Estimate the big$-$O complexity for each of these algorithms, and justify your answer.

To confirm your calculations, answers are provided at the end of the rubric. Your justification can be mathematical or written, formal or informal.

$1)$

for $($int i $=0$; i $<10$; i$++)\{$

sum$++$;

$\}$

Big$-$O Category

Justification $($why did you pick the way you did?$)$

$2)$

String strVar $=$Hello$$;

Int length $=$ strVar.length$()$;

for $($int j $=0$; j $<$ length; j$++)\{$

System.out.println$($strVar$.$charAt$($j$))$;

$\}$

Big$-$O Category

Justification $($why did you pick the way you did?$)$

$3)$

list : array of items

n : size of list

for $($i $=1$; i $<$ n; i$++)\{$

$/*$ set current element as minimum$*/$

min $=$ i

$/*$ check the element to be minimum $*/$

for $($j $=$ i$+1$; j $<$ n; j$++)\{$

if list$[$j$]<$ list$[$min$]$ then

min $=$ j;

$\}$

$/*$ swap the minimum element with the current element$*/$

if indexMin $!=$ i then

swap list$[$min$]$ and list$[$i$]$

$\}$

Big$-$O Category

Justification $($why did you pick the way you did?$)$

$4)$

k$=1$;

while $($k $<20)\{$

sum$++$;

avg$++$;

k$++$;

$\}$

Big$-$O Category

Justification $($why did you pick the way you did?$)$