$1.$ When calling recursively, how does the stack manage the return address and local variables of each call? Please explain the relationship between recursion and stack.

$2.$ Consider the following code for recursive factorial calculation:

$```$

java

public static int factorial$($int n$)\{$

if $($n $==0)$ return $1$;

return n $*$ factorial$($n $-1)$;

$\}$

$```$

a$.$ Please draw a diagram of the function call stack when $\backslash (\backslash$mathrm$\{$n$\}=3\backslash ),$ showing the order and return process of each recursive call.

b$.$ Using the principle of the stack, explain the "stack overflow" phenomenon that may occur when large$-$scale recursive calls are made.

$3.$ What are the advantages and limitations of stacks and recursion? Please discuss the differences in their application in program design and give scenarios where each method is suitable.