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Problem 3 : 1 . For each of the following algorithms, in 2 . dicate ( i ) a natural size metric for its inputs,

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.Euclids 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 \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.

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