9/24/2023 0 Comments String permutation![]() In the j loop, we proceed through all the characters that match A, and we need to be able to find unique indices in B that match for them (including the i-th position). The idea here is that we have already validated that we have a permutation of the characters before i in the outer loop. In C-style code for the whole routine: for (int i = 0 i nĪnd function findNextValue searches in B for a value starting from an index, and returns the index where it was found (or n+1 if not found). Using double hashing (or for overkill even more) by changing the value of R would successfully identify them as permutations with very high probability. The product (computed using 32-bit ints) is This is an arbitrary choice, doing someĮxperiments should show if a given R is good or bad. The division by 2 at theĮnd is because the product will always be odd, hence the division justĮ.g. The factor 2 in (R + 2e) guarantees that all factors are odd, henceĪvoiding that the product will ever become 0. For eachĮlement e you want to hash compute the factor (R + 2*e). ![]() If the two hashes of the strings differ, they're not permutations of each other. This hashing function would work, andĮ for any letter would be its ascii value. If they differ anywhere, they're not permutations of each other.įor an O(n) solution, hashing could be used. Sort the two strings, and compare them index by index. When elements are allowed to repeat, we modify the algorithm as follows:Ĭompute the minimum values $m_$, and that the counts are identical. Given the $k$th smallest element, we can find the $(k+1)$st smallest element by finding the minimal value larger than the $k$th smallest element (here we use the fact that all elements are distinct). Here is an algorithm that uses $O(1)$ space:Ĭompute the minimum values of both arrays, and check that they are identical.Ĭompute the second minimum values of both arrays, and check that they are identical.Ĭomputing the minimum value of an array clearly uses $O(1)$ space. ![]() Suppose first that the values in each array are distinct. Denote the arrays by $A,B$, and suppose they are of length $n$.
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