19.2 Recursion

Objective

Show awareness of what a compiler has to do to translate recursive programming code.

What is Recursion?

Recursion is a programming technique where a function calls itself within its own definition. It's a powerful way to solve problems that can be broken down into smaller, self-similar subproblems.

A recursive solution typically involves two parts:

1. Base Case: A condition that stops the recursion. Without a base case, the recursion would continue indefinitely, leading to a stack overflow error.
2. Recursive Step: The part of the function where it calls itself with a modified input, moving closer to the base case.

How a Compiler Handles Recursive Code

When a compiler encounters recursive function calls, it needs to perform specific steps to ensure the code is translated and executed correctly. These steps involve managing the call stack.

• Creating a new frame on the call stack for the recursive call.
• Passing the modified input to the recursive call.
• The function then waits for the recursive call to return.

Step	Description
1. Function Definition	The compiler parses the recursive function definition, identifying the function name, parameters, and the recursive call.
2. Symbol Table Entry	An entry is created in the symbol table for the function, storing information like its name, parameters, and return type.
3. Call Stack Management	When a recursive function is called, a new frame is pushed onto the call stack. This frame stores the function's parameters, local variables, and the return address (the address to return to after the function completes).
4. Base Case Handling	The compiler checks if the base case condition is met. If it is, the function returns a value without making another recursive call.
5. Recursive Step Handling	If the base case is not met, the function executes the recursive step. This involves:
6. Return Value Propagation	Once the recursive call returns, its result is used to calculate the return value of the current function call. This value is then propagated back up the call stack.
7. Stack Unwinding	As each recursive call returns, its frame is popped off the call stack. This process continues until the initial function call returns, and the program can continue execution.

Example (Conceptual)

Consider a recursive function to calculate the factorial of a number:

$$ \text{factorial}(n) = \begin{cases} 1 & \text{if } n = 0 \text{ (base case)} \\ n \times \text{factorial}(n-1) & \text{if } n > 0 \text{ (recursive step)} \end{cases} $$

When the compiler encounters a call to factorial(3), it will:

1. Create a stack frame for factorial(3).
2. The base case (n=0) is not met.
3. It calls factorial(2), creating a new frame on top of the previous one.
4. The base case (n=0) is not met in factorial(2).
5. It calls factorial(1), creating another frame.
6. The base case (n=0) is not met in factorial(1).
7. It calls factorial(0), creating a frame.
8. The base case (n=0) is met.
9. factorial(0) returns 1.
10. factorial(1) returns 1 * 1 = 1.
11. factorial(2) returns 2 * 1 = 2.
12. factorial(3) returns 3 * 2 = 6.

The call stack unwinds, and the final result (6) is returned.