(a) Consider the following algorithm segment: for i :=1 to n for j := 1 to i a:= 5-i+8-j next j пеxt i How many additions and multiplications are performed when the inner loop of this algo- rithm segment is executed? How many additions and multiplications are performed when the entire algorithm segment is executed? (b) Find an order for this algorithm segment from among the following: log2 n, n, n - log2 n, n², n², and nª. Give a reason for your answer.
(a) Consider the following algorithm segment: for i :=1 to n for j := 1 to i a:= 5-i+8-j next j пеxt i How many additions and multiplications are performed when the inner loop of this algo- rithm segment is executed? How many additions and multiplications are performed when the entire algorithm segment is executed? (b) Find an order for this algorithm segment from among the following: log2 n, n, n - log2 n, n², n², and nª. Give a reason for your answer.
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![Express the following statement using N-notation.:
| 12(3r + 4
for all real numbers r > 2.
z+2
5.
Express the following statement using 0-notation:
| 12x*(3r | 1)|
< 36 ||
for all real numbers r> 2.
z+2
6.
Express the following statement using O-notation:
| 12*(3r + 4)|
s 36||
for all real numbers r> 2.
r+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2c468b4-e4ef-442f-9a01-985fb3fa35fd%2F7ab81c34-7c7e-47b3-9e6c-64b7b1a006f2%2Ff09fo9_processed.png&w=3840&q=75)
Transcribed Image Text:Express the following statement using N-notation.:
| 12(3r + 4
for all real numbers r > 2.
z+2
5.
Express the following statement using 0-notation:
| 12x*(3r | 1)|
< 36 ||
for all real numbers r> 2.
z+2
6.
Express the following statement using O-notation:
| 12*(3r + 4)|
s 36||
for all real numbers r> 2.
r+2
![(a) Find the total number of additions and multiplications that must be performed when the
following algorithm is executed. Show your work carefully.
for i := 1 to n
for j = i to n
a := 2 · (5 - i+j+ 1)
next j
next i
(b) Find an order for the algorithm segment of part (a) from among the following: log, n, n,
n- log, n, n², nº, and nº. Give a reason for your answer.
2.
(a) Consider the following algorithm segment:
for i := 1 to n
for j := 1 to i
ar:= 5.i+8.j
next j
next i
How many additions and multiplications are performed when the inner loop of this algo-
rithm segment is executed? How many additions and multiplications are performed when
the entire algorithm segment is executed?
(b) Find an order for this algorithm segment from among the following: log, n, n, n - log, n,
n2, nº, and n, Give a reason for your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2c468b4-e4ef-442f-9a01-985fb3fa35fd%2F7ab81c34-7c7e-47b3-9e6c-64b7b1a006f2%2Fxwzhbvt_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Find the total number of additions and multiplications that must be performed when the
following algorithm is executed. Show your work carefully.
for i := 1 to n
for j = i to n
a := 2 · (5 - i+j+ 1)
next j
next i
(b) Find an order for the algorithm segment of part (a) from among the following: log, n, n,
n- log, n, n², nº, and nº. Give a reason for your answer.
2.
(a) Consider the following algorithm segment:
for i := 1 to n
for j := 1 to i
ar:= 5.i+8.j
next j
next i
How many additions and multiplications are performed when the inner loop of this algo-
rithm segment is executed? How many additions and multiplications are performed when
the entire algorithm segment is executed?
(b) Find an order for this algorithm segment from among the following: log, n, n, n - log, n,
n2, nº, and n, Give a reason for your answer.
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