The C++ Algorithm Libraries A standard collection of generic algorithms Applicable to various types and containers E.g., sorting integers (int) vs. intervals (pair<int, int>) E.g., sorting elements in a vector vs. in a C-style array Polymorphic even without inheritance relationships Types substituted need not have a common base class Must only provide the operators the algorithm needs Significantly used with the sequence containers To reorder elements within a container’s sequence To store/fetch values into/from a container To calculate various values and properties from it

Motivating Example: Searching a String From Austern: “Generic Programming and the STL” Sequential (linear) search: find char c in string s char * strchr (char* s, char c) { while (*s != 0 && *s != c){ ++s; } return *s == c ? s : (char *) 0; Problem: not very general “Range” of iteration is always defined up to ‘\0’ character Only works for a “zero terminated” string in C/C++ What make strchr not very general? 1. You can only search for a specific type 2. The data structure you can search in is limited to the null-terminated array

Improving Linear Search with Ranges First generalization (Austern, pp. 11): use a range (something that sequential containers can give us!) char * find1 (char* first, char* last, char c){ while (first != last && *first != c) ++first; return first; } Gives an explicit range (calculate its length – how?) Assumes first is before last (can check – how?) Note how caller checks for success changed: why? What make strchr not very general? 1. You can only search for a specific type 2. The data structure you can search in is limited to the null-terminated array

Linear Search over Parameterized Types Second generalization: use templates to parameterize the function argument types template <typename T> T * find2(T * first, T * last, const T & value){ while (first != last && *first != value) ++first; return first; } How much did the find1 code need to change? One last problem What if we want to apply this to a container (e.g., list) whose range can’t be traversed via simple pointers?

Linear Search with Generic Iterators Third generalization: separate iterator type parameter We arrive at the find algorithm (Austern pp. 13): template <typename Iterator, typename T> Iterator find (Iterator first, Iterator last, const T & value) { while (first != last && *first != value) ++first; return first; } Notice how algorithm depends on the iterators Notice how refinements made algorithm more abstract … but still essentially does the same thing i.e., algorithm structure (and time complexity) is the same

Organization of C++ Algorithm Libraries The <algorithm> header file contains Non-modifying sequence operations Do some calculation but don’t change sequence itself Examples include count, count_if Mutating sequence operations Modify the order or values of the sequence elements Examples include copy, random_shuffle Sorting and related operations Modify the order in which elements appear in a sequence Examples include sort, next_permutation The <numeric> header file contains General numeric operations Scalar and matrix algebra, especially used with vector<T> Examples include accumulate, inner_product

Example of Using Non-Modifying Algorithms count algorithm Moves through iterator range Checks each position for equality Increases count if equal #include <iostream> #include <vector> #include <algorithm> using namespace std; int main (int, char * []) { vector<int> v; v.push_back(1); v.push_back(2); v.push_back(3); int i = 7; cout << i << " appears " << count(v.begin(), v.end(), i) << " times in v" << endl; i = 2; return 0; } /* output is 7 appears 0 times in v 2 appears 2 times in v */

Example of Using Mutating Algorithms copy algorithm Copies from an input iterator range into an output iterator Note use of default constructor to get an “off-the-end” (here, “end-of-file”) input iterator Note use of noskipws (need to make sure container behavior matches what you want to do) ifstream input_file (input_file_name.c_str()); ofstream output_file (output_file_name.c_str()); input_file >> noskipws; istream_iterator<char> i (input_file); ostream_iterator<char> o (output_file); copy (i, istream_iterator<char>(), o); cout << "copied input file: " << input_file_name << endl << " to output file: " << output_file_name << endl; return 0; } /* output: cdgill@hive> ./copytest Makefile Makefile2 copied input file: Makefile to output file: Makefile2 cdgill@hive> diff Makefile Makefile2 cdgill@hive> */ #include <iostream> #include <string> #include <fstream> #include <iterator> #include <algorithm> using namespace std; int main (int argc, char * argv[]) { if (argc != 3) {return 1;} string input_file_name (argv[1]); string output_file_name (argv[2]);

Example of Using Sorting Algorithms sort algorithm Reorders a given range Can also plug in a functor to change the ordering function next_permutation algorithm Generates a specific kind of reordering, called a “permutation” Can use to generate all possible orders of a given sequence #include <iostream> #include <string> #include <algorithm> using namespace std; int main (int, char * []) { string s = "asdf"; cout << "original: " << s << endl; sort (s.begin(), s.end()); cout << "sorted: " << s << endl; string t (s); cout << "permutations:" << endl; do { next_permutation (s.begin(), s.end()); cout << s << " "; } while (s != t); cout << endl; return 0; } /* output is original: asdf sorted: adfs permutations: adsf afds afsd asdf asfd dafs dasf dfas dfsa dsaf dsfa fads fasd fdas fdsa fsad fsda sadf safd sdaf sdfa sfad sfda adfs */

Example of Using Numeric Algorithms accumulate algorithm Sums up elements in a range (based on a starting sum value) inner_product algorithm Computes the inner (also known as “dot”) product of two matrixes: sum of the products of their respective elements #include <iostream> #include <vector> #include <numeric> using namespace std; int main (int, char * []) { vector<int> v; v.push_back(1); v.push_back(2); v.push_back(3); cout << "v contains "; for (size_t s = 0; s < v.size(); ++s) { cout << v[s] << " "; } cout << endl; cout << "the sum of the elements in v is " << accumulate (v.begin(), v.end(), 0) << endl; cout << "the inner product of v and itself is " << inner_product (v.begin(), v.end(), v.begin(), 0) << endl; return 0; /* output is: v contains 1 2 3 2 the sum of the elements in v is 8 the inner product of v and itself is 18 */

Concluding Remarks C++ libraries give you useful, generic algorithms Combine easily with a variety of containers/iterators Support many common data structure manipulations Finding and modifying values, re-ordering, numeric operations Reusing them saves you from writing code Many STL algorithms can be extended further Especially by plugging callable entities into them Next time we’ll look at how callables work, and how to use them, as well as at algorithms and iterators in more detail