Problem $3$:

$1.$For each of the following algorithms, in

$2.$dicate $($i$)$a natural size metric for its

inputs, $($ii$)$its basic operation, and $($iii$)$whether the basic operation count can

be different for inputs of the same size:

a$.$computing the sum of n numbers

b$.$computing n$!$

c$.$finding the largest element in a list of n numbers

d$.$Euclid$$s algorithm

e$.$sieve of Eratosthenes

f$.$pen$-$and$-$pencil algorithm for multiplying two n$-$digit decimal integers

Problem $4$

$2.$a$.$Consider the definition$-$based algorithm for adding two n $\backslash$times n matrices.

What is its basic operation? How many times is it performed as a function

of the matrix order n$?$As a function of the total number of elements in the

input matrices?

b$.$Answer the same questions for the definition$-$based algorithm for matrix

multiplication.