數據結構基礎(21) --DFS與BFS

DFS

    從圖中某個頂點V0 出發，訪問此頂點，然後依次從V0的各個未被訪問的鄰接點出發深度優先搜索遍歷圖，直至圖中所有和V0有路徑相通的頂點都被訪問到(使用堆棧).

 

//使用鄰接矩陣存儲的無向圖的深度優先遍歷
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);
        }
    }

    //使其還可以再深/廣度優先搜索
    for (int i = 0; i < nVerts; ++i)
        vertexList[i]->wasVisted = false;
}

BFS

   從圖中的某個頂點V0出發，並在訪問此頂點之後依次訪問V0的所有未被訪問過的鄰接點，之後按這些頂點被訪問的先後次序依次訪問它們的鄰接點，直至圖中所有和V0有路徑相通的頂點都被訪問到.

  若此時圖中尚有頂點未被訪問，則另選圖中一個未曾被訪問的頂點作起始點，重複上述過程，直至圖中所有頂點都被訪問到爲止(使用隊列)。

 

//使用鄰接矩陣存儲的無向圖的廣度優先遍歷
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-完整代碼

const int MAX_VERTS = 20;
//頂點
template <typename Type>
class Vertex
{
public:
    Vertex(const Type &_node = Type())
        : node(_node), wasVisted(false) {}

public:
    bool wasVisted; //增加一個訪問位
    Type node;
};
//圖
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);
        }
    }

    //使其還可以再深度優先搜索
    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;
}
//獲取下一個尚未訪問的連通節點
template <typename Type>
int Graph<Type>::getAdjUnvisitedVertex(int v)
{
    for (int j = 0; j < nVerts; ++j)
    {
        //首先是鄰接的, 並且是未訪問過的
        if ((adjMatrix[v][j] == 1) &&
                (vertexList[j]->wasVisted == false))
            return j;
    }
    return -1;
}
//打印節點信息
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)
{
    //無向圖
    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;
    }
}

//測試代碼
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;
}

原文地址：http://blog.csdn.net/zjf280441589/article/details/42710977