Question $8$

Both of the following algorithms, A and B$,$ calculate the sum of the elements of the diagonal of a square matrix.

$345678910111213141516171812$

M: square matrix

N: number of rows $($columns$)$ of M

function A$($M$,$N$)$

sum$=0$

for $0<=$ i $<$ N

for $0<=$ j $<$ N

if i$=$j

sum $=$ sum $+$ M$[$i$,$j$]$

return sum

Which algorithm would you recommend to implement? Why?

$10$ points

algorithm A$,$ because its time complexity $$

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Theta$($N$)$ is lower than the complexity of algorithm B $$

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Theta$($N

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any of them, because both have the same time complexity $$

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algorithm B$,$ because its time complexity $$

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Theta$($N$)$ is lower than the complexity of algorithm A $$

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$2$

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Theta$($N

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none of the others

any of them, because both have the same time complexity $$

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Theta$($N$)$