Can you explain what asymptotic complexity O means in algorithm analysis?

Asymptotic complexity, denoted as O (big O), describes how the running time or memory usage of an algorithm grows with respect to the size of the input data as this size approaches infinity. This allows for evaluating the efficiency of an algorithm without considering specific implementation details or hardware features.

For example, if an algorithm has a complexity of O(n), it means that the running time grows linearly with the increase in input data size n. If it is O(n²), the time grows proportionally to the square of n.

Example in C++:

// Find the maximum in an array in O(n)
int findMax(const std::vector<int>& data) {
    int maxVal = data[0];
    for (int val : data) {
        if (val > maxVal) maxVal = val;
    }
    return maxVal;
}

Here, the running time depends linearly on the size of the array, so the complexity is O(n).