Version 5.0 The LEDA User Manual

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[85] R.E. Tarjan: “Depth First Search an Linear Graph Algorithms”. SIAM Journal of Computing, Vol. 1, 146-160, 1972 [86] R.E. Tarjan: “Data Structures and Network Algorithms”. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 44, 1983 [87] J.S. Vitter: “Dynamic Huffman Coding”. ACM Transactions on Mathematical Software, Vol. 15, No. 2, 158-167, 1989 [88] M. Wenzel: “Wörterbücher für ein beschränktes Universum”. Diplomarbeit, Fachbereich Informatik, Universität des Saarlandes, 1992 [89] A.G. White: “Graphs,Groups, and Surfaces”. North Holland, 1973 [90] D.E. Willard: “New Data Structures for Orthogonal Queries”. SIAM Journal of Computing, 232-253, 1985 [91] J.W.J. Williams: “Algorithm 232 (heapsort). Communications of the ACM, Vol. 7, 347-348, 1964 [92] I.H. Witten, M. Radford and J.G. Cleary: “Arithmetic Coding for Data Compression”. Communications of the ACM, Vol. 30, 520-540, 1987 [93] J. Ziv and A. Lempel: “A universal algorithm for sequential data compression”. IEEE Transactions on Information <strong>The</strong>ory, Vol. 30(3), 337-343, 1977 [94] J. Ziv and A. Lempel: “Compression of individual sequences via variable-rate coding” IEEE Transactions on Information <strong>The</strong>ory, Vol. 24(5), 530-536, 1978 [95] S. Näher, O. Zlotowski: “Design and Implementation of Data Types for Static Graphs”. ESA, 2002
Index Symbols L A TEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 Apr date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Aug date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 colons date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Dec date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 english date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Feb date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 french date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 FULL r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 german date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 german standard date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 hyphens date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Jul date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Jun date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 local date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Mar date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 May date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 mr cut off PPMIICoder . . . . . . . . . . . . . . . . . . . . 189 mr freeze PPMIICoder . . . . . . . . . . . . . . . . . . . . 189 NON TRIVIAL r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 NOT WEAKLY SIMPLE r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 Nov date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Oct date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 RESPECT ORIENTATION r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 second r circle point . . . . . . . . . . . . . . . . . . . . 521 Sep date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 SIMPLE r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 US standard date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 WEAKLY SIMPLE r circle gen polygon . . . . . . . . . . . . . .533 r circle polygon . . . . . . . . . . . . . . . . . .528 A A() d3 plane . . . . . . . . . . . . . . . . . . . . . . . . 567 d3 rat plane . . . . . . . . . . . . . . . . . . . . . 591 A0Coder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 A0sCoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 abs(...) . . . . . . . . . . . . . . . . 67, 69, 73, 78, 88 absolute(...) residual . . . . . . . . . . . . . . . . . . . . . . . . . . 88 accept() leda socket . . . . . . . . . . . . . . . . . . . . . . . 41 access(...) dictionary . . . . . . . . . . . . . . . . 152 763
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Version 5.0 The LEDA User Manual Al
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4.14 Socket Streambuffer ( socket s
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9.11 Move-To-Front Coder II ( MTF2C
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13.1.2 Handles and Iterators . . .
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16.7 Simplices in 3D-Space ( d3 sim
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License Terms and Availability Any
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7. LEDA is available from Algorithm
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Chapter 2 Basics An extended versio
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XYZ y(x1, ... ,xt); ,tk > and uses
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2.3.1 Linear Orders Many data types
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dictionary D0; // default ordering
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2.3.3 Implementation Parameters Man
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lookup returned the location where
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list::iterator defines the iterator
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• internal (LEDA/incl/internal/)
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string s(const char ∗ p); string
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ool bool bool bool istream& ostream
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string buffer, i.e., all output ope
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andom source& S ≫ char& x random
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int R.set weight(int i, int g) sets
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4.10 Memory Allocator ( leda alloca
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4.11 Error Handling ( error ) LEDA
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4.12 Files and Directories ( file )
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4.13 Sockets ( leda socket ) 1. Def
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ool S.receive string(string& s) rec
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ool sb.failed( ) returns whether a
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4.15 Some Useful Functions ( misc )
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4.16 Timer ( timer ) 1. Definition
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unsigned fibonacci(unsigned n) { st
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unsigned fibonacci(unsigned n) { st
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int Hash(const two tuple& p) hash f
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3. Creation four tuple p; creates a
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4.21 A date interface ( date ) 1. D
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3. Creation date D; creates an inst
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string D.get month name( ) returns
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Now we show an example in which dif
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integer integer a(const char ∗ s)
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5.2 Rational Numbers ( rational ) 1
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5.3 The data type bigfloat ( bigflo
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ounding modes bigfloat :: get round
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ostream& ostream& os ≪ const bigf
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double x.get double error( ) bigflo
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int int real roots(const Polynomial
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√ y v = b 1 c 2 + b 2 c 1 ± sign
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5.5 Interval Arithmetic in LEDA ( i
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void x.set midpoint(VOLATILE I doub
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5.7 The mod kernel of type residual
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int residual :: required primetable
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5.9 A Floating Point Filter ( float
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5.10 Double-Valued Vectors ( vector
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double v.zcoord( ) returns the seco
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matrix matrix matrix vector M + con
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5.12 Vectors with Integer Entries (
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5.13 Matrices with Integer Entries
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integer matrix inverse(const intege
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distinct representatives and linear
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at vector v(const array& A); introd
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int compare by angle(const rat vect
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5.15 Real-Valued Vectors ( real vec
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int compare by angle(const real vec
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eal matrix M + const real matrix& M
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5.17.2 Integration double integrate
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array A(int low, const E& x, const
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int A.binary locate(int (∗cmp)(co
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6.3 Stacks ( stack ) 1. Definition
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6.5 Bounded Stacks ( b stack ) 1. D
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6.7 Linear Lists ( list ) 1. Defini
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const E& L.pop front( ) same as L.p
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Sorting and Searching void L.sort(i
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Input and Output void L.read(istrea
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6.8 Singly Linked Lists ( slist ) 1
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6.9 Sets ( set ) 1. Definition An i
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4. Implementation Sets are implemen
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int set S | const int set& T return
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d int set S − const d int set& T
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6.12 Partitions ( partition ) 1. De
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6.13 Parameterized Partitions ( Par
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void D.evert(vertex v) makes v the
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4. Implementation Dynamic collectio
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dictionary D(int (∗cmp)(const K&
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7.2 Dictionary Arrays ( d array ) 1
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{ d_array dic; dic["hello"] = "hall
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ool A.empty( ) returns true if A is
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Note that it is not possible to ite
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void M.clear( ) clears M by making
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p dictionary D.change inf(p dic ite
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void D.del(const K& k) deletes the
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3. Creation sortseq S; creates an i
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seq item S.max item( ) returns the
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Iteration forall items(it, S) { “
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Chapter 8 Priority Queues 8.1 Prior
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6. Example Dijkstra’s Algorithm (
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int Q.size( ) returns the size of Q
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Assume that you want to send the fi
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9.1 Adaptive Arithmetic Coder ( A0C
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uint32 C.get scale threshold( ) uin
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uint32 C.decode memory chunk(const
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3. Creation PPMIICoder C(streambuf
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9.4 Deflation/Inflation Coder ( Def
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void C.set compression level(int le
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void void C.set src stream(streambu
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streambuf ∗ C.get src stream( ) r
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streambuf ∗ C.get src stream( ) r
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uint32 C.decode memory chunk(const
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uint32 C.encode memory chunk(const
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9.10 Move-To-Front Coder ( MTFCoder
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9.11 Move-To-Front Coder II ( MTF2C
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9.12 RLE for Runs of Zero ( RLE0Cod
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9.13 Checksummers ( checksummer bas
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ool C.checksum is valid( ) returns
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9.19 Encoding Output Stream ( encod
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ostream& os.seekp(streamoff off , i
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9.23 Coder Pipes ( CoderPipe2 ) 1.
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void C.set coder1(Coder1 ∗ c1 , b
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void void C.set src stream(streambu
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3. Operations Standard Operations v
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string out_file1 = tmp_file_name(),
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void mb.truncate(streamsize n) also
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e able to change your message witho
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Then you can use the CryptAutoDecod
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10.1 Secure Byte String ( CryptByte
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CryptKey k(const byte ∗ bytes, ui
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10.3 Encryption and Decryption with
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10.4 Example for a Stream-Cipher (
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uint16 void C.get accepted key size
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3. Operations Standard Operations v
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10.6 Automatic Decoder supporting C
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void C.add keys in file(const char
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secure socket streambuf sb(leda soc
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Chapter 11 Graphs and Related Data
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2. Creation graph G; creates an obj
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edge G.first in edge(node v) return
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void G.hide node(node v) removes no
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void G.bucket sort nodes(int l, int
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edge G.new map edge(edge e1 , edge
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edge edge edge G.new edge(node v, e
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void void G.print(string s, ostream
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graph algorithms, i.e., algorithms
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void void G.sort nodes(const list&
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• Opposite Graphs (opposite graph
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4. Operations The interface consist
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int main () { static_graph G; array
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3. Implementation see section 11.2.
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list M.triangulate( ) triangulates
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void M.assign(face f, const ftype&
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void A.init(const graph t& G, int n
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ool M.use node data(const graph t&
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ool M.use edge data(const graph t&
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E& M[face f] returns the variable M
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4. Implementation Node matrices for
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4. Implementation Node maps are imp
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11.17 Sets of Edges ( edge set ) 1.
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node L.cyclic pred(node v) returns
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11.20 Node Priority Queues ( node p
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11.21 Bounded Node Priority Queues
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11.22 Graph Generators ( graph gen
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uedges. For n > 3, a random maximal
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void random planar graph(graph& G,
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ool Is Bidirected(const graph& G) r
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list Delete Loops(graph& G) returns
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11.25 Dynamic Markov Chains ( dynam
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has a source and a target. These ar
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void parser.append(const char ∗ k
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11.27 The LEDA graph input/output f
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arithmetic demand for each function
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GRAPH TRANSITIVE CLOSURE(const gra
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template bool SHORTEST PATH T(cons
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template bool ALL PAIRS SHORTEST P
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The algorithms have the following a
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inline NT MAX FLOW GRH T(const grap
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12.5 Minimum Cut ( min cut ) A cut
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that the bipartition (A, B) is give
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The pre-instantiations for number t
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template bool CHECK MIN WEIGHT ASS
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in general graph. You may skip the
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Worst-Case Running Time: All functi
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list MIN WEIGHT PERFECT MATCHING T(
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12.10 Stable Matching ( stable matc
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12.11 Minimum Spanning Trees ( min
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12.13 Algorithms for Planar Graphs
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ool bool Is CCW Ordered(const graph
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ool void void void TUTTE EMBEDDING(
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Chapter 13 Graphs and Iterators 13.
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The purpose of each iterator is the
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template void set_and_check (graph
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In addition to the algorithm mentio
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13.3 Edge Iterators ( EdgeIt ) 1. D
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#include < LEDA/graph/graph iterato
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OutAdjIt OutAdjIt OutAdjIt it(const
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OutAdjIt& −−it performs one ste
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ool it.eol( ) returns !it.valid( )
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void it.del( ) deletes the marked l
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3. Operations void fc.init(const le
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We would have to write something li
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Equal is a class that compares two
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used only as a “Trojan horse,”
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typename DataAccessor :: value type
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13.14 Constant Accessors ( constant
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13.16 Node Attribute Accessors ( no
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GIT BFS< OutAdjIt, Queuetype, Mark
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3. dfs grow depth: a new adjacency
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• indegree stores for every node
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• Mark is a data accessor that ha
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OutAdjIt algorithm.curr adj( ) retu
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14.1 Points ( point ) 1. Definition
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point p.reflect(const point& q, con
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ool contained in simplex(const arra
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4. Operations point s.start( ) retu
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segment s.rotate90(const point& q,
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double r.direction( ) returns the d
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14.4 Straight Lines ( line ) 1. Def
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line l.translate(const vector& v) r
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14.5 Circles ( circle ) 1. Definiti
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circle C + const vector& v returns
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14.6 Polygons ( POLYGON ) 1. Defini
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const list& P.segments( ) returns t
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ool P.inside(const POINT & p) bool
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14.7 Generalized Polygons ( GEN POL
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GEN POLYGON GEN POLYGON :: make wea
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int P.side of(const POINT & p) regi
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14.8 Triangles ( triangle ) 1. Defi
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triangle t.rotate90(const point& q,
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double r.height( ) returns the heig
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14.10 Rational Points ( rat point )
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at point p.reflect(const rat point&
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int side of halfspace(const rat poi
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at segment s(const segment& s1 , in
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ational s.y abs( ) returns the y-ab
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14.12 Rational Rays ( rat ray ) 1.
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ool r.contains(const rat segment& s
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void l.normalize( ) simplifies the
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at line p bisector(const rat point&
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at circle C(const circle& c, int pr
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14.15 Rational Triangles ( rat tria
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at triangle t − const rat vector&
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list r.vertices( ) returns the vert
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list r.intersection(const rat recta
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int p.orientation(const real point&
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eal area(const real point& a, const
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14.18 Real Segments ( real segment
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ool s.intersection(const real segme
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14.19 Real Rays ( real ray ) 1. Def
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Non-Member Functions int orientatio
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4. Operations real point l.point1(
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int cmp slopes(const real line& l1
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eal circle C(const circle& c, int p
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ool radical axis(const real circle&
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eal point t.point3( ) returns the t
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14.23 Iso-oriented Real Rectangles
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eal rectangle r.translate(real dx,
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14.24 Geometry Algorithms ( geo alg
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edge TRIANGULATE PLANE MAP(GRAPH &
Page 520 and 521:
gen polygon MINKOWSKI SUM(const pol
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ool MIN WIDTH ANNULUS(const list& L
Page 524 and 525:
double CLOSEST PAIR(list& L, point&
Page 526 and 527:
14.25 Transformation ( TRANSFORM )
Page 528 and 529:
TRANSFORM reflection(const POINT& q
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void random points in unit cube(int
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void random points on unit circle(i
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const rat point& p.to rat point( )
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circle segment cs(const rat circle&
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list cs.intersection(const r circle
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14.29 Polygons with circular edges
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CHECK TYPE P.check simplicity( ) ch
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ool P.inside(const r circle point&
Page 546 and 547:
circle gen polygon P (KIND k); crea
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list P.intersection(const rat line&
Page 550 and 551:
double P.approximate area( ) approx
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const I& D.inf(dic2 item it) return
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15.2 Point Sets and Delaunay Triang
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ool T.is hull edge(edge e) as above
Page 558 and 559:
list T.range search(node v, const P
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15.3 Sets of Intervals ( interval s
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15.4 Sets of Parallel Segments ( se
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15.5 Sets of Parallel Rational Segm
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15.6 Planar Subdivisions ( subdivis
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16.1 Points in 3D-Space ( d3 point
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d3 point midpoint(const d3 point& a
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ool outside sphere(const d3 point&
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ool bool r.project xz(ray& m) if th
Page 576 and 577:
segment s.project xy( ) returns the
Page 578 and 579:
ool l.project(const d3 point& p, co
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double p.sqr dist(const d3 point& q
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16.6 Spheres in 3D-Space ( d3 spher
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16.7 Simplices in 3D-Space ( d3 sim
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16.8 Rational Points in 3D-Space (
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d3 rat point p.translate(const rat
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ool coplanar(const d3 rat point& a,
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d3 rat point random d3 rat point in
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void random d3 rat points on segmen
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ool r.project xy(rat ray& m) bool r
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ool l.project yz(rat line& m) if th
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16.11 Rational Segments in 3D-Space
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d3 rat segment s + const rat vector
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d3 plane p.to float( ) returns a fl
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16.13 Rational Spheres ( d3 rat sph
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16.14 Rational Simplices ( d3 rat s
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16.15 3D Convex Hull Algorithms ( d
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Chapter 17 Graphics This section de
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17.2 Windows ( window ) 1. Definiti
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18. The buttons per line parameter
Page 619 and 620:
void W.display(window& W 0 , int x,
Page 621 and 622:
void W.set show coord object(const
Page 623 and 624:
int W.menu bar height( ) returns th
Page 625 and 626:
void W.draw ray(point p, point q, l
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void W.draw filled ellipse(double x
Page 629 and 630:
void void void void void W.draw rou
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void void void W.draw edge(double x
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void W.screenshot(string fname, boo
Page 635 and 636:
int W.read mouse seg(const point& p
Page 637 and 638:
int W.read event(int& val, double&
Page 639 and 640:
window& W ≫ segment& s reads a se
Page 641 and 642:
panel item W.bool item(string s, bo
Page 643 and 644:
panel item W.int item(string s, int
Page 645 and 646:
int W.button(string s, const char
Page 647 and 648:
int W.button(string s, window& M, c
Page 649 and 650:
void void void W.redraw panel(panel
Page 651 and 652:
17.4 Menues ( menu ) 1. Definition
Page 653 and 654:
17.5 Postscript Files ( ps file ) 1
Page 655 and 656:
shape: the shape of the node (type
Page 657 and 658:
void gw.display(int x, int y) displ
Page 659 and 660:
param type gw.set param(node v, par
Page 661 and 662:
string gw.set edge index format(str
Page 663 and 664:
void void gw.transform layout(node
Page 665 and 666:
int bool bool gw.load layout(istrea
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void void gw.set edge slider handle
Page 669 and 670:
int bool bool bool bool bool bool g
Page 671 and 672:
void gw.restore all attributes( ) .
Page 673 and 674:
6. edge index format format This li
Page 675 and 676:
of GraphWin) are 0 (central pos) 1
Page 677 and 678:
17.7.1 A complete example LEDA.GRAP
Page 679 and 680:
17.8 Geometry Windows ( GeoWin ) 1.
Page 681 and 682:
0 will be drawn on top in the order
Page 683 and 684:
geowin new scene and geowin get obj
Page 685 and 686:
e inserted in the result scene. In
Page 687 and 688:
geo_scene sc_points = gw.new_scene(
Page 689 and 690:
} }; int main() { GeoWin gw; list L
Page 691 and 692:
virtual bool is_running(const GeoWi
Page 693 and 694:
geo scene void int GW.get scene wit
Page 695 and 696:
color GW.get fill color(geo scene s
Page 697 and 698:
void∗ GW.set client data(geo scen
Page 699 and 700:
color GW.set obj color(GeoBaseScene
Page 701 and 702:
template string GW.set obj label(G
Page 703 and 704:
string string GW.get bg pixmap( ) r
Page 705 and 706:
• A DRAG (button not released)
Page 707 and 708:
template bool GW.set post del hand
Page 709 and 710:
geowin_gui_rat_transform geowin_gui
Page 711 and 712:
ool GW.del(geo scenegroup GS , geo
Page 713 and 714:
void GW.set d3 fcn(geo scene sc, vo
Page 715 and 716:
17.9 Windows for 3d visualization (
Page 717 and 718:
int D.move( ) animates the contents
Page 719 and 720:
Chapter 18 Implementations 18.1 Lis
Page 721 and 722:
void clear(); int size() const; };
Page 723: 18.2.3 Sorted Sequences Any class s
Page 726 and 727: libGeoW is the LEDA library providi
Page 728 and 729: (b) Type VCVARS32 (VSVARS32). 2. Go
Page 730 and 731: LEDA MEMORY STD: If this is set, th
Page 732 and 733: When using graphics on Solaris syst
Page 734 and 735: (7) Double click on prog.cpp If you
Page 736 and 737: • extend LIB by Otherwise add ne
Page 738 and 739: and at least one of the following d
Page 740 and 741: • Copy leda .dll to the bin\ subd
Page 742 and 743: Preparations To install LEDA you on
Page 744 and 745: • libg .lib libl .lib for program
Page 746 and 747: cl -TP prog.c Programs using grap
Page 748 and 749: Automatic Setting Include header fi
Page 750 and 751: The default value is ”/MLd”, al
Page 752 and 753: 2. Windows 95/98: (a) Add the line
Page 754 and 755: Preparations To install LEDA you on
Page 756 and 757: A.16 Platforms When this manual was
Page 758 and 759: (b) For objects x and y of an indep
Page 760 and 761: A and B are different objects: A ==
Page 762 and 763: if (p.y > q.y) return 1; return 0;
Page 764 and 765: partypes={no, yes} Determines how p
Page 766 and 767: Stacks ( stack ) 1. Definition An i
Page 769 and 770: Bibliography [1] H. Alt, N. Blum, K
Page 771 and 772: [31] I. Fary: “On Straight Line R
Page 773: [67] M. Mignotte: Mathematics for C
Page 777 and 778: adj nodes(...) graph . . . . . . .
Page 779 and 780: circle gen polygon . . . . . . . .
Page 781 and 782: at ray . . . . . . . . . . . . . .
Page 783 and 784: CBCCoder< BlkCipher > . . . . . . .
Page 785 and 786: disconnect() leda socket . . . . .
Page 787 and 788: edges() GEN POLYGON . . . . . . . .
Page 789 and 790: finger locate pre...(...) sortseq .
Page 791 and 792: checksummer base . . . . . . . . .
Page 793 and 794: OMACCoder< BlkCipher > . . . . . .
Page 795 and 796: get stack() GIT DFS . . . . . . . .
Page 797 and 798: in pred(...) graph . . . . . . . .
Page 799 and 800: eal triangle . . . . . . . . . . .
Page 801 and 802: at segment . . . . . . . . . . . .
Page 803 and 804: eal rectangle . . . . . . . . . . .
Page 805 and 806: mw matching . . . . . . . . . . . .
Page 807 and 808: outdeg(...) graph . . . . . . . . .
Page 809 and 810: pos(...) POINT SET . . . . . . . .
Page 811 and 812: eal matrix . . . . . . . . . . . .
Page 813 and 814: FaceIt . . . . . . . . . . . . . .
Page 815 and 816: save gw(...) GraphWin . . . . . . .
Page 817 and 818: set edge index fo...(...) GraphWin
Page 819 and 820: GeoWin . . . . . . . . . . . . . .
Page 821 and 822: DeflateCoder . . . . . . . . . . .
Page 823 and 824: planar map . . . . . . . . . . . .
Page 825 and 826:
d3 rat point . . . . . . . . . . .
Page 827 and 828:
GraphWin . . . . . . . . . . . . .
Page 829 and 830:
at segment . . . . . . . . . . . .
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