Question $1(40$ points$)$

Find the computational complexity for the following four loops. You must explain and show your work for partial credit consideration

a$)$

int count $=0$;

for $($int $i=1$;$in$; $i++)$

for $($int $j=1$;$j1$;$j++)$

count$++$;

b$)$

int count $=0$;

for $($int $i=1$;$in$; $i=i**2)$

for $($int $j=1$;$jn$;$j++$

count$++$;

c$)$

int count $=0$;

for $($int $i=1$;$in$;$i=i**2)$

for $($int $j=1$;$ji$;$j++$

count$++$;