Consider the following pseudocode:

$1$ Algorithm r o u n d R o b i n T o u r n a m e n t $($ a $)$

$2$ This algorithm generates the list of matches that must be

$3$ played in a round $-$ robin pirate $-$ dueling tournament $($ a tournament where

$4$ each pirate duels each other pirate exactly once $).$

$5$

$6$ a is an array of strings containing names of pirates in the tournament

$7$

$8$ n $=$ a $.$ length

$9$ for i $=0$ to n $-1$

$10$ for j $=$ i $+1$ to n $-1$

$11$ print a $[$ i $]+"$ duels $"+$ a $[$ j $]+",$ Yarrr $!"$

Note: the pseudocode for i $=$ a to b means that the loop runs for all values of i between a and b$,$ inclusive,

that is$,$ including the values a and b$.$

$($a$)(6$ points$)$ Use the statement counting approach to determine the exact number of statements that

are executed by this pseudocode as a function of n$.$ Show all of your calculations.

$($b$)(1$ point$)$ Express the answer you obtained in part a$)$ in big$-\backslash$Theta notation $($since$,$ again, the best and

worst cases are the same$)$