$(12$ points$)$ Consider the definition.

$h(0)=0$

$h(1)=1$

$h(2)=2$

$h(n)=h(n-1)+h(n-2)+h(n-3)$ for $n3$

$($a$)$ Write a recursive function to compute $h,$ directly based on the defining equations.

$($b$)$ Is that algorithm efficient? Why or why not? Justify your answer.

If not, write one or more function$($s$)$ to implement a linear time $O(n)$ algorithm.