数据结构基础(21) --DFS与BFS

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‘);   //0
    g.addVertex(‘B‘);   //1
    g.addVertex(‘C‘);   //2
    g.addVertex(‘D‘);   //3
    g.addVertex(‘E‘);   //4

    g.addEdge(0, 1);    //A-B
    g.addEdge(0, 3);    //A-D
    g.addEdge(1, 0);    //B-A
    g.addEdge(1, 4);    //B-E
    g.addEdge(2, 4);    //C-E
    g.addEdge(3, 0);    //D-A
    g.addEdge(3, 4);    //D-E
    g.addEdge(4, 1);    //E-B
    g.addEdge(4, 2);    //E-C
    g.addEdge(4, 3);    //E-D

    g.printMatrix();

    cout << "DFS: ";
    g.DFS();
    cout << "\nBFS: ";
    g.BFS();
    return 0;
}