Version 5.0 The LEDA User Manual

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ool coplanar(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d) returns true if points a, b, c, d are coplanar and false otherwise. int side of sphere(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& e) returns +1 (−1) if point e lies on the positive (negative) side of the oriented sphere through points a, b, c, and d, and 0 if e is contained in this sphere. int region of sphere(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& x) determines whether the point x lies inside (= +1), on (= 0), or outside (= −1) the sphere through points a, b, c, d, (equivalent to orientation(a, b, c, d) ∗ side of sphere(a, b, c, d, x)) Precondition: orientation(A) ≠ 0 bool contained in simplex(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& x) determines whether x is contained in the simplex spanned by the points a, b, c, d. Precondition: a, b, c, d are affinely independent. bool contained in simplex(const array& A, const d3 rat point& x) determines whether x is contained in the simplex spanned by the points in A. Precondition: A must have size ≤ 4 and the points in A must be affinely independent. bool contained in affine hull(const list& L, const d3 rat point& x) determines whether x is contained in the affine hull of the points in L. bool contained in affine hull(const array& A, const d3 rat point& x) determines whether x is contained in the affine hull of the points in A. int affine rank(const array& L) int affine rank(const array& A) computes the affine rank of the points in L. computes the affine rank of the points in A.
ool affinely independent(const list& L) decides whether the points in A are affinely independent. bool affinely independent(const array& A) decides whether the points in A are affinely independent. bool inside sphere(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& e) returns true if point e lies in the interior of the sphere through points a, b, c, and d, and false otherwise. bool outside sphere(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& e) returns true if point e lies in the exterior of the sphere through points a, b, c, and d, and false otherwise. bool on sphere(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c, const d3 rat point& d, const d3 rat point& e) returns true if points a, b, c, d, and e lie on a common sphere. d3 rat point point on positive side(const d3 rat point& a, const d3 rat point& b, const d3 rat point& c) returns a point d with orientation(a, b, c, d) > 0. Point Generators d3 rat point random d3 rat point in cube(int maxc) returns a point whose coordinates are random integers in [−maxc .. maxc]. void random d3 rat points in cube(int n, int maxc, list& L) returns a list L of n points . . . . d3 rat point random d3 rat point in square(int maxc) returns a point whose x and y-coordinates are random integers in [−maxc .. maxc]. <strong>The</strong> z-coordinate is zero. In 2d, this function is equivalent to random rat point in cube. void random d3 rat points in square(int n, int maxc, 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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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 &
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gen polygon MINKOWSKI SUM(const pol
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ool MIN WIDTH ANNULUS(const list& L
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double CLOSEST PAIR(list& L, point&
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14.25 Transformation ( TRANSFORM )
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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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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
Page 576 and 577: segment s.project xy( ) returns the
Page 578 and 579: ool l.project(const d3 point& p, co
Page 580 and 581: double p.sqr dist(const d3 point& q
Page 582 and 583: 16.6 Spheres in 3D-Space ( d3 spher
Page 584 and 585: 16.7 Simplices in 3D-Space ( d3 sim
Page 586 and 587: 16.8 Rational Points in 3D-Space (
Page 588 and 589: d3 rat point p.translate(const rat
Page 592 and 593: d3 rat point random d3 rat point in
Page 594 and 595: void random d3 rat points on segmen
Page 596 and 597: ool r.project xy(rat ray& m) bool r
Page 598 and 599: ool l.project yz(rat line& m) if th
Page 600 and 601: 16.11 Rational Segments in 3D-Space
Page 602 and 603: d3 rat segment s + const rat vector
Page 604 and 605: d3 plane p.to float( ) returns a fl
Page 606 and 607: 16.13 Rational Spheres ( d3 rat sph
Page 608 and 609: 16.14 Rational Simplices ( d3 rat s
Page 610 and 611: 16.15 3D Convex Hull Algorithms ( d
Page 613 and 614: Chapter 17 Graphics This section de
Page 615 and 616: 17.2 Windows ( window ) 1. Definiti
Page 617 and 618: 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
Page 627 and 628: void W.draw filled ellipse(double x
Page 629 and 630: void void void void void W.draw rou
Page 631 and 632: void void void W.draw edge(double x
Page 633 and 634: 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
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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
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 and 774:
[67] M. Mignotte: Mathematics for C
Page 775 and 776:
Index Symbols L A TEX . . . . . . .
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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Version 5.0 The LEDA User Manual

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