How to Solve any linked list problem

Here’s a guide to help you tackle linked list problems:

1️⃣ Understand the Problem Statement

• Read Carefully: Make sure you fully understand what the problem is asking. Identify whether it's a singly or doubly linked list, whether it has additional pointers (like random pointers), and what operations need to be performed.
• Clarify Edge Cases: Consider edge cases like an empty list, a single-node list, a list with cycles, or lists that intersect.

2️⃣ Plan Your Approach

• Identify the Core Operation: Determine the main operation you need to perform (e.g., insertion, deletion, reversing, detecting loops).
• Think About the Data Structure: Understand how the data structure works, particularly how pointers need to be manipulated.
• Decide on the Technique: Common techniques for solving linked list problems include:
  • Two-pointer Technique: Useful for problems like finding the middle of a linked list or detecting cycles.
  • Dummy Nodes: Simplifies edge cases, especially for problems involving head node deletion or insertion.
  • Recursive Approach: Suitable for problems like reversing a linked list recursively or merging two sorted lists.

3️⃣ Write the Algorithm Step-by-Step

• Break Down the Problem: Write down each step you need to perform. For example, if you are reversing a linked list, steps might include iterating through the list, reversing pointers one by one, and keeping track of the previous node.
• Pseudo Code: Before jumping into code, write pseudo code to outline your approach. This helps in structuring your thoughts and ensuring you don't miss any steps.

4️⃣ Implement the Solution

• Start Simple: Begin with a straightforward solution that is easy to implement, even if it's not the most optimized.
• Handle Edge Cases: Ensure your implementation handles edge cases like an empty list or a list with only one node.
• Use Comments: Comment your code to explain what each section does, particularly for complex pointer manipulations.

5️⃣ Test Your Solution

• Test With Simple Cases: Start by testing your solution with simple, small linked lists to ensure the basic functionality works.
• Test Edge Cases: Include tests for edge cases, such as empty lists, single-node lists, and lists with duplicate values.
• Test Performance: For larger inputs, consider the time and space complexity of your solution.

6️⃣ Optimize the Solution

• Evaluate Complexity: Review your solution’s time and space complexity. For linked list problems, the goal is often O(n) time complexity and O(1) space complexity.
• Refactor Code: Look for ways to simplify and optimize your code. Avoid unnecessary loops or recursive calls that could be converted to iterative ones.

Creation of Simple Linked List

We can create a simple linked list either using structure or class in c++.

Here is the very basic prototype of an linked list using structure in c++.

Linked List using Structure:

// Define a Node using a struct
struct Node {
    int data;       // Data stored in the node
    Node* next;     // Pointer to the next node in the list

    // Constructor to initialize the node with data and set next to nullptr
    Node(int data) {
    	this->data = data;
    	next = nullptr;
    }
};

int main() {
	Node* head = new Node(1);
	head->next = new Node(2);
	head->next->next = new Node(3);
	head->next->next->next = new Node(4);
	head->next->next->next->next = new Node(5);

// Print the Linked List 	
 	Node* curr = head;
	while(curr != nullptr) {
		cout << curr->data << " -> ";
		curr = curr->next;
	}
    cout << "nullptr" << endl;
}

Linked List using Class:

// Define a Node using a class
class Node {
public:
    int data;       // Data stored in the node
    Node* next;     // Pointer to the next node in the list

    // Constructor to initialize the node with data and set next to nullptr
    Node(int data) {
    	this->data = data;
    	next = nullptr;
    }
};

int main() {
	Node* head = new Node(1);
	head->next = new Node(2);
	head->next->next = new Node(3);
	head->next->next->next = new Node(4);
	head->next->next->next->next = new Node(5);

// Print the Linked List 	
 	Node* curr = head;
	while(curr != nullptr) {
		cout << curr->data << " -> ";
		curr = curr->next;
	}
    cout << "nullptr" << endl;

}

Common Patterns

Two-pointer Technique:

The Two Pointer Technique is a powerful strategy in linked list manipulation, enabling efficient solutions to many common problems. In linked lists, this technique usually involves using two pointers that traverse the list at different speeds or start from different points, allowing us to solve problems with reduced time complexity and memory usage.

1️⃣ Fast and Slow Pointers (Tortoise and Hare):

Purpose: This technique involves using two pointers that move at different speeds to find specific elements or detect cycles within a linked list.

Common Use Cases:

• Cycle Detection: Determine if a linked list has a loop.
• Finding the Middle of a Linked List: Locate the middle node in a single traversal.
• Finding the Start of a Cycle: Identify the entry point of a loop after detecting a cycle.

2️⃣ Lag and Lead Pointers (N-Pointer Distance):

Purpose: This variation finds a node based on its position from the end of the linked list. It involves using two pointers that start at different positions or with a certain distance apart however traverse in same speed.

Common Use Cases:

• Finding the Nth Node from the End: Retrieve the node that is a certain distance from the end.
• Removing the Nth Node from the End: Remove a node based on its position from the end.

Resources

1️⃣ Become Master In Linked List - LeetCode Discuss