Precomputation Increases Rabin-Karp Algorithm Efficiency A common string matching approach for locating a substring inside a bigger text is the Rabin-Karp algorithm. Despite having an excellent average-case performance, this algorithm's temporal complexity can be problematic when working with lengthy text strings. This article will investigate using precomputation to reduce the Rabin-Karp algorithm's execution time. Precomputation's fundamental premise is to employ a recurrence equation to precompute hashes for all text substrings with lengths equal to the pattern's length. The algorithm operates in the same way as the original Rabin-Karp algorithm after the hashes have been precomputed. The hashes are fetched from the precomputed array rather than being computed as part of the search process, which enhances the algorithm's overall efficiency and saves time. Let's examine the precompute hashes function to understand how precomputation functions. The text, pattern length, prime number utilized in the polynomial hash function, and polynomial hash function generator are all inputs for this function. The array H, which will hold the hash values of the substrings, must first be initialized as the first step in the function. The text length less the pattern length plus one makes up the length of the array H. There are only so many text substrings that are the same length as the pattern, which is the cause of this. The final substring of the text, which has length equal to the pattern's length, is used by the function to initialize the string S after that. The polynomial hash method is then used to directly calculate the hash value for this specific substring. This component of the algorithm operates in time O since the polyhash technique requires time proportional to the length of the string S, which is equal to the length of the pattern (length of pattern). The calculation of x to the power of the pattern's length, modulo the prime integer, comes next. This is accomplished by setting y to 1 and then executing a straightforward for loop. The loop multiplies y by x modulo the prime number for each iteration. By the time the loop is finished, y will equal x to the power of the pattern's length modulo the prime number. Since each action in the loop is performed exactly once and takes a certain amount of time, this results in an additional length of pattern operations. The array H's values are computed using the recurrence equation as the last step. The recurrence equation is used to calculate H[i] in each iteration of the last for loop, given H[i+1] and the value of y, which is equal to x to the power of the pattern's length modulo the prime integer. Constant time is used to perform this calculation. This final for loop iterates exactly length of text minus length of pattern times, resulting in an extra length of text minus length of pattern operations. Last but not least, the precomputation of H computes the polyhash in time O(length of pattern), x to the power of the length of the pattern in time O(length of pattern), and the remaining values in the array H in time O. (length of text minus length of pattern). In contrast to the earlier estimate of O, the total calculation time for the precomputation of H is consequently O(length of text + length of pattern) (length of text times length of pattern).