Java Recursion Methods: Principles and Examples of Recursive Calls, from Factorial to Fibonacci

Recursion is a process in programming where a method calls itself directly or indirectly. Its core consists of the **base case** (when to stop) and the **recursive relation** (how to decompose the problem). The principle can be analogized to "peeling an onion": the problem is broken down into smaller subproblems until the base case is triggered, with execution and return occurring layer by layer through the method call stack. Classic examples include factorial (\(n! = n \times (n-1)!\), base case \(n=0\) or \(n=1\) returns 1) and the Fibonacci sequence (\(F(n) = F(n-1) + F(n-2)\), base cases \(n=0\) returns 0, \(n=1\) returns 1). Advantages of recursion are clear logic and concise code. Disadvantages include stack overflow with excessive depth and repeated calculations in some scenarios (e.g., Fibonacci). Key considerations: always set a base case, ensure parameters decrease stepwise, and use appropriate data types for large results (e.g., `long` for factorials). Recursion is suitable for solving self-similar problems. It requires mastery of base cases and call stack logic. For complex scenarios, optimization with loops or dynamic programming can be combined.