What is the time complexity for this problem in Python?

Question

I have the following code that checks if the sum of three positions in an array v of integers is equal to a given number x .

def triplet(array, sum):

    array_size = len(array) # 1

    for i in range( 0, array_size-2): 

        for j in range(i + 1, array_size-1):  

            for k in range(j + 1, array_size): 
                if array[i] + array[j] + array[k] == sum: 
                    return True # 1

    return False # 1

What would be the time complexity of the nested loops inside the code as well as the worst-case complexity? As far as I understand, the worst-case complexity for the whole function is O(n^3) since the function needs to perform a linear time operation for each value in the input data. Is that correct?

I have commented out the lines with the constant complexity as # 1 . What would be the time complexity for other individual for loops as well as for the if condition in the last for loop?

Answer 1

The time complexity is O(n^3).

To calculate it you have to add up how many machine instructions it will execute as a function of the size of its input, and then simplify the expression to the largest (when N is very large) term and can include any simplifying constant factor.

For reference and deeper explanation check out->

How to find time complexity of an algorithm