Pattern Bias

I bought the Leetcode course for the datastructures and algorithms. I went through the Pointers section. When the practice problems were provided, they had already told that two pointers can be used. However I felt very difficult to just blindly apply two pointer approach because there were other elements that needs to be combined. The problem I was working through was the Squares of a Sorted Array.

  • Does knowing the approach you need to apply in advance hinder your problem solving?
  • Should we solve the problems from first principles without attaching any names to certain patterns?

You bring up some really good points about problem solving approaches and patterns. Here are a few thoughts:

  • Knowing the approach upfront can be a double-edged sword. On one hand, it provides a hint and direction to explore. But on the other hand, it can lead to trying to force-fit a pattern without fully understanding the problem.

  • I think solving problems from first principles is extremely valuable, especially when learning new patterns. Coming up with your own solution helps strengthen problem solving skills and intuition.

  • That said, patterns do provide useful abstraction and vocabulary to apply known techniques. But patterns shouldn’t be used as blind templates without comprehension.

  • For tricky problems, I find it helpful to first reason through the requirements from basics before thinking about patterns. Once I have an initial solution, then I can try to match it to known patterns or optimizations.

  • LeetCode-style questions are a bit artificial in providing the expected pattern upfront. In reality, you need to deduce the techniques to apply based on the problem.

  • So in summary, use patterns as guiding templates once you have internalized the underlying methods. But avoid starting from patterns without fundamental understanding, especially when learning. Finding your own solutions is key for developing stronger intuition.

Does this help provide some perspective on balancing patterns with problem solving fundamentals? I’d be happy to discuss further. Let me know your thoughts!

Does knowing the approach you need to apply in advance hinder your problem solving?

Knowing the approach in advance can be a double-edged sword. On one side, it can guide you, offering a starting point and reducing the scope of the problem. On the other, it can also limit your thinking, causing you to overlook other potential solutions or misunderstand the problem’s complexities.

In the case of the LeetCode problem “Squares of a Sorted Array,” knowing that a two-pointer approach is useful may make you focus too narrowly on that approach, even when other elements need to be combined, as you mentioned.

Should we solve the problems from first principles without attaching any names to certain patterns?

Solving problems from first principles can be valuable, especially for understanding the core mechanics of a problem. This way, you dissect the problem into its most basic parts and think critically about how to solve it. It can also make you more adaptable in solving different kinds of problems.

However, named patterns like “two-pointer technique,” “dynamic programming,” or “breadth-first search” exist because they’re effective for certain types of problems. Learning them helps you build a toolkit of strategies for tackling different problems more efficiently.

Insight

  1. Balancing Act: The key is to balance your approach. Use named patterns as tools, not as the only lens through which to view a problem.

  2. Understanding: Before applying a pattern, understand why it’s suitable for the given problem. This helps you adapt the pattern as needed.

  3. Flexibility: Being flexible in your approach allows you to navigate the complexities that might not be apparent when you first read the problem description.

In summary, both first-principles reasoning and the use of named patterns have their places in problem solving. Being adept at both will make you a more effective problem solver.