Difference between member functions,non member functions and friend functions ?

In C++, we know that private members cannot be accessed from the outside class.
That is a non-member function cannot have an access to the private data of a class.
However there could be a situation where we would like two classes to share a particular function.
For example consider a case where two classes, manager and scientist have been defined.
We would like to use a function income_ tax () to operate on the objects of both these classes.
In such situation, C++ allows the common function to be made friendly with both the classes. Such a function needs not be member of any these classes.
To make outside function friendly to a class, we have to simply declare this function as a friend of a class as shown below:
Class ABC
{
……
…..
Public:
……..
……..
Friend void xyz (void); //declaration
};

When the function is logically coupled with the class (like your maze connectedness example)
When the function needs to access private or protected members, it's better to make it a member than a friend. when it's a generic function that can be templatized to naturally work on other classes (look at the header for good example) .