Question

Consider the following piece of code:

sum = 0;

for (i=1; i<= f(n); i++)

sum +=i;

where f (n) is a function call. Give a tight big-oh bound on the running of this piece of code as a function of n, on the assumption that

(a) The running time of f (n) is O(n), and the value of f (n) is n!

(b) The running time of f (n) is O(n), and the value of f (n) is n

(c) The running time of f (n) is O(n2), and the value of f(n) is n

(d) The running time of f (n) is O(1), and the value of f(n) is 0

Answer 1

Code:
--------
sum = 0;
for (i=1; i<= f(n); i++)
    sum +=i;


This code has a for loop running for f(n) times.
sum is total sum of all numbers between 1 and f(n)

Both the running time and value f(n) are same values.
(b) The running time of f (n) is O(n), and the value of f (n) is n

Option b