To implement recursion in MATLAB functions, follow these steps and consider

To implement recursion in MATLAB functions, follow these steps and considerations:

1. Function Structure

• Define the function in an .m file with the same name as the function.
• Use the function keyword, specifying input and output arguments.

2. Base Case

• Identify the simplest instance of the problem (base case) which can be solved directly without recursion.
• Ensure the function checks for the base case first to terminate the recursion.

3. Recursive Call

• For non-base cases, call the function itself with modified parameters that progress toward the base case.

Example: Factorial Calculation

function result = my_factorial(n)
    if n == 0
        result = 1; % Base case
    else
        result = n * my_factorial(n - 1); % Recursive call
    end
end

Example: Fibonacci Sequence

function fib = my_fibonacci(n)
    if n == 0
        fib = 0; % Base case 1
    elseif n == 1
        fib = 1; % Base case 2
    else
        fib = my_fibonacci(n-1) + my_fibonacci(n-2); % Recursive calls
    end
end

4. Considerations

• Recursion Depth: MATLAB has a default recursion limit (500). Adjust with set(0, 'RecursionLimit', N) cautiously.
• Efficiency: Recursive methods can be inefficient (e.g., Fibonacci). Consider iteration or memoization for optimization.
• Edge Cases: Handle inputs like n = 0 or negative numbers to avoid errors.

Example: Sum of First N Natural Numbers

function total = sum_n(n)
    if n <= 0
        total = 0; % Handles edge cases
    elseif n == 1
        total = 1; % Base case
    else
        total = n + sum_n(n - 1); % Recursive call
    end
end

5. Advanced Example: Towers of Hanoi

function hanoi(n, source, target, auxiliary)
    if n > 0
        hanoi(n-1, source, auxiliary, target);
        fprintf('Move disk %d from %s to %s\n', n, source, target);
        hanoi(n-1, auxiliary, target, source);
    end
end
% Call: hanoi(3, 'A', 'C', 'B')

Key Takeaways

• Base Cases: Essential to prevent infinite recursion.
• Parameter Adjustment: Each recursive call should move closer to the base case.
• Testing: Validate with small inputs and edge cases.
• Alternatives: Use iteration for deep recursion to avoid stack overflow.

By adhering to these principles, you can effectively implement recursive solutions in MATLAB