I changed O(n²) as if it was O(n), but is it actually O(n²)?

Is the time complexity of nested for, while, and if statements the same? Suppose a is given as an array of length n.

for _ in range(len(a)):
    for _ in range(len(a)):
        do_something

The for statement above will be O(n²).

i = 0
while i < len(a) * len(a):
    do_something
    i += 1

At first glance, the above loop can be thought of as O(n), but in the end I think that it is also O(n²).

Am I right?

>Solution :

Am I right?

Yes!

The double loop:

for _ in range(len(a)):
    for _ in range(len(a)):
        do_something

has a time complexity of O(n) * O(n) = O(n²) because each loop runs until n.

The single loop:

i = 0
while i < len(a) * len(a):
    do_something
    i += 1

has a time complexity of O(n * n) = O(n²), because the loop runs until i = n * n = n².