Скачать или смотреть How to Assign Numbers to Letters for Efficient Anagram Search

Learn how to use the modified Rabin-Karp algorithm to assign numbers to letters for anagram searches with O(n) complexity. Streamline your string comparison tasks!
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This video is based on the question https://stackoverflow.com/q/65079733/ asked by the user 'MAG' ( https://stackoverflow.com/u/1636300/ ) and on the answer https://stackoverflow.com/a/65080246/ provided by the user 'David Eisenstat' ( https://stackoverflow.com/u/2144669/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Introduction

Searching for anagrams effectively can be a challenging task, especially when dealing with longer strings. An anagram is a word formed by rearranging the letters of another, which makes traditional search methods insufficient due to their higher time complexity. However, a clever approach using the modified Rabin-Karp algorithm allows us to assign unique numbers to each letter, enhancing our search efficiency to O(n). In this guide, we will walk you through the steps to achieve this.

Understanding the Problem

Anagrams are positional independent, which means that the order of letters doesn’t matter—only their frequency does. To search for anagrams effectively, we can utilize a hash function where:

The hash value is the sum of the letter values in the string.

We can map each lowercase letter (a-z) to specific numbers.

Key Points

Efficiency: We aim to execute string comparison in linear time, O(n).

Position Irrelevance: Since anagrams only rely on letter counts, positional weighting (as employed in traditional Rabin-Karp) isn’t necessary.

The Solution: Assigning Numbers to Letters

So how do we assign numbers to letters effectively? Here’s a step-by-step approach:

Step 1: Choose a Prime Modulus

Select a suitable large prime number as a modulus, for example:

p ≈ 2^31 − 1

This helps in minimizing collisions when hashing different strings.

Step 2: Map Letters to Numbers

Next, create a mapping for each letter (a through z) to random numbers within the range of 0 to p−1. Here’s how you can do this:

Random Number Generation: For each letter, generate a random number, ensuring no duplicates.

Example Mapping:

a → 3

b → 19

c → 12

…

z → 25

Step 3: Implement the Hash Function

You can compute the hash value of a given string by summing the assigned number values of its letters.

Hash Function Formula:

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

Where s[i] is the assigned number of the i-th letter.

Step 4: Handling Collisions

Collision refers to two distinct strings producing the same hash value. Although we've chosen a large prime, here's what we can do to manage this:

Collision Probability: It can be shown that the probability of spurious collisions occurring when using this method is approximately 1/p. Therefore, the larger the value of p, the lower the chance of collision.

Conclusion

With this method, you can efficiently assign numbers to letters for anagram searches. By utilizing a modified Rabin-Karp approach, we can ensure that our anagram search operates in linear time—crucial for performance with larger datasets.

This systematic approach not only streamlines the process but also reduces the likelihood of errors through strategic number assignments and prime number selection.

Feel free to implement this in your next text analysis or string manipulation project, and watch your anagram search become faster and more effective!