P$5.(25$ points$)$ Write a function int follow$\_$path$($link root, int $*$ A$,$ int F$)$ that takes as

arguments a tree $($given by the root node, root$),$ an array, A$,$ and a number, F$,$ and returns the item found in the

tree, following the path given by the first F elements of A:

$-$ if you see a $0$ in A$,$ go left in the tree;

$-$ if you see a $1$ in A go right in the tree.

Continue the same way. For the function calls below, assume that root is pointing to the root, $8,$ of the tree

below.

$8$

$-$ follow$\_$path $($root$,[0,1],2)$ returns $3($from root, go left, then right$)$

$-$ follow$\_$path $($root$,[1,0],2)$ returns $4$

$-$ follow$\_$path $($root$,[0,1,1,0],2)$ returns $3$

$-$ follow$\_$path $($root$,[1],1)$ returns $5$

$-$ follow$\_$path $($root$,[0,1],0)$ returns $8$

$0$

$95$

$2$

You can only assume that A has at least F elements in it whenever it is called.

$1$

$3$

$4$

If anything goes wrong in the function call, it should return $-1.$

$5$

$7$

$4$

You can use a helper function if you want. The nodes and links are defined as follows:

typedef struct node $*$ link;

struct node$\{$

int data;

link left;

link right;

$(6$ points$)$ What special cases are there? Focus especially on cases that can crash your code. Give an

example $($function call and tree$)$ that show each special case.

$\}$;

a$)$ b$)(4$ points$)$ Fill in the time complexity of the code you wrote for part c$).($If needed, you can assume the

tree has N nodes in total.$)$

O $(\_\_\_\_\_\_\_\_\_\_\_\_)$

c$)(15$ points$)$ Write the complete code for the function. It should deal with the special cases that you

mentioned. Each line or section that deals with a special case, should clearly indicate what case it deals

with.