What methods do you use to determine the time complexity of an algorithm?

The determination of an algorithm's time complexity usually involves analyzing the number of operations the algorithm performs depending on the size of the input data (usually denoted as n).

Main methods:

1. Analytical approach — studying the algorithm's code and counting the number of basic operations depending on n. For example, if there is a nested loop iterating over n elements, the complexity will be approximately O(n²).

2. Using Big O notation — to estimate the asymptotic behavior of the algorithm, ignoring constants and less significant terms.

3. Experimental approach — measuring the execution time of the algorithm on input data of different sizes and plotting a graph of time versus n to empirically determine the complexity.

Example of analytical determination:

def example(arr):
    for i in range(len(arr)):
        for j in range(len(arr)):
            print(arr[i], arr[j])

Here, two nested loops over n elements, so the time complexity is O(n²).

Thus, to determine the time complexity, you need to understand how the number of operations grows with increasing input size.