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  2. Recursion (computer science) - Wikipedia

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

    In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. [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 ...

  3. 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.

  4. Recursion - Wikipedia

    en.wikipedia.org/wiki/Recursion

    A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...

  5. 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 nth Fibonacci number, is defined with the recursion equations =, =,

  6. Tail call - Wikipedia

    en.wikipedia.org/wiki/Tail_call

    For example, in the Java virtual machine (JVM), tail-recursive calls can be eliminated (as this reuses the existing call stack), but general tail calls cannot be (as this changes the call stack). [13] [14] As a result, functional languages such as Scala that target the JVM can efficiently implement direct tail recursion, but not mutual tail ...

  7. Primitive recursive function - Wikipedia

    en.wikipedia.org/wiki/Primitive_recursive_function

    For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1] In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. [ 2 ]

  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 ...