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This section covers some basic function templates in the STL We cannot give you a comprehensive description of them all here, but we will present a large enough sample to give you a good feel for what is contained in the STL and to give you suf cient detail to start using these template functions These template functions are sometimes called generic algorithms The term algorithm is used for a reason Recall that an algorithm is just a set of instructions for performing a task An algorithm can be presented in any language, including a programming language like C++ But, when using the word algorithm, programmers typically have in mind a less formal presentation given in English or pseudocode As such, it is often thought of as an abstraction of the code de ning a function It gives the important details but not the ne details of the coding The STL speci es certain details about the algorithms underlying the STL template functions, which is why they are sometimes called generic algorithms These STL function templates do more than just deliver a value in any way that the implementers wish The function templates in the STL come with minimum requirements that must be satis ed by their implementations if they are to satisfy the standard In most cases they must be implemented with a guaranteed running time This adds an entirely new dimension to the idea of a function interface In the STL the interface not only tells a programmer what the function does and how to use the functions, but also how rapidly the task will be done In some cases the standard even speci es the particular algorithm that is used, although not the exact details of the coding Moreover, when it does specify the particular algorithm, it does so because of the known ef ciency of the algorithm The key new point is the speci cation of an ef ciency guarantee for the code In this chapter we will use the terms generic algorithm, generic function, and STL function template to all mean the same thing
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In order to have some terminology to discuss the ef ciency of these template functions or generic algorithms, we rst present some background on how the ef ciency of algorithms is usually measured
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If you ask a programmer how fast his or her program is, you might expect an answer like two seconds However, the speed of a program cannot be given by a single number A program will typically take a longer amount of time on larger inputs than it will on smaller inputs You would expect that a program for sorting numbers would take less time to sort ten numbers than it would to sort one thousand numbers Perhaps it takes two seconds to sort ten numbers, but ten seconds to sort one thousand numbers How then should the programmer answer the question How fast is your program The programmer would have to give a table of values showing how long the program took for different sizes of input For example, the table might be as shown in Display 1914 This table does not give a single time, but instead gives different times for a variety of different input sizes The table is a description of what is called a function in mathematics Just as a (non-void) C++ function takes an argument and returns a value, so too does this function take an argument, which is an input size, and returns a number, which is the time the program takes on an input of that size If we call this function T, then T(10) is 2 seconds, T(100) is 21 seconds, T(1,000) is 10 seconds, and T(10,000) is 25 minutes The table is just a sample of some of the values of this function T The program will take some amount of time on inputs of every size So although they are not shown in the table, there are also values for T(1), T(2), , T(101), T(102), and so forth For any positive integer N, T(N) is the amount of time it takes for the program to sort N numbers The function T is called the running time of the program So far we have been assuming that this sorting program will take the same amount of time on any list of N numbers That need not be true Perhaps it takes much less time if the list is already sorted or almost sorted In that case, T(N) is de ned to be the time taken by the hardest list, that is, the time taken on that list of N numbers that makes the program run the longest This is called the worst-case running time In this
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