10/21/2023 0 Comments Palindrome permutation![]() The number of ways to do that is exactly the Multinomial coefficient (a quotient of certain factorials), which Mathematica has built-in. ![]() If there are, then i represents the counts of distinct characters in the left half of the permutations, which can be arranged arbitrarily. We can test for that by simply adding up all the elements of t-i (using Tr): if the answer is less than 1, there are palindromic permutations, otherwise not. Note that palindromic permutations of the input exist exactly when there is at most one odd number among the original counts, that is, when there is at most one fraction in t. Therefore, to decide if a string is a permutation of a palindrome, we need to know if it can be written such that it’s the same forwards and backwards. Not as short as Martin Ender's Mathematica answer, but it's a cute approach nonetheless, which seems to be the same approach as in smls's Perl 6 answer.įirst, computes the counts of all the distinct characters in the input, divided by 2 then i=Floor rounds down any fractions occurring in t. Hello Guys, In this tutorial we gone see how to get the permutations of all the words and to check if any permutation of the word is palindrome and print. A palindrome is a string that is the same forwards and backwards. Mathematica, 68 bytes function taking a list of characters as input and returning an integer. ![]() A simple solution is to run two loops, the outer loop picks all characters one by one, and the inner loop counts the number of occurrences of the picked character. %“µɲ€’ - mod 666013, as in the brute force version. A set of characters can form a palindrome if at most one character occurs an odd number of times and all characters occur an even number of times. first check to see if any palindromes will be possible: ĠL€ - Link 2, count characters: string a e.g. Μ - start a new monadic chain - call that p Ñ - call the next link (2) as a monad(a) e.g. I believe that this will do it more efficiently, but it's 30 bytes (edit: this pdf seems to confirm it, courtesy of smls's answer): ÑHḞµS!÷!P$ - Link 1, palindrome count: string a e.g. If a question asks if strings are permutations of each other, it is asking if they have the same characters in a different order. For example, a 3 letter word will have 6 ( 3 3 2 1) permutations. Thanks to Allan for saving a byte! -> Changed the import styleĪ brute forcer. A permutation is a different ordering of a string's characters. In Floroid, this is (almost) z(T(a=aDKaIW(cb(L)))%666013), but prints the result instead, and takes input through the command line. Perl 6, 104 108 88 84 bytes ) to keep only distinct permutations inside.
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