Rabin-Karp Algorithm

Preview

1. What is the basic idea behind the Rabin-Karp algorithm?
2. How is the rolling hash function used in the Rabin-Karp algorithm?
3. What is the worst-case time complexity of the Rabin-Karp algorithm?
4. How does the Rabin-Karp algorithm compare to other string matching algorithms in terms of efficiency?
5. How would you modify the Rabin-Karp algorithm to handle multiple pattern searches in a single text string?

Explain

The Rabin-Karp algorithm is a string searching algorithm that matches a pattern in a text by comparing hash values of substrings of the text and the pattern. It is considered a probabilistic algorithm as it may have false positives, but it has average-case time complexity of O(n+m), where n is the length of the text and m is the length of the pattern.

The algorithm works as follows:

1. Compute the hash value of the pattern.

2. Compute the hash values of all substrings of the text with the same length as the pattern.

3. Compare the hash value of the pattern with the hash values of the substrings. If there is a match, compare the actual characters of the pattern and substring to ensure it is not a false positive.

4. If the pattern is not found, slide the pattern over the text one character at a time and repeat steps 2-3.

Example:

Text: ABCDEFGHJKLFGFGFGFGFGFGFGFGFGFGFGFGHIJKLMN

Pattern: FGFGFGFGFG

Hash function: sum of ASCII values of characters

Step 1: Compute the hash value of the pattern

FGFGFGFGFG = 70+71+70+71+70+71+70+71+70+71 = 700

Step 2: Compute the hash values of all substrings of the text with the same length as the pattern

Substrings: ABCDEFGHJKL, BCDEFGHJKLF, CDEFGHJKLFG, DEFGHJKLFGF, EFGHJKLFGFG, FG…

Hash values: 65+66+67+68+69+70+71+72+74+75+76+70 = 804
66+67+68+69+70+71+72+74+75+76+70+71 = 810
67+68+69+70+71+72+74+75+76+70+71+70 = 812
…

Step 3: Compare the hash value of the pattern with the hash values of the substrings

The hash value of FGFGFGFGFG is 700. One of the substrings with the same hash value is FGFGFGFGFG. We then compare the actual characters of the pattern and substring to confirm it is not a false positive.

Step 4: If the pattern is not found, slide the pattern over the text one character at a time and repeat steps 2-3

We continue to slide the pattern over the text one character at a time until we find all occurrences of the pattern.

Keypoint

1. Rabin-Karp Algorithm is a pattern matching algorithm.
2. It uses hash values and rolling hash technique to find a pattern in a text string.
3. It has a time complexity of O(n+m), where n is the length of the text and m is the length of the pattern.
4. It is particularly useful when the pattern has many characters in common with the text.
5. Rabin-Karp Algorithm uses a sliding window technique to calculate hash values of substrings of the text.
6. It compares the hash value of the pattern with the hash value of each substring to find a match.
7. In case of a hash collision, it verifies the match by comparing the pattern with substring character by character.
8. The algorithm can be optimized by using a prime number for the hash function and implementing a rolling hash technique.
9. It is a versatile algorithm and can be used in various applications such as plagiarism detection, spell checking, and DNA sequence analysis.

Review

1. What is the basic idea behind the Rabin-Karp algorithm?
   Answer: The Rabin-Karp algorithm is a string matching algorithm that uses hashing to compare the pattern to the text. It performs pattern matching by comparing the hash values of the pattern and substrings of the text.

2. What is the worst-case time complexity of the Rabin-Karp algorithm?
   Answer: The worst-case time complexity of the Rabin-Karp algorithm is O(mn), where m is the length of the pattern and n is the length of the text.

3. How does the Rabin-Karp algorithm handle collisions in hash values?
   Answer: The Rabin-Karp algorithm uses a rolling hash function that allows it to handle collisions by rehashing only the affected substrings, rather than recomputing the hash values of all substrings.

4. What is the role of modular arithmetic in the Rabin-Karp algorithm?
   Answer: The Rabin-Karp algorithm uses modular arithmetic to reduce the hash values to a fixed range, which helps to prevent overflow and ensures that the hash values are uniformly distributed.

5. How does the Rabin-Karp algorithm compare to other string matching algorithms, such as the Knuth-Morris-Pratt algorithm?
   Answer: The Rabin-Karp algorithm is generally slower than the Knuth-Morris-Pratt algorithm for small patterns, but it can be faster for larger patterns or when multiple patterns need to be matched simultaneously. Additionally, the Rabin-Karp algorithm is more flexible because it can be easily adapted to handle different types of patterns (e.g., regular expressions).