How is the time complexity of inserting an element into a std::unordered_map container determined?

The time complexity of inserting an element into a std::unordered_map in average case is O(1) (constant time). This is achieved by using a hash table, where the element is placed into a bucket based on the hash of the key.

However, in the worst case, due to collisions and uneven hash distribution, the complexity can degrade to O(n), where n is the number of elements in the container, if all elements end up in one bucket.

Example of insertion:

#include <unordered_map>
#include <string>

int main() {
    std::unordered_map<std::string, int> map;
    map.insert({"key", 42}); // amortized O(1) insertion
    return 0;
}

Thus, std::unordered_map provides efficient average insertion, but depends on hash function quality and load factor.