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  2. Corecursion - Wikipedia

    en.wikipedia.org/wiki/Corecursion

    A classic example of recursion is computing the factorial, which is defined recursively by 0! := 1 and n! := n × (n - 1)!. To recursively compute its result on a given input, a recursive function calls (a copy of) itself with a different ("smaller" in some way) input and uses the result of this call to construct its result.

  3. Recursion (computer science) - Wikipedia

    en.wikipedia.org/wiki/Recursion_(computer_science)

    [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. [3] The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite ...

  4. Mutual recursion - Wikipedia

    en.wikipedia.org/wiki/Mutual_recursion

    This example is mutual single recursion, and could easily be replaced by iteration. In this example, the mutually recursive calls are tail calls, and tail call optimization would be necessary to execute in constant stack space. In C, this would take O(n) stack space, unless rewritten to use jumps instead of calls. [4]

  5. Tail call - Wikipedia

    en.wikipedia.org/wiki/Tail_call

    If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack.

  6. Course-of-values recursion - Wikipedia

    en.wikipedia.org/wiki/Course-of-values_recursion

    This recursion is a primitive recursion because it computes the next value (n+1)! of the function based on the value of n and the previous value n! of the function. On the other hand, the function Fib( n ), which returns the n th Fibonacci number , is defined with the recursion equations

  7. Primitive recursive function - Wikipedia

    en.wikipedia.org/wiki/Primitive_recursive_function

    A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...

  8. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    In the recursive calls to the algorithm, the prime number theorem can again be invoked to prove that the numbers of bits in the corresponding products decrease by a constant factor at each level of recursion, so the total time for these steps at all levels of recursion adds in a geometric series to (⁡).

  9. Memoization - Wikipedia

    en.wikipedia.org/wiki/Memoization

    function factorial (n is a non-negative integer) if n is 0 then return 1 [by the convention that 0! = 1] else if n is in lookup-table then return lookup-table-value-for-n else let x = factorial(n – 1) times n [recursively invoke factorial with the parameter 1 less than n] store x in lookup-table in the n th slot [remember the result of n! for ...