How is the time and computational complexity of an algorithm determined?

The time and computational complexity of an algorithm is determined by analyzing the number of operations the algorithm performs depending on the size of the input data.

• Time complexity shows how the execution time of the algorithm changes as the volume of data increases. It is usually expressed in Big O notation (e.g., O(n), O(n²)).

• Computational (space) complexity reflects how much memory the algorithm requires to process data.

To estimate complexity, cycles, recursion, and nested operations are analyzed. For example, if an algorithm has one loop over n elements, the time complexity is O(n). If there are two nested loops over n, then O(n²).

Example:

# Time complexity O(n)
def sum_list(lst):
    total = 0
    for item in lst:
        total += item
    return total

Here, the execution time grows linearly with the size of the list.