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+==============================================================================+ | | | VERSION 2.1.1 | | | +==============================================================================+ -------------------------------------------------------------------------------- vector/matrix -------------------------------------------------------------------------------- 1. Assignment (=) and comparison (==/!=) operators now can be applied to vectors/matrices with different dimensions. 2. The default initialization for arrays of vectors/matrices is the vector/matrix of dimension 0. 3. Problems with vector/matrix typ parameters fixed. -------------------------------------------------------------------------------- graphics -------------------------------------------------------------------------------- graph_edit(window W, GRAPH(point,int) G, bool directed = true); Graph editor, edges are represented by arrows if directed = true and by segments if directed = false (declaration in <LEDA/graph_edit.h>) see example program "prog/graphics/matching.c" for details. -------------------------------------------------------------------------------- string -------------------------------------------------------------------------------- string(const char*, ...) new printf/form - like constructor e.g. s = string("x = %5.2f",x); -------------------------------------------------------------------------------- graph algorithms -------------------------------------------------------------------------------- list(edge) MAX_CARD_MATCHING(graph G) Maximum cardinality matching for general graphs, implemented by Edmond's Algorithm, returns list of matched edges. (source in "src/graph_alg/_mc_matching.c") (worst-case running time O(n*m) ) +==============================================================================+ | | | VERSION 2.1.0 | | | +==============================================================================+ -------------------------------------------------------------------------------- !!!!!!!!!!!! CHANGES IN HEADER FILES !!!!!!!!!!!!!!!!!! -------------------------------------------------------------------------------- I. <LEDA/graph.h> Header file <LEDA/graph.h> has been split into <LEDA/graph.h> : graph, GRAPH, node_array, edge_array <LEDA/ugraph.h> : ugraph, UGRAPH <LEDA/planar_map.h> : planar_map, PLANAR_MAP <LEDA/graph_alg.h> : graph algorithms + predefined node/edge array types node_array(int) edge_array(int) node_array(edge) edge_array(edge) node_array(bool) edge_array(bool); node_array(real) edge_array(real) node_matrix(bool) node_matrix(int) node_matrix(real) <LEDA/node_set.h> : node_set <LEDA/edge_set.h> : edge_set <LEDA/node_partition.h> : node_partition <LEDA/node_pq.h> : node_pq -------------------------------------------------------------------------------- II. <LEDA/plane.h> Header file <LEDA/plane.h> has been split into <LEDA/plane.h> : basic geometric objects (point,segment, ...) and predefined types list(point), list(segment), ... <LEDA/plane_alg.h> : plane algorithms, predefined type GRAPH(point,point) -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- data type "string" -------------------------------------------------------------------------------- int s.pos (string s_1, int i ) returns the first position of s_1 in s right of position i (-1 if no such position exists) string s.insert (string s_1, int i ) returns s(0,i-1) + s_1 + s(i+1,s.length()) Precondition:0 <= i <= s.length()-1 string s.replace (string s_1, string s_2, int i=1 ) returns the string created from s by replacing the i-th occurence of s_1 in s by s_2 string s.replace_all (string s_1, string s_2 ) returns the string created from s by replacing all occurences of s_1 in s by s_2 string s.replace (int i, int j, string s_1 ) returns the string created from s by replacing s(i,j) by s_1 string s.replace (int i, string s_1 ) returns the string created from s by replacing s[i] by s_1 string s.del (string s_1, int i=1 ) returns s.replace(s_1,"",i) string s.del_all (string s_1 ) returns s.replace_all(s_1,"") string s.del (int i, int j ) returns s.replace(i,j,"") string s.del (int i ) returns s.replace(i,"") void s.read (istream I, char delim = ' ' ) reads characters from input stream I into s until the first occurence of character delim void s.read (char delim = ' ' ) read(cin,delim) void s.readline (istream I ) read(I,'\n') void s.readline () readline(cin) -------------------------------------------------------------------------------- matrix -------------------------------------------------------------------------------- Operations matrix matrix::inv() O(n^3) vector matrix::solve(vector) O(n^2) double matrix::det() O(n^2) are now implemented by Gaussian eliminiation. matrix M.solve(matrix A) solves M*x_i = b_i simultaneously for all columns b_i of A, returns matrix (x_0,...,x_n-1) Preconditions: a) M is quadratic b) A.dim2() = M.dim1() -------------------------------------------------------------------------------- list -------------------------------------------------------------------------------- list_item L[int i] returns i-th item (nil if i<0 or i>L.length()-1) cost: O(i) -------------------------------------------------------------------------------- sortseq -------------------------------------------------------------------------------- void S.split (seq_item it, sortseq& S_1, sortseq& S_2 ) splits S at item it into sequences S_1 and S_2 and makes S empty. More precisely, if S = x_1,...,x_k-1,it,x_k+1,...,x_n then S1 = x_1,...,x_k-1,it and S2 = x_k+1,...,x_n Precondition: it is an item in S. sortseq& S.conc (sortseq& S_1 ) appends S_1 to S, makes S_1 empty, and returns S. Precondition: S.key(S.max()) <= S_1.key(S_1.min()). -------------------------------------------------------------------------------- graph G -------------------------------------------------------------------------------- void G.sort_nodes (node_array(T) A ) the nodes of G are sorted according to the entries of node_array A (cf. section 5.7) Precondition: T must be linearly ordered void G.sort_edges (edge_array(T) A ) the edges of G are sorted according to the entries of edge_array A (cf. section 5.7) Precondition: T must be linearly ordered pretty printing: void G.print(string s, ostream O) void G.print(string s) void G.print(ostream O) void G.print() void G.print_node(node v, ostream O = cout) void G.print_edge(edge e, ostream O = cout) -------------------------------------------------------------------------------- GRAPH(vtype,etype) G -------------------------------------------------------------------------------- void G.sort_nodes () the nodes of G are sorted according to their informations. Precondition: vtype is linearly ordered. void G.sort_edges () the edges of G are sorted according to their informations. Precondition: etype is linearly ordered. -------------------------------------------------------------------------------- node/edge_array -------------------------------------------------------------------------------- Creation of a node array (edge array):: a) ... b) ... c) ... d) node/edge_array(E) A(graph G, int n, E x) array for n nodes/edges of G Precondition: n >= |V| (|E|) +==============================================================================+ | | | VERSION 2.0.1 | | | +==============================================================================+ -------------------------------------------------------------------------------- GENERAL -------------------------------------------------------------------------------- forall_items(x,...) can be used for all kinds of items Read and Write functions for user defined I/O (cf. User Manual, section 1.5) must have an additional stream argument: Read(T&, istream&) defines an input function for reading objects of type T from an input stream. Write(T&,ostream&) defines an output function for printing objects of type T to an output stream. -------------------------------------------------------------------------------- string (section 2.3) -------------------------------------------------------------------------------- string s.tail(int i) returns the last i characters of s string s.head(int i) returns the first i characters of s -------------------------------------------------------------------------------- array (section 3.1) -------------------------------------------------------------------------------- void A.sort (int (*cmp)(E&, E&), int l, int h ) applies the sorting operation to the sub-array [l..h]. void A.read (istream I ) reads b-a+1 objects of type E from the input stream I into the array A using the overloaded Read function (section 1.5) void A.read () Calls A.read(cin) to read A from the standard input stream cin. void A.read (string s ) As above, but uses string s as a prompt. void A.print (ostream O, char space = ' ' ) Prints the contents of array A to the output stream O using the overload Print function (section 1.5) to print each element. The elements are separated by the space character space. void A.print (char space = ' ' ) Calls A.print(cout, space) to print A on the standard output stream cout. void A.print (string s, char space = ' ' ) As above, but uses string s as a header. -------------------------------------------------------------------------------- list (section 3.7) -------------------------------------------------------------------------------- void L.read (istream I, char delim = '\n' ) reads a sequence of objects of type E terminated by the delimiter delim from the input stream I using the overloaded Read function (section 1.5) L is made a list of appropriate length and the sequence is stored in L. void L.read (char delim = '\n' ) Calls L.read(cin, delim) to read L from the standard input stream cin. void L.read (string s, char delim = '\n' ) As above, but uses string s as a prompt. void L.print (ostream O, char space = ' ' ) Prints the contents of list L to the output stream O using the overload Print function (section 1.5) to print each element. The elements are separated by the space character space. void L.print (char space = ' ' ) Calls L.print(cout, space) to print L on the standard output stream cout. void L.print (string s, char space = ' ' ) As above, but uses string s as a header. void L.write (string fname ) writes G to the file with name fname. The overloaded functions Print(vtype,ostream) and Print(etype,ostream) (cf. section 1.6) are used to write the node and edge entries of G respectively. void L.read (string fname ) reads G from the file with name fname. The overloaded functions Read(vtype,istream) and Read(etype,istream) (cf. section 1.6) are used to read the node and edge entries of G respectively. -------------------------------------------------------------------------------- priority_queue (section 4.1) -------------------------------------------------------------------------------- Operation del_min has been overloaded K del_min() void del_min(K& k, I& i) removes an item x with minimal information assigns key(x) to k and inf(x) to i. -------------------------------------------------------------------------------- sortseq (section 4.6) -------------------------------------------------------------------------------- Operations "succ" and "pred" have been overloaded: seq_item S.succ(seq_item x) seq_item S.succ(K k) seq_item S.pred(seq_item x) seq_item S.pred(K k) NEW DATA TYPE: -------------------------------------------------------------------------------- 4.7 Persistent Dictionaries (p_dictionary) -------------------------------------------------------------------------------- 1. DEFINITION The difference between dictionaries (cf. section~4.3) and persistent dictionaries lies in the fact that update operations performed on a persistent dictionary D do not change D but create and return a new dictionary D'. For example, D.del(k) returns the dictionary D' containing all items it of D with key(it) != k. An instance D of the data type p_dictionary is a set of items (type p_dic_item). Every item in D contains a key from a linearly ordered data type K, called the key type of D, and an information from a data type I, called the information type of D. The number of items in D is called the size of D. A dictionary of size zero is called empty. We use <k,i> to denote an item with key k and information i (i is said to be the information associated with key k). For each k in K there is at most one item <k,i> in D. 2. DECLARATION declare2(p_dictionary,K,I) introduces a new data type with name p_dictionary(K,I) consisting of all persistent dictionaries with key type K and information type I. precond K is linearly ordered. 3. CREATION p_dictionary(K,I) D ; creates an instance D of type p_dictionary(K,I) and initializes D to an empty persistent dictionary. 4. OPERATIONS K D.key (dic_item it ) returns the key of item it. Precondition: it in D. I D.inf (dic_item it ) returns the information of item it. Precondition: it in D. dic_item D.lookup (K k ) returns the item with key k (nil if no such item exists in D). I D.access (K k ) returns the information associated with key k Precondition: there is an item with key k in D. p_dictionary(K,I) D.del (K k ) returns { x in D | key(x) != k }. p_dictionary(K,I) D.del_item (dic_item it ) returns { x in D | x != it }. p_dictionary(K,I) D.insert (K k, I i ) returns D.del(k) cup {<k,i>}. p_dictionary(K,I) D.change_inf (dic_item it, I i ) Let k = key(it), returns D.del_item(it) cup {<k,i>}. Precondition: it in D. p_dictionary(K,I) D.clear () returns an empty persistent dictionary. bool D.empty () returns true if D is empty, false otherwise. int D.size () returns the size of D. 5. ITERATION forall_items(i,D) { ``the items of D are successively assigned to i '' } 6. IMPLEMENTATION Persistent Dictionaries are implemented by leaf oriented persistent red black trees (cf. [DSST89]). Operations insert, lookup, del_item, del take time O(log n), key, inf, empty, size, change_inf and clear take time O(1). The space requirement is O(n). Here n is the number of all created persistent dictionaries (= number of all performed update operations). -------------------------------------------------------------------------------- GRAPH (section 5.4) -------------------------------------------------------------------------------- void G.write (string fname ) writes G to the file with name fname. The overloaded functions Print(vtype,ostream) and Print(etype,ostream) (cf. section 1.6) are used to write the node and edge entries of G respectively. int G.read (string fname ) reads G from the file with name fname. The overloaded functions Read(vtype,istream) and Read(etype,istream) (cf. section 1.6) are used to read the node and edge entries of G respectively. Returns error code 1 if file fname does not exist 2 if graph is not of type GRAPH(vtype,etype) 3 if file fname does not contain a graph 0 otherwise. -------------------------------------------------------------------------------- PLANE (section 6.1.6) -------------------------------------------------------------------------------- Function VORONOI (cf. section 6.1.6) has a new interface: void VORONOI(list(point), double R, GRAPH(point,point) ) VORONOI takes as input a list of points sites and a real number R. It computes a directed graph G representing the planar subdivision defined by the Voronoi-diagram of sites where all ``infinite" edges have length R. For each node v G.inf(v) is the corresponding Voronoi vertex (point) and for each edge e G.inf(e) is the site (point) whose Voronoi region is bounded by e. -------------------------------------------------------------------------------- point_set (section 6.3) -------------------------------------------------------------------------------- list(ps_item) S.convex_hull () returns the list of items containing all points of the convex hull of in clockwise order. -------------------------------------------------------------------------------- graphic windows (section 6.7) -------------------------------------------------------------------------------- Data type gwindow no longer exists, it is replaced by data type window The data type window provides an interface for the input and output of basic two-dimensinal geometric objects (cf. section 5.1) using the X11 (xview) or SunView window system. There are two object code libraries (libWs.a, libWx.a) containing implementations for different environments. Application programs using data type window have to be linked with one of these libraries (cf. section~1.6): a) For the SunView window system: CC prog.c -lWs -lP -lG -lL -lm -lsuntool -lsunwindow -lpixrect b) For the X11 (open windows) window system: CC prog.c -lWx -lP -lG -lL -lm -lxview -lolgx -lX11 -------------------------------------------------------------------------------- Creation of a graphic window -------------------------------------------------------------------------------- a) window W(int xpix, int ypix, int xpos, int ypos); b) window W(int xpix, int ypix); c) window W(); Variant a) creates a window W of physical size xpix times ypix pixels with its upper left corner at position (xpos,ypos) on the screen, variant b) places W into the upper right corner of the screen, and variant c) creates a 850 times 850 pixel window positioned into the upper right corner. All three variants initialize the coordinates of W to x0 = 0, x1 = 100 and y0 = 0. The init operation (see below) can later be used to change the window coordinates and scaling. -------------------------------------------------------------------------------- Additional operations -------------------------------------------------------------------------------- int W.read_panel (string h, int n, string* S ) displays a panel with header h and an array S[n] of n string buttons, returns the index of the selected button. int W.read_vpanel (string h, int n, string* S ) read_panel with vertical button layout int W.read_int (string p ) displays a panel with prompt p for integer input, returns the input real W.read_real (string p ) displays a panel with prompt p for real input returns the input string W.read_string (string p ) displays a panel with prompt p for string input, returns the input string W.read_string (string p, list(string) menu) as above, adds an additional menu button which can be used to select a string from menu. string W.read_string (string p, string label, list(string) menu) as above, the menu button is labelled with label. -------------------------------------------------------------------------------- PANELS -------------------------------------------------------------------------------- Creation: -------- panel P(string header); panel P; Operations: ---------- void P.text_item(string s) void P.bool_item(string label, bool& x) void P.real_item(string label, real& x) void P.color_item(string label, color& x) void P.int_item(string label, int& x) void P.int_item(string label, int& x, int min, int max) // slider void P.int_item(string label, int& x, int low, int high, int step) // choice void P.string_item(string label, string& x) void P.string_item(string label,string& x,list(string) L) // menu void P.choice_item(string label, int& x, list(string) L) void P.choice_item(string label, int& x, int l, string* L) void P.choice_item(string label, int& x, string, ... ) void P.button(string label) void P.new_button_line() void P.new_button_line(list(string) buttons) int P.open() int P.open(list(string)& buttons) -------------------------------------------------------------------------------- 7. Miscellaneous -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- Command input streams (cmd_istream) -------------------------------------------------------------------------------- An instance I of the data type cmd_istream is an C++ istream connected to the output of a shell command cmd, i.e., all input operations or operators applied to I read from the standard output of command cmd. 1. Creation of a command input stream cmd_istream in(string cmd); creates an instance in of type cmd_istream connected to the output of command cmd. 2. Operations All operations and operators (>>) defined for C++ istreams can be applied to command input streams as well. -------------------------------------------------------------------------------- Command output streams (cmd_ostream) -------------------------------------------------------------------------------- An instance O of the data type cmd_ostream is an C++ ostream connected to the input of a shell command cmd, i.e., all output operations or operators applied to O write into the standard input of command cmd. 1. Creation of a command output stream} cmd_ostream out(string cmd); creates an instance out of type cmd_ostream connected to the input of command cmd. 2. Operations All operations and operators (<<) defined for C++ ostreams can be applied to command output streams as well.