图的基本算法实现（邻接矩阵与邻接表两种方法）

本博客前面文章已对图有过简单的介绍，本文主要是重点介绍有关图的一些具体操作与应用

阅读本文前，可以先参考本博客 各种基本算法实现小结（四）—— 图及其遍历

一、无向图

1 无向图——邻接矩阵

测试环境：VS2008

#include "stdafx.h" #include <stdlib.h> #include <malloc.h> #define MAX_VEX 20 #define INFINITY 65535 int *visited; struct _node { int vex_num; struct _node *next; }; typedef struct _node node, *pnode; struct _graph { char *vexs; int arcs[MAX_VEX][MAX_VEX]; int vexnum, arcnum; }; typedef struct _graph graph, *pgraph; int locate(graph g, char ch) { int i; for(i=1; i<=g.vexnum; i++) if(g.vexs[i]==ch) return i; return -1; } graph create_graph() { int i, j, w, p1, p2; char ch1, ch2; graph g; printf("Enter vexnum arcnum: "); scanf("%d %d", &g.vexnum, &g.arcnum); getchar(); for(i=1; i<=g.vexnum; i++) for(j=1; j<g.vexnum; j++) g.arcs[i][j]=INFINITY; g.vexs=(char *)malloc(sizeof(char)); printf("Enter %d vexnum.../n", g.vexnum); for(i=1; i<=g.vexnum; i++) { printf("vex %d: ", i); scanf("%c", &g.vexs[i]); getchar(); } printf("Enter %d arcnum.../n", g.arcnum); for(i=1; i<=g.arcnum; i++) { printf("arc %d: ", i); scanf("%c %c %d", &ch1, &ch2, &w); getchar(); p1=locate(g, ch1); p2=locate(g, ch2); g.arcs[p1][p2]=g.arcs[p2][p1]=w; } return g; } int firstvex_graph(graph g, int i) { int k; if(i>=1 && i<=g.vexnum) for(k=1; k<=g.vexnum; k++) if(g.arcs[i][k]!=INFINITY) return k; return -1; } int nextvex_graph(graph g, int i, int j) { int k; if(i>=1 && i<=g.vexnum && j>=1 && j<=g.vexnum) for(k=j+1; k<=g.vexnum; k++) if(g.arcs[i][k]!=INFINITY) return k; return -1; } void dfs(graph g, int i) { int k, j; if(!visited[i]) { visited[i]=1; printf("%3c", g.vexs[i]); for(j=firstvex_graph(g, i); j>=1; j=nextvex_graph(g, i, j)) if(!visited[j]) dfs(g, j); } } void dfs_graph(graph g) { int i; visited=(int *)malloc((g.vexnum+1)*sizeof(int)); for(i=1; i<=g.vexnum; i++) visited[i]=0; for(i=1; i<g.vexnum; i++) if(!visited[i]) dfs(g, i); } int _tmain(int argc, _TCHAR* argv[]) { graph g; g=create_graph(); printf("DFS: "); dfs_graph(g); printf("/n"); return 0; }

运行结果：

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2 无向图—— 邻接表

测试环境：VS2008

#include "stdafx.h" #include <stdlib.h> #include <malloc.h> #define MAX_VEX 20 int *visited; typedef struct _ArcNode { int ivex; /* next ivex */ struct _ArcNode *nextarc; /* next node */ int *info; /* arc weight */ }; typedef struct _ArcNode ArcNode, *pArcNode; struct _VNode { char adjvex; /* note vex */ ArcNode *firstarc; }; typedef struct _VNode VNode; struct _ALGraph { VNode AdjList[MAX_VEX]; int vexnum, arcnum; int kink; }; typedef struct _ALGraph ALGraph; int locate(ALGraph g, char ch) { int i; for(i=1; i<=g.vexnum; i++) if(g.AdjList[i].adjvex==ch) return i; return -1; } ALGraph create_graph() { int i, j, w, p1, p2; char ch1, ch2; pArcNode pnode, pnode1, pnode2; ALGraph g; printf("Enter vexnum arcnum: "); scanf("%d %d", &g.vexnum, &g.arcnum); getchar(); printf("Enter %d vexnum.../n", g.vexnum); for(i=1; i<=g.vexnum; i++) { printf("vex %d: ", i); scanf("%c", &g.AdjList[i].adjvex); getchar(); g.AdjList[i].firstarc=NULL; } printf("Enter arc.../n"); for(i=1; i<=g.arcnum; i++) { printf("arc %d: ", i); scanf("%c %c", &ch1, &ch2); getchar(); p1=locate(g, ch1); p2=locate(g, ch2); pnode1=(pArcNode)malloc(sizeof(ArcNode)); pnode2=(pArcNode)malloc(sizeof(ArcNode)); pnode1->ivex=p2; /* next ivex */ pnode1->nextarc=g.AdjList[p1].firstarc; g.AdjList[p1].firstarc=pnode1; pnode2->ivex=p1; /* next ivex */ pnode2->nextarc=g.AdjList[p2].firstarc; g.AdjList[p2].firstarc=pnode2; } return g; } int firstvex_graph(ALGraph g, int i) { int k; if(i>=1 && i<=g.vexnum) if(g.AdjList[i].firstarc) return g.AdjList[i].firstarc->ivex; return -1; } int nextvex_graph(ALGraph g, int i, int k) { pArcNode pnode; if(i>=1 && i<=g.vexnum && k>=1 && k<=g.vexnum) { pnode=g.AdjList[i].firstarc; while(pnode->nextarc) { k=pnode->nextarc->ivex; if(!visited[k]) return k; else pnode=pnode->nextarc; } } return -1; } void dfs(ALGraph g, int i) { int k; if(!visited[i]) { visited[i]=1; printf("%c", g.AdjList[i].adjvex); for(k=firstvex_graph(g, i); k>=1; k=nextvex_graph(g, i, k)) if(!visited[k]) dfs(g, k); } } void dfs_graph(ALGraph g) { int i; visited=(int *)malloc((g.vexnum+1)*sizeof(int)); for(i=1; i<=g.vexnum; i++) visited[i]=0; for(i=1; i<=g.vexnum; i++) if(!visited[i]) dfs(g, i); } int _tmain(int argc, _TCHAR* argv[]) { ALGraph g; g=create_graph(); dfs_graph(g); printf("/n"); return 0; }

运行结果：

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