**Problem : **
What does the following function do?

int mystery(int a, int b)
{
if (b==1) return a;
else return a + mystery(a, b-1);
}

How would you categorize it?

This function returns the result of multiplying two positive integers.
It is a linear recursive function (it only makes one call to itself).
Some might also consider it tail recursion, although technically the
last thing it does is add

`a` to the result of the function call, so
it isn't really.

**Problem : **
Suppose we wrote a function to see if a tree node is part of a tree whose
root has a specified name:

int root_named_x(tree_node_t *node, char* x)
{
if (strcmp(node->name, x) == 0) return 1;
else if (node->parent == NULL) return 0;
else return root_named_x(node->parent, x);
}

How would you categorize this function?

This function is linearly recursive, and is tail recursive. The last
thing it does if it makes a recursive call is to make the recursive call.

**Problem : **
Convert the following tail-recursive function into an iterative function:

int pow(int a, int b)
{
if (b==1) return a;
else return a * pow(a, b-1);
}

int pow(int a, int b)
{
int i, total=1;
for(i=0; i<b; i++) total *= a;
return total;
}

**Problem : **
What category would the following function fit into? How many function
calls will there be in total if the function is called with `func(10)`?

void func(int n)
{
if (n!=1) {
func(n-1);
func(n-1);
}
}

It is a binary recursive function. There will be 1023 function calls
(including the initial call

`func(10)`).

**Problem : **
Continuing from the last problem, with a call `func(10)`, how many
function calls will there be in total with the following function?

void func(int n)
{
if (n!=1) {
func(n-1);
func(n-1);
func(n-1);
}
}

There will be

3^{1}0 - 1 function calls.