Understanding the Recurrent Situation Between Hash Values of Substrings in the Raven Cars Algorithm In the discipline of computer science, the Raven Cars method is a well-known optimization tool. This article examines the recurring relationship between the hash values of substrings in the Raven Cars algorithm and how it contributes to algorithm optimization. What is the Raven Cars Algorithm? A piece of software called the Raven Cars algorithm is used to look for patterns in a text input. Numerous applications, such as text analysis, cryptography, and information retrieval, can benefit from this approach. The Convenience of Polynomial Hashing The polynomial hash function is one of the fundamental elements of the Raven Cars algorithm. This hash function is useful for both strings and the substrings of those strings. The polynomial hash's general formula is as follows: $H(i) = "sum j=0n-1" T[i+j] x "j"$ Where $n$ is the length of the pattern $P$ and $T[i+j]$ is the code of the character at position $i+j$ in the text $T$. The Function of Polynomial Hash The polynomial hash value can be calculated when text is encoded using a numerical coding in which each letter is given a number between 0 and 25. For instance, the encoded code for the word "beach" in the string $T$ would be [1, 4, 0, 2, 7]. Assume the pattern is three lengths long. Next, we would calculate the hash values for each substring of the three-character text $T$. The hash value would have coefficients for $1x and $x2$ with degrees of $x$ ranging from 0 to 2 for the final substring of length 3, "ach." The respective coefficients would be 0, 2, and 7. The previous substring, "eac," had a length of 3, therefore its hash value would also include coefficients for $1x and $x2 with values of 4, 0, and 2, respectively. The final two terms of the hash polynomial for "eac" are identical to the opening two terms of the polynomial for "ach," multiplied by $x$, as can be seen. The Recurrence Equation We may derive a recurrence equation between the hash values thanks to the polynomial hash function's characteristic. The hash of the substring beginning at position 2, "ach," for instance, is $H(2)$, which equals 0 + 2$x$ plus 7$x2$ (mod $b$). The hash value for "eac" is $H(1)$, which equals 4 plus $x$ plus $x2$ times. This equation can be rewritten as 0 + 2$x$ times the first two terms of $H(2)$ multiplied by 4 plus $x$. After that, we may rewrite it as 4 plus $x times the entire hash of "ach." This recurrence equation considerably improves the Raven Cars technique by enabling us to swiftly compute one hash value given the value of another hash value. In order to optimize the Raven Cars algorithm, it is essential to understand the recurring relationship between the hash values of the substrings. This optimization is enabled by the polynomial hash and its characteristics.