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In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time. Sometimes the term "inductive data type" is used for algebraic data types which are not necessarily recursive.
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
Conceptually, short-circuiting can be considered to either have the same base case and recursive step, checking the base case only before the recursion, or it can be considered to have a different base case (one step removed from standard base case) and a more complex recursive step, namely "check valid then recurse", as in considering leaf ...
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 ...
As with direct recursion, tail call optimization is necessary if the recursion depth is large or unbounded, such as using mutual recursion for multitasking. Note that tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult to implement than the ...
That way, a nested call can modify its local variables without affecting any of the suspended calls variables. Recursion allows direct implementation of functionality defined by mathematical induction and recursive divide and conquer algorithms. Here is an example of a recursive function in C/C++ to find Fibonacci numbers:
We can make only one traversal at a time. It is more prone to errors when both the children are not present and both values of nodes point to their ancestors. Morris traversal is an implementation of in-order traversal that uses threading: [9] Create links to the in-order successor. Print the data using these links.