Counting Similar Substrings for Each Query in Python

💡 Problem Formulation: The task is to count the occurrences of substring patterns within a given string or set of strings based on varied queries. For instance, if given the string ‘ababa’ and queries like ‘aba’ or ‘bab’, the program would output the counts of these substrings in the original string – which would be 2 for ‘aba’ and 1 for ‘bab’.

Method 1: Brute Force Search

The brute force search method involves checking for the occurrence of the query substring in the main string starting at each position. To implement this, we loop through the main string for each query and check for matches. It’s straightforward but can be inefficient for large strings or numerous queries.

Here’s an example:

def count_substrings(s, query):
    return sum(1 for i in range(len(s)) if s.startswith(query, i))
    
# Example usage:
main_string = "ababa"
queries = ["aba", "bab"]
counts = [count_substrings(main_string, q) for q in queries]
print(counts)

Output: [2, 1]

This code defines a function count_substrings() that takes a string and a query substring as its arguments. It uses a generator expression with startswith() to check if the main string starts with the query at any given index. This process is repeated for each query, and the counts are collected in a list.

Method 2: Using Regular Expressions

Regular expressions can be used to count overlapping occurrences of a substring within a string. The re module in Python has a findall() method, which can be utilized to search for all instances of the pattern, also capturing the overlaps by using lookaheads.

Here’s an example:

import re

def count_substrings_regex(s, query):
    return len(re.findall('(?=' + query + ')', s))

# Example usage:
main_string = "ababa"
queries = ["aba", "bab"]
counts = [count_substrings_regex(main_string, q) for q in queries]
print(counts)

Output: [2, 1]

In the count_substrings_regex() function, a regex pattern is constructed using a lookahead to search for the query substring in a way that counts overlap. The findall() function then returns all matches, and the length of this list is the count of occurrences.

Method 3: Using String Count Method

Python’s native str.count() method counts non-overlapping occurrences of a substring within a string. It’s very efficient for non-overlapping patterns but won’t work for substrings that overlap.

Here’s an example:

def count_substrings_count_method(s, query):
    return s.count(query)

# Example usage:
main_string = "ababa"
queries = ["aba", "bab"]
counts = [count_substrings_count_method(main_string, q) for q in queries]
print(counts)

Output: [1, 1]

The count_substrings_count_method() function uses str.count() to find the occurrences of each query in the main string. This method is simple and time-efficient for non-overlapping cases but, as the output shows, it doesn’t account for overlapping occurrences of the substring ‘aba’.

Method 4: Using Suffix Tree/Array

For a more advanced and efficient approach, especially with large data sets or when performing multiple queries, a suffix tree or array can be utilized. This data structure allows for fast substring queries after an initial expensive building phase.

Here’s an example:

# Placeholder for actual suffix tree/array implementation.
# Due to complexity, this is just to illustrate the usage.

def build_suffix_array(s):
    # Normally here would be the algorithm to build
    # the suffix array from the string `s`.
    pass

def count_substrings_suffix_array(suffix_array, query):
    # This function would use the suffix array to
    # quickly count occurrences of the query.
    pass

# Note: Real implementation and example are significantly more complex.

This section represents a conceptual framework, as implementing a suffix tree/array is beyond the scope of this simple tutorial. Using such data structures is highly efficient for repetitive searching once constructed.

Bonus One-Liner Method 5: Functional Programming Approach

A one-liner using functional programming with map() and lambda can be used to achieve the same result in a concise but less readable manner.

Here’s an example:

main_string = "ababa"
queries = ["aba", "bab"]
counts = list(map(lambda q: len(re.findall('(?=' + q + ')', main_string)), queries))
print(counts)

Output: [2, 1]

This one-liner maps a lambda function over the queries, applying the regular expression method discussed earlier directly within the lambda function. It is very succinct, but the drawback is that it might be less clear to those unfamiliar with functional programming paradigms.

Summary/Discussion

• Method 1: Brute Force Search. Simple and straightforward. Inefficient for larger strings or numerous queries.
• Method 2: Using Regular Expressions. Captures overlapping occurrences well. Might be less efficient than other methods for very large strings.
• Method 3: Using String Count Method. Fast and simple for non-overlapping substrings. Does not count overlaps.
• Method 4: Using Suffix Tree/Array. Highly efficient after construction. Initial setup is complex and not trivial to implement.
• Bonus Method 5: Functional Programming Approach. Compact and efficient one-liner. Readability could be an issue for some developers.