Generating permutations is a frequently occurring problem in both coding challenges and real-world problems.  Any time you encounter the need to enum

Permutation Generation Algorithms

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2022-07-05 00:30:05

Generating permutations is a frequently occurring problem in both coding challenges and real-world problems.  Any time you encounter the need to enumerate the arrangements of a set of items, you're considering permutations.  

In addition to that, permutation generation algorithms are an important building block in more complicated algorithms.  It's important to have a good understanding of the base algorithm in order to use it in more complicated situations.  Enumerating all the permutations of a set of $n$ elements takes $O(n!)$ time, but that's impractical for reasonable sizes of $n$.  Therefore it's important to be able to reason about permutation generation algorithms to be able to improve the time complexity of any practical algorithm.

Lastly, permutation generation algorithms are a great example of recursion and backtracking.  They are a quintessential application of these techniques and demonstrate some of the tradeoffs of different approaches.

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