Question 1

Consider the following algorithm:

sum = 0

For j starting at 1 and ending with 13: sum = sum + (8*j + 4) print(sum)

What is printed as a result of executing this algorithm?

Question 2

Consider the following algorithm:

g₁ = 5

g₂ = 9

For k starting at 3 and ending with 8:

g_k = (k-1)g_k-1 + g_k-2

What is the last term, g₈, of the recursive sequence generated as a result of executing this algorithm?

Question 3

Suppose a computer program has been initialized such that the following sets have been stored for use in any algorithm:

A = {1, 2, 3, ..., 49} B = {-7, -6, -5, ..., 28}

Consider the following algorithm, which represents one part of the whole computer program (comments may occur after the # symbol on any line and are not used in computations):

#Part 1: computes A - B and its cardinality

AminusB = set() for element in A: # this line runs through every element in A if not(element in B): #A - B is the set of elements that are in A and are not in B AminusB.add(element) # Add to AminusB every element in A if the element is also not in B

n = len(AminusB) #len() returns the number of elements in the array print(n)

What value is printed as a result of executing this algorithm?

Question 4

Consider the following algorithm:

g₁ = 7

g₂ = 4

for k > 2:

g_k = (k-1)g_k-1 - g_k-2

What is term g₆of the recursive sequence generated as a result of executing this algorithm?

Question 5

Consider the following algorithm:

sum = 0

for j in range(1,16): sum = sum + (8*j - 3) print(sum)

What is printed as a result of executing this algorithm?