深度优先遍历DFS用邻接表表示的图

深度优先遍历用邻接表表示的图

DFS the Adjacency List Graph

[email protected]

一、简介

创建了图之后，我们希望从图中某个顶点出发访遍图中其余顶点，且使每个顶点仅被访问一次。这一过程就是图的遍历（Traversing Graph）。图的遍历算法是求解图的连通性问题、拓朴排序和求解关键路径等算法的基础。

深度优先搜索（Depth First Search）是一种递归的遍历方法。其过程为从图中任意一顶点出发，访问与其相连接的未被访问的顶点。因此，遍历图的过程实质上是对每个顶点查找其邻接点的过程。

 

二、实现代码

依然使用邻接表来表示图的存储结构，深度优先遍历程序如下代码所示：

  1: //------------------------------------------------------------------------------
  2: //	Copyright (c) 2012 eryar All Rights Reserved.
  3: //
  4: //		File    : Main.cpp
  5: //		Author  : [email protected]
  6: //		Date    : 2012-8-25 17:11
  7: //		Version : 0.1v
  8: //
  9: //	Description : Use Adjacency List data structure to store Digraph.
 10: //
 11: //==============================================================================
 12: 
 13: #include <vector>
 14: #include <string>
 15: #include <iostream>
 16: using namespace std;
 17: 
 18: struct SVertexNode
 19: {
 20:     bool          bIsVisited;
 21:     string        data;
 22:     vector<int> vecLoc;
 23: };
 24: 
 25: typedef struct SEdge
 26: {
 27:     int iInitialNode;
 28: 
 29:     int iTerminalNode;
 30: 
 31: }Edge;
 32: 
 33: typedef struct SGraph
 34: {
 35:     int iVertexNum;
 36:     int iEdgeNum;
 37:     vector<SVertexNode> vecVertex;
 38: }Graph;
 39: 
 40: ///////////////////////////////////////////////////////////////////////////////
 41: // Functions of Graph
 42: void    Initialize(Graph& g, int v);
 43: Edge    MakeEdge(int v, int w);
 44: void    InsertEdge(Graph& g, const Edge& e);
 45: void    ShowGraph(const Graph& g);
 46: 
 47: // Use Depth First Search method to Traverse the graph.
 48: void    DepthFirstSearch(Graph& g);
 49: void    DepthFirstSearch(Graph& g, int v);
 50: 
 51: ///////////////////////////////////////////////////////////////////////////////
 52: // Main function.
 53: 
 54: int main(int agrc, char* argv[])
 55: {
 56:     Graph   aGraph;
 57: 
 58:     // Initialize the graph.
 59:     Initialize(aGraph, 4);
 60: 
 61:     // Insert some edges to make graph.
 62:     InsertEdge(aGraph, MakeEdge(0, 1));
 63:     InsertEdge(aGraph, MakeEdge(0, 2));
 64:     InsertEdge(aGraph, MakeEdge(2, 3));
 65:     InsertEdge(aGraph, MakeEdge(3, 0));
 66: 
 67:     // Show the graph.
 68:     ShowGraph(aGraph);
 69: 
 70:     // DFS traverse the graph.
 71:     DepthFirstSearch(aGraph);
 72: 
 73:     return 0;
 74: }
 75: 
 76: ///////////////////////////////////////////////////////////////////////////////
 77: 
 78: /**
 79: * brief	Initialize the graph.
 80: *
 81: *       v: vertex number of the graph.
 82: */
 83: void Initialize( Graph& g, int v )
 84: {
 85:     char    szData[6];
 86:     SVertexNode node;
 87: 
 88:     g.iVertexNum    = v;
 89:     g.iEdgeNum      = 0;
 90: 
 91:     for (int i = 0; i < v; i++)
 92:     {
 93:         sprintf(szData, "V%d", i+1);
 94:         node.data   = szData;
 95:         node.bIsVisited = false;
 96:         g.vecVertex.push_back(node);
 97:     }
 98: }
 99: 
100: /**
101: * brief	Make an edge by initial node and terminal node.
102: */
103: Edge MakeEdge( int v, int w )
104: {
105:     Edge    e;
106: 
107:     e.iInitialNode  = v;
108:     e.iTerminalNode = w;
109: 
110:     return e;
111: }
112: 
113: /**
114: * brief	Insert an edge to the graph.
115: */
116: void InsertEdge( Graph& g, const Edge& e )
117: {
118:     g.vecVertex.at(e.iInitialNode).vecLoc.push_back(e.iTerminalNode);
119: 
120:     // If the graph is Undigraph, need do something here...
121:     //g.vecVertex.at(e.iTerminalNode).vecLoc.push_back(e.iInitialNode);
122: 
123:     g.iEdgeNum++;
124: }
125: 
126: /**
127: * brief	Show the graph.
128: */
129: void ShowGraph( const Graph& g )
130: {
131:     cout<<"Show the graph: "<<endl;
132: 
133:     for (int i = 0; i < g.iVertexNum; i++)
134:     {
135:         cout<<"Node "<<i<<"("<<g.vecVertex.at(i).data<<")";
136: 
137:         for (int j = 0; j < g.vecVertex.at(i).vecLoc.size(); j++)
138:         {
139:             cout<<"->"<<g.vecVertex.at(i).vecLoc.at(j);
140:         }
141: 
142:         cout<<endl;
143:     }
144: }
145: 
146: void DepthFirstSearch( Graph& g )
147: {
148:     cout<<"Depth First Search the graph:"<<endl;
149: 
150:     for (int i = 0; i < g.iVertexNum; i++)
151:     {
152:         if (!(g.vecVertex.at(i).bIsVisited))
153:         {
154:             DepthFirstSearch(g, i);
155:         }
156:     }
157: }
158: 
159: void DepthFirstSearch(Graph& g, int v)
160: {
161:     int     iAdjacent   = 0;
162:     SVertexNode node    = g.vecVertex.at(v);
163: 
164:     // Visit the vertex and mark it.
165:     cout<<g.vecVertex.at(v).data<<endl;
166:     g.vecVertex.at(v).bIsVisited = true;
167: 
168:     // Visit the adjacent vertex.
169:     for (int i = 0; i < node.vecLoc.size(); i++)
170:     {
171:         iAdjacent   = node.vecLoc.at(i);
172: 
173:         if (!(g.vecVertex.at(iAdjacent).bIsVisited))
174:         {
175:             DepthFirstSearch(g, iAdjacent);
176:         }
177:     }
178: 
179: }
180: 
181: 

三、输出结果

  1: Show the graph:
  2: Node 0(V1)->1->2
  3: Node 1(V2)
  4: Node 2(V3)->3
  5: Node 3(V4)->0
  6: Depth First Search the graph:
  7: V1
  8: V2
  9: V3
 10: V4