When do we have to use copy constructors?

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The copy constructor generated by the compiler does member-wise copying. Sometimes that is not sufficient. For example:

class Class {
public:
    Class( const char* str );
    ~Class();
private:
    char* stored;
};

Class::Class( const char* str )
{
    stored = new char[srtlen( str ) + 1 ];
    strcpy( stored, str );
}

Class::~Class()
{
    delete[] stored;
}

in this case member-wise copying of stored member will not duplicate the buffer (only the pointer will be copied), so the first to be destroyed copy sharing the buffer will call delete[] successfully and the second will run into undefined behavior. You need deep copying copy constructor (and assignment operator as well).

Class::Class( const Class& another )
{
    stored = new char[strlen(another.stored) + 1];
    strcpy( stored, another.stored );
}

void Class::operator = ( const Class& another )
{
    char* temp = new char[strlen(another.stored) + 1];
    strcpy( temp, another.stored);
    delete[] stored;
    stored = temp;
}

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