数据结构精品课程ppt 16

Set of Neighbors B A B E C 4 2 3 4 1 E 2 C 7 D 6
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vertexInfo Object A vertexInfo object consists of seven data members. The first two members, called vtxMapLoc and edges, identify the vertex in the map and its adjacency set.

Graph Categories A graph is connected if each pair of vertices have a path between them A complete graph is a connected graph in which each pair of vertices are linked by an edge
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Adjacency Set
Vertices Set of Neighbors B C B 1 1 1 D 1 C 1
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Vertices A
locA edges inDegree = 1 A B locB C D locD locB vtxMap 3(D) 1 edges inDegree = 1 .... 2(C) 1 locD edges inDegree = 1 .... 3 locC 2 0 1 2 3 1 locA vInfo 0 .... 1(B) 1 2(C) 1 locC edges inDegree = 2 .... 0(A) 1
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Class Graph
Class graph{ { private: typedef map<T,int> vertexMap; vertexMap vtxMap; vector<vertexInfo<T> > vInfo; int numVertices; int numEdges; stack<int> availStack; int getvInfoIndex(const T& v) const;
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Class Neighbor
class neighbor { public: int dest; int weight;
neighbor(int d=0, int c=0): dest(d), weight(c){} friend bool operator< (const neighbor& lhs, const neighbor& rhs) { return lhs.dest < rhs.dest; } friend bool operator== (const neighbor& lhs, const neighbor& rhs) { return lhs.dest == rhs.dest; } };
container, called vtxMap, where a vertex name is the key of type T. The int field of a map object is an index into a vector of vertexInfo objects, called vInfo. The size of the vector is initially the number of vertices in the graph, and there is a 1-1 correspondence between an entry in the map and a vertexInfo entry in the vector
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Class Graph
public: void insertEdge(const T& v1, const T& v2, int w); void insertVertex(const T& v); void eraseEdge(const T& v1, const T& v2); void eraseVertex(const T& v); void clear(); iterator begin(); iterator end(); const_iterator begin() const; const_iterator end() const; }
Adjacency Set
Vertex v in a map vertexInfo Object
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Vertex Map and Vector vInfo

To store the vertices in a graph, we provide a map<T,int>
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Class Graph
public: graph(); graph(const graph<T>& g); int numberOfVertices() const; int numberOfEdges() const; bool empty() const; int getWeight(const T& v1, const T& v2) const; void setWeight(const T& v1, const T& v2, int w); int inDegree(const T& v) const; int outDegree(const T& v) const; set<T> getNeighbors(const T& v) const;
const set<neighbor>& edgeSet = vInfo[pos1].edges; set<neighbor>::const_iterator setIter;
if ((setIter = edgeSet.find(neighbor(pos2))) != edgeSet.end()) return (*setIter).weight; else return -1; }
vt xMapLoc edges inDegree occupied color mIt er (it erat or locat ion) vert ex index dat aValue dist ance
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vt xMap
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index
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VtxMap and Vinfo Example
Adjacency Matrix Adjacency Set vertexInfo Object Vertex Map and Vector vInfo
VtxMap and Vinfo Example
Breadth-First Search Algorithm Dfs()
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Class VertexInfo
template <typename T> class vertexInfo { public: enum vertexColor { WHITE, GRAY, BLACK }; map<T,int>::iterator vtxMapLoc; set<neighbor> edges; int inDegree; bool occupied; vertexColor color; int dataValue; int parent; vertexInfo(): inDegree(0), occupied(true){} vertexInfo(map<T,int>::iterator iter): vtxMapLoc(iter), inDegree(0), occupied(true){} };
(a: Connected)
(b: Disconnected)
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(c: Complete)
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Example of Digraph Graph with ordered edges are called directed graphs or digraphs
A C B D E Vertices V = {A, B, C, D, E} Edges E = {(A,B), (A,C), (A,D), (B,D), (B,E), (C,A), (D,E)}
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Connectedness of Digraph Strongly connected if there is a path from any vertex to any other vertex. Weakly connected if, for each pair of vertices vi and vj, there is either a path P(vi, vj) or a path P(vi,vj).