A. Consider the following algorithm segment: for i := 1 to 4, for j := 1 to i, [Statements in body of inner loop. None contain b

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A. Consider the following algorithm segment: for i := 1 to 4, for j := 1 to i, [Statements in body of inner loop. None contain b

ranching statements that lead outside the loop.] next j, next i. How many times will the inner loop be iterated when the algorithm is implemented and run?
b. Let n be a positive integer, and consider the following algorithm segment: for i := 1 to n, for j := 1 to i, [Statements in body of inner loop. None contain branching statements that lead outside the loop.], next j, next i. How many times will the inner loop be iterated when the algorithm is implemented and run?

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-03-04T00:52:00+03:00

Answer:

(a) 4i iterations

(b) "i × n" iterations

Step-by-step explanation:

(a) The provided algorithm segment shows:

for i:= 1 to 4, (Outer loop)

for j:= 1 to i (Inner loop)

next j,

next i

The inner loop executes i times while the outer loop completes 4 cycles.

The inner loop’s total execution when the full algorithm runs is:

= i × 4

= 4i iterations

(b) In the given algorithm segment;

for i:= 1 to n, (Outer loop)

for j:= 1 to i (Inner loop)

next j,

next i

where n denotes a set of positive integers.

= i × n

= "i × n" iterations

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