A Question about modulus R in Rabin Karp Algorithm

In summary, setting a value q as a prime number larger than the length of the pattern in the Rabin-Karp Algorithm can greatly reduce the time complexity of the function. The optimal prime number for q is determined by the length of the pattern and a larger value of q can result in a slower search while a smaller value can result in a faster search.
  • #1
Sunwoo Bae
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Hello, I am learning trying to set up a code that searches for a certain pattern in the text by implementing Rabin-Karp Algorithm.
When setting up the Rabin Karp hash function, I have been told that I should set a value q in order to lower the time complexity of the function, and that q should be a prime number that is larger than the length of the pattern that I want to find in the text.

1) Why exactly is it that the time complexity of the function is reduced when mod q is performed?
2) How do you determine the optimal prime number for q? Can it be any prime number that is bigger than the pattern length? For instance, if the pattern length is 3, what would be an optimal prime number?
3)Will value of q affect the time complexity of code in any way?

Thank you for your help!
 
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  • #2
1) Mod q is performed to reduce the time complexity of the Rabin Karp hash function. This works because when mod q is applied, the hash value of the pattern will be a much smaller number than the actual length of the pattern. This means that when the hash values of the text and the pattern are compared, the comparison can be done much faster since it is comparing much smaller numbers. 2) The optimal prime number for q is determined by the length of the pattern. Any prime number larger than the length of the pattern is suitable. For instance, if the pattern length is 3, the optimal prime number for q could be 5, 11, 17, etc. 3) Yes, the value of q will affect the time complexity of the code. A larger prime number for q will result in a slower search, whereas a smaller prime number for q will result in a faster search.
 

1. What is the purpose of modulus R in the Rabin-Karp algorithm?

The modulus R in the Rabin-Karp algorithm is used to reduce the size of the hash value, making it easier to compare and match patterns in a string. It also helps to avoid integer overflow when dealing with large strings and patterns.

2. How is the modulus R chosen in the Rabin-Karp algorithm?

The modulus R is typically chosen as a prime number that is larger than the size of the alphabet being used in the string and pattern. This helps to reduce the chance of hash collisions and improves the accuracy of the algorithm.

3. Can the modulus R be changed during the execution of the Rabin-Karp algorithm?

No, the modulus R should remain constant throughout the execution of the algorithm. Changing the modulus R can result in incorrect hash values and lead to incorrect pattern matching.

4. Is the choice of modulus R important in the Rabin-Karp algorithm?

Yes, the choice of modulus R can significantly impact the performance and accuracy of the algorithm. A poorly chosen modulus R can result in a higher number of hash collisions and slower execution times.

5. Are there any limitations to using the Rabin-Karp algorithm with a specific modulus R?

Yes, using a modulus R that is too small can lead to an increased chance of hash collisions, while using a modulus R that is too large can result in a larger hash table and slower execution times. It is important to choose a suitable modulus R based on the size of the strings and patterns being used.

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