How is the efficiency of algorithmic solutions determined?

The efficiency of algorithmic solutions is usually determined by two main criteria: execution time (time complexity) and memory usage (space complexity). To evaluate time complexity, the notation "O" (Big O) is often used, which describes how the execution time of an algorithm grows with an increase in input size.

For example, the bubble sort algorithm has a time complexity of O(n²), which means that the execution time grows quadratically with the input size. Meanwhile, quicksort typically operates in O(n log n) on average.

An example of estimating time complexity in Python:

# Example: summing elements of a list
def sum_list(lst):
    total = 0
    for item in lst:
        total += item
    return total

The time complexity is O(n), where n is the length of the list.

Thus, the efficiency of an algorithm is determined by analyzing its time and space complexities, which allows for comparing algorithms and selecting optimal solutions for specific tasks.