Question

How many times the operation inside the while loop will be executed? n is a positive number.

void fun (int n)
{int j=1;
while (ja) (n log n)
b) (j)
c) None of the answers are correct
d) ( log n)
e) (1)
f) (n * j)
g) (n)
h) (n/4)

Answer 1

The number of times the operation inside the while loop will be executed is
`\( \mathbf{(n \log n)} \).`

Step-by-step explanation:

The given while loop is conditioned on
`\(j \leq n \log n\), where \(j\)` starts at 1. The loop will continue executing as long as
`\(j\)` is less than or equal to
`\(n \log n\).` Initially,
`\(j\)` is 1, and it will increment by 1 in each iteration.

Therefore, the loop will run
`\(n \log n\)` times before the condition becomes false. The complexity of the loop is determined by the expression
`\(n \log n\),`indicating that the number of iterations is proportional to the product of
`\(n\)` and the logarithm of \(n\).

The choices (a)
`\((n \log n)\), (b) \((j)\), (d) \((\log n)\), (e) \((1)\), (f) \((n \cdot j)\), (g) \((n)\), and (h) \((n/4)\)`are all incorrect because they do not accurately represent the loop's iteration count. The correct answer is (c) ("None of the answers are correct") as the loop's complexity is
`\(n \log n\)`. In conclusion, the while loop will execute
`\(n \log n\)` times, making option (c) the accurate choice for the number of loop iterations.