Version 5.0 The LEDA User Manual

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License Terms and Availability Any use of <strong>LEDA</strong> requires a license which is distributed by Algorithmic Solutions Software GmbH Schützenstrasse 3–5 66123 Saarbrücken Germany phone: +49 681 876470 fax: +49 681 8764729 email: leda@algorithmic-solutions.com For the current price list, license terms, available packages, supported platforms, and other information please visit http://www.algorithmic-solutions.com and follow the PRODUCTS link. 1
Page 1: Version 5.0 The LEDA User Manual Al
Page 4 and 5: 4.14 Socket Streambuffer ( socket s
Page 6 and 7: 9.11 Move-To-Front Coder II ( MTF2C
Page 8 and 9: 13.1.2 Handles and Iterators . . .
Page 10 and 11: 16.7 Simplices in 3D-Space ( d3 sim
Page 15 and 16: Chapter 1 Preface One of the major
Page 17: - A new class timer for facilitatin
Page 20 and 21: When executed it reads a sequence o
Page 22 and 23: defines the interface of the access
Page 24 and 25: double get_x() {return x;} double g
Page 26 and 27: cmp_edges_by_length cmp(G); list E
Page 28 and 29: • Argument Passing There are two
Page 30 and 31: 2.6 Iteration For many (container)
Page 33 and 34: Chapter 3 Modules During the last y
Page 35 and 36: Chapter 4 Simple Data Types and Bas
Page 37 and 38: string s.replace(int i, const strin
Page 39 and 40: 4.2 File Input Streams ( file istre
Page 41 and 42: 4.6 Random Sources ( random source
Page 43 and 44: 4.7 Random Variates ( random variat
Page 45 and 46: 4.9 Memory Management LEDA offers a
Page 47 and 48: size type A.max size( ) the largest
Page 49 and 50: ool leda assert(bool cond, const ch
Page 51 and 52: ool int is link(string fname) retur
Page 53 and 54: string S.get host( ) returns the ho
Page 55 and 56: 4.14 Socket Streambuffer ( socket s
Page 57 and 58: if (! sock.listen()) { cerr
Page 59 and 60: template const T & min(const T & a
Page 61 and 62: 3. Creation timer t(const string& n
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4.17 Counter ( counter ) 1. Definit
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4.18 Two Tuples ( two tuple ) 1. De
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C& p.third( ) returns the C-compone
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#define pq_item() third() #define p
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Table 4.1: Token Overview token inp
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format date :: get input format( )
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4.3 Arithmetic Operations date D +
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Chapter 5 Number Types and Linear A
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Non-member functions double to doub
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double to float( ) returns a double
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double x.to double( ) returns the d
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ool ispInf(const bigfloat& x) bool
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5.4 The data type real ( real ) 1.
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int x.sign(const integer& q) void x
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integer floor(const real& x) intege
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Without this assistance, reals auto
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interval x(const bigfloat& a); crea
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5.6 Modular Arithmetic in LEDA ( re
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5.8 The smod kernel of type residua
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void x.add(const residual& a, const
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int Sign(const floatf & f) 4. Imple
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vector v.rotate90(int i = 1) return
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5.11 Double-Valued Matrices ( matri
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y x = M.solve(b) it is not necessar
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integer vector integer vector integ
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integer vector M.col(int i) returns
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ool linear solver(const integer mat
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5.14 Rational Vectors ( rat vector
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at vector rat vector :: d3(integer
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at vector& rat vector rat vector& v
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eal vector v.norm( ) returns v norm
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5.16 Real-Valued Matrices ( real ma
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5.17 Numerical Analysis Functions (
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Chapter 6 Basic Data Types 6.1 One
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void A.permute( ) the elements of A
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6.2 Two Dimensional Arrays ( array2
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6.4 Queues ( queue ) 1. Definition
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6.6 Bounded Queues ( b queue ) 1. D
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list item L.cyclic succ(list item i
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void L.split(list item it, list& L1
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void L.merge(list& L1 , int (∗cmp
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Iteration forall items(it, L) { “
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const E& L.head( ) const E& L.tail(
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set S % const set& T returns S.symd
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6.10 Integer Sets ( int set ) 1. De
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6.11 Dynamic Integer Sets ( d int s
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insert and del also take time O(b
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for split) takes time O(m α(m, n))
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6.14 Dynamic Trees ( dynamic trees
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6.15 Dynamic Collections of Trees (
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Chapter 7 Dictionary Types 7.1 Dict
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int D.size( ) returns the size of D
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int A.size( ) returns |dom(A)|. voi
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7.3 Hashing Arrays ( h array ) 1. D
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7.4 Maps ( map ) 1. Definition An i
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7.5 Two-Dimensional Maps ( map2 ) 1
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7.6 Persistent Dictionaries ( p dic
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7.7 Partially Persistent Dictionari
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7.8 Sorted Sequences ( sortseq ) 1.
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seq item S.succ(const K& k) equival
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void S.del(const K& k) removes the
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int main() { sortseq S; string s1,
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p queue Q(int (∗cmp)(const P & ,
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8.2 Bounded Priority Queues ( b pri
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Chapter 9 Lossless Compression Befo
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pression module available. Then you
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uint32 C.encode memory chunk(const
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9.2 Static Arithmetic Coder ( A0sCo
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9.3 Prediction by Partial Matching
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void void C.set tgt file(const char
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9.5 Dictionary Based Coder ( DictCo
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9.6 Static Huffman Coder ( HuffmanC
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9.7 Adaptive Huffman Coder ( Adapti
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9.8 Run-Length Coder ( RLECoder ) 1
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9.9 Burrows-Wheeler Transform ( BWT
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4. Implementation Our implementatio
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uint32 C.decode memory chunk(const
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uint32 C.decode memory chunk(const
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9.17 MD5 Checksum ( MD5SumCoder ) 1
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void is.close( ) detaches is from i
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3. Operations bool is.is open( ) re
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9.24 Automatic Decoder ( AutoDecode
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9.25 Block Coder ( BlockCoder ) 1.
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string C.get description( ) provide
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9.26 Memory Streambuffer ( memory s
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Chapter 10 Symmetric Key Cryptograp
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in.get_coder()->get_coder3()->set_k
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We want to address another importan
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CryptByteString s(uint16 idx start,
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CryptKey CryptByteString CryptKey C
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corresponding block in the plaintex
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10.5 Authentication ( OMACCoder ) 1
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void C.reset(bool keep parameters =
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void void streambuf ∗ void void C
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10.7 Secure Socket Streambuffer ( s
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ool sb.sends acknowledge( ) returns
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there is an edge (v, w) ∈ E; in a
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list G.adj edges(node v) returns ad
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edge edge G.new edge(node v, edge e
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void void G.move edge(edge e, node
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c) Reversal Edges and Maps void G.m
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const list& G.all faces( ) returns
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void G.write(ostream& O = cout) wri
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forall adj nodes(v, w) { “the nod
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edge G.new edge(node v, node w, con
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11.3 Static Graphs ( static graph )
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When using the data types node slot
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node G.outdeg(node v) returns the n
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11.4 Undirected Graphs ( ugraph ) 1
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11.6 Planar Maps ( planar map ) 1.
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11.7 Parameterized Planar Maps ( PL
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11.8 Node Arrays ( node array ) 1.
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11.9 Edge Arrays ( edge array ) 1.
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11.10 Face Arrays ( face array ) 1.
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11.11 Node Maps ( node map ) 1. Def
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11.12 Edge Maps ( edge map ) 1. Def
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11.13 Face Maps ( face map ) 1. Def
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11.14 Two Dimensional Node Arrays (
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11.15 Two-Dimensional Node Maps ( n
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11.16 Sets of Nodes ( node set ) 1.
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11.18 Lists of Nodes ( node list )
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11.19 Node Partitions ( node partit
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const P & Q.inf(node v) returns the
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} { int dv = dist[v]; edge e; foral
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void random bigraph(graph& G, int a
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void triangulation map(graph& G, in
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11.23 Miscellaneous Graph Functions
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ool Is Triconnected(const graph& G,
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11.24 Markov Chains ( markov chain
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11.26 GML Parser for Graphs ( gml g
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ool (*gml node rule)(const gml obje
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void parser.add graph done rule(gml
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Chapter 12 Graph Algorithms This ch
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list BFS(const graph& G, node s, no
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12.2 Shortest Path Algorithms ( sho
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template void DIJKSTRA T(const gra
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12.3 Maximum Flow ( max flow ) Let
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inline bool CHECK MAX FLOW T(const
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12.4 Min Cost Flow Algorithms ( min
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12.6 Maximum Cardinality Matchings
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• to compute maximum and minimum
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template list MAX WEIGHT ASSIGNMEN
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or connects two nodes labeled with
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Heuristics for Initial Matching Con
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list MAX WEIGHT PERFECT MATCHING T(
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ool CHECK WEIGHTS T(const graph& G,
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void CreateInputGraph(graph& G, lis
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12.12 Euler Tours ( euler tour ) An
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int KURATOWSKI(graph& G, list& V, l
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12.14 Graph Drawing Algorithms ( gr
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int bool bool ORTHO EMBEDDING(const
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• Iterators are not bound to a lo
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• Classes GRAPH and UGRAPH (sects
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An example for an algorithm that su
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void it.update(leda :: node n) it m
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EdgeIt& bool it = const EdgeIt& it2
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ool it.valid( ) returns true if and
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void it.reset end( ) resets it to G
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void it.init(const leda :: graph& G
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#include < LEDA/graph/graph iterato
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AdjIt& ++it performs one step forwa
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13.9 Filter Node Iterator ( FilterN
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2. Creation CompPred cp(const DA& d
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4. Example First two simple observe
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Note: There are specialized version
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4. Implementation Constant Overhead
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2. Creation node member da da; intr
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13.17 Breadth First Search (flexibl
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With this iterator you can easily i
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void algorithm.finish algo( ) execu
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Initialization of get queue() with
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13.21 Dijkstra(flexible) ( GIT DIJK
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Chapter 14 Basic Data Types for Two
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double p.sqr dist(const point& q) i
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ool collinear(const point& a, const
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14.2 Segments ( segment ) 1. Defini
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ool s.contains(const point& p) bool
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14.3 Straight Rays ( ray ) 1. Defin
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ay r.reflect(const point& p) return
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double l.direction( ) returns the d
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int cmp slopes(const line& l1 , con
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circle C(const circle& c, int); 4.
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double C.distance(const circle& D)
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POLYGON POLYGON P (const list& pl,
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list P.simple parts( ) returns the
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POLYGON n gon(int n, CIRCLE C, doub
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GEN POLYGON P (const POLYGON & p, C
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list P.intersection(const SEGMENT &
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The following functions are only av
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int t.side of(const point& p) regio
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14.9 Iso-oriented Rectangles ( rect
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ectangle r.rotate90(const point& p,
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at point p(const point& p1 , int pr
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int cmp signed dist(const rat point
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14.11 Rational Segments ( rat segme
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integer s.W2( ) returns the third h
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at segment s.rotate90(int i = 1) re
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at point r.source( ) returns the so
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14.13 Straight Rational Lines ( rat
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at line l.reflect(const rat point&
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14.14 Rational Circles ( rat circle
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at circle C.translate(integer dx, i
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at point t[int i] returns the i-th
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14.16 Iso-oriented Rational Rectang
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at rectangle r.include(const rat re
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14.17 Real Points ( real point ) 1.
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eal point p.reflect(const real poin
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int compare by angle(const real poi
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4. Operations real point s.start( )
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eal segment s.reverse( ) returns s
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eal point r.point2( ) returns a poi
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14.20 Straight Real Lines ( real li
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eal line l.translate(const real vec
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14.21 Real Circles ( real circle )
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eal circle C + const real vector& v
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14.22 Real Triangles ( real triangl
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eal triangle t + const real vector&
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eal r.xmin( ) returns the minimal x
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list r.intersection(const real rect
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double WIDTH(const list& L, line& l
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edge CONVEX COMPONENTS(const gen po
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ool Is Delaunay Diagram(const GRAPH
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void SWEEP SEGMENTS(const list& S,
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template bool Is CCW Ordered Plane
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TRANSFORM T (const TRANSFORM & T1 )
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14.26 Point Generators ( point gene
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void random points near circle(int
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14.27 Point on Rational Circle ( r
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14.28 Segment of Rational Circle (
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ool cs.contains(const r circle poin
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void SWEEP SEGMENTS(const list& L,
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circle polygon P (const list& chain
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circle polygon P.reflect(const rat
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14.30 Generalized polygons with cir
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circle gen polygon P (const rat cir
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circle polygon P.to r circle polygo
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Chapter 15 Advanced Data Types for
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4. Implementation Two-dimensional d
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POINT SET POINT SET T (const list&
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node T.lookup(POINT p, const list&
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void T.draw edge(edge e, void (∗d
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void S.change inf(is item it, const
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list S.intersection sorted(const se
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list S.intersection sorted(const ra
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Chapter 16 Basic Data Types for Thr
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double p.ydist(const d3 point& q) r
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int region of sphere(const d3 point
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16.2 Straight Rays in 3D-Space ( d3
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16.3 Segments in 3D-Space ( d3 segm
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16.4 Straight Lines in 3D-Space ( d
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16.5 Planes ( d3 plane ) 1. Definit
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ool p.contains(const d3 point& q) b
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d3 sphere S.translate(double dx, do
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ool S.insphere(const d3 point& p) r
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integer p.W( ) returns the fourth h
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int orientation(const d3 rat point&
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ool affinely independent(const list
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d3 rat point random d3 rat point on
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16.9 Straight Rational Rays in 3D-S
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16.10 Rational Lines in 3D-Space (
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ool l.intersection(const d3 rat lin
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ational s.dy( ) returns ycoord2 ( )
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16.12 Rational Planes ( d3 rat plan
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ool p.contains(const d3 rat point&
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d3 rat sphere S.translate(const rat
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ool S.in simplex(const d3 rat point
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16.16 3D Triangulation and Voronoi
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3. Operations void col.set rgb(int
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4. Minimal and maximal coordinates
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All four variants initialize the co
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line style W.set line style(line st
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int W.get node width( ) returns the
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void void void W.draw segment(const
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void void W.draw bezier arrow(const
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void W.draw rectangle(double x 0 ,
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double W.text box(double x 0 , doub
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int void void void void void void W
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3.5 Input The main input operation
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int W.read mouse arc(double x 0 , d
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int W.read int(string p) displays a
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in this section add panel items or
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panel item W.lstyle item(string s,
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panel item panel item panel item W.
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int W.button(char ∗ pr1 , char
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void W.disable button(int b) disabl
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17.3 Panels ( panel ) 1. Definition
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int M.open(window& W, int x, int y)
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17.6 Graph Windows ( GraphWin ) 1.
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The corresponding types are: gw_nod
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void gw.set frame label(const char
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int gw.set gen edges(int m) sets th
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ool gw.is selected(edge e) returns
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void gw.place into box(double x0 ,
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void gw.add edge menu(string label,
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void void void int gw.add separator
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ool gw.wait(const char ∗ msg) dis
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17.7 The GraphWin (GW) File Format
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order color an attribute of type in
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direction an attribute of type int
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0.9074733 1 0 0 1 1 1 5 (0,0) (0,0)
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changes. The contents of the result
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The geometric objects The objects s
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• (rat )gen polygon or a d3 point
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ool write postscript(const CONTAINE
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eturn 0; } template void GW.set up
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void GW.set selected objects(GeoEdi
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ool GW.get show status( ) return bo
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string string color GW.get name(geo
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ool GW.set visible(geo scene sc, bo
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#include #include using namespace
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template line style GW.set obj lin
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template bool GW.get obj text(GeoB
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ool GW.set show position(bool sp) s
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• Pre add handler • Pre add cha
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ool GW.set post rotate handler(GeoE
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void void void void void int int GW
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void GW.add dependence(geo scene sc
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int GW.set limit(GeoEditScene ∗ e
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#include < LEDA/graphics/d3 window.
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string D.set message(string msg) se
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18.2 User Implementations In additi
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18.2.2 Priority Queues Any class pr
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Appendix A Technical Information Th
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A.3 Source Code on UNIX Platforms S
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A.5 Source Code on Windows with Bor
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Preparations Unpacking the LEDA dis
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Files and Directories To compile an
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(13) Choose ”Directories” (14)
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Possible values for are ”-ML”,
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(5’) In the ”File” menu click
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1. Change the file autoexec.bat as
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Compiling and Linking in Microsoft
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Compiling and Linking Application P
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Preparations To install LEDA you on
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(9b) Click on ”C/C++” and ”Pr
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2. Restart Windows 95/98 for the ch
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Programs using graph data types: bc
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• Make sure that there is a file
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Appendix B The golden LEDA rules Th
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(c) If y is the copy of a value x o
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4. list_item it = L.first(); L.del_
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Appendix C The LEDA Tools for Manua
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#ifndef LEDA_STACK_H #define LEDA_S
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foo.[lw|nw|w] lextract ❄ foo.man
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[15] C. Burnikel, R. Fleischer, K.
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[49] T. Iwata, K. Kurosawa: “OMAC
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[85] R.E. Tarjan: “Depth First Se
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acknowledge(...) GraphWin . . . . .
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BELLMAN FORD T(...) . . . . . . . .
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point . . . . . . . . . . . . . . .
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dynamic markov chain . . . . . . .
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del min() b node pq . . . . . . . .
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draw hull(...) POINT SET . . . . .
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MTFCoder . . . . . . . . . . . . .
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forall in edges(...). . . . . . . .
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get edit edge() GraphWin . . . . .
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get param(...) GraphWin . . . . . .
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eal . . . . . . . . . . . . . . . .
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dictionary . . . . . . . . . . . .
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is hidden(...) graph . . . . . . .
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language date . . . . . . . . . . .
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maximal planar graph(...). . . . .
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at triangle . . . . . . . . . . . .
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eal triangle . . . . . . . . . . .
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project yz(...) d3 line . . . . . .
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d3 plane . . . . . . . . . . . . .
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circle segment . . . . . . . . . .
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window . . . . . . . . . . . . . .
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set keys in file(...) CryptAutoDeco
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GraphWin . . . . . . . . . . . . .
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priority queue. . . . . . . . . . .
Page 824 and 825:
STRONG COMPONENTS(...) . . . . . .
Page 826 and 827:
d3 sphere . . . . . . . . . . . . .
Page 828 and 829:
W1() rat segment . . . . . . . . .
Page 830:
eal rectangle . . . . . . . . . . .
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Version 5.0 The LEDA User Manual

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