拓扑排序

拓扑排序

/*** C++: 无回路有向图(Directed Acyclic Graph)的拓扑排序* 该DAG图是通过邻接表实现的。** @author skywang* @date 2014/04/22*/#include <iomanip>#include <iostream>#include <vector>#include <cstring>using namespace std;#define MAX 100// 邻接表class ListDG{private: // 内部类 // 邻接表中表对应的链表的顶点class ENode{int ivex; // 该边所指向的顶点的位置ENode *nextEdge; // 指向下一条弧的指针friend class ListDG;};// 邻接表中表的顶点class VNode{char data; // 顶点信息ENode *firstEdge; // 指向第一条依附该顶点的弧friend class ListDG;};private: // 私有成员int mVexNum; // 图的顶点的数目int mEdgNum; // 图的边的数目VNode *mVexs; // 图的顶点数组public:// 创建邻接表对应的图(自己输入)ListDG();// 创建邻接表对应的图(用已提供的数据)ListDG(char vexs[], int vlen, char edges[][2], int elen);~ListDG();// 深度优先搜索遍历图void DFS();// 广度优先搜索（类似于树的层次遍历）void BFS();// 打印邻接表图void print();// 拓扑排序int topologicalSort();private:// 读取一个输入字符char readChar();// 返回ch的位置int getPosition(char ch);// 深度优先搜索遍历图的递归实现void DFS(int i, int *visited);// 将node节点链接到list的最后void linkLast(ENode *list, ENode *node);};/** 创建邻接表对应的图(自己输入)*/ListDG::ListDG(){char c1, c2;int v, e;int i, p1, p2;ENode *node1, *node2;// 输入"顶点数"和"边数"cout << "input vertex number: ";cin >> mVexNum;cout << "input edge number: ";cin >> mEdgNum;if (mVexNum < 1 || mEdgNum < 1 || (mEdgNum >(mVexNum * (mVexNum - 1)))){cout << "input error: invalid parameters!" << endl;return;}// 初始化"邻接表"的顶点mVexs = new VNode[mVexNum];for (i = 0; i<mVexNum; i++){cout << "vertex(" << i << "): ";mVexs[i].data = readChar();mVexs[i].firstEdge = NULL;}// 初始化"邻接表"的边for (i = 0; i<mEdgNum; i++){// 读取边的起始顶点和结束顶点cout << "edge(" << i << "): ";c1 = readChar();c2 = readChar();p1 = getPosition(c1);p2 = getPosition(c2);// 初始化node1node1 = new ENode();node1->ivex = p2;// 将node1链接到"p1所在链表的末尾"if (mVexs[p1].firstEdge == NULL)mVexs[p1].firstEdge = node1;elselinkLast(mVexs[p1].firstEdge, node1);}}/** 创建邻接表对应的图(用已提供的数据)*/ListDG::ListDG(char vexs[], int vlen, char edges[][2], int elen){char c1, c2;int i, p1, p2;ENode *node1, *node2;// 初始化"顶点数"和"边数"mVexNum = vlen;mEdgNum = elen;// 初始化"邻接表"的顶点mVexs = new VNode[mVexNum];for (i = 0; i<mVexNum; i++){mVexs[i].data = vexs[i];mVexs[i].firstEdge = NULL;}// 初始化"邻接表"的边for (i = 0; i<mEdgNum; i++){// 读取边的起始顶点和结束顶点c1 = edges[i][0];c2 = edges[i][1];p1 = getPosition(c1);p2 = getPosition(c2);// 初始化node1node1 = new ENode();node1->ivex = p2;// 将node1链接到"p1所在链表的末尾"if (mVexs[p1].firstEdge == NULL)mVexs[p1].firstEdge = node1;elselinkLast(mVexs[p1].firstEdge, node1);}}/** 析构函数*/ListDG::~ListDG(){ENode *node;for (int i = 0; i<mEdgNum; i++){node = mVexs[i].firstEdge;while (node != NULL){delete node;node = node->nextEdge;}}delete[] mVexs;}/** 将node节点链接到list的最后*/void ListDG::linkLast(ENode *list, ENode *node){ENode *p = list;while (p->nextEdge)p = p->nextEdge;p->nextEdge = node;}/** 返回ch的位置*/int ListDG::getPosition(char ch){int i;for (i = 0; i<mVexNum; i++)if (mVexs[i].data == ch)return i;return -1;}/** 读取一个输入字符*/char ListDG::readChar(){char ch;do {cin >> ch;} while (!((ch >= 'a'&&ch <= 'z') || (ch >= 'A'&&ch <= 'Z')));return ch;}/** 深度优先搜索遍历图的递归实现*/void ListDG::DFS(int i, int *visited){ENode *node;visited[i] = 1;cout << mVexs[i].data << " ";node = mVexs[i].firstEdge;while (node != NULL){if (!visited[node->ivex])DFS(node->ivex, visited);node = node->nextEdge;}}/** 深度优先搜索遍历图*/void ListDG::DFS(){int i;int *visited; // 顶点访问标记visited = new int[mVexNum];// 初始化所有顶点都没有被访问for (i = 0; i < mVexNum; i++)visited[i] = 0;cout << "== DFS: ";for (i = 0; i < mVexNum; i++){if (!visited[i])DFS(i, visited);}cout << endl;delete[] visited;}/** 广度优先搜索（类似于树的层次遍历）*/void ListDG::BFS(){int head = 0;int rear = 0;int *queue; // 辅组队列int *visited; // 顶点访问标记int i, j, k;ENode *node;queue = new int[mVexNum];visited = new int[mVexNum];for (i = 0; i < mVexNum; i++)visited[i] = 0;cout << "== BFS: ";for (i = 0; i < mVexNum; i++){if (!visited[i]){visited[i] = 1;cout << mVexs[i].data << " ";queue[rear++] = i; // 入队列}while (head != rear){j = queue[head++]; // 出队列node = mVexs[j].firstEdge;while (node != NULL){k = node->ivex;if (!visited[k]){visited[k] = 1;cout << mVexs[k].data << " ";queue[rear++] = k;}node = node->nextEdge;}}}cout << endl;delete[] visited;delete[] queue;}/** 打印邻接表图*/void ListDG::print(){int i, j;ENode *node;cout << "== List Graph:" << endl;for (i = 0; i < mVexNum; i++){cout << i << "(" << mVexs[i].data << "): ";node = mVexs[i].firstEdge;while (node != NULL){cout << node->ivex << "(" << mVexs[node->ivex].data << ") ";node = node->nextEdge;}cout << endl;}}/** 拓扑排序** 返回值：* -1 -- 失败(由于内存不足等原因导致)* 0 -- 成功排序，并输入结果* 1 -- 失败(该有向图是有环的)*/int ListDG::topologicalSort(){int i, j;int index = 0;int head = 0; // 辅助队列的头int rear = 0; // 辅助队列的尾int *queue; // 辅组队列int *ins; // 入度数组char *tops; // 拓扑排序结果数组，记录每个节点的排序后的序号。ENode *node;ins = new int[mVexNum];queue = new int[mVexNum];tops = new char[mVexNum];memset(ins, 0, mVexNum * sizeof(int));memset(queue, 0, mVexNum * sizeof(int));memset(tops, 0, mVexNum * sizeof(char));// 统计每个顶点的入度数for (i = 0; i < mVexNum; i++){node = mVexs[i].firstEdge;while (node != NULL){ins[node->ivex]++;node = node->nextEdge;}}// 将所有入度为0的顶点入队列for (i = 0; i < mVexNum; i++)if (ins[i] == 0)queue[rear++] = i; // 入队列while (head != rear) // 队列非空{j = queue[head++]; // 出队列。j是顶点的序号tops[index++] = mVexs[j].data; // 将该顶点添加到tops中，tops是排序结果node = mVexs[j].firstEdge; // 获取以该顶点为起点的出边队列   // 将与"node"关联的节点的入度减1；   // 若减1之后，该节点的入度为0；则将该节点添加到队列中。while (node != NULL){// 将节点(序号为node->ivex)的入度减1。ins[node->ivex]--;// 若节点的入度为0，则将其"入队列"if (ins[node->ivex] == 0)queue[rear++] = node->ivex; // 入队列node = node->nextEdge;}}if (index != mVexNum){cout << "Graph has a cycle" << endl;delete queue;delete ins;delete tops;return 1;}// 打印拓扑排序结果cout << "== TopSort: ";for (i = 0; i < mVexNum; i++)cout << tops[i] << " ";cout << endl;delete queue;delete ins;delete tops;return 0;}int main(){char vexs[] = { 'A', 'B', 'C', 'D', 'E', 'F', 'G' };char edges[][2] = {{ 'A', 'G' },{ 'B', 'A' },{ 'B', 'D' },{ 'C', 'F' },{ 'C', 'G' },{ 'D', 'E' },{ 'D', 'F' } };int vlen = sizeof(vexs) / sizeof(vexs[0]);int elen = sizeof(edges) / sizeof(edges[0]);ListDG* pG;// 自定义"图"(输入矩阵队列)//pG = new ListDG();// 采用已有的"图"pG = new ListDG(vexs, vlen, edges, elen);pG->print(); // 打印图 //pG->DFS(); // 深度优先遍历 //pG->BFS(); // 广度优先遍历pG->topologicalSort(); // 拓扑排序system("pause");return 0;}

== List Graph:0(A): 6(G)1(B): 0(A) 3(D)2(C): 5(F) 6(G)3(D): 4(E) 5(F)4(E):5(F):6(G):== TopSort: B C A D G E F请按任意键继续. . .