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Short-circuiting the base case, also known as arm's-length recursion, consists of checking the base case before making a recursive call – i.e., checking if the next call will be the base case, instead of calling and then checking for the base case. Short-circuiting is particularly done for efficiency reasons, to avoid the overhead of a ...
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
Another technical point is that, in the case of left folds using lazy evaluation, the new initial parameter is not being evaluated before the recursive call is made. This can lead to stack overflows when one reaches the end of the list and tries to evaluate the resulting potentially gigantic expression.
For these cases, optimizing tail recursion remains trivial, but general tail-call optimization may be harder to implement efficiently. 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).
Divide-and-conquer algorithms are naturally implemented as recursive procedures. In that case, the partial sub-problems leading to the one currently being solved are automatically stored in the procedure call stack. A recursive function is a function that calls itself within its definition.
In this case the tree function calls the forest function by single recursion, but the forest function calls the tree function by multiple recursion. Using the Standard ML datatype above, the size of a tree (number of nodes) can be computed via the following mutually recursive functions: [5]
A simple recursive inner function is created, which behaves as the algorithm's main loop, while the outer function performs startup actions that only need to be done once. In more complex cases, a number of mutually recursive functions may be created as inner functions.
This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest: t: v [t[1], ..., t[k]] A tree t consists of a pair of a value v and a list of trees (its children). This definition is more compact, but somewhat messier: a tree consists of a pair of one type and a list another, which ...