Version 5.0 The LEDA User Manual

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TRANSFORM reflection(const POINT& q, const POINT & r) TRANSFORM reflection(const POINT& q) returns the reflection across the straight line passing through q and r. returns the reflection across point q.
14.26 Point Generators ( point generators ) All generators are available for point, rat point, real point, d3 point, and d3 rat point. We use POINT to stand for any of these classes. The corresponding header files are called random point.h, random rat point.h, random real point.h, random d3 point.h, and random d3 rat point.h, respectively. These header files are included in the corresponding kernel header files, e.g., random rat point.h is part of rat kernel.h. We use the following naming conventions: square, circle, segment, and disk refer to twodimensional objects (even in 3d) and cube, ball, and sphere refer to full-dimensional objects, i.e, in 2d cube and square, ball and disk, and circle and sphere are synonymous. void random point in square(POINT & p, int maxc) returns a point whose x and y-coordinates are random integers in [−maxc .. maxc]. The z-coordinate is zero. void random points in square(int n, int maxc, list& L) returns a list L of n points . . . . void random point in unit square(POINT & p, int D = (1 ≪ 30) − 1) returns a point whose coordinates are random rationals of the form i/D where i is a random integer in the range [0 .. D]. The default value of D is 2 30 − 1. void random points in unit square(int n, int D, list& L) returns a list L of n points . . . . void random points in unit square(int n, list& L) void returns a list L of n points . . . . The default value of D is used. random point in cube(POINT & p, int maxc) returns a point whose coordinates are random integers in [−maxc .. maxc]. In 2d this function is equivalent to random point in square. void random points in cube(int n, int maxc, list& L) returns a list L of n points . . . . void random point in unit cube(POINT & p, int D = (1 ≪ 30) − 1) returns a point whose coordinates are random rationals of the form i/D where i is a random integer in the range [0 .. D]. The default value of D is 2 30 − 1. void random points in unit cube(int n, int D, list& L) returns a list L of n points . . . .
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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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Page 480 and 481: at circle C(const circle& c, int pr
Page 482 and 483: 14.15 Rational Triangles ( rat tria
Page 484 and 485: at triangle t − const rat vector&
Page 486 and 487: list r.vertices( ) returns the vert
Page 488 and 489: list r.intersection(const rat recta
Page 490 and 491: int p.orientation(const real point&
Page 492 and 493: eal area(const real point& a, const
Page 494 and 495: 14.18 Real Segments ( real segment
Page 496 and 497: ool s.intersection(const real segme
Page 498 and 499: 14.19 Real Rays ( real ray ) 1. Def
Page 500 and 501: Non-Member Functions int orientatio
Page 502 and 503: 4. Operations real point l.point1(
Page 504 and 505: int cmp slopes(const real line& l1
Page 506 and 507: eal circle C(const circle& c, int p
Page 508 and 509: ool radical axis(const real circle&
Page 510 and 511: eal point t.point3( ) returns the t
Page 512 and 513: 14.23 Iso-oriented Real Rectangles
Page 514 and 515: eal rectangle r.translate(real dx,
Page 516 and 517: 14.24 Geometry Algorithms ( geo alg
Page 518 and 519: edge TRIANGULATE PLANE MAP(GRAPH &
Page 520 and 521: gen polygon MINKOWSKI SUM(const pol
Page 522 and 523: 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 530 and 531: void random points in unit cube(int
Page 532 and 533: void random points on unit circle(i
Page 534 and 535: const rat point& p.to rat point( )
Page 536 and 537: circle segment cs(const rat circle&
Page 538 and 539: list cs.intersection(const r circle
Page 540 and 541: 14.29 Polygons with circular edges
Page 542 and 543: CHECK TYPE P.check simplicity( ) ch
Page 544 and 545: ool P.inside(const r circle point&
Page 546 and 547: circle gen polygon P (KIND k); crea
Page 548 and 549: list P.intersection(const rat line&
Page 550 and 551: double P.approximate area( ) approx
Page 552 and 553: const I& D.inf(dic2 item it) return
Page 554 and 555: 15.2 Point Sets and Delaunay Triang
Page 556 and 557: ool T.is hull edge(edge e) as above
Page 558 and 559: list T.range search(node v, const P
Page 560 and 561: 15.3 Sets of Intervals ( interval s
Page 562 and 563: 15.4 Sets of Parallel Segments ( se
Page 564 and 565: 15.5 Sets of Parallel Rational Segm
Page 566 and 567: 15.6 Planar Subdivisions ( subdivis
Page 568 and 569: 16.1 Points in 3D-Space ( d3 point
Page 570 and 571: d3 point midpoint(const d3 point& a
Page 572 and 573: ool outside sphere(const d3 point&
Page 574 and 575: ool bool r.project xz(ray& m) if th
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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
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void W.display(window& W 0 , int x,
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void W.set show coord object(const
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int W.menu bar height( ) returns th
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void W.draw ray(point p, point q, l
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void W.draw filled ellipse(double x
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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
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int W.read mouse seg(const point& p
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int W.read event(int& val, double&
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window& W ≫ segment& s reads a se
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panel item W.bool item(string s, bo
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panel item W.int item(string s, int
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int W.button(string s, const char
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int W.button(string s, window& M, c
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void void void W.redraw panel(panel
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17.4 Menues ( menu ) 1. Definition
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17.5 Postscript Files ( ps file ) 1
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shape: the shape of the node (type
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void gw.display(int x, int y) displ
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param type gw.set param(node v, par
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string gw.set edge index format(str
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void void gw.transform layout(node
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int bool bool gw.load layout(istrea
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void void gw.set edge slider handle
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int bool bool bool bool bool bool g
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void gw.restore all attributes( ) .
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6. edge index format format This li
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of GraphWin) are 0 (central pos) 1
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17.7.1 A complete example LEDA.GRAP
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17.8 Geometry Windows ( GeoWin ) 1.
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0 will be drawn on top in the order
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geowin new scene and geowin get obj
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e inserted in the result scene. In
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geo_scene sc_points = gw.new_scene(
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} }; int main() { GeoWin gw; list L
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virtual bool is_running(const GeoWi
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geo scene void int GW.get scene wit
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color GW.get fill color(geo scene s
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void∗ GW.set client data(geo scen
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color GW.set obj color(GeoBaseScene
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template string GW.set obj label(G
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string string GW.get bg pixmap( ) r
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• A DRAG (button not released)
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template bool GW.set post del hand
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geowin_gui_rat_transform geowin_gui
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ool GW.del(geo scenegroup GS , geo
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void GW.set d3 fcn(geo scene sc, vo
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17.9 Windows for 3d visualization (
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int D.move( ) animates the contents
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Chapter 18 Implementations 18.1 Lis
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void clear(); int size() const; };
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18.2.3 Sorted Sequences Any class s
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libGeoW is the LEDA library providi
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(b) Type VCVARS32 (VSVARS32). 2. Go
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LEDA MEMORY STD: If this is set, th
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When using graphics on Solaris syst
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(7) Double click on prog.cpp If you
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• extend LIB by Otherwise add ne
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and at least one of the following d
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• Copy leda .dll to the bin\ subd
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Preparations To install LEDA you on
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• libg .lib libl .lib for program
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cl -TP prog.c Programs using grap
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Automatic Setting Include header fi
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The default value is ”/MLd”, al
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2. Windows 95/98: (a) Add the line
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Preparations To install LEDA you on
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A.16 Platforms When this manual was
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(b) For objects x and y of an indep
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A and B are different objects: A ==
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if (p.y > q.y) return 1; return 0;
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partypes={no, yes} Determines how p
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Stacks ( stack ) 1. Definition An i
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Bibliography [1] H. Alt, N. Blum, K
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[31] I. Fary: “On Straight Line R
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[67] M. Mignotte: Mathematics for C
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Index Symbols L A TEX . . . . . . .
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adj nodes(...) graph . . . . . . .
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circle gen polygon . . . . . . . .
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at ray . . . . . . . . . . . . . .
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CBCCoder< BlkCipher > . . . . . . .
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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 . . . . . . . . . . . .
show all

Version 5.0 The LEDA User Manual

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