5: STL Algorithms

The other half of the STL is the algorithms, which are templatized functions designed to work with the containers (or, as you will see, anything that can behave like a container, including arrays and string objects).

The STL was originally designed around the algorithms. The goal was that you use algorithms for almost every piece of code that you write. In this sense it was a bit of an experiment, and only time will tell how well it works. The real test will be in how easy or difficult it is for the average programmer to adapt. At the end of this chapter you’ll be able to decide for yourself whether you find the algorithms addictive or too confusing to remember. If you’re like me, you’ll resist them at first but then tend to use them more and more.

Before you make your judgment, however, there’s one other thing to consider. The STL algorithms provide a vocabulary with which to describe solutions. That is, once you become familiar with the algorithms you’ll have a new set of words with which to discuss what you’re doing, and these words are at a higher level than what you’ve had before. You don’t have to say “this loop moves through and assigns from here to there ... oh, I see, it’s copying!” Instead, you say copy( ). This is the kind of thing we’ve been doing in computer programming from the beginning – creating more dense ways to express what we’re doing and spending less time saying how we’re doing it. Whether the STL algorithms and generic programming are a great success in accomplishing this remains to be seen, but that is certainly the objective.

A concept that is used heavily in the STL algorithms is the function object, which was introduced in the previous chapter. A function object has an overloaded operator( ), and the result is that a template function can’t tell whether you’ve handed it a pointer to a function or an object that has an operator( ); all the template function knows is that it can attach an argument list to the object as if it were a pointer to a function:

} ///:~

The template callFunc( ) says “give me an f and an x, and I’ll write the code f(x).” In main( ), you can see that it doesn’t matter if f is a pointer to a function (as in the case of g( )), or if it’s a function object (which is created as a temporary object by the expression UFunc( )). Notice you can only accomplish this genericity with a template function; a non-template function is too particular about its argument types to allow such a thing. The STL algorithms use this flexibility to take either a function pointer or a function object, but you’ll usually find that creating a function object is more powerful and flexible.

The function object is actually a variation on the theme of a callback, which is described in the design patterns chapter. A callback allows you to vary the behavior of a function or object by passing, as an argument, a way to execute some other piece of code. Here, we are handing callFunc( ) a pointer to a function or a function object.

The following descriptions of function objects should not only make that topic clear, but also give you an introduction to the way the STL algorithms work.

Just as the STL classifies iterators (based on their capabilities), it also classifies function objects based on the number of arguments that their operator( ) takes and the kind of value returned by that operator (of course, this is also true for function pointers when you treat them as function objects). The classification of function objects in the STL is based on whether the operator( ) takes zero, one or two arguments, and if it returns a bool or non-bool value.

Generator: Takes no arguments, and returns a value of the desired type. A RandomNumberGenerator is a special case.

UnaryFunction: Takes a single argument of any type and returns a value which may be of a different type.

BinaryFunction: Takes two arguments of any two types and returns a value of any type.

A special case of the unary and binary functions is the predicate, which simply means a function that returns a bool. A predicate is a function you use to make a true/false decision.

Predicate: This can also be called a UnaryPredicate. It takes a single argument of any type and returns a bool.

BinaryPredicate: Takes two arguments of any two types and returns a bool.

StrictWeakOrdering: A binary predicate that says that if you have two objects and neither one is less than the other, they can be regarded as equivalent to each other.

In addition, there are sometimes qualifications on object types that are passed to an algorithm. These qualifications are given in the template argument type identifier name:

LessThanComparable: A class that has a less-than operator<.

Assignable: A class that has an assignment operator= for its own type.

EqualityComparable: A class that has an equivalence operator== for its own type.

The STL has, in the header file <functional>, a set of templates that will automatically create function objects for you. These generated function objects are admittedly simple, but the goal is to provide very basic functionality that will allow you to compose more complicated function objects, and in many situations this is all you’ll need. Also, you’ll see that there are some function object adapters that allow you to take the simple function objects and make them slightly more complicated.

Here are the templates that generate function objects, along with the expressions that they effect.

Name	Type	Result produced by generated function object
plus	BinaryFunction	arg1 + arg2
minus	BinaryFunction	arg1 - arg2
multiplies	BinaryFunction	arg1 * arg2
divides	BinaryFunction	arg1 / arg2
modulus	BinaryFunction	arg1 % arg2
negate	UnaryFunction	- arg1
equal_to	BinaryPredicate	arg1 == arg2
not_equal_to	BinaryPredicate	arg1 != arg2
greater	BinaryPredicate	arg1 > arg2
less	BinaryPredicate	arg1 < arg2
greater_equal	BinaryPredicate	arg1 >= arg2
less_equal	BinaryPredicate	arg1 <= arg2
logical_and	BinaryPredicate	arg1 && arg2
logical_or	BinaryPredicate	arg1 || arg2
logical_not	UnaryPredicate	!arg1
not1( )	Unary Logical	!(UnaryPredicate(arg1))
not2( )	Binary Logical	!(BinaryPredicate(arg1, arg2))

The following example provides simple tests for each of the built-in basic function object templates. This way, you can see how to use each one, along with their resulting behavior.

} ///:~

To keep this example small, some tools are created. The print( ) template is designed to print any vector<T>, along with an optional message. Since print( ) uses the STL copy( ) algorithm to send objects to cout via an ostream_iterator, the ostream_iterator must know the type of object it is printing, and therefore the print( ) template must know this type also. However, you’ll see in main( ) that the compiler can deduce the type of T when you hand it a vector<T>, so you don’t have to hand it the template argument explicitly; you just say print(x) to print the vector<T> x.

The next two template functions automate the process of testing the various function object templates. There are two since the function objects are either unary or binary. In testUnary( ), you pass a source and destination vector, and a unary function object to apply to the source vector to produce the destination vector. In testBinary( ), there are two source vectors which are fed to a binary function to produce the destination vector. In both cases, the template functions simply turn around and call the transform( ) algorithm, although the tests could certainly be more complex.

For each test, you want to see a string describing what the test is, followed by the results of the test. To automate this, the preprocessor comes in handy; the T( ) and B( ) macros each take the expression you want to execute. They call that expression, then call print( ), passing it the result vector (they assume the expression changes a vector named r and br, respectively), and to produce the message the expression is “string-ized” using the preprocessor. So that way you see the code of the expression that is executed followed by the result vector.

The last little tool is a generator object that creates random bool values. To do this, it gets a random number from rand( ) and tests to see if it’s greater than RAND_MAX/2. If the random numbers are evenly distributed, this should happen half the time.

In main( ), three vector<int> are created: x and y for source values, and r for results. To initialize x and y with random values no greater than 50, a generator of type URandGen is used; this will be defined shortly. Since there is one operation where elements of x are divided by elements of y, we must ensure that there are no zero values of y. This is accomplished using the transform( ) algorithm, taking the source values from y and putting the results back into y. The function object for this is created with the expression:

bind2nd(plus<int>(), 1)

This uses the plus function object that adds two objects together. It is thus a binary function which requires two arguments; we only want to pass it one argument (the element from y) and have the other argument be the value 1. A “binder” does the trick (we will look at these next). The binder in this case says “make a new function object which is the plus function object with the second argument fixed at 1.”

Another of the tests in the program compares the elements in the two vectors for equality, so it is interesting to guarantee that at least one pair of elements is equivalent; in this case element zero is chosen.

Once the two vectors are printed, T( ) is used to test each of the function objects that produces a numerical value, and then B( ) is used to test each function object that produces a Boolean result. The result is placed into a vector<bool>, and when this vector is printed it produces a ‘1’ for a true value and a ‘0’ for a false value.

It’s common to want to take a binary function object and to “bind” one of its arguments to a constant value. After binding, you get a unary function object.

For example, suppose you want to find integers that are less than a particular value, say 20. Sensibly enough, the STL algorithms have a function called find_if( ) that will search through a sequence; however, find_if( ) requires a unary predicate to tell it if this is what you’re looking for. This unary predicate can of course be some function object that you have written by hand, but it can also be created using the built-in function object templates. In this case, the less template will work, but that produces a binary predicate, so we need some way of forming a unary predicate. The binder templates (which work with any binary function object, not just binary predicates) give you two choices:

bind1st(const BinaryFunction& op, const T& t);
bind2nd(const BinaryFunction& op, const T& t);

Both bind t to one of the arguments of op, but bind1st( ) binds t to the first argument, and bind2nd( ) binds t to the second argument. With less, the function object that provides the solution to our exercise is:

bind2nd(less<int>(), 20);

This produces a new function object that returns true if its argument is less than 20. Here it is, used with find_if( ):

} ///:~

The vector<int> a is filled with random numbers between 0 and max. find_if( ) finds the first element in a that satisfies the predicate (that is, which is less than 20) and returns an iterator to it (here, the type of the iterator is actually just int* although I could have been more precise and said vector<int>::iterator instead).

A more interesting algorithm to use is copy_if( ), which isn’t part of the STL but is defined at the end of this chapter. This algorithm only copies an element from the source to the destination if that element satisfies a predicate. So the resulting vector will only contain elements that are less than 20.

Here’s a second example, using a vector<string> and replacing strings that satisfy particular conditions:

} ///:~

This uses another pair of STL algorithms. The first, replace_copy_if( ), copies each element from a source range to a destination range, performing replacements on those that satisfy a particular unary predicate. The second, replace_if( ), doesn’t do any copying but instead performs the replacements directly into the original range.

A binder doesn’t have to produce a unary predicate; it can also create a unary function (that is, a function that returns something other than bool). For example, suppose you’d like to multiply every element in a vector by 10. Using a binder with the transform( ) algorithm does the trick:

} ///:~

Since the third argument to transform( ) is the same as the first, the resulting elements are copied back into the source vector. The function object created by bind2nd( ) in this case produces an int result.

The “bound” argument to a binder cannot be a function object, but it does not have to be a compile-time constant. For example:

} ///:~

Here, an array is filled with random numbers between 0 and 100, and the user provides a value on the command line. In the copy_if( ) call, you can see that the bound argument to bind2nd( ) is the result of the function call atoi( ) (from <cstdlib>).

Any place in an STL algorithm where a function object is required, it’s very conceivable that you’d like to use a function pointer instead. Actually, you can use an ordinary function pointer – that’s how the STL was designed, so that a “function object” can actually be anything that can be dereferenced using an argument list. For example, the rand( ) random number generator can be passed to generate( ) or generate_n( ) as a function pointer, like this:

} ///:~

The “iterators” in this case are just the starting and past-the-end pointers for the array v, and the generator is just a pointer to the standard library rand( ) function. The program repeatedly generates a group of random numbers, then it uses the STL algorithm count_if( ) and a predicate that tells whether a particular element is greater than RAND_MAX/2. The result is the number of elements that match this criterion; this is divided by the total number of elements and multiplied by 100 to produce the percentage of elements greater than the midpoint. If the random number generator is reasonable, this value should hover at around 50% (of course, there are many other tests to determine if the random number generator is reasonable).

The ptr_fun( ) adapters take a pointer to a function and turn it into a function object. They are not designed for a function that takes no arguments, like the one above (that is, a generator). Instead, they are for unary functions and binary functions. However, these could also be simply passed as if they were function objects, so the ptr_fun( ) adapters might at first appear to be redundant. Here’s an example where using ptr_fun( ) and simply passing the address of the function both produce the same results:

} ///:~

The goal of this program is to convert an array of char* which are ASCII representations of floating-point numbers into a vector<double>. After defining this array and the print( ) template (which encapsulates the act of printing a range of elements), you can see transform( ) used with atof( ) as a “naked” pointer to a function, and then a second time with atof passed to ptr_fun( ). The results are the same. So why bother with ptr_fun( )? Well, the actual effect of ptr_fun( ) is to create a function object with an operator( ). This function object can then be passed to other template adapters, such as binders, to create new function objects. As you’ll see a bit later, the SGI extensions to the STL contain a number of other function templates to enable this, but in the Standard C++ STL there are only the bind1st( ) and bind2nd( ) function templates, and these expect binary function objects as their first arguments. In the above example, only the ptr_fun( ) for a unary function is used, and that doesn’t work with the binders. So ptr_fun( ) used with a unary function in Standard C++ really is redundant (note that Gnu g++ uses the SGI STL).

With a binary function and a binder, things can be a little more interesting. This program produces the squares of the input vector d:

} ///:~

Here, ptr_fun( ) is indispensable; bind2nd( ) must have a function object as its first argument and a pointer to function won’t cut it.

A trickier problem is that of converting a member function into a function object suitable for using in the STL algorithms. As a simple example, suppose we have the “shape” problem and would like to apply the draw( ) member function to each pointer in a container of Shape:

} ///:~

The for_each( ) function does just what it sounds like it does: passes each element in the range determined by the first two (iterator) arguments to the function object which is its third argument. In this case we want the function object to be created from one of the member functions of the class itself, and so the function object’s “argument” becomes the pointer to the object that the member function is called for. To produce such a function object, the mem_fun( ) template takes a pointer to member as its argument.

The mem_fun( ) functions are for producing function objects that are called using a pointer to the object that the member function is called for, while mem_fun_ref( ) is used for calling the member function directly for an object. One set of overloads of both mem_fun( ) and mem_fun_ref( ) are for member functions that take zero arguments and one argument, and this is multiplied by two to handle const vs. non-const member functions. However, templates and overloading takes care of sorting all of that out; all you need to remember is when to use mem_fun( ) vs. mem_fun_ref( ).

Suppose you have a container of objects (not pointers) and you want to call a member function that takes an argument. The argument you pass should come from a second container of objects. To accomplish this, the second overloaded form of the transform( ) algorithm is used:

} ///:~

Because the container is holding objects, mem_fun_ref( ) must be used with the pointer-to-member function. This version of transform( ) takes the start and end point of the first range (where the objects live), the starting point of second range which holds the arguments to the member function, the destination iterator which in this case is standard output, and the function object to call for each object; this function object is created with mem_fun_ref( ) and the desired pointer to member. Notice the transform( ) and for_each( ) template functions are incomplete; transform( ) requires that the function it calls return a value and there is no for_each( ) that passes two arguments to the function it calls. Thus, you cannot call a member function that returns void and takes an argument using transform( ) or for_each( ).

Any member function works, including those in the Standard libraries. For example, suppose you’d like to read a file and search for blank lines; you can use the string::empty( ) member function like this:

} ///:~

The blank( ) function uses find_if( ) to locate the first blank line in the given range using mem_fun_ref( ) with string::empty( ). After the file is opened and read into the list, blank( ) is called repeated times to find every blank line in the file. Notice that subsequent calls to blank( ) use the current version of the iterator so it moves forward to the next one. Each time a blank line is found, it is replaced with the characters “A BLANK LINE.” All you have to do to accomplish this is dereference the iterator, and you select the current string.

The SGI STL (mentioned at the end of the previous chapter) also includes additional function object templates, which allow you to write expressions that create even more complicated function objects. Consider a more involved program which converts strings of digits into floating point numbers, like PtrFun2.cpp but more general. First, here’s a generator that creates strings of integers that represent floating-point values (including an embedded decimal point):

#endif // NUMSTRINGGEN_H ///:~

You tell it how big the strings should be when you create the NumStringGen object. The random number generator is used to select digits, and a decimal point is placed in the middle.

The following program (which works with the Standard C++ STL without the SGI extensions) uses NumStringGen to fill a vector<string>. However, to use the Standard C library function atof( ) to convert the strings to floating-point numbers, the string objects must first be turned into char pointers, since there is no automatic type conversion from string to char*. The transform( ) algorithm can be used with mem_fun_ref( ) and string::c_str( ) to convert all the strings to char*, and then these can be transformed using atof:

} ///:~

The SGI extensions to the STL contain a number of additional function object templates that accomplish more detailed activities than the Standard C++ function object templates, including identity (returns its argument unchanged), project1st and project2nd (to take two arguments and return the first or second one, respectively), select1st and select2nd (to take a pair object and return the first or second element, respectively), and the “compose” function templates.

If you’re using the SGI extensions, you can make the above program denser using one of the two “compose” function templates. The first, compose1(f1, f2), takes the two function objects f1 and f2 as its arguments. It produces a function object that takes a single argument, passes it to f2, then takes the result of the call to f2 and passes it to f1. The result of f1 is returned. By using compose1( ), the process of converting the string objects to char*, then converting the char* to a floating-point number can be combined into a single operation, like this:

} ///:~

You can see there’s only a single call to transform( ) now, and no intermediate holder for the char pointers.

The second “compose” function is compose2( ), which takes three function objects as its arguments. The first function object is binary (it takes two arguments), and its arguments are the results of the second and third function objects, respectively. The function object that results from compose2( ) expects one argument, and it feeds that argument to the second and third function objects. Here is an example:

} ///:~

The vector<int> v is first filled with random numbers. To cut these down to size, the transform( ) algorithm is used to divide each value by RAND_MAX/100, which will force the values to be between 0 and 100 (making them more readable). The copy_if( ) algorithm defined later in this chapter is then used, along with a composed function object, to copy all the elements that are greater than or equal to 30 and less than or equal to 40 into the destination vector<int> r. Just to show how easy it is, r is sorted, and then displayed.

The arguments of compose2( ) say, in effect:

(x >= 30) && (x <= 40)

You could also take the function object that comes from a compose1( ) or compose2( ) call and pass it into another “compose” expression ... but this could rapidly get very difficult to decipher.

Instead of all this composing and transforming, you can write your own function objects (without using the SGI extensions) as follows:

} ///:~

There are a few more lines of code, but you can’t deny that it’s much clearer and easier to understand, and therefore to maintain.

We can thus observe two drawbacks to the SGI extensions to the STL. The first is simply that it’s an extension; yes, you can download and use them for free so the barriers to entry are low, but your company may be conservative and decide that if it’s not in Standard C++, they don’t want to use it. The second drawback is complexity. Once you get familiar and comfortable with the idea of composing complicated functions from simple ones you can visually parse complicated expressions and figure out what they mean. However, my guess is that most people will find anything more than what you can do with the Standard, non-extended STL function object notation to be overwhelming. At some point on the complexity curve you have to bite the bullet and write a regular class to produce your function object, and that point might as well be the point where you can’t use the Standard C++ STL. A stand-alone class for a function object is going to be much more readable and maintainable than a complicated function-composition expression (although my sense of adventure does lure me into wanting to experiment more with the SGI extensions...).

As a final note, you can’t compose generators; you can only create function objects whose operator( ) requires one or two arguments.

This section provides a quick reference for when you’re searching for the appropriate algorithm. I leave the full exploration of all the STL algorithms to other references (see the end of this chapter, and Appendix XX), along with the more intimate details of complexity, performance, etc. My goal here is for you to become rapidly comfortable and facile with the algorithms, and I will assume you will look into the more specialized references if you need more depth of detail.

Although you will often see the algorithms described using their full template declaration syntax, I am not doing that here because you already know they are templates, and it’s quite easy to see what the template arguments are from the function declarations. The type names for the arguments provide descriptions for the types of iterators required. I think you’ll find this form is easier to read, while you can quickly find the full declaration in the template header file if for some reason you feel the need.

The names of the iterator classes describe the iterator type they must conform to. The iterator types were described in the previous chapter, but here is a summary:

InputIterator. You (or rather, the STL algorithm and any algorithms you write that use InputIterators) can increment this with operator++ and dereference it with operator* to read the value (and only read the value), but you can only read each value once. InputIterators can be tested with operator== and operator!=. That’s all. Because an InputIterator is so limited, it can be used with istreams (via istream_iterator).

OutputIterator. This can be incremented with operator++, and dereferenced with operator* to write the value (and only write the value), but you can only dereference/write each value once. OutputIterators cannot be tested with operator== and operator!=, however, because you assume that you can just keep sending elements to the destination and that you don’t have to see if the destination’s end marker has been reached. That is, the container that an OutputIterator references can take an infinite number of objects, so no end-checking is necessary. This requirement is important so that an OutputIterator can be used with ostreams (via ostream_iterator), but you’ll also commonly use the “insert” iterators insert_iterator, front_insert_iterator and back_insert_iterator (generated by the helper templates inserter( ), front_inserter( ) and back_inserter( )).

With both InputIterator and OutputIterator, you cannot have multiple iterators pointing to different parts of the same range. Just think in terms of iterators to support istreams and ostreams, and InputIterator and OutputIterator will make perfect sense. Also note that InputIterator and OutputIterator put the weakest restrictions on the types of iterators they will accept, which means that you can use any “more sophisticated” type of iterator when you see InputIterator or OutputIterator used as STL algorithm template arguments.

ForwardIterator. InputIterator and OutputIterator are the most restricted, which means they’ll work with the largest number of actual iterators. However, there are some operations for which they are too restricted; you can only read from an InputIterator and write to an OutputIterator, so you can’t use them to read and modify a range, for example, and you can’t have more than one active iterator on a particular range, or dereference such an iterator more than once. With a ForwardIterator these restrictions are relaxed; you can still only move forward using operator++, but you can both write and read and you can write/read multiple times in each location. A ForwardIterator is much more like a regular pointer, whereas InputIterator and OutputIterator are a bit strange by comparison.

BidirectionalIterator. Effectively, this is a ForwardIterator that can also go backward. That is, a BidirectionalIterator supports all the operations that a ForwardIterator does, but in addition it has an operator--.

RandomAccessIterator. An iterator that is random access supports all the same operations that a regular pointer does: you can add and subtract integral values to move it forward and backward by jumps (rather than just one element at a time), you can subscript it with operator[ ], you can subtract one iterator from another, and iterators can be compared to see which is greater using operator<, operator>, etc. If you’re implementing a sorting routine or something similar, random access iterators are necessary to be able to create an efficient algorithm.

The names used for the template parameter types consist of the above iterator types (sometimes with a ‘1’ or ‘2’ appended to distinguish different template arguments), and may also include other arguments, often function objects.

When describing the group of elements that an operation is performed on, mathematical “range” notation will often be used. In this, the square bracket means “includes the end point” while the parenthesis means “does not include the end point.” When using iterators, a range is determined by the iterator pointing to the initial element, and the “past-the-end” iterator, pointing past the last element. Since the past-the-end element is never used, the range determined by a pair of iterators can thus be expressed as [first, last), where first is the iterator pointing to the initial element and last is the past-the-end iterator.

Most books and discussions of the STL algorithms arrange them according to side effects: non-mutating algorithms don’t change the elements in the range, mutating algorithms do change the elements, etc. These descriptions are based more on the underlying behavior or implementation of the algorithm – that is, the designer’s perspective. In practice, I don’t find this a very useful categorization so I shall instead organize them according to the problem you want to solve: are you searching for an element or set of elements, performing an operation on each element, counting elements, replacing elements, etc. This should help you find the one you want more easily.

Note that all the algorithms are in the namespace std. If you do not see a different header such as <utility> or <numerics> above the function declarations, that means it appears in <algorithm>.

It’s useful to create some basic tools with which to test the algorithms.

Displaying a range is something that will be done constantly, so here is a templatized function that allows you to print any sequence, regardless of the type that’s in that sequence:

#endif // PRINTSEQUENCE_H ///:~

There are two forms here, one that requires you to give an explicit range (this allows you to print an array or a sub-sequence) and one that prints any of the STL containers, which provides notational convenience when printing the entire contents of that container. The second form performs template type deduction to determine the type of T so it can be used in the copy( ) algorithm. That trick wouldn’t work with the first form, so the copy( ) algorithm is avoided and the copying is just done by hand (this could have been done with the second form as well, but it’s instructive to see a template-template in use). Because of this, you never need to specify the type that you’re printing when you call either template function.

The default is to print to cout with newlines as separators, but you can change that. You may also provide a message to print at the head of the output.

Next, it’s useful to have some generators (classes with an operator( ) that returns values of the appropriate type) which allow a sequence to be rapidly filled with different values.

#endif // GENERATORS_H ///:~

To create some interesting values, the SkipGen generator skips by the value skp each time its operator( ) is called. You can initialize both the start value and the skip value in the constructor.

URandGen (‘U’ for “unique”) is a generator for random ints between 0 and mod, with the additional constraint that each value can only be produced once (thus you must be careful not to use up all the values). This is easily accomplished with a set.

CharGen generates chars and can be used to fill up a string (when treating a string as a sequence container). You’ll note that the one member function that any generator implements is operator( ) (with no arguments). This is what is called by the “generate” functions.

The use of the generators and the print( ) functions is shown in the following section.

Finally, a number of the STL algorithms that move elements of a sequence around distinguish between “stable” and “unstable” reordering of a sequence. This refers to preserving the original order of the elements for those elements that are equivalent but not identical. For example, consider a sequence { c(1), b(1), c(2), a(1), b(2), a(2) }. These elements are tested for equivalence based on their letters, but their numbers indicate how they first appeared in the sequence. If you sort (for example) this sequence using an unstable sort, there’s no guarantee of any particular order among equivalent letters, so you could end up with { a(2), a(1), b(1), b(2), c(2), c(1) }. However, if you used a stable sort, it guarantees you will get { a(1), a(2), b(1), b(2), c(1), c(2) }.

To demonstrate the stability versus instability of algorithms that reorder a sequence, we need some way to keep track of how the elements originally appeared. The following is a kind of string object that keeps track of the order in which that particular object originally appeared, using a static map that maps NStrings to Counters. Each NString then contains an occurrence field that indicates the order in which this NString was discovered:

#endif // NSTRING_H ///:~

In the constructors (one that takes a string, one that takes a char*), the simple-looking initialization occurrence(occurMap[s]++) performs all the work of maintaining and assigning the occurrence counts (see the demonstration of the map class in the previous chapter for more details).

To do an ordinary ascending sort, the only operator that’s necessary is NString::operator<( ), however to sort in reverse order the operator>( ) is also provided so that the greater template can be used.

As this is just a demonstration class I am getting away with the convenience of putting the definition of the static member occurMap in the header file, but this will break down if the header file is included in more than one place, so you should normally relegate all static definitions to cpp files.

These algorithms allow you to automatically fill a range with a particular value, or to generate a set of values for a particular range (these were introduced in the previous chapter). The “fill” functions insert a single value multiple times into the container, while the “generate” functions use an object called a generator (described earlier) to create the values to insert into the container.

void fill(ForwardIterator first, ForwardIterator last, const T& value);
void fill_n(OutputIterator first, Size n, const T& value);

fill( ) assigns value to every element in the range [first, last). fill_n( ) assigns value to n elements starting at first.

void generate(ForwardIterator first, ForwardIterator last, Generator gen);
void generate_n(OutputIterator first, Size n, Generator gen);

generate( ) makes a call to gen( ) for each element in the range [first, last), presumably to produce a different value for each element. generate_n( ) calls gen( ) n times and assigns each result to n elements starting at first.

The following example fills and generates into vectors. It also shows the use of print( ):

} ///:~

A vector<string> is created with a pre-defined size. Since storage has already been created for all the string objects in the vector, fill( ) can use its assignment operator to assign a copy of “howdy” to each space in the vector. To print the result, the second form of print( ) is used which simply needs a container (you don’t have to give the first and last iterators). Also, the default newline separator is replaced with a space.

The second vector<string> v2 is not given an initial size so back_inserter must be used to force new elements in instead of trying to assign to existing locations. Just as an example, the other print( ) is used which requires a range.

The generate( ) and generate_n( ) functions have the same form as the “fill” functions except that they use a generator instead of a constant value; here, both generators are demonstrated.

All containers have a method size( ) that will tell you how many elements they hold. The following two algorithms count objects only if they satisfy certain criteria.

IntegralValue count(InputIterator first, InputIterator last,
const EqualityComparable& value);

Produces the number of elements in [first, last) that are equivalent to value (when tested using operator==).

IntegralValue count_if(InputIterator first, InputIterator last, Predicate pred);

Produces the number of elements in [first, last) which each cause pred to return true.

Here, a vector<char> v is filled with random characters (including some duplicates). A set<char> is initialized from v, so it holds only one of each letter represented in v. This set is used to count all the instances of all the different characters, which are then displayed:

} ///:~

The count_if( ) algorithm is demonstrated by counting all the lowercase letters; the predicate is created using the bind2nd( ) and greater function object templates.

These algorithms allow you to move sequences around.

OutputIterator copy(InputIterator, first InputIterator last, OutputIterator destination);

Using assignment, copies from [first, last) to destination, incrementing destination after each assignment. Works with almost any type of source range and almost any kind of destination. Because assignment is used, you cannot directly insert elements into an empty container or at the end of a container, but instead you must wrap the destination iterator in an insert_iterator (typically by using back_inserter( ), or inserter( ) in the case of an associative container).

The copy algorithm is used in many examples in this book.

BidirectionalIterator2 copy_backward(BidirectionalIterator1 first,
BidirectionalIterator1 last, BidirectionalIterator2 destinationEnd);

Like copy( ), but performs the actual copying of the elements in reverse order. That is, the resulting sequence is the same, it’s just that the copy happens in a different way. The source range [first, last) is copied to the destination, but the first destination element is destinationEnd - 1. This iterator is then decremented after each assignment. The space in the destination range must already exist (to allow assignment), and the destination range cannot be within the source range.

void reverse(BidirectionalIterator first, BidirectionalIterator last);
OutputIterator reverse_copy(BidirectionalIterator first, BidirectionalIterator last,
OutputIterator destination);

Both forms of this function reverse the range [first, last). reverse( ) reverses the range in place, while reverse_copy( ) leaves the original range alone and copies the reversed elements into destination, returning the past-the-end iterator of the resulting range.

ForwardIterator2 swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2);

Exchanges the contents of two ranges of equal size, by moving from the beginning to the end of each range and swapping each set of elements.

void rotate(ForwardIterator first, ForwardIterator middle, ForwardIterator last);
OutputIterator rotate_copy(ForwardIterator first, ForwardIterator middle,
ForwardIterator last, OutputIterator destination);

Swaps the two ranges [first, middle) and [middle, last). With rotate( ), the swap is performed in place, and with rotate_copy( ) the original range is untouched and the rotated version is copied into destination, returning the past-the-end iterator of the resulting range. Note that while swap_ranges( ) requires that the two ranges be exactly the same size, the “rotate” functions do not.

bool next_permutation(BidirectionalIterator first, BidirectionalIterator last);
bool next_permutation(BidirectionalIterator first, BidirectionalIterator last,
StrictWeakOrdering binary_pred);
bool prev_permutation(BidirectionalIterator first, BidirectionalIterator last);
bool prev_permutation(BidirectionalIterator first, BidirectionalIterator last,
StrictWeakOrdering binary_pred);

A permutation is one unique ordering of a set of elements. If you have n unique elements, then there are n! (n factorial) distinct possible combinations of those elements. All these combinations can be conceptually sorted into a sequence using a lexicographical ordering, and thus produce a concept of a “next” and “previous” permutation. Therefore, whatever the current ordering of elements in the range, there is a distinct “next” and “previous” permutation in the sequence of permutations.

The next_permutation( ) and prev_permutation( ) functions re-arrange the elements into their next or previous permutation, and if successful return true. If there are no more “next” permutations, it means that the elements are in sorted order so next_permutation( ) returns false. If there are no more “previous” permutations, it means that the elements are in descending sorted order so previous_permutation( ) returns false.

The versions of the functions which have a StrictWeakOrdering argument perform the comparisons using binary_pred instead of operator<.

void random_shuffle(RandomAccessIterator first, RandomAccessIterator last);
void random_shuffle(RandomAccessIterator first, RandomAccessIterator last
RandomNumberGenerator& rand);

This function randomly rearranges the elements in the range. It yields uniformly distributed results. The first form uses an internal random number generator and the second uses a user-supplied random-number generator.

BidirectionalIterator partition(BidirectionalIterator first, BidirectionalIterator last,
Predicate pred);
BidirectionalIterator stable_partition(BidirectionalIterator first,
BidirectionalIterator last, Predicate pred);

The “partition” functions use pred to organize the elements in the range [first, last) so they are before or after the partition (a point in the range). The partition point is given by the returned iterator. If pred(*i) is true (where i is the iterator pointing to a particular element), then that element will be placed before the partition point, otherwise it will be placed after the partition point.

With partition( ), the order of the elements is after the function call is not specified, but with stable_parition( ) the relative order of the elements before and after the partition point will be the same as before the partitioning process.

This gives a basic demonstration of sequence manipulation:

} ///:~

The best way to see the results of the above program is to run it (you’ll probably want to redirect the output to a file).

The vector<int> v1 is initially loaded with a simple ascending sequence and printed. You’ll see that the effect of copy_backward( ) (which copies into v2, which is the same size as v1) is the same as an ordinary copy. Again, copy_backward( ) does the same thing as copy( ), it just performs the operations in backward order.

reverse_copy( ), however, actually does created a reversed copy, while reverse( ) performs the reversal in place. Next, swap_ranges( ) swaps the upper half of the reversed sequence with the lower half. Of course, the ranges could be smaller subsets of the entire vector, as long as they are of equivalent size.

After re-creating the ascending sequence, rotate( ) is demonstrated by rotating one third of v1 multiple times. A second rotate( ) example uses characters and just rotates two characters at a time. This also demonstrates the flexibility of both the STL algorithms and the print( ) template, since they can both be used with arrays of char as easily as with anything else.

To demonstrate next_permutation( ) and prev_permutation( ), a set of four characters “abcd” is permuted through all n! (n factorial) possible combinations. You’ll see from the output that the permutations move through a strictly-defined order (that is, permuting is a deterministic process).

A quick-and-dirty demonstration of random_shuffle( ) is to apply it to a string and see what words result. Because a string object has begin( ) and end( ) member functions that return the appropriate iterators, it too may be easily used with many of the STL algorithms. Of course, an array of char could also have been used.

Finally, the partition( ) and stable_partition( ) are demonstrated, using an array of NString. You’ll note that the aggregate initialization expression uses char arrays, but NString has a char* constructor which is automatically used.

When partitioning a sequence, you need a predicate which will determine whether the object belongs above or below the partition point. This takes a single argument and returns true (the object is above the partition point) or false (it isn’t). I could have written a separate function or function object to do this, but for something simple, like “the object is greater than ‘b’”, why not use the built-in function object templates? The expression is:

bind2nd(greater<NString>(), "b")

And to understand it, you need to pick it apart from the middle outward. First,

greater<NString>()

produces a binary function object which compares its first and second arguments:

return first > second;

and returns a bool. But we don’t want a binary predicate, and we want to compare against the constant value “b.” So bind2nd( ) says: create a new function object which only takes one argument, by taking this greater<NString>( ) function and forcing the second argument to always be “b.” The first argument (the only argument) will be the one from the vector ns.

You’ll see from the output that with the unstable partition, the objects are correctly above and below the partition point, but in no particular order, whereas with the stable partition their original order is maintained.

All of these algorithms are used for searching for one or more objects within a range defined by the first two iterator arguments.

InputIterator find(InputIterator first, InputIterator last,
const EqualityComparable& value);

Searches for value within a range of elements. Returns an iterator in the range [first, last) that points to the first occurrence of value. If value isn’t in the range, then find( ) returns last. This is a linear search, that is, it starts at the beginning and looks at each sequential element without making any assumptions about the way the elements are ordered. In contrast, a binary_search( ) (defined later) works on a sorted sequence and can thus be much faster.

InputIterator find_if(InputIterator first, InputIterator last, Predicate pred);

Just like find( ), find_if( ) performs a linear search through the range. However, instead of searching for value, find_if( ) looks for an element such that the Predicate pred returns true when applied to that element. Returns last if no such element can be found.

ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last);
ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last,
BinaryPredicate binary_pred);

Like find( ), performs a linear search through the range, but instead of looking for only one element it searches for two elements that are right next to each other. The first form of the function looks for two elements that are equivalent (via operator==). The second form looks for two adjacent elements that, when passed together to binary_pred, produce a true result. If two adjacent elements cannot be found, last is returned.

ForwardIterator1 find_first_of(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
ForwardIterator1 find_first_of(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate binary_pred);

Like find( ), performs a linear search through the range. The first form finds the first element in the first range that is equivalent to any of the elements in the second range. The second form finds the first element in the first range that produces true when passed to binary_pred along with any of the elements in the second range. When a BinaryPredicate is used with two ranges in the algorithms, the element from the first range becomes the first argument to binary_pred, and the element from the second range becomes the second argument.

ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2 BinaryPredicate binary_pred);

Attempts to find the entire range [first2, last2) within the range [first1, last1). That is, it checks to see if the second range occurs (in the exact order of the second range) within the first range, and if so returns an iterator pointing to the place in the first range where the second range begins. Returns last1 if no subset can be found. The first form performs its test using operator==, while the second checks to see if each pair of objects being compared causes binary_pred to return true.

ForwardIterator1 find_end(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
ForwardIterator1 find_end(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate binary_pred);

The forms and arguments are just like search( ) in that it looks for the second range within the first range, but while search( ) looks for the first occurrence of the second range, find_end( ) looks for the last occurrence of the second range within the first.

ForwardIterator search_n(ForwardIterator first, ForwardIterator last,
Size count, const T& value);
ForwardIterator search_n(ForwardIterator first, ForwardIterator last,
Size count, const T& value, BinaryPredicate binary_pred);

Looks for a group of count consecutive values in [first, last) that are all equal to value (in the first form) or that all cause a return value of true when passed into binary_pred along with value (in the second form). Returns last if such a group cannot be found.

ForwardIterator min_element(ForwardIterator first, ForwardIterator last);
ForwardIterator min_element(ForwardIterator first, ForwardIterator last,
BinaryPredicate binary_pred);

Returns an iterator pointing to the first occurrence of the smallest value in the range (there may be multiple occurrences of the smallest value). Returns last if the range is empty. The first version performs comparisons with operator< and the value r returned is such that
*e < *r
is false for every element e in the range. The second version compares using binary_pred and the value r returned is such that binary_pred (*e, *r) is false for every element e in the range.

ForwardIterator max_element(ForwardIterator first, ForwardIterator last);
ForwardIterator max_element(ForwardIterator first, ForwardIterator last,
BinaryPredicate binary_pred);

Returns an iterator pointing to the first occurrence of the largest value in the range (there may be multiple occurrences of the largest value). Returns last if the range is empty. The first version performs comparisons with operator< and the value r returned is such that
*r < *e
is false for every element e in the range. The second version compares using binary_pred and the value r returned is such that binary_pred (*r, *e) is false for every element e in the range.

void replace(ForwardIterator first, ForwardIterator last,
const T& old_value, const T& new_value);
void replace_if(ForwardIterator first, ForwardIterator last,
Predicate pred, const T& new_value);
OutputIterator replace_copy(InputIterator first, InputIterator last,
OutputIterator result, const T& old_value, const T& new_value);
OutputIterator replace_copy_if(InputIterator first, InputIterator last,
OutputIterator result, Predicate pred, const T& new_value);

Each of the “replace” forms moves through the range [first, last), finding values that match a criterion and replacing them with new_value. Both replace( ) and replace_copy( ) simply look for old_value to replace, while replace_if( ) and replace_copy_if( ) look for values that satisfy the predicate pred. The “copy” versions of the functions do not modify the original range but instead make a copy with the replacements into result (incrementing result after each assignment).

To provide easy viewing of the results, this example will manipulate vectors of int. Again, not every possible version of each algorithm will be shown (some that should be obvious have been omitted).

} ///:~

The example begins with two predicates: PlusOne which is a binary predicate that returns true if the second argument is equivalent to one plus the first argument, and MulMoreThan which returns true if the first argument times the second argument is greater than a value stored in the object. These binary predicates are used as tests in the example.

In main( ), an array a is created and fed to the constructor for vector<int> v. This vector will be used as the target for the search and replace activities, and you’ll note that there are duplicate elements – these will be discovered by some of the search/replace routines.

The first test demonstrates find( ), discovering the value 4 in v. The return value is the iterator pointing to the first instance of 4, or the end of the input range (v.end( )) if the search value is not found.

find_if( ) uses a predicate to determine if it has discovered the correct element. In the above example, this predicate is created on the fly using greater<int> (that is, “see if the first int argument is greater than the second”) and bind2nd( ) to fix the second argument to 8. Thus, it returns true if the value in v is greater than 8.