$.$ For each of the following program fragments:

a$.$ Give an analysis of the running time $($Big O will do$)$

b$.$ Implement the code in the language of your choice, and give the

running time for several values of N$.$

c$.$ Compare your analysis with the actual running times.

$1.$ sum $=0$;

for $($i $=0$; i $<$ n; $++$i$)$

$++$sum;

$2.$ sum $=0$;

for $($i $=0$; i $<$ n; $++$i$)$

for $($j $=0$; j $<$ n; $++$j$)$

$++$sum;

$3.$ sum $=0$;

for $($i $=0$; i $<$ n; $++$i$)$

for $($j $=0$; j $<$ n $*$ n; $++$j$)$

$++$sum;