How Can Recursion Be Used to Generate All Permutations of a String or Integer?

The arrangement of the string and integer

A common algorithm challenge is to generate all possible arranges to generate string or integer. This problem often appears in programming interviews and needs to be able to identify and implement recursive solutions.

Recursive: The step -by -step method

recursion is the foundation for arranging. The key is to understand two different steps:

The first step is to treat a single element as its own arrangement.

Subsequent steps include connecting each element with each arrangement of the remaining elements.
• A intuitive example

For the collection of character "A", "B" and "C", we can apply this recursive principle:

For a single element, the arrangement is the element itself:

a

• For two elements, for each element:

• "A" and "B" are connected:

  AB

  ,
  BA
  • "B" and "A" are connected: BA ,
  ab
  For three elements, for each element:
• "A" and "BC" are arranged:

  ABC

  ,
  ACB
  • , BAC , BCA , CAB , cba "B" and "AC" are arranged: BAC , BCA
  ,
  • ABC , ACB , CAB , cba "C" and "AB" are arranged: Cab , CBA ,
  ABC
  • , ACB , BAC , BCA pseudo code and implementation
  Converting this logic into a code, we can use the following pseudo -code as guidance:

C# more detailed examples

This C#example uses a clearer output method, directly output the string, and modify some logical details to make it easier to understand and run. It should be noted that the time complexity of this recursive algorithm is O (n!), Where n is the length of the string or integer. For longer string or integers, the calculation time will be very long.

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