实用数据结构---图的操作和算法

图算法的源代码、包含大量的注释，和最小生成树、最短路径、邻接表图深度广度优先搜索，邻接矩阵图深度广度优先搜索，欢迎借鉴

#include<stdio.h>#include<stdlib.h>#define MAXVEX 20#define INFINITY 65535typedef char vertexType;typedef int edgeType;typedef int Boolean;typedef int Pathmatirx[MAXVEX];//用于存储最短路径下标的数组typedef int ShortPathTabl[MAXVEX];//用于存数最短路径权值和的数组Boolean visited[MAXVEX];//图的邻接矩阵结构typedef struct{vertexType vexs[MAXVEX];edgeType arc[MAXVEX][MAXVEX];int numVertexs, numEdges;}Mgraph;//邻接矩阵图的创建void creatGraph(Mgraph *G){int i, j,k,w;printf("输入顶点数和边数\n");scanf_s("%d%d", &(G->numVertexs), &(G->numEdges));printf("输入顶点信息\n");getchar();for (i = 0; i < G->numVertexs; i++)scanf_s("%c", &(G->vexs[i]));//矩阵初始化for (i = 0; i < G->numVertexs;i++)for (j = 0; j < G->numVertexs; j++)G->arc[i][j] = INFINITY;printf("输入顶点上下标i,j和权重w\n");getchar();for (k = 0; k < G->numEdges; k++){scanf_s("%d%d%d", &i, &j, &w);G->arc[i][j] = w;G->arc[j][i] = w;//无向图，矩阵对称}}////顺序队列节点//typedef struct{//char data[MAXVEX];//int front;//int rear;//}Queue;//////初始化队列//void InitQueue(Queue* q){//q->front = 0;//q->rear = 0;//}//////返回队列长度//int QueueLength(Queue *q){//return (q->rear - q->front + MAXVEX) % MAXVEX;//}//////判断队列是否已满//bool isFull(Queue *q){//if ((q->rear + 1) % MAXVEX == q->front)//return true;//else//return false;//}//////入队列//bool enQueue(Queue *q,char e){//if (!isFull(q)){//q->data[q->rear] = e;//q->rear = (q->rear+1) % MAXVEX;//return true;//}//else//return false;//}//////出队列//bool Dequeue(Queue *q, char *e){//if (q->front == q->rear)//return false;//*e = q->data[q->front];//q->front = (q->front + 1) % MAXVEX;//return true;//}////图的邻接表结构//边节点//typedef struct edgeNode{//int adjvex;//当前点的下标//edgeType weight;//struct edgeNode *next;//指向下一个邻接点//}edgeNode;//typedef struct vertexNode{//vertexType data;//顶点数据域//struct edgeNode *firstEdge;//}vertexNode,AdjList[MAXVEX];//typedef struct{//AdjList adjList;//int numVertexes, numEdges;//图中当前顶点数和边数//}GraphAdjList;//邻接表图的创建//void creatGraph(GraphAdjList *g){//int i, j, k;//edgeNode *e;//printf("输入顶点数和边数\n");//scanf_s("%d%d", &g->numVertexes, &g->numEdges);//getchar();//for (i = 0; i < g->numVertexes; i++){//scanf_s("%c", &g->adjList[i].data);//g->adjList[i].firstEdge = NULL;//}//for (k = 0; k < g->numEdges; k++){//printf("输入边上的顶点序号\n");//scanf_s("%d%d", &i, &j);//e = (edgeNode*)malloc(sizeof(edgeNode));//e->adjvex = j;//e->next = g->adjList[i].firstEdge;//g->adjList[i].firstEdge = e;//e = (edgeNode*)malloc(sizeof(edgeNode));//e->adjvex = i;//e->next = g->adjList[j].firstEdge;//g->adjList[j].firstEdge = e;//}//}//邻接矩阵的深度优先算法//void DFS(Mgraph *g,int i){//visited[i] = true;//printf("%c ", g->vexs[i]);//for (int j = 0; j < g->numVertexs; j++){//if (g->arc[i][j] == 1 && !visited[j])//DFS(g, j);//}//}//void DFSTraverse(Mgraph *g){//int i;//for (i = 0; i < g->numVertexs; i++)//visited[i] = false;//for (i = 0; i < g->numVertexs; i++){//if (!visited[i])//DFS(g, i);//}//}//邻接表的深度优先遍历算法//void DFS(GraphAdjList *a,int i){//visited[i] = true;//edgeNode *p;//p = a->adjList[i].firstEdge;//printf("%c ", a->adjList[i].data);//while (p){//if (!visited[p->adjvex])//DFS(a, p->adjvex);//p = p->next;//}//}//void DFSTraverse(GraphAdjList *a){//int i;//for (i = 0; i < a->numVertexes; i++)//visited[i] = false;//for (i = 0; i < a->numVertexes; i++)//{//if (!visited[i])//DFS(a, i);//}//}//删除邻接表图//void del(GraphAdjList *a, int i){//edgeNode *p;//visited[i] = true;//p = a->adjList[i].firstEdge->next;//free(a->adjList[i].firstEdge);//a->adjList[i].firstEdge->next = p->next;//while (p){//if (!visited[p->adjvex])//del(a, p->adjvex);//p = p->next;//}//}//void delGraph(GraphAdjList *a){//int i;//for (i = 0; i < a->numVertexes; i++){//if (!visited[i])//del(a, i);//}//}//邻接矩阵图的广度优先遍历//void BFS(Mgraph G){//int i;//char e;//for (i = 0; i < G.numVertexs; i++)//visited[i] = false;//Queue p;//Queue *q = &p;//InitQueue(q);//for (i = 0; i < G.numVertexs; i++){//if (!visited[i]){//visited[i] = true;//enQueue(q, G.vexs[i]);//while (q->front != q->rear){//Dequeue(q, &e);//printf("%c ", e);//for (int j = 0; j < G.numVertexs; j++){//if (!visited[j] && G.arc[i][j] == 1){//visited[j] = true;//enQueue(q, G.vexs[j]);//}////}//}//}////}//}//prim最小生成树算法void MinSpanTree_prim(Mgraph G){int min, i, j, k;int adjvex[MAXVEX];int lowcost[MAXVEX];lowcost[0] = 0;adjvex[0] = 0;for (i = 1; i < G.numVertexs; i++){lowcost[i] = G.arc[0][i];adjvex[i] = 0;}for (i = 1; i < G.numVertexs; i++){min = INFINITY;j = 1;k = 0;while (j < G.numVertexs){if (lowcost[j] != 0 && lowcost[j] < min){min = lowcost[j];k = j;}j++;}printf("(%d %d) ", adjvex[k], k);lowcost[k] = 0;for (j = 1; j < G.numVertexs; j++){if (lowcost[j] != 0 && G.arc[k][j] < lowcost[j]){lowcost[j] = G.arc[k][j];adjvex[j] = k;}}}}//void MinSpanTree_prim(Mgraph G){//int i, j, k, min;//int adjvex[MAXVEX];//int lowcost[MAXVEX];//lowcost[0] = 0;//adjvex[0] = 0;//for (i = 1; i < G.numVertexs; i++){//lowcost[i] = G.arc[0][i];//adjvex[i] = 0;//}//for (i = 1; i < G.numVertexs; i++){//min = INFINITY;//k = 0;//j = 1;//while (j < G.numVertexs){//if (lowcost[j] != 0 && lowcost[j]<min){//min = lowcost[j];//k = j;//}//j++;//}//lowcost[k] = 0;//printf("(%d,%d)", adjvex[k], k);//for (j = 1; j < G.numVertexs; j++){//if (lowcost[j] != 0 && lowcost[j] > G.arc[k][j]){//lowcost[j] = G.arc[k][j];//adjvex[j] = k;//}//}//}//}//迪杰斯特拉//迪杰斯特拉最短路径算法//p[v]的值为前驱顶点下标,D[v]表示从v0到v最短路径长度和void ShotestPath_Dijkstra(Mgraph G, int v0, Pathmatirx *P, ShortPathTabl *D){int v, w, k, min;int visited[MAXVEX];//visited[i]=1表示求得v0到vi的最短路径for (v = 0; v < G.numVertexs; v++){visited[v] = 0;//全部顶点初始化为未知最短路径状态(*D)[v] = G.arc[v0][v];//将与v0点有连线的顶点加上权值(*P)[v] = 0;//初始化路径数组p为0}(*D)[v0] = 0;//v0到v0的路径为0visited[v0] = 1;//v0到v0不需要求路径//开始主循环，每次求得v0到某个v的最短路径for (v = 1; v < G.numVertexs; v++){min = INFINITY;//寻找离v0最近的顶点for (w = 0; w < G.numVertexs; w++){if (!visited[w] && (*D)[w] < min){k = w;min = (*D)[w];//w顶点离v0点更近}}visited[k] = 1;//修正当前最短路径及距离for (w = 0; w < G.numVertexs; w++){//如果经过v顶点的路径比现在这条路径的长度短的话if (!visited[w] && (min + G.arc[k][w]) < (*D)[w]){//说明找到了更短的路径，修正D[w]和P[w](*D)[w] = min + G.arc[k][w];(*P)[w] = k;}}}}//输出最小路径void print(Pathmatirx *P,int n){if (n == 0){printf("0\n");return;}printf("%d<-", n);print(P, (*P)[n]);}int main(){Pathmatirx P[MAXVEX];ShortPathTabl D[MAXVEX];int v0 = 0;Mgraph G;creatGraph(&G);//MinSpanTree_prim(G);ShotestPath_Dijkstra(G, v0, P, D);print(P,8);system("pause");return 0;}