rekurzivního

Rekurzivní refers to a concept where something is defined in terms of itself. In mathematics and computer science, a recursive definition is one that uses the object being defined as part of its own definition. This often leads to a process that repeats itself, breaking down a problem into smaller, identical subproblems until a simple base case is reached.

A classic example in mathematics is the factorial function. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Recursively, n! can be defined as n multiplied by (n-1)!, with the base case that 0! equals 1. So, to calculate 5!, we would calculate 5 * 4!, then 4 * 3!, and so on, until we reach the base case of 1! or 0!.

In computer programming, recursion is implemented through functions that call themselves. A recursive function must have at least one base case to prevent infinite loops. When the function encounters the base case, it stops calling itself and returns a value. Otherwise, it performs some operations and then calls itself with modified arguments, moving closer to the base case. This approach can lead to elegant and concise solutions for problems that have a naturally recursive structure, such as traversing tree-like data structures or solving certain types of puzzles. However, it's important to manage recursion carefully, as excessive depth can lead to stack overflow errors due to memory limitations.