By what methods is the efficiency and complexity of an algorithm determined?

Efficiency and complexity of an algorithm are usually evaluated using analysis of time and space complexity.

• Time complexity indicates how the execution time of an algorithm depends on the size of the input data. It is usually expressed in Big O notation, for example, O(n), O(n²), O(log n).
• Space complexity reflects how much memory the algorithm requires depending on the size of the input data.

To determine complexity, the number of basic operations (such as comparisons, assignments) is analyzed in the worst, average, and best cases.

Example: Bubble sort has a time complexity of O(n²), as in the worst case, it requires about n² comparisons.

Efficiency can also be measured empirically by running the algorithm on different data volumes and measuring the time and memory consumption.