Resource Management in Action
- Topological Sort
- Resource-Management Approach
- Conclusion
- Bibliography
Resource management pops up in virtually every nontrivial programming exercise. Not long ago, I had the opportunity to listen to an interesting talk given by Andrew Koenig at the C++ World conference. He spoke about the standard library and, to round things up, gave an example of a simple implementation of a topological sort. What made the implementation simple and elegant was the use of the facilities of the standard library—string, vectors, maps, and iterators.
I liked his implementation, but it wasn't the kind of solution I would have come up with. In particular, it cleverly avoided all memory-management problems. Obviously, if you can avoid memory management, you should. But that's not always possible—and besides, it's not always most efficient. I started thinking about an alternative approach that would deal explicitly with the problems of allocating and deallocating objects.
I'll first describe the implementation based on Andrew Koenig's talk (I call it string-based) and then transform it into a more explicitly resource-management–based solution. In the process, I'll explain some of the tradeoffs and unveil some of the resource-management tricks of the standard library.
I would like to thank Andrew Koenig for letting me use his example and discussing the tradeoffs with me.
Topological Sort
Here's a short description of the problem. The program is given a list of pairs of strings. The second element of each pair, the successor, is meant to depend on the first element of the pair, the predecessor. After reading all the pairs, the program outputs the strings in an order that fulfills the following condition: No successor is output before its predecessor. There could be many acceptable orderings, or, in the case of cyclic dependencies, there could be none. In the latter case, the program should print the appropriate failure message.
This problem arises whenever you have to schedule several interdependent tasks. For instance, you might think of the process of dressing—putting on a shirt, pants, socks, shoes, and so on. Some of these items can be put on in any order; others depend on each other. For instance, it's impractical to put on shoes before putting on socks. The dependencies between various items of clothing can be expressed as a list of pairs, like this:
LeftSock LeftShoe RightSock RightShoe Pants LeftShoe Pants RightShoe
Our program, given a list like that, should produce the output that describes one possible order of putting on various items of dress. For instance, this list fulfills the constraints of our problem:
LeftSock RightSock Pants LeftShoe RightShoe
The algorithm that creates such a list, given a list of dependencies, is called a topological sort. Here's how it works.
For each item, store a count of predecessors and a list of successors. For instance, for Pants you'd store zero predecessors and a list of LeftShoe, RightShoe as successors. For LeftShoe, you'd count one predecessor (LeftSock) and store an empty list of successors, and so on. Items whose predecessor count is zero can be immediately output—they have no dependencies. Each time you output such an item, go through its list of successors and decrement their predecessor count. Again, those items whose predecessor count goes to zero are ready to be output. You know you've been successful if you're able to output all items using this procedure.
String-Based Approach
This is my version of Andrew Koenig's implementation. The information about each item is stored inside the Item object. It's just a count of predecessors and a list of successors, together with methods to manipulate and access them:
class Item
{
public:
typedef vector<string>::iterator iter;
Item () : _predCount (0) {}
int PredCount () const { return _predCount; }
void IncPred () { _predCount++; }
void DecPred () { _predCount--; }
void AddSucc (string str)
{
_succ.push_back (str);
}
iter begin () { return _succ.begin (); }
iter end () { return _succ.end (); }
private
int _predCount;
vector<string> _succ;
};
Notice that successors are stored by name in a vector of strings. Access to successors is given by means of an iterator. It's a standard vector iterator that we typedef'd for convenience to Item::iter.
The name of the item itself is not stored in the Item. That's because the main data structure in this implementation is a standard map that maps names to Items.
Here's how this map is filled with the initial data:
void InputData (map<string, Item> & itemMap)
{
string pred, succ;
while (cin >> pred >> succ)
{
itemMap [pred].AddSucc (succ);
itemMap [succ].IncPred ();
}
}
An important point to remember, when dealing with maps, is that the mere action of subscripting a map creates a new entry, if one is not already there. In such a case, the default constructor is used to initialize the Item.
After filling the map with string/item pairs, we create a vector, zeroes, of items whose predecessor count is zero. Again, notice that items are stored in this vector by name, using strings. These items are ready to be output at any time, since they have no dependencies:
vector<string> zeroes;
map<string, Item>::iterator it;
for (it = itemMap.begin (); it != itemMap.end (); ++it)
{
pair<string, Item> p = *it;
if (p.second.PredCount () == 0)
zeroes.push_back (p.first);
}
The map iterator returns key/value pairs. You access the key part of the pair as its first element, and the value part as its second element. In our case, the key is a string and the value is an Item.
Now we're ready to start outputting the elements. We pop them from our vector of zeroes. Notice that it's a two-step process—we access the top element of the vector using back, and destroy it using pop_back. The standard library is designed in such a way that the method pop_back doesn't return the popped element.
After an element has been output, we go through its list of successors and decrement their respective predecessor counts. Those items whose predecessor counts go to zero become ready to be output during the following iterations. We add them to our vector of zeroes:
int count = 0;
while (zeroes.size () != 0)
{
string str = zeroes.back ();
cout << str << endl;
count++;
zeroes.pop_back ();
// Iterate over successors
Item & item = itemMap [str];
for (Item::iter itSuc = item.begin ();
itSuc != item.end (); ++itSuc)
{
Item & suc = itemMap [*itSuc];
suc.DecPred ();
if (suc.PredCount () == 0)
zeroes.push_back (*itSuc);
}
}
Finally, the measure of our success is the equality between the original number of items in the map and the number of items that we have output:
return count == itemMap.size ();
Discussion
This is an elegant and reasonably efficient implementation of a topological sort. But there's something very non–C about it. Notice the way items are indirectly addressed using strings. The traditional C way would be to use pointers. Why isn't the list of successors, for instance, implemented as a vector of pointers? Same with the vector of zeroes. Pointer implementation would eliminate all these redundant map lookups. Innocent-looking statements like this are not what they seem:
Item & suc = itemMap [*itSuc];
Indexing into a map is not a constant-time operation. It's not a big deal—a log-time search in a balanced tree involving some string comparisons. But do we really have to sacrifice performance, and for what reason?
C programmers are usually very aware of little inefficiencies like these. So there must have been a good reason why this solution was chosen. Well, do you see any explicit memory allocation in this whole program? There is none! All the resource management is done behind the scenes. The design of this program was influenced by the attempt to avoid dealing with dynamic resources. It was possible to attain this goal by judicious use of value semantics and a very clever resource-management scheme implemented by the standard library's string. In fact, most implementations of the standard string come very close to what other languages call garbage collection.
Standard containers were designed to work with values. In this program, both items and strings are being internally treated as values—they're copied and passed around as if they were integers or doubles. For instance, when necessary, the map allocates a node with enough room to hold a string and an Item. The string is then copied into its space and the Item initialized using its default constructor. Since the map was designed to take care of the management of its nodes, the client doesn't have to worry about any allocations or deallocations.
In terms of resource management, the usual implementation of the standard string is in terms of a strong reference-counting pointer with a twist. Internally it contains a pointer to the actual storage area for the characters. This storage area has room for reference count (in most implementations, it's in the same array at offset –1). So whenever you're passing a string "by value," or assigning it to another string, you're not actually copying the characters—you're just incrementing their reference count.
The twist is that the characters are copied when you're trying to write into a string whose internal storage is shared with other strings. This is called copy-on-write, or COW for short. From the clients' point of view, it looks like they're always dealing with separate copies of strings, but they only pay the cost of copying when it actually matters. The downside of this scheme is that such behind-the-scenes manipulations of shared data might get ugly when multiple threads are involved. Synchronizing access at such a low level might be costly.