Effective STL: Item 21: Always have comparison functions return

Let me show you something kind of cool. Create a set where less_equal

is the comparison type, then insert 10 into the set:

set<int, less_equal<int> > s; // s is sorted by “<=”

s.insert(10); // insert the value 10

Now try inserting 10 again:

s.insert(10);

For this call to insert, the set has to figure out whether 10 is already

present. We know that it is, but the set is dumb as toast, so it has to

check. To make it easier to understand what happens when the set

does this, we’ll call the 10 that was initially inserted 10 A and the 10

that we’re trying to insert 10 B .

The set runs through its internal data structures looking for the place

to insert 10 B . It ultimately has to check 10 B to see if it’s the same as

10 A . The definition of “the same” for associative containers is equiva-lence

(see Item 19), so the set tests to see whether 10 B is equivalent to

10 A . When performing this test, it naturally uses the set’s comparison

function. In this example, that’s operator<=, because we specified

less_equal as the set’s comparison function, and less_equal means oper-ator<=.

The set thus checks to see whether this expression is true:

!(10 A <= 10 B ) && !(10 B <= 10 A ) // test 10 A and 10 B for equivalence

Well, 10 A and 10 B are both 10, so it’s clearly true that 10 A <= 10 B .

Equally clearly, 10 B <= 10 A . The above expression thus simplifies to

!(true) && !(true)

and that simplifies to

false && false

which is simply false. That is, the set concludes that 10 A and 10 B are

not equivalent, hence not the same,and itthus goes aboutinserting

10 B into the container alongside 10 A . Technically, this action yields

undefined behavior, but the nearly universal outcome is that the set

ends up with two copies of the value 10, and that means it’s not a set

any longer. By using less_equal as our comparison type, we’ve cor-rupted

the container! Furthermore, any comparison function whereഊequal values return true will do the same thing. Equal values are, by

definition, not equivalent! Isn’t that cool?

Okay, maybe your definition of cool isn’t the same as mine. Even so,

you’ll still want to make sure that the comparison functions you use

for associative containers always return false for equal values. You’ll

need to be vigilant, however. It’s surprisingly easy to run afoul of this

constraint.

For example, Item 20 describes how to write a comparison function

for containers of string* pointers such that the container sorts its con-tents

by the values of the strings insteadofthe valuesofthepointers.

That comparison function sorts them in ascending order, but let’s

suppose you’re in need of a comparison function for a container of

string* pointers that sorts in descending order. The natural thing to do

is to grab the existing code and modify it. If you’re not careful, you

might come up with this, where I’ve highlighted the changes to the

code in Item 20:

struct StringPtrGreater: // highlights show how

public binary_function<const string*, // this code was changed

const string*, // from page 89. Beware,

bool> { // this code is flawed!

bool operator()(const string *ps1, const string *ps2) const

{

return !( *ps1 < *ps2); // just negate the old test;

} // this is incorrect!

};

The idea here is to reverse the sort order by negating the test inside

the comparison function. Unfortunately, negating “<” doesn’t give you

“>” (which is what you want), it gives you “>=”. And you now under-stand

that “>=”, because it will return true for equal values, is an

invalid comparison function for associative containers.

The comparison type you really want is this one:

struct StringPtrGreater: // this is a valid

public binary_function<const string*, // comparison type for

const string*, // associative containers

bool> {

bool operator()(const string *ps1, const string *ps2) const

{

return *ps2 < *ps1; // return whether *ps2

} // precedes *ps1 (i.e., swap

// the order of the

}; // operands)ഊTo avoid falling into this trap, all you need to remember is that the

return value of a comparison function indicates whether one value

precedes another in the sort order defined by that function. Equal val-ues

never precede one another, so comparison functions should

always return false for equal values.

Sigh.

I know what you’re thinking. You’re thinking, “Sure, that makes sense

for set and map, because those containers can’t hold duplicates. But

what about multiset and multimap? Those containers may contain

duplicates, so what do I care if the container thinks that two objects of

equal value aren’t equivalent? It will store them both, which is what

the multi containers are supposed to do. No problem, right?”

Wrong. To see why, let’s go back to the original example, but this time

we’ll use a multiset:

multiset<int, less_equal<int> > s; // s is still sorted by “<=”

s.insert(10); // insert 10 A

s.insert(10); // insert 10 B

s now has two copies of 10 in it, so we’d expect that if we do an

equal_range on it, we’ll get back a pair of iterators that define a range

containing both copies. But that’s not possible. equal_range,itsname

notwithstanding, doesn’t identify a range of equal values, it identifies

a rangeofequivalent values. In this example, s’s comparison function

says that 10 A and 10 B are not equivalent, so there’s no way that both

can be in the range identified by equal_range.

You see? Unless your comparison functions always return false for

equal values, you break all standard associative containers, regard-less

of whether they are allowed to store duplicates.

Technically speaking, comparison functions used to sort associative

containers must define a “strict weak ordering” over the objects they

compare. (Comparison functions passed to algorithms like sort (see

Item 31) are similarly constrained.) If you’re interested in the details of

what it means to be a strict weak ordering, you can find them in many

comprehensive STL references, including Josuttis’ The C++ Standard

Library [3], Austern’s Generic Programming and the STL [4], and the

SGI STL Web Site [21]. I’ve never found the details terribly illuminat-ing,

but one of the requirements of a strict weak ordering bears

directly on this Item. That requirement is that any function defining a

strict weak ordering must return false if it’s passed two copies of the

same value.

Hey! That is this Item!