Can you explain what the term 'O big' means in the context of algorithm theory?

The term "Big O" notation is used to describe the asymptotic estimate of an algorithm's complexity, that is, how the execution time or memory usage grows depending on the size of the input data. For example, if an algorithm has a complexity of O(n), it means that the execution time grows linearly with the increase in input size n.

Big O helps compare algorithms in terms of efficiency, ignoring constants and less significant terms. Main complexity classes:

• O(1) — constant time
• O(log n) — logarithmic
• O(n) — linear
• O(n log n) — linear-logarithmic
• O(n²), O(n³) — polynomial
• O(2^n), O(n!) — exponential

Example in Python:

# Searching for an element in a list — O(n)
def find_element(lst, target):
    for item in lst:
        if item == target:
            return True
    return False

Here, the execution time grows proportionally to the length of the list.