第7章 图

leetcode刷了一大半，数组，链表，树，队列和栈的题目已经做了好多，感觉比较扎实了。突然发现后面好多关于图算法的问题，没办法，又继续开始学习“图”这种数据结构。折腾了一天，把图的创建，深度优先级遍历（DFS）和广度优先级遍历（BFS）都用c++写出来了，算法参照了《算法导论》和《数据结构和算法》。
遍历是各种图操作的基本思路，所以一定要熟练掌握。

注：

1. 图的表示采用了邻接链表，因为这种结构在存储方面比较节约空间，在遍历时的时间复杂度也比用邻接矩阵时更好，两种遍历都为O(V+E)

2.下面以有向图来展示遍历的过程，无向图类似，只是在添加边调用addEdge()函数时再加一条相反的边即可。

/*A C++ Program to demonstrate adjacency list representation of graphsCreate a adjacency list representation of graphsBFS based on adjacency list representation of graphsBFS based on adjacency list representation of graphs*/#include <iostream>#include <queue>#include <vector>using namespace std;// A structure to represent an adjacency list nodestruct AdjListNode{    int dest;    AdjListNode* next;    AdjListNode(int d): dest(d), next(NULL) {}};// A structure to represent an adjacency liststruct AdjList{    AdjListNode *head;  // pointer to head node of list    AdjList(): head(NULL) {}};// A structure to represent a graph. A graph is an array of adjacency lists.// Size of array will be V (number of vertices in graph)struct Graph{    int V;    AdjList* array;    Graph(int vertex): V(vertex)    {        array = new AdjList[V];        for(int i = 0; i < vertex; i++)            array[i].head = new AdjListNode(i);    }    ~Graph()    {        AdjListNode* it;        AdjListNode* prev;        for(int i = 0; i < V; i++)        {            it = array[i].head;            while(it)            {                prev = it;                it = it->next;                delete prev;            }        }        delete[] array;    }};// A utility function to create a new adjacency list nodeAdjListNode* newAdjListNode(int dest){    AdjListNode* node = new AdjListNode(dest);    return node;}// A utility function that creates a graph of V verticesGraph* createGraph(int V){    Graph* graph = new Graph(V);    return graph;}// Adds an edge to an directed graphvoid addEdge(struct Graph* graph, int src, int dest){    //src to dest    AdjListNode* node = newAdjListNode(dest);    node->next = graph->array[src].head->next;    graph->array[src].head->next = node;    /*    //dest to src (if it's an undirected graph)    node = newAdjListNode(src);    node->next = graph->array[dest].head;    graph->array[dest].head = node;    */}// A utility function to print the adjacenncy list representation of graphvoid printGraph(struct Graph* graph){    for (int v = 0; v < graph->V; ++v)    {        AdjListNode* pCrawl = graph->array[v].head;        cout << endl << " Adjacency list of vertex " << v << endl << " ";        while (pCrawl)        {            cout << pCrawl->dest << "-> ";            pCrawl = pCrawl->next;        }        cout << "#" << endl;    }}void BreadthFirstSearch(Graph* graph){    cout << "BreadthFirstSearch print: " << endl;    queue<AdjListNode*> q;    vector<bool> visited(graph->V, false);    AdjListNode* cur = NULL;    for(int i = 0; i < graph->V; i++)    {        if(!visited[i])        {            visited[i] = true;            cout << i << " -> ";            cur = graph->array[i].head;            q.push(cur);            while(!q.empty())            {                cur = q.front();                if(cur->dest < graph->V)                    cur = graph->array[cur->dest].head;                q.pop();                while(cur)                {                    if(!visited[cur->dest])                    {                        visited[cur->dest] = true;                        cout << cur->dest << " -> ";                        q.push(cur);                    }                    cur = cur->next;                }            }        }    }    cout << "#" << endl;}void DFS_helper(Graph* graph, int v, vector<bool>& visited){    cout << v << " -> ";    if(v >= graph->V || v < 0)        return;    visited[v] = true;    AdjListNode* cur = graph->array[v].head->next;    while(cur)    {        DFS_helper(graph, cur->dest, visited);        cur = cur->next;    }}void DepthFirstSearch(Graph* graph){    cout << "DepthFirstSearch print: " << endl;    vector<bool> visited(graph->V, false);    for(int i = 0; i < graph->V; i++)    {        if(!visited[i])            DFS_helper(graph, i, visited);    }    cout << "#" << endl;}// Driver program to test above functionsint main(){    // create the graph given in above fugure    int V = 7;    struct Graph* graph = createGraph(V);    addEdge(graph, 0, 2);    addEdge(graph, 0, 1);    addEdge(graph, 1, 4);    addEdge(graph, 1, 3);    addEdge(graph, 2, 6);    addEdge(graph, 2, 5);    addEdge(graph, 3, 7);    // print the adjacency list representation of the above graph    printGraph(graph);    //BFS and DFS    BreadthFirstSearch(graph);    DepthFirstSearch(graph);    return 0;}