/*** C++: 無回路有向圖(Directed Acyclic Graph)的拓撲排序* 該DAG圖是通過鄰接表實現的。 ** @author judyge* @date 2014/04/22*/#include <iomanip> #include <iostream> #include <vector> #include <cstring> using namespace std;#define MAX 100 // 鄰接表 class ListDG {private: // 內部類// 鄰接表中表對應的鏈表的頂點class ENode{int ivex; // 該邊所指向的頂點的位置ENode *nextEdge; // 指向下一條弧的指針friend class ListDG;};// 鄰接表中表的頂點class VNode{char data; // 頂點信息ENode *firstEdge; // 指向第一條依附該頂點的弧friend class ListDG;};private: // 私有成員int mVexNum; // 圖的頂點的數目int mEdgNum; // 圖的邊的數目VNode *mVexs; // 圖的頂點數組public:// 創建鄰接表對應的圖(自己輸入)ListDG();// 創建鄰接表對應的圖(用已提供的數據)ListDG(char vexs[], int vlen, char edges[][2], int elen);~ListDG();// 深度優先搜索遍歷圖void DFS();// 廣度優先搜索（類似于樹的層次遍歷）void BFS();// 打印鄰接表圖void print();// 拓撲排序int topologicalSort();private:// 讀取一個輸入字符char readChar();// 返回ch的位置int getPosition(char ch);// 深度優先搜索遍歷圖的遞歸實現void DFS(int i, int *visited);// 將node節點鏈接到list的最后void linkLast(ENode *list, ENode *node); };/** 創建鄰接表對應的圖(自己輸入)*/ ListDG::ListDG() {char c1, c2;int v, e;int i, p1, p2;ENode *node1, *node2;// 輸入"頂點數"和"邊數"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"鄰接表"的頂點mVexs = new VNode[mVexNum];for(i=0; i<mVexNum; i++){cout << "vertex(" << i << "): ";mVexs[i].data = readChar();mVexs[i].firstEdge = NULL;}// 初始化"鄰接表"的邊for(i=0; i<mEdgNum; i++){// 讀取邊的起始頂點和結束頂點cout << "edge(" << i << "): ";c1 = readChar();c2 = readChar();p1 = getPosition(c1);p2 = getPosition(c2);// 初始化node1node1 = new ENode();node1->ivex = p2;// 將node1鏈接到"p1所在鏈表的末尾"if(mVexs[p1].firstEdge == NULL)mVexs[p1].firstEdge = node1;elselinkLast(mVexs[p1].firstEdge, node1);} }/** 創建鄰接表對應的圖(用已提供的數據)*/ ListDG::ListDG(char vexs[], int vlen, char edges[][2], int elen) {char c1, c2;int i, p1, p2;ENode *node1, *node2;// 初始化"頂點數"和"邊數"mVexNum = vlen;mEdgNum = elen;// 初始化"鄰接表"的頂點mVexs = new VNode[mVexNum];for(i=0; i<mVexNum; i++){mVexs[i].data = vexs[i];mVexs[i].firstEdge = NULL;}// 初始化"鄰接表"的邊for(i=0; i<mEdgNum; i++){// 讀取邊的起始頂點和結束頂點c1 = edges[i][0];c2 = edges[i][1];p1 = getPosition(c1);p2 = getPosition(c2);// 初始化node1node1 = new ENode();node1->ivex = p2;// 將node1鏈接到"p1所在鏈表的末尾"if(mVexs[p1].firstEdge == NULL)mVexs[p1].firstEdge = node1;elselinkLast(mVexs[p1].firstEdge, node1);} }/* * 析構函數*/ 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; }/** 將node節點鏈接到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; }/** 讀取一個輸入字符*/ char ListDG::readChar() {char ch;do {cin >> ch;} while(!((ch>='a'&&ch<='z') || (ch>='A'&&ch<='Z')));return ch; }/** 深度優先搜索遍歷圖的遞歸實現*/ 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;} }/** 深度優先搜索遍歷圖*/ void ListDG::DFS() {int i;int *visited; // 頂點訪問標記visited = new int[mVexNum];// 初始化所有頂點都沒有被訪問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; }/** 廣度優先搜索（類似于樹的層次遍歷）*/ void ListDG::BFS() {int head = 0;int rear = 0;int *queue; // 輔組隊列int *visited; // 頂點訪問標記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; // 入隊列}while (head != rear) {j = queue[head++]; // 出隊列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; }/** 打印鄰接表圖*/ 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;} }/** 拓撲排序** 返回值：* -1 -- 失敗(由于內存不足等原因導致)* 0 -- 成功排序，并輸入結果* 1 -- 失敗(該有向圖是有環的)*/ int ListDG::topologicalSort() {int i,j;int index = 0;int head = 0; // 輔助隊列的頭int rear = 0; // 輔助隊列的尾int *queue; // 輔組隊列int *ins; // 入度數組char *tops; // 拓撲排序結果數組，記錄每個節點的排序后的序號。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));// 統計每個頂點的入度數for(i = 0; i < mVexNum; i++){node = mVexs[i].firstEdge;while (node != NULL){ins[node->ivex]++;node = node->nextEdge;}}// 將所有入度為0的頂點入隊列for(i = 0; i < mVexNum; i ++)if(ins[i] == 0)queue[rear++] = i; // 入隊列while (head != rear) // 隊列非空{j = queue[head++]; // 出隊列。j是頂點的序號tops[index++] = mVexs[j].data; // 將該頂點添加到tops中，tops是排序結果node = mVexs[j].firstEdge; // 獲取以該頂點為起點的出邊隊列// 將與"node"關聯的節點的入度減1；// 若減1之后，該節點的入度為0；則將該節點添加到隊列中。while(node != NULL){// 將節點(序號為node->ivex)的入度減1。ins[node->ivex]--;// 若節點的入度為0，則將其"入隊列"if( ins[node->ivex] == 0)queue[rear++] = node->ivex; // 入隊列node = node->nextEdge;}}if(index != mVexNum){cout << "Graph has a cycle" << endl;delete queue;delete ins;delete tops;return 1;}// 打印拓撲排序結果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;// 自定義"圖"(輸入矩陣隊列)//pG = new ListDG();// 采用已有的"圖"pG = new ListDG(vexs, vlen, edges, elen);pG->print(); // 打印圖//pG->DFS(); // 深度優先遍歷//pG->BFS(); // 廣度優先遍歷pG->topologicalSort(); // 拓撲排序return 0; }

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