Question

How many times the operation BP will be executed? n is a positive number.

void fun (int n )
{
for (int i=0;ifor (int j=0;jexecute operation BP
}
A. O(n²)
B. O(i*n)
C. BP will never be executed
D. infinite number of times
E. Depends on the values of i and j
F. O(i*j)
G. O(n)
H. None of the answers provided is correct

Answer 1

Operation BP in the nested loops will be executed O(n²) times as the complexity of the function scales with the square of the size of the input n. The sum of the arithmetic series from 0 to n-1 contributes to this quadratic complexity.

Step-by-step explanation:

The question you've asked is about understanding how many times a certain operation, referred to as "operation BP", will be executed within a nested loop in a given function. The function you've provided is written in C or a C-like language and contains two nested loops. Usually, the outer loop runs "n" times, where "n" is the parameter of the function, and the inner loop runs "i" times for each iteration of the outer loop, where "i" varies from 0 to "n-1".

The operation BP will be executed for each iteration of the inner loop. Since the inner loop runs from 0 to "i-1" and the outer loop runs from 0 to "n-1", we can conclude that the operation BP will be executed for a total of 0+1+2+...+(n-1) times. This is a sum of an arithmetic series and equals n*(n-1)/2. Therefore, the number of times operation BP will be executed is of order O(n²), which represents the complexity of a function that scales with the square of the size of the input.

The correct answer to how many times the operation BP will be executed is A. O(n²).