Question

Find an expression in terms of n for the exact number of times

the ""Hello"" message is printed by the following system of
loops.
a. for k ← 1 to n − 1 do
b. print ""Hello""
c. for j ← k to n − 1 do
d. print

Answer 1

The expression in terms of n for the exact number of times the "Hello" message is printed can be represented as n(n - 1) / 2.

Step-by-step explanation:

The expression in terms of n for the exact number of times the "Hello" message is printed by the system of loops can be found by evaluating the sum of the number of times the inner loop runs for each iteration of the outer loop. Let's break down the steps:

1. The outer loop runs from k = 1 to n - 1. This means it will run (n - 1) - 1 + 1 = n - 1 times.
2. For each iteration of the outer loop, the inner loop runs from j = k to n - 1. The number of times the inner loop runs can be calculated as (n - 1) - k + 1 = n - k.
3. Since the "Hello" message is printed once in each iteration of the inner loop, the total number of times it is printed in one iteration of the outer loop is n - k.

Therefore, the expression in terms of n for the exact number of times the "Hello" message is printed can be represented as:

n - 1 + n - 2 + n - 3 + ... + 2 + 1

This simplifies to:

n(n - 1) / 2