![]() If it has, continue to the next iteration.įix current character: If the character has not been visited, mark it as visited and append it to the current string. Iterate through characters: Iterate through each character of the original string using a loop.Ĭheck visited characters: For each character, check if it has been visited. Print or store the current string and return from the current recursion. If they are equal, it means we have generated a permutation. visited: A boolean array to keep track of the characters that have been visited.īase case: Check if the length of the current string is equal to the length of the original string.current: A string representing the current permutation being generated.string: The original string for which we want to generate permutations.Here is a step-by-step explanation of the algorithm:ĭefine a recursive function: Start by defining a recursive function, let’s call it generatePermutations(), that takes the following parameters: The idea behind this approach is to fix one character at a time and recursively generate permutations for the remaining characters. One of the most common and efficient algorithms to obtain all permutations of a string is recursive backtracking. For example, if we have the string “abc,” its permutations would be “abc,” “acb,” “bac,” “bca,” “cab,” and “cba.” Approach: Using Recursive Backtracking In the context of strings, a permutation refers to all possible rearrangements of the characters in a given string. What are Permutations?īefore diving into the algorithm, let’s first define what permutations are. Whether you are a beginner or an experienced professional, this guide will help you understand the concept and implementation details of this algorithm. In this article, we will explore an algorithmic approach to obtain all permutations of a string efficiently. Permutations are all possible arrangements of the characters in a given string. So T(1) = 1.| Miscellaneous Getting All Permutations of a String: Explained for Data ScientistsĪs a data scientist or software engineer, you often come across situations where you need to generate permutations of a string. The first call to permute is permute(a, n, 0). Each invocation of permute(a, n, k) calls permute(a, n, k+1) recursively n-k times. ![]() Let the number of times permute is called when we pass in a string of length n be T(n). If it runs in O(n!) steps, then our function above is as efficient as it can get. How efficient is the function permute? We know that for a string of length n, there are n! permutations, so the function permute should be at least n!. When we are done, we swap back the original a, this is to ensure that the string remains unchanged after permute is called. Lines 9-13 is a for loop which loops through all characters a to a, and swaps each one to the position of a, and recursively permutes the string a. Line 8 permutes the remaining string, a to a, with character a intact. Since there is only one possible permutation, we do not need to do anything except to print out the permutated string. Lines 3-6 above corresponds to the base case, where we have reached the end of the string, there is only one character left to permutate. Void permute ( char a, long len, long curr ) The idea above is implemented as the following: Similarly, we get the permutations cab and cba by considering c as the first character and permutating ba. We generate all permutations of the string ac. ![]() We start with a as the first character, and generate all the permutations of the string bc. We have n-1 characters left, which we solve recursively, generating all possible permutations with i as the first character.įor example, consider a string length 3, abc. Here is what we do to generate all permutations of a string of length n.įor each character i in the string, we move i to the first position in the string. There is only one possible permutation! Now, by wishful thinking, we assume that we know how to generate all permutations of a string of length n-1. The trivial case is when we generate the permutation of a string with one character. A simpler version of the problem is to permute a string of length n-1. To formulate a recursive solution, as usual, let's simplify the problem. For simplicity, we assume that there is no repetition in the string. Let's see a simple example of this: generate all permutations of the characters in a string of length n. ![]() ![]() In this unit, let's look at another useful application of recursion: to generate all possible permutations or combinations of items. We have been using recursions to either compute or find a solution to a problem. Appendix: Complete Code Written in Lecture ![]()
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