I assume that you have necessary programming skills to implement this basic idea yourself, in particular solving problems using recursive calls. 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. lets write a program to print all permutations of a String in Java, for example if input is xyz then it. Depending on whether you start counting your permutations from 0 or 1, the answers is (2, 7, 8, 3, 9, 1, 5, 6, 0, 4) or (2, 7, 8, 3, 9, 1, 5, 6, 4, 0). This program provides a easy recursive solution. The following picture should clarify the basic idea: Essentially, this finds the first element of the k-th permutation of S, and then recurses on the remaining string to find its first element. String permutations have applications ranging from security and encryption to optimization and analysis. 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 $3$. However, it does not need to be an existing word, but can simply be a re-arrangement of the characters. A string permutation is similar to an anagram. 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 every string has a number of permutations into which its characters could be re-arranged. So, basically, what you do is build incrementally all permutations. 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).
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