute prev to indicate the previous node in the linked list. Assume all nodes in the linked list are 0-indexed.

Implement the MyLinkedList class:

MyLinkedList() Initializes the MyLinkedList object. int get(int index) Get the value of the indexth node in the linked list. If the index is invalid, return -1. void addAtHead(int val) Add a node of value val before the first element of the linked list. After the insertion, the new node will be the first node of the linked list. void addAtTail(int val) Append a node of value val as the last element of the linked list. void addAtIndex(int index, int val) Add a node of value val before the indexth node in the linked list. If index equals the length of the linked list, the node will be appended to the end of the linked list. If index is greater than the length, the node will not be inserted. void deleteAtIndex(int index) Delete the indexth node in the linked list, if the index is valid.

Example 1:

Input [“MyLinkedList”, “addAtHead”, “addAtTail”, “addAtIndex”, “get”, “deleteAtIndex”, “get”] [[], [1], [3], [1, 2], [1], [1], [1]] Output [null, null, null, null, 2, null, 3]

Explanation MyLinkedList myLinkedList = new MyLinkedList(); myLinkedList.addAtHead(1); myLinkedList.addAtTail(3); myLinkedList.addAtIndex(1, 2); // linked list becomes 1->2->3 myLinkedList.get(1); // return 2 myLinkedList.deleteAtIndex(1); // now the linked list is 1->3 myLinkedList.get(1); // return 3

Constraints:

0 <= index, val <= 1000 Please do not use the built-in LinkedList library. At most 2000 calls will be made to get, addAtHead, addAtTail, addAtIndex and deleteAtIndex.

Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Identifying Problem Isomorphism

Can you help me with finding the isomorphism for this problem?

Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?

How did you identify that this problem is a variation of problem?

Clarification Questions

What are the clarification questions we can ask about this problem?

Problem Analysis and Key Insights

What are the key insights from analyzing the problem statement?

Problem Boundary

What is the scope of this problem?

How to establish the boundary of this problem?

Distilling the Problem to Its Core Elements

Can you identify the fundamental concept or principle this problem is based upon? Please explain. What is the simplest way you would describe this problem to someone unfamiliar with the subject? What is the core problem we are trying to solve? Can we simplify the problem statement? Can you break down the problem into its key components? What is the minimal set of operations we need to perform to solve this problem?

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Provide names by categorizing these cases

What are the edge cases?

How to visualize these cases?

What are the key insights from analyzing the different cases?

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Simple Explanation

Can you explain this problem in simple terms or like you would explain to a non-technical person? Imagine you’re explaining this problem to someone without a background in programming. How would you describe it? If you had to explain this problem to a child or someone who doesn’t know anything about coding, how would you do it? In layman’s terms, how would you explain the concept of this problem? Could you provide a metaphor or everyday example to explain the idea of this problem?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

Can you identify the key terms or concepts in this problem and explain how they inform your approach to solving it? Please list each keyword and how it guides you towards using a specific strategy or method. How can I recognize these properties by drawing tables or diagrams?

How did you infer from the problem statement that this problem can be solved using ?

Simple Explanation of the Proof

I’m having trouble understanding the proof of this algorithm. Could you explain it in a way that’s easy to understand?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Identify Invariant

What is the invariant in this problem?

Identify Loop Invariant

What is the loop invariant in this problem?

Is invariant and loop invariant the same for this problem?

Thought Process

Can you explain the basic thought process and steps involved in solving this type of problem?

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

Establishing Preconditions and Postconditions

Parameters:
- What are the inputs to the method?
- What types are these parameters?
- What do these parameters represent in the context of the problem?
Preconditions:
- Before this method is called, what must be true about the state of the program or the values of the parameters?
- Are there any constraints on the input parameters?
- Is there a specific state that the program or some part of it must be in?
Method Functionality:
- What is this method expected to do?
- How does it interact with the inputs and the current state of the program?
Postconditions:
- After the method has been called and has returned, what is now true about the state of the program or the values of the parameters?
- What does the return value represent or indicate?
- What side effects, if any, does the method have?
Error Handling:
- How does the method respond if the preconditions are not met?
- Does it throw an exception, return a special value, or do something else?

Problem Decomposition

Problem Understanding:
- Can you explain the problem in your own words? What are the key components and requirements?
Initial Breakdown:
- Start by identifying the major parts or stages of the problem. How can you break the problem into several broad subproblems?
Subproblem Refinement:
- For each subproblem identified, ask yourself if it can be further broken down. What are the smaller tasks that need to be done to solve each subproblem?
Task Identification:
- Within these smaller tasks, are there any that are repeated or very similar? Could these be generalized into a single, reusable task?
Task Abstraction:
- For each task you’ve identified, is it abstracted enough to be clear and reusable, but still makes sense in the context of the problem?
Method Naming:
- Can you give each task a simple, descriptive name that makes its purpose clear?
Subproblem Interactions:
- How do these subproblems or tasks interact with each other? In what order do they need to be performed? Are there any dependencies?

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Code Explanation and Design Decisions

Identify the initial parameters and explain their significance in the context of the problem statement or the solution domain.
Discuss the primary loop or iteration over the input data. What does each iteration represent in terms of the problem you’re trying to solve? How does the iteration advance or contribute to the solution?
If there are conditions or branches within the loop, what do these conditions signify? Explain the logical reasoning behind the branching in the context of the problem’s constraints or requirements.
If there are updates or modifications to parameters within the loop, clarify why these changes are necessary. How do these modifications reflect changes in the state of the solution or the constraints of the problem?
Describe any invariant that’s maintained throughout the code, and explain how it helps meet the problem’s constraints or objectives.
Discuss the significance of the final output in relation to the problem statement or solution domain. What does it represent and how does it satisfy the problem’s requirements?

Remember, the focus here is not to explain what the code does on a syntactic level, but to communicate the intent and rationale behind the code in the context of the problem being solved.

Coding Constructs

Consider the code for the solution of this problem.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.