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

This algorithm generates the list of matches that must be

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

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

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

n $=$ a $.$ length

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

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

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$).$

Using the active operation approach, determine the time complexity of the pseudocode in question $5.$

Show all your work and express your final answer in big$-\backslash$Theta notation.