Question

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 (ignoring comparisons used to test the conditions in the while or for loop). a) t := 0 for i := 1 to n for j := 1 to m t := t + i + j b) t := 0 for i := 1 to n t := t · 2 for j := 1 to m t := t + j c) t := 0 i := 1 while i ? n t := t - i i := i · 3

          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 (ignoring comparisons used to test the conditions in the while or for loop).

a)
t := 0
for i := 1 to n
for j := 1 to m
t := t + i + j

b)
t := 0
for i := 1 to n
t := t · 2
for j := 1 to m
t := t + j

c)
t := 0
i := 1
while i ? n
t := t - i
i := i · 3

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 (ignoring comparisons used to test the conditions in the while or for loop).

a)
t := 0
for i := 1 to n
for j := 1 to m
t := t + i + j

b)
t := 0
for i := 1 to n
t := t · 2
for j := 1 to m
t := t + j

c)
t := 0
i := 1
while i ? n
t := t - i
i := i · 3

Added by Melissa F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/21/2022

Step 1

In this segment, there are 2 operations for each iteration of the inner loop (i + j), and there are n * m total iterations of the inner loop. Therefore, the total number of operations in this segment is O(n * m). Show more…

Show all steps

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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 (ignoring comparisons used to test the conditions in the while or for loop). a) t := 0 for i := 1 to n for j := 1 to m t := t + i + j b) t := 0 for i := 1 to n t := t · 2 for j := 1 to m t := t + j c) t := 0 i := 1 while i ≤ n t := t - i i := i · 3