10/7/2023 0 Comments All permutations of a stringThe cookie is used to store the user consent for the cookies in the category "Analytics". This cookie is set by GDPR Cookie Consent plugin. These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. Note that the constants, in this case, can have a significant influence on the performance of the algorithm, but anyway, the performance of this algorithm will be much better than our naive algorithm. currentHash += primesĭropping the constants, we get it done on linear time – O(b). result.append(longer.substring(left, right))ī. Pseudocode Implementation procedure getAllPermutations(a, b)Ģ. Now the only thing left is to check if the sum of substrings on the longer string is equal to the sum of the sorter string. This allows us to assign each character to a prime number, where the prime number is the hash key, the sum of all permutations of the shorter string characters keys are equal. Then S is the only possible entirely prime multiset of size N, whose elements can sum to Q. Let the sum of the numbers in S equal some integer Q. Let S = be a multiset list of size N that contains only prime numbers. As with many exponential runtimes’ algorithms, such as the famous Fibonacci sequence algorithm, we could improve it by implementing a hash table. To optimize our algorithm we could implement something similar to the Rabin-Karp algorithm. Try to run this JS implementation where a.length >= 10, and you’ll probably get a timeout error. These algorithms may be more suitable for generating permutations of larger strings. There are more efficient algorithms for generating permutations that have a lower time complexity, such as the Heap’s algorithm, which has a time complexity of O(n * n!), or the Steinhaus–Johnson–Trotter algorithm, which has a time complexity of O(n * n). This time complexity is not very efficient, especially for larger strings, as the number of permutations grows very quickly with the size of the string. For example, a string with 4 characters has 4! = 24 permutations, and a string with 5 characters has 5! = 120 permutations. This is because there are n! (n factorial) possible permutations of a string with n characters. The time complexity of a naive solution to generate all permutations of a string would be at least exponential, specifically O(n!), where n is the length of the string. if permutations index of b.substring(i, a.length) > -1Ī.1 push b.substring(i, a.length) to resultĤ return result JavaScript Implementation permutations = // array of all a permutationsĪ. Reslut = Brute Force Solution procdure getAllPermutations(a, b)ġ. We assume that both strings contain only ASCII characters. Find all permutations of A that occur on B. Given a short string A and a longer string B.
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