Summary of last lecture. Basics of programming II. (8th lect) C++ iterators, special data structures. Revision of List template

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1 Summary of last lecture Basics of programming II. (8th lect) C++ iterators, special data structures Péter Dóbé BME IIT Budapesti Mőszaki Egyetem C++ programming language BME-IIT Sz.I With the use of generic classes and functions we can get general structures: Type defined by parameter. Generic class or function can be instantiated by a type. Using specialization an instance can be got that differs from the default. Template type can be deduced from function parameters. Template function can be redefined. C++ programming language BME-IIT Sz.I Summary of last lecture / With predicates the behaviour of an algorithm can be changed. This helps writing general algorithms that can be specialized. Clumsy usage of templates may result in unnecessarily huge code. Eg: template<class T, int n> void copy(t a[n])... template<class T> void copy(t a[], int n)... Revision of List template For each element, print what other elements it can divide with no remainder!. We print the element, then traverse the list.. Print the next, but which one is next? C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Revision of List template / Putting there a new pointer? How many new pointers? Should we make the pointer public? ListElem should really be public? We should better hide it in the class! Solution: Generalized pointer that does not give out unnecessary information. Iterator C++ programming language BME-IIT Sz.I Iterators Abstract pointer object referencing elements of a generalized data sequence. Most important operations: accessing actual element (*, ->) getting next element (++) comparing pointers ( ==,!= ) creating object pointer pointing to the first element ( begin() ) creating object pointer pointing to the last element ( end() ) List<int> L; List<int>::iterator i, i; for (i = L.begin(); i!= L.end(); i++) int x = *i; Container object (list) C++ programming language BME-IIT Sz.I

2 Encapsulating the pointer object This is also encapsulated template<class T> class List struct ListElem // private structure, no need for friend T data; // data ListElem *next; // pointer to next ListElem(ListElem *p = ) :next(p) ; ListElem *first; // pointer to first public: no act List() first = new ListElem; // creating guard bool Compare(T d, T d) return(d<d); void Insert(const T& dat); // inserting element class iterator; // forward declaration iterator begin() // creating, and positioning it to first return(iterator(*this)); iterator end() // creating, and positioning it after last return(iterator()); Encapsulating iterator / // Inside class List... class iterator // inner class ListElem *act; // pointer to actual element public: Here is act iterator() : act() ; // sets act to end () iterator(const List& l) : act(l.first) // sets to first if (act->next == ) act = ; // trick because of the guard This is easier than traversing to the end. iterator& operator++() // incrementing iterator (pre) if (act) act = act->next; // to next if (act->next == ) act = ; // because of guard return(*this); C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Encapsulating iterator / iterator operator++(int) // incrementing iterator (post) iterator tmp = *this; // previous value operator++(); // increment return(tmp); // return with previous bool operator!=(const iterator &i) const // compare return(act!= i.act); T operator*() // indirection if (act) return(act->data); else throw( List iteration error"); T* operator->() // indirection if (act) return(&act->data); else throw( List iteration error"); ; ; It has to return a pointer C++ programming language BME-IIT Sz.I Using Iterator #include "generic_list_iter.hpp" int main() Traverses to the end, List<int> L; no need to know data type. List<int>::iterator i; for (i = L.begin(); i!= L.end(); i++) increments int x = *i; accessing actual element List<Complex> Lc; List<Complex>::iterator ic(lc); ic->abs(); Complex c = ic->; // wrong return(); -> single operand postfix operator. Formal rules require fieldname to be written! C++ programming language BME-IIT Sz.I Iterators - summary Containers -> storing data sequences accessing elements of a data sequence typical operation: give the next" Iterator: abstract pointer pointing to the elements of general data sequence. Most important operations: accessing the actual element (* ->) stepping to next element (++) comparing pointers ( ==,!= ) creating pointer object to first element ( begin() ) creating pointer object pointing to element after last ( end() ) C++ programming language BME-IIT Sz.I Special data structures Choosing the proper data representation, finding the proper data structure is a very important design and implementation issue. A clumsy data store can ruin the results of the most prudent design. Different aspects are to be considered: model, speed, size. C++ programming language BME-IIT Sz.I

3 Arrays If size and dimension is known, no problem. If dimension might vary, there is no default language construct storing row- or columnwise, dynamic allocation of memory element address is to be calculated according to the index-expression (last index runs fastest) In C index runs from to n-, but not in every language. C++ programming language BME-IIT Sz.I I-,, I-,J-, j Arrays/,J-, i,, I-,,K- M[I][J][K] sized D matrix[i][j][k] element address= J*K*i+K*j+k+base C++ programming language BME-IIT Sz.I k,,k-,j-,k- N dimensional array Let Li be the minimal index of the i-th dimension of an N dimensional array, Ui the maximal index. The address of element with indices i, i, i, i,... is: S*S*... *Sn*(i-L) + S*...Sn*(i-L) (in-ln) + base where: Si = Ui Li + Huge arrays Storing huge sparse array (many similar elements) matrices, saving space might be important. If the number of non-null elements is known, solution is easy with static tables With the element the dimensions are also stored. C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Row: Value: Huge arrays / C++ programming language BME-IIT Sz.I ColFirst: Huge arrays / Row: Value: ColFirst: 7 int elem(int i, int j) // eg:, for (k = ColFirst[j]; k < ColFirst[j+]; k++) if (Row[k] == i) return(value[k]); return(); C++ programming language BME-IIT Sz.I

4 Huge array with list Huge array with orthogonal list Instead of static array circular orthogonal linked list. (comb) In each list element the index and data are to be stored. Zero, or other repetitive data is not stored. For each row and column there is a head (guard), which is signed by a special index. 8 9 C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Queues and stacks Queue: FIFO (First-In-First-Out) Stack: LIFO (Last-In-First-Out) implementation with array or list Using Queues Natural means for implementing waiting queues. Natural means for buffering (balancing consumer-supplier speed difference) C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Using Stacks Because of behaviour (shrinks and grows dynamically, LIFO) Typical implementation of function call and parameter passing. Helper for implementing recursion. For storing local variables. Evaluating postfix expressions. Helper for backtrack algorithms. Hash function Creates a fixed length extract that is characteristic to the data. h = H(z). features: one-way it is hard to find a z z' for h, where h=h(z') it is hard to find a z z' where H(z)=H(z') Use: mapping index to a finite range. (e.g. indexing with a string) C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I

5 Hash table Hash table / Store, where storing is helped by hash function. The key serving as base for storage (usually the data itself) is extracted by a hash function. Storing is based on this value, but expecting collisions. Example for H: z H Ht: m - domain [ m( mod ) ] H ( z) = zθ, where : θ = collision C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Resolving Hash collisions Linear search The solution shown is logical, but it s not the usual solution. Searching for the next free space. Eg. choosing from next elements is done with linear search. Disadvantage: clusters are formed This is why multiple hash is used instead int Test(int s, Key k) int i = s; do if (Ht[i] == k) return(i); i = (i + ) % m; while (i!= s); return(-); Special key int Store(Key k) int h = Hash(k); int i = Test(h, Empty); if (i < ) return(); Ht[i] = k; return(); Key Search(Key k) int h = Hash(k); int i = Test(h, k); if (i < ) return(empty); return(ht[i]); C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Multiple hash In the loop of Test we use d = Hash instead of d=+. Eg: in Hash we use -θ instead of θ. int Test(int s, Key k) int i = s; int d = Hash(k); do if (Ht[i] == k) return(i); i = (i + d) % m; while (i!= s); return(-); Single linked Multiple linked Circular linked Sorted Unsorted Comb (orthogonal) Lists C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I

6 Doubly-linked data structure Comb list FIRST NULL FIRST NULL C++ programming language BME-IIT Sz.I TK TK NAME,AVG TK TK TK TK NAME,AVG TK C++ programming language BME-IIT Sz.I Tree structures Binary tree Sorted, key pointers Heap special binary tree also represented by an array N-tree N- keys, N pointers if k < k -> p if ki < k < ki+ -> pi if kn- < k -> pn- k k, k, k p p p p Traversing a binary tree (rep). If tree_not_empty Then print_left_subtree print_element print_right_subtree End 6 9 C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Heap Submerging a a i <= a i if i <= n/ a i <= a i+ if i < n/ a = a i <= a i if i <= n/ a i <= a i+ if i < n/ a a a =8 a = a a a 6 a 7 a =9 a = a 6 = a 7 =8 a 8 a 9 a 8 =88 a 9 = Traversing lesser branch while we can swap. C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I

7 Sorting algorithm (heap) Creating a heap smallest element on top Taking off top, and submerging, thus we have a new heap with the smallest element on top. Questions How to make a heap? a n/+... a n is already a heap, then submerging a n/, a n/-, etc. How to represent? array: element index = array index 6 7 C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I Questions () B-tree What to use instead of? Let it be the largest element! Thus we swap the first element, the size of the heap decreases by one, but it is still a heap. smallest swap B-tree balanced an N-tree, that has at least n/ and at most n siblings. k, k, k p p p p remaining heap C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I B-tree example (N=) B-tree example / should come here, but maximum sibling number is reached new key, split,,,,,,,, leaves are on same level. C++ programming language BME-IIT Sz.I C++ programming language BME-IIT Sz.I