(I won't give you this last part of how to compute the answer. This is a classic permutation problem (I think it's called the "multinomial coefficient" or something fancy). So, the number of answers is precisely the number of ways you can permute the left side.You can permute the characters in any way on the left, and then there is a single choice of permutation on the right, so that they appear as a mirror image.Of the remaining characters, half of them must appear on the left, half on the right.If there is an odd-occurring letter, one occurrence of it must be in the middle.All letters must occur an even number of times (except possibly one letter, which may be odd).Start by counting how many times each letter appears.Once you know the order of the letters on the left, the remaining letters on the right have only one choice (they must appear as the mirror image of the left side). You can choose any order of them on the left. So, in the above example, we must have 1 a, 1 b, and 1 c appear on the left, and similarly on the right (of the middle a). For everything else, there is (and must be) an even number, and half of them appear on the right, and half of them appear on the left. In fact, ALL palindromes of abbacac have this property: acbabcaĪnyway, the point is, since there are an odd number of a's, that odd "a" has to be in the middle. You will notice that it has 1 "a" in the middle, and then the remainder of the letters appear around the middle "a" in a mirrored fashion. Using the "abbacac" example above, can you think of examples of palindromes from this string?įor example: "abcacba" is such a palindrome. Secondly, a palindrome is special because it is "symmetric" (by definition). Also, the original order doesn't matter (since you will be permuting them.) So the "counts" of the characters are important - how many of each character appear in the string. Intuitively, these will have the same answer (number of palindromic permutations). Similarly the second string has 3 x's, 2 y's and 2 z's. The first string has 3 a's, 2 b's and 2 c's. They share a similar "pattern" in terms of their characters. What do the following strings have in common? abbacac xyyxzxz Once you are thinking this way, here is an example to get you thinking about it. It seems more like a combinatorics / counting problem than anything else (recall permutations and combinations from high school or in an introductory algebra class). If so, what are your constraints? If the string is guaranteed to be shorter than about 11 characters long then you should definitely do the "brute force" solution as you mentioned (try every permutation and check if it's a palindrome), if it is a programming problem.īut, there is most certainly a better way. It does not store any personal data.Is this a programming problem? Or is it a math problem? The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. If the length of the string is 1, return a list containing the string Otherwise, for each character in the string: a. The cookie is used to store the user consent for the cookies in the category "Performance". This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other. The cookies is used to store the user consent for the cookies in the category "Necessary". The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. swap character at index `i` with the current character Void get_permutations(string str, int i, int n) Then we find all the permutation of the remaining characters using a recursion. Here we will swap each of the characters in the string with the first character. To solve this problem we shall use the concept of backtracking. You are given a string, you need to find all the permutations of it.
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