Question

Let T(n) be the running time of function select_even. Find the equation of T(n) and find the complexity of T(n) using big-O notation.

def select_even(L):
output = []
for x in L:
if x%2==0:
output.append(x)
return output

Answer 1

def select_even(L):
    output = [] // 1
    for x in L: // n
        if x%2==0:  // k times. assuming there are k numbers in L list.
            output.append(x)    // 1
    return output   // 1

if there are n elements in L list, and k elements in the list.
x%2==0, indicates that x is even
so, T(n) = 2 + n + k.
we know that k <= n
so, T(n) <= 2+n+n
= 2+2n
hence time complexity is O(n)

Answer: O(n)