Question$1$

We saw that in the case that $p$ is $8,$ Core $0$ had $7$ receives and adds for algorithm $1($Core $0$ does all the additions

for global sum$)$ and $3$ for algorithm$2($tree$-5$tructured addition$).$

a$)$ Complete the following table with the numbers of receives and additions as $p$ varies

b$)$ Derive formulas $($based on p$)$ for the number of receives and additions that core $0$ carries out for algorithm $1$

and algorithm$2$