Output: Print all permutations of the string. A string of length n has n permutation ( Source: Mathword ) Below are the permutations of string ABC. Algorithm stringPermutation (str, left, right) Input: The string and left and right index of characters. I assume that you have necessary programming skills to implement this basic idea yourself, in particular solving problems using recursive calls. A permutation, also called an arrangement number or order, is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. Moving one level up the tree is what we call the backtracking in this case.Īs for implementation, the backtracking is usually implemented using recursive call(s) as in your example. Then you backtrack one level up, and try another option. In other words, you simply traverse the tree, and when you reach the leaf you print the permutation. This is one way to generate permutations with recursion, you can understand the code easily by taking strings a,ab & abc as input. The following picture should clarify the basic idea: You backtrack again, but you have already used $2$ and $3$, so you backtrack again (one level up where), and choose $2$ instead of $1$, then you select $1$, and finally $3$, so you have $213$. Then you backtrack and select $3$ instead of $2$, then select $2$, and you have $132$. At that point you have built the first permutation $123$. Then you move forward an choose $2$ (since $1$ has already been chosen), and then you choose $3$. Given a string, str, you are required to output an array containing all the possible permutations of that string. As soon as as you build a single permutation, you backtrack and build another one, and so on until you generate all $n!$ possible permutations, say, on $n$ symbols. So, basically, what you do is build incrementally all permutations. Backtracking is an algorithm for finding all the possible solutions by exploring all possible ways. Approach: Backtracking Using a backtracking approach, all the permutations of the given string can be printed. Backtracking is a general algorithm "that incrementally builds candidates to the solutions, and abandons each partial candidate (" backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution." (Wikipedia). Input: S abc Output: abc, acb, bac, bca, cba, cab Explanation: All the permutations of the given string are given.
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