DFS

从图中某个顶点V0 出发，访问此顶点，然后依次从V0的各个未被访问的邻接点出发深度优先搜索遍历图，直至图中所有和V0有路径相通的顶点都被访问到(使用堆栈).

//使用邻接矩阵存储的无向图的深度优先遍历
template <typename Type>
void Graph<Type>::DFS()
{stack<int> iStack;showVertex(0);vertexList[0]->wasVisted = true;iStack.push(0);while (!iStack.empty()){int top = iStack.top();int v = getAdjUnvisitedVertex(top);if (v == -1){iStack.pop();}else{showVertex(v);vertexList[v]->wasVisted = true;iStack.push(v);}}//使其还可以再深/广度优先搜索for (int i = 0; i < nVerts; ++i)vertexList[i]->wasVisted = false;
}

BFS

从图中的某个顶点V0出发，并在访问此顶点之后依次访问V0的所有未被访问过的邻接点，之后按这些顶点被访问的先后次序依次访问它们的邻接点，直至图中所有和V0有路径相通的顶点都被访问到.

若此时图中尚有顶点未被访问，则另选图中一个未曾被访问的顶点作起始点，重复上述过程，直至图中所有顶点都被访问到为止(使用队列)。

//使用邻接矩阵存储的无向图的广度优先遍历
template <typename Type>
void Graph<Type>::BFS()
{queue<int> iQueue;showVertex(0);vertexList[0]->wasVisted = true;iQueue.push(0);while (!iQueue.empty()){int front = iQueue.front();iQueue.pop();int v = getAdjUnvisitedVertex(front);while (v != -1){showVertex(v);vertexList[v]->wasVisted = true;iQueue.push(v);v = getAdjUnvisitedVertex(front);}}for (int i = 0; i < nVerts; ++i)vertexList[i]->wasVisted = false;
}

附-完整代码

const int MAX_VERTS = 20;
//顶点
template <typename Type>
class Vertex
{
public:Vertex(const Type &_node = Type()): node(_node), wasVisted(false) {}public:bool wasVisted;  //增加一个访问位Type node;
};
//图
template <typename Type>
class Graph
{
public:Graph();~Graph();void addVertex(const Type &vertex);void addEdge(int start, int end);void printMatrix();void showVertex(int v);void DFS();void BFS();private:int getAdjUnvisitedVertex(int v);private:Vertex<Type>* vertexList[MAX_VERTS];int nVerts;int adjMatrix[MAX_VERTS][MAX_VERTS];
};
template <typename Type>
void Graph<Type>::DFS()
{stack<int> iStack;showVertex(0);vertexList[0]->wasVisted = true;iStack.push(0);while (!iStack.empty()){int top = iStack.top();int v = getAdjUnvisitedVertex(top);if (v == -1){iStack.pop();}else{showVertex(v);vertexList[v]->wasVisted = true;iStack.push(v);}}//使其还可以再深度优先搜索for (int i = 0; i < nVerts; ++i)vertexList[i]->wasVisted = false;
}template <typename Type>
void Graph<Type>::BFS()
{queue<int> iQueue;showVertex(0);vertexList[0]->wasVisted = true;iQueue.push(0);while (!iQueue.empty()){int front = iQueue.front();iQueue.pop();int v = getAdjUnvisitedVertex(front);while (v != -1){showVertex(v);vertexList[v]->wasVisted = true;iQueue.push(v);v = getAdjUnvisitedVertex(front);}}for (int i = 0; i < nVerts; ++i)vertexList[i]->wasVisted = false;
}
//获取下一个尚未访问的连通节点
template <typename Type>
int Graph<Type>::getAdjUnvisitedVertex(int v)
{for (int j = 0; j < nVerts; ++j){//首先是邻接的, 并且是未访问过的if ((adjMatrix[v][j] == 1) &&(vertexList[j]->wasVisted == false))return j;}return -1;
}
//打印节点信息
template <typename Type>
void Graph<Type>::showVertex(int v)
{cout << vertexList[v]->node << ' ';
}template <typename Type>
Graph<Type>::Graph():nVerts(0)
{for (int i = 0; i < MAX_VERTS; ++i)for (int j = 0; j < MAX_VERTS; ++j)adjMatrix[i][j] = 0;
}
template <typename Type>
Graph<Type>::~Graph()
{for (int i = 0; i < nVerts; ++i)delete vertexList[i];
}
template <typename Type>
void Graph<Type>::addVertex(const Type &vertex)
{vertexList[nVerts ++] = new Vertex<Type>(vertex);
}
template <typename Type>
void Graph<Type>::addEdge(int start, int end)
{//无向图adjMatrix[start][end] = 1;adjMatrix[end][start] = 1;
}
template <typename Type>
void Graph<Type>::printMatrix()
{for (int i = 0; i < nVerts; ++i){for (int j = 0; j < nVerts; ++j)cout << adjMatrix[i][j] << ' ';cout << endl;}
}//测试代码
int main()
{Graph<char> g;g.addVertex('A');   //0g.addVertex('B');   //1g.addVertex('C');   //2g.addVertex('D');   //3g.addVertex('E');   //4g.addEdge(0, 1);    //A-Bg.addEdge(0, 3);    //A-Dg.addEdge(1, 0);    //B-Ag.addEdge(1, 4);    //B-Eg.addEdge(2, 4);    //C-Eg.addEdge(3, 0);    //D-Ag.addEdge(3, 4);    //D-Eg.addEdge(4, 1);    //E-Bg.addEdge(4, 2);    //E-Cg.addEdge(4, 3);    //E-Dg.printMatrix();cout << "DFS: ";g.DFS();cout << "\nBFS: ";g.BFS();return 0;
}