Скачать или смотреть Understanding Backtracking: Why Is Your Haskell Code Returning an empty list?

Discover why your Haskell backtracking function always returns an empty list and learn how to fix it effectively.
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This video is based on the question https://stackoverflow.com/q/64688672/ asked by the user 'tree' ( https://stackoverflow.com/u/12874005/ ) and on the answer https://stackoverflow.com/a/64689308/ provided by the user 'Li-yao Xia' ( https://stackoverflow.com/u/6863749/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding Backtracking: Why Is Your Haskell Code Returning an empty list?

Backtracking is a powerful algorithmic technique used for solving problems incrementally, where solutions are built step by step and abandoned as soon as it's determined that the solution cannot be completed. However, even seasoned developers can find themselves puzzled when their backtracking implementation yields an empty list, indicating no valid solution was found. In this post, we'll delve into a specific Haskell backtracking scenario, unpack the code, and explore how to resolve the issue.

The Problem

You are attempting to create a function in Haskell that returns a maximal independent set based on a specific predicate. With the function defined as:

[[See Video to Reveal this Text or Code Snippet]]

You expected to receive tuples from a list (like [2..11]) that satisfied the predicate (e.g., (\x -> \y -> x*y < 45)). However, when you run your backtracking script, it always returns an empty list, despite there being valid solutions.

Analyzing Your Backtracking Script

Let’s take a look at the core function that’s causing the trouble:

[[See Video to Reveal this Text or Code Snippet]]

The Issue

The crucial part of this code relies on two conditions:

Guard Statement: You check if the pair can be added to the final list.

Checking Final Length: You check if you've reached the desired length of the final list.

However, there is a logical flaw in the order of these checks. As it stands, if you reach the length of the final list first, the guard condition will fail since the final list cannot hold more pairs.

The Solution

We can fix this by reorganizing how we check for the length of the final list. Specifically, we need to prioritize this check before the guard:

[[See Video to Reveal this Text or Code Snippet]]

Explanation of Changes

Early Return: We check first if the length of final equals the desired len. If it does, we return final.

Using tails: By using tails, we ensure that duplicates do not arise as we explore combinations.

Guard Placement: The guard statement now only comes into play after confirming that more elements can be added, which allows for proper backtracking.

Conclusion

Backtracking can be challenging, especially regarding ensuring your implementation correctly approaches the problem. By understanding the issue with your original order of checks and reorganizing your function accordingly, you can effectively resolve it. Make sure to always check your conditional logic and the flow of your program to ensure it aligns with the backtracking methodology.

Incorporating these adjustments should set your backtracking function on the right path to return valid solutions, transforming that frustrating empty list into a comprehensive list of maximal independent tuples.

Feel free to reach out with your implementation details, and let’s solve any further issues you might encounter!