Question 1

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is
pqr.
-Whatand 7 ×is 3,therespbestectivorderely?to form the product ABC if A, B and C are matrices with dimensions 2 × 5, 5 × 7

Accepted Answer

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Question 2

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-An algorithm that ﬁnds the average of n numbers by adding them and dividing by n.

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Question 3

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-$$\text { An iterative algorithm to compute } n ! \text {, (counting the number of multiplications). }$$

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Question 4

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-The number of print statements in the following: while $n > 1$
print "hello";
$$n : = \lfloor n / 2 \rfloor$$

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Question 5

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is
pqr.
-What is the most eﬃcient way to multiply the matrices $$\mathbf { A } _ { 1 } , \mathbf { A } _ { 2 } , \mathbf { A } _ { 3 } \text { of sizes } 10 \times 50,50 \times 10,10 \times 40 \text { ? }$$

Accepted Answer

The answer of assume that the number of multiplications of...

Question 6

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-An algorithm that prints all subsets of size three of the set {1, 2, 3, . . . , n}.

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Question 7

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is
pqr.
-Whatand 6 ×is 12,therespbestectivorderely?to form the product ABC if A, B and C are matrices with dimensions 8 × 3, 3 × 6

Accepted Answer

The answer of assume that the number of multiplications of...

Question 8

Give a big-O estimate for the number of operations (where an operation is an addition or a multiplication)
used in this segment of an algorithm: $$\begin{array} { l } 
t : = 1 \
\text { for } i = n \text { to } n ^ { 2 } \
t : = t + 2 i t
\end{array}$$

Accepted Answer

The answer of Give a big-O estimate for the number...

Question 9

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is
pqr.
-What is the most eﬃcient way to multiply the matrices $$\mathbf { A } _ { 1 } , \mathbf { A } _ { 2 } , \mathbf { A } _ { 3 } \text { of sizes } 20 \times 5,5 \times 50,50 \times 5 \text { ? }$$

Accepted Answer

The answer of assume that the number of multiplications of...

Question 10

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-The best-case analysis of a linear search of a list of size n (counting the number of comparisons).

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Question 11

Give a big-O estimate for the number of operations (where an operation is an addition or a multiplication)
used in this segment of an algorithm: $$\begin{array} { l } 
t : = 0 \
\text { for } i = 1 \text { to } n \
\quad \text { for } j = 1 \text { to } n \
\quad t : = ( i t + j t + 1 ) ^ { 2 }
\end{array}$$

Accepted Answer

The answer of Give a big-O estimate for the number...

Question 12

In questions ﬁnd the "best" big-O notation to describe the complexity of the algorithm. Choose your
answers from the following:
1, $$\log _ { 2 } n , n , n \log _ { 2 } n , n ^ { 2 } , n ^ { 3 } , \ldots , 2 ^ { n } , n !$$
-The worst-case analysis of a linear search of a list of size n (counting the number of comparisons).

Accepted Answer

The answer of In questions ﬁnd the "best" big-O notation...

Quiz 3: Algorithms

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is pqr. -Whatand 7 ×is 3,therespbestectivorderely?to form the product ABC if A, B and C are matrices with dimensions 2 × 5, 5 × 7

assume that the number of multiplications of entries used to multiply a p × q and a q × r matrix is pqr. -Whatand 6 ×is 12,therespbestectivorderely?to form the product ABC if A, B and C are matrices with dimensions 8 × 3, 3 × 6

Give a big-O estimate for the number of operations (where an operation is an addition or a multiplication) used in this segment of an algorithm: $\begin{array} { l } t : = 1 \\\text { for } i = n \text { to } n ^ { 2 } \\t : = t + 2 i t\end{array}$