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Iteration And Recursion Homework Help

Recursion Defined

Recursion is a way of determining information data structures or algorithms in terms of themselves. A recursive algorithm is a form of decomposition where rather than selecting an arbitrary subtask of the issue to do, select a simpler problem that has the same form as the original (self-similarity). A recursive description has two parts:

  1. The base case - a stopping condition
  2. The recursive step - an expression of the calculation or definition in terms of itself

Example of a Recursive Definition:

  • There are many recursive definitions in mathematics. Consider the factorial function:
    • n! = n * (n-1) * (n -2) * … * 2 * 1
  • The same function can be defined recursively by giving a base case and a recursive step:
    • 0! = 1 (by definition)
    • n! = n * (n - 1)! (the recursive step)

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