$(12$ 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 n$>=3$

$($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.