Decompress File Paths in Python with Time Complexity Analysis

A comma separated list of strings can be compressed by finding common substrings and grouping those strings together into Token Lists

More formally, a Token List is a list where each item can be one of the following:

a string
a concatenation of Token Lists

Examples:

ab,ac => a{b,c}
ac,ad,bc,bd => {a,b}{c,d}
axc,axd,bxc,bxd => {a,b}x{c,d}

This technique is used to compress folder paths since a folder like

README.md
resources/
    js/
        app.js
        boot.js
        comp/
            a.js
            b.js

can be represented as a list of strings:

[
    "README.md",
    "resources/js/app.js",
    "resources/js/boot.js",
    "resources/js/comp/a.js",
    "resources/js/comp/b.js"
]

and further encoded into comma separated string

“README.md,resources/js/app.js,resources/js/boot.js,resources/js/comp/a.js,resources/js/comp/b.js”

and then we can compress them to the following Token List:

README.md,resources/js/{app,boot,comp/{a,b}}.js

Given a Token List representing a compressed folder, return the initial list of paths.

Example 1:

Input:
"resources/{js/{app.js,comp/{a.js,b.js},boot.js}},README.md"

Output: [
    "README.md",
    "resources/js/app.js",
    "resources/js/boot.js",
    "resources/js/comp/a.js",
    "resources/js/comp/b.js"
]

Example 2:

Input:
"my_{first,second}_folder/{a,b}{.js,.py}"

Output: [
    "my_first_folder/a.js,
    "my_first_folder/a.py,
    "my_first_folder/b.js,
    "my_first_folder/b.py,
    "my_second_folder/a.js,
    "my_second_folder/a.py,
    "my_second_folder/b.js,
    "my_second_folder/b.py
]

Note: The resulting array can be in any order

Understanding the Problem

The core challenge of this problem is to expand a compressed representation of file paths into their full list of paths. This involves parsing the input string, identifying the token lists, and generating all possible combinations of paths.

This problem is significant in scenarios where file paths or similar hierarchical data structures need to be efficiently stored and transmitted. Common applications include file system management, data serialization, and configuration management.

Potential pitfalls include incorrectly parsing nested token lists and not handling edge cases such as empty strings or malformed input.

Approach

To solve this problem, we need to recursively parse the input string and generate all possible combinations of paths. Here’s a step-by-step approach:

Identify the base case: If the input string does not contain any braces, return it as a single-element list.
Find the first pair of braces and split the string into three parts: the prefix before the braces, the content inside the braces, and the suffix after the braces.
Recursively expand the content inside the braces and concatenate each expanded result with the prefix and suffix.
Combine all results and return the final list of paths.

Algorithm

Here’s a step-by-step breakdown of the algorithm:

Initialize an empty list to store the results.
Iterate through the input string to find the first pair of braces.
Split the string into prefix, content inside the braces, and suffix.
Recursively expand the content inside the braces.
Concatenate each expanded result with the prefix and suffix.
Combine all results and return the final list of paths.

Code Implementation

def decompress_paths(token_list):
    # Helper function to recursively expand the token list
    def expand(s):
        # Base case: if no braces, return the string as a single-element list
        if '{' not in s:
            return [s]
        
        # Find the first pair of braces
        start = s.index('{')
        end = start
        count = 0
        while end < len(s):
            if s[end] == '{':
                count += 1
            elif s[end] == '}':
                count -= 1
                if count == 0:
                    break
            end += 1
        
        # Split the string into prefix, content inside braces, and suffix
        prefix = s[:start]
        content = s[start+1:end]
        suffix = s[end+1:]
        
        # Recursively expand the content inside the braces
        expanded_content = []
        for part in content.split(','):
            expanded_content.extend(expand(part))
        
        # Concatenate each expanded result with the prefix and suffix
        result = []
        for item in expanded_content:
            result.extend(expand(prefix + item + suffix))
        
        return result
    
    # Split the input token list by commas and expand each part
    parts = token_list.split(',')
    result = []
    for part in parts:
        result.extend(expand(part))
    
    return result

# Example usage
print(decompress_paths("resources/{js/{app.js,comp/{a.js,b.js},boot.js}},README.md"))
print(decompress_paths("my_{first,second}_folder/{a,b}{.js,.py}"))

Complexity Analysis

The time complexity of this approach is O(n * 2^m), where n is the length of the input string and m is the maximum depth of nested braces. The space complexity is also O(n * 2^m) due to the recursive calls and the storage of intermediate results.

Compared to a naive approach that might involve generating all possible combinations without recursion, this approach is more efficient in terms of both time and space.

Edge Cases

Potential edge cases include:

Empty input string: The function should return an empty list.
Malformed input (e.g., unmatched braces): The function should handle such cases gracefully, possibly by raising an error or returning an empty list.
Nested braces with varying depths: The function should correctly handle multiple levels of nested braces.

Examples of edge cases and their expected outputs:

Input: ""
Output: []

Input: "a{b,c{d,e}}f"
Output: ["abf", "acdf", "acef"]

Testing

To test the solution comprehensively, we can use a variety of test cases, from simple to complex:

def test_decompress_paths():
    assert decompress_paths("resources/{js/{app.js,comp/{a.js,b.js},boot.js}},README.md") == [
        "README.md",
        "resources/js/app.js",
        "resources/js/boot.js",
        "resources/js/comp/a.js",
        "resources/js/comp/b.js"
    ]
    assert decompress_paths("my_{first,second}_folder/{a,b}{.js,.py}") == [
        "my_first_folder/a.js",
        "my_first_folder/a.py",
        "my_first_folder/b.js",
        "my_first_folder/b.py",
        "my_second_folder/a.js",
        "my_second_folder/a.py",
        "my_second_folder/b.js",
        "my_second_folder/b.py"
    ]
    assert decompress_paths("") == []
    assert decompress_paths("a{b,c{d,e}}f") == ["abf", "acdf", "acef"]
    print("All tests passed.")

# Run tests
test_decompress_paths()

We can use testing frameworks like unittest or pytest to automate the testing process.

Thinking and Problem-Solving Tips

When approaching such problems, it’s important to:

Break down the problem into smaller, manageable parts.
Identify the base case and recursive case for recursive solutions.
Use helper functions to keep the code clean and modular.
Test the solution with a variety of test cases, including edge cases.

To develop problem-solving skills, practice solving similar problems, study algorithms, and participate in coding challenges on platforms like LeetCode, HackerRank, and CodeSignal.

Conclusion

In this blog post, we discussed how to decompress file paths represented as token lists. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for efficient data management and manipulation. We encourage readers to practice and explore further to enhance their problem-solving skills.

Additional Resources

For further reading and practice problems related to this topic, check out the following resources: