Here's how you can master advanced algorithms with the best online resources.

Before starting to practice with algorithms, ensure you have a solid understanding of fundamental data structures like arrays, linked lists, stacks, and queues. Familiarize yourself with basic algorithms, including sorting and searching. For instance, Gauss's formula for the sum of the first (n) natural numbers (sum = n(n + 1) / 2) can be a helpful example. Once you're comfortable with data structures, focus on specific patterns like BFS (Breadth-First Search) and DFS (Depth-First Search). Practice regularly, and read books on algorithms and dynamic programming to deepen your knowledge.

While mastering the basics of algorithms and data structures is essential, the ultimate goal should be to solve problems efficiently and effectively. It's crucial to understand fundamental concepts like arrays, linked lists, stacks, and queues, as well as basic sorting and searching algorithms, because they provide the foundation for tackling more complex challenges. However, the true measure of success lies in finding the simplest and most performant solution to a given problem. Emphasizing simplicity and performance ensures that your solutions are not only correct but also practical and scalable in real-world applications.

Start with easy problems and review the solutions to understand how they’re done. Revisit these problems after a few days to see if you can recall the logic or if they seem familiar. This will help you get accustomed to problem-solving. Once you’ve solved a problem, consider if there’s a better way to do it. Scribble on paper as much as you can, and write comments outlining the entire algorithm before coding to stay on track.

In recent time online platforms are playing major role in developing skills. Today whatever resources we want we can get it online . Today learning has became easier. We can get various good materials on internet to enhance our algorithm and also we can practice online over the platforms like: Hackerrank, leetcode etc…

Many online resources offer practice exercises for common patterns and algorithm solutions, categorized by data structure or pattern. Carefully follow courses, online resources, and videos to master and refine your skills. Remember, you don't have to reinvent the wheel; just ride the wheel!

MIT OCW offers free course materials from MIT's extensive catalog. The "6.006 Introduction to Algorithms" and "6.046J Design and Analysis of Algorithms" courses are particularly valuable. Pros: Free access to high-quality course materials. Cons: Self-study format without interactive elements.

These are the two best platforms according to me for practising problems: 1)LeetCode is a popular platform among competitive programmers. It provides a vast collection of problems categorized by difficulty and topic, with solutions and discussions. Pros: Extensive problem set, community discussions. Cons: Subscription required for premium content. 2) Codeforces is a competitive programming platform that hosts regular contests. It’s an excellent place to practice under timed conditions and improve problem-solving speed. Pros: Regular contests, active community. Cons: Steep learning curve for beginners.

One helpful approach is to break down the problem into simpler parts. You can create an example to visualize the flow or algorithm, or use pen and paper to note down the steps, both at a high level and in detail.

Anytime you solve a problem, don't start coding. Even if you have thought of an approach, don't start coding. Even if it is an optimised approach don't start coding. Ask one more question to yourself, why the algorithm you thought of will produce the correct results? Can you prove the correctness of the algorithm/approach which you have thought of? If you can answer both of them, still don't start coding. Figure out the time complexity and space complexity, prove the expression for both. Now start coding. Doing this way will take you to the next level and it will help you in the long run.

Start solving algorithm problems with the brute-force method to understand the basics. Then, identify common patterns like dynamic programming, which solves complex problems by breaking them into simpler subproblems, storing their solutions to avoid recomputation. Learn other techniques like the sliding window for optimizing array problems and backtracking for exploring permutations and combinations. Use resources like LeetCode, HackerRank, Codewars and CodeSignal to practice and gradually increase problem difficulty, enhancing your problem-solving speed and efficiency.

While not an online resource, books like "Introduction to Algorithms" by Cormen, Leiserson, Rivest, and Stein (commonly known as CLRS) and "The Algorithm Design Manual" by Steven Skiena are essential reads for mastering algorithms.

Don’t be afraid to look at solutions. Spend 10-15 minutes trying to solve the problem. If nothing comes to mind, check out the solution (high-level steps or logic) and implement it on your own. Focus on solving more problems rather than spending too much time on a single problem. Many problems have similar or repeated logic. Becoming accustomed to this way of thinking will enhance your problem-solving abilities.

Tips for Mastering Advanced Algorithms Understand the Basics: Ensure you have a solid understanding of basic algorithms and data structures before tackling advanced topics. Practice Regularly: Consistent practice on platforms like LeetCode, HackerRank, and Codeforces is key to mastery. Analyze and Optimize: Focus on analyzing the time and space complexity of algorithms and strive to optimize them. Participate in Contests: Regular participation in coding contests helps improve problem-solving skills and speed. Join Study Groups: Engaging with study groups or online communities can provide support and different perspectives on solving problems.