Below are the pseudo codes of $3$ algorithms.

Alg$1($n$)$:

if n $=0$

return $1$

else

return $2*$Alg$1($n$-1)$

end

Alg$2($n$)$:

if n $=0$

return $1$

else

return Alg$2($n$-1)+$ Alg$2($n$-1)$

end

Alg$3($n$)$:

if n $=0$

return $1$

else

m$=[$n$/2]$

p$=$ Alg$3($m$)$

p$=$p$*$p

if n is odd

return $2*$p

else

return p

end

end

a$)$ What does each algorithm compute?

b$)$ What is the running time of each algorithm.