Explain the principle of evaluating the execution time of operations using Big O notation in data structures.

Big O notation is used to estimate the asymptotic complexity of algorithms, that is, how the execution time of an operation changes as the size of the input data increases.

For example, if an operation has a complexity of O(1), the execution time does not depend on the size of the data — this is very efficient.

If the complexity is O(n), the time grows linearly with the size of the data.

For data structures, this helps understand how quickly operations can be performed:

• Searching in an array — O(n), since each element must be checked.
• Searching in a hash table — O(1) on average.
• Inserting into a balanced tree — O(log n).

Thus, Big O shows the upper bound of execution time, allowing comparison of the efficiency of different structures and algorithms without being tied to specific hardware.