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I read C++ Primer, and it says function template specialization is an advanced topic, but I am totally lost. Can anybody offer an example why function template specialization is important and necessary?

Why don't function templates support partial specialization while class templates do? What's the underlying logic?

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Your question of why functions do not support partial specialization can be answered here. The code below shows how to implement the different specializations.

template<typename T>
bool Less(T a, T b)
{
    cout << "version 1 ";
    return a < b;
}
// Function templates can't be partially specialized they can overload instead.
template<typename T>
bool Less(T* a, T* b)
{
    cout << "version 2 ";
    return *a < *b;
}

template<>
bool Less<>(const char* lhs, const char* rhs)
{
    cout << "version 3 ";
    return strcmp(lhs, rhs) < 0;
}

int a = 5, b = 6;

cout << Less<int>(a, b) << endl;
cout << Less<int>(&a, &b) << endl;
cout << Less("abc", "def") << endl;

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