BSP FSP

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   和  图的一些基本算法

 

无向图——邻接矩阵的深度优先和广度优先算法实现

测试环境：VS2008（C）

#include "stdafx.h"
#include <stdlib.h>
#include <malloc.h>
#define INFINITY INT_MAX
#define MAX_VEX 20
#define VRType int
#define VertexType char
#define InfoType int
int *visited;
/********************************/
/****      图的结构定义      ****/
/********************************/
typedef enum
{
    DG,
    DN,
    UDG,
    UDN
}GraphKind;
struct _ArcCell
{
    VRType adj; /* note weight */
    InfoType *info;
};
typedef struct _ArcCell ArcCell, AdjMatrix[MAX_VEX][MAX_VEX];
struct _MGraph
{
    VertexType vexs[MAX_VEX];
    AdjMatrix arcs;
    int vexnum, arcnum;
    GraphKind kind;
};
typedef struct _MGraph MGraph;
/********************************/
/****      栈的结构定义      ****/
/********************************/
struct _node
{
    int ivex;
    struct _node *next;
};
typedef struct _node node, *pnode;
struct _stack
{
    int size;
    pnode ptop;
};
typedef struct _stack stack, *pstack;
/********************************/
/****      堆的结构定义      ****/
/********************************/
struct _queue
{
    pnode front;
    pnode rear;
};
typedef struct _queue queue, *pqueue;
/********************************/
/****         栈的实现       ****/
/********************************/
pstack init_stack(int size)
{
    pnode pn=NULL;
    pstack ps=NULL;
    pn=(pnode)malloc(sizeof(node));
    ps=(pstack)malloc(sizeof(stack));
    pn->ivex=-1;
    pn->next=NULL;
    ps->size=size;
    ps->ptop=pn;
    return ps;
}
int empty_stack(pstack ps)
{
    if(ps->ptop->next==NULL)
        return 1;
    else
        return 0;
}
void push_stack(pstack ps, int ivex)
{
    pnode pn=NULL;
    pn=(pnode)malloc(sizeof(node));
    pn->ivex=ivex;
    pn->next=ps->ptop;
    ps->ptop=pn;
}
int pop_stack(pstack ps)
{
    int ivex=-1;
    pnode pn=NULL;
    if(!empty_stack(ps))
    {
        pn=ps->ptop;
        ps->ptop=ps->ptop->next;
        ivex=pn->ivex;
        free(pn);
    }
    return ivex;
}
/********************************/
/****         堆的实现       ****/
/********************************/
queue init_queue()
{
    pnode pn=NULL;
    queue qu;
    pn=(pnode)malloc(sizeof(node));
    pn->next;
    pn->ivex=-1;
    qu.front=qu.rear=pn;
    return qu;
}
int empty_queue(queue qu)
{
    if(qu.front==qu.rear)
        return 1;
    else
        return 0;
}
void en_queue(queue qu, int ivex)
{
    pnode pn=NULL;
    pn=(pnode)malloc(sizeof(node));
    pn->ivex=ivex;
    pn->next=qu.rear->next;
    qu.rear=pn;
}
int de_queue(queue qu)
{
    int ivex=-1;
    pnode pn=NULL;
    if(!empty_queue(qu))
    {
        pn=qu.front;
        qu.front=qu.front->next;
        ivex=pn->ivex;
        free(pn);
    }
    return ivex;
}
/********************************/
/****         图的实现       ****/
/********************************/
int LocateVex(MGraph g, char ch)
{
    int i;
    for(i=1; i<=g.vexnum; i++)
        if(ch==g.vexs[i])
            return i;
    return -1;
}
MGraph Create_UDG()
{
    int i, j, w, p1, p2;
    char ch1, ch2;
    MGraph 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].adj=g.arcs[j][i].adj=INFINITY; /* UDG should define i-j and j-i */
    printf("Enter %d vex.../n", g.vexnum);
    for(i=1; i<=g.vexnum; i++)
    {
        printf("vex %d: ", i);
        scanf("%c", &g.vexs[i]);
        getchar();
    }
    printf("Enter %d arc.../n", g.arcnum);
    for(i=1; i<=g.arcnum; i++)
    {
        printf("arc %d: ", i);
        scanf("%c %c %d", &ch1, &ch2, &w);
        getchar();
        p1=LocateVex(g, ch1);
        p2=LocateVex(g, ch2);
        g.arcs[p1][p2].adj=g.arcs[p2][p1].adj=w;
    }
    return g;
}
int FirstVex(MGraph g, int i)
{
    int k;
    if(i>=1 && i<=g.vexnum)
        for(k=1; k<=g.vexnum; k++)
            if(g.arcs[i][k].adj!=INFINITY)
                return k;
    return -1;
}
int NextVex(MGraph 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].adj!=INFINITY)
                return k;
    return -1;
}
void DFS(MGraph g, int i)
{
    int j;
    if(!visited[i])
    {
        visited[i]=1;
        printf("%3c", g.vexs[i]);
        for(j=FirstVex(g, i); j>=1; j=NextVex(g, i, j))
            if(!visited[j])
                DFS(g, j);
    }
}
void DFS_Graph(MGraph 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);
}
void DFS2_Graph(MGraph g)
{
    int i, j, k;
    pstack ps=NULL;
    ps=init_stack(g.vexnum);
    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])
        {
            visited[i]=1;
            printf("%3c", g.vexs[i]);
            push_stack(ps, i);
            k=i;
            while (!empty_stack(ps))
            {
                for(j=FirstVex(g, k); j>=1; j=NextVex(g, k, j))
                {
                    if(!visited[j])
                    {
                        visited[j]=1;
                        printf("%3c", g.vexs[j]);
                        push_stack(ps, j); /* push all visited ivex */
                        k=j; /* newer node */
                    }
                }
                k=pop_stack(ps);
            }
        }
}
void BFS_Graph(MGraph g)
{
    int i, j, k;
    queue qu;
    qu=init_queue();
    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])
        {
            visited[i]=1;
            printf("%3c", g.vexs[i]);
            en_queue(qu, i);
            while (!empty_queue(qu))
            {
                k=de_queue(qu);
                for(j=FirstVex(g, k); j>=1; j=NextVex(g, k, j))
                    if(!visited[j])
                    {
                        visited[j]=1;
                        printf("%3c", g.vexs[j]);
                        en_queue(qu, j);
                    }
            }
        }
}
/********************************/
/****          主函数        ****/
/********************************/
int _tmain(int argc, _TCHAR* argv[])
{
    MGraph g;
    g=Create_UDG();
    printf("/nDFS: ");
    DFS_Graph(g);       /* recursion */
    printf("/nDFS: ");
    DFS2_Graph(g);      /* non recursion */
    printf("/nBFS: ");
    BFS_Graph(g);
    printf("/n");
    return 0;
}

#include "stdafx.h" #include <stdlib.h> #include <malloc.h> #define INFINITY INT_MAX #define MAX_VEX 20 #define VRType int #define VertexType char #define InfoType int int *visited; /********************************/ /**** 图的结构定义 ****/ /********************************/ typedef enum { DG, DN, UDG, UDN }GraphKind; struct _ArcCell { VRType adj; /* note weight */ InfoType *info; }; typedef struct _ArcCell ArcCell, AdjMatrix[MAX_VEX][MAX_VEX]; struct _MGraph { VertexType vexs[MAX_VEX]; AdjMatrix arcs; int vexnum, arcnum; GraphKind kind; }; typedef struct _MGraph MGraph; /********************************/ /**** 栈的结构定义 ****/ /********************************/ struct _node { int ivex; struct _node *next; }; typedef struct _node node, *pnode; struct _stack { int size; pnode ptop; }; typedef struct _stack stack, *pstack; /********************************/ /**** 堆的结构定义 ****/ /********************************/ struct _queue { pnode front; pnode rear; }; typedef struct _queue queue, *pqueue; /********************************/ /**** 栈的实现 ****/ /********************************/ pstack init_stack(int size) { pnode pn=NULL; pstack ps=NULL; pn=(pnode)malloc(sizeof(node)); ps=(pstack)malloc(sizeof(stack)); pn->ivex=-1; pn->next=NULL; ps->size=size; ps->ptop=pn; return ps; } int empty_stack(pstack ps) { if(ps->ptop->next==NULL) return 1; else return 0; } void push_stack(pstack ps, int ivex) { pnode pn=NULL; pn=(pnode)malloc(sizeof(node)); pn->ivex=ivex; pn->next=ps->ptop; ps->ptop=pn; } int pop_stack(pstack ps) { int ivex=-1; pnode pn=NULL; if(!empty_stack(ps)) { pn=ps->ptop; ps->ptop=ps->ptop->next; ivex=pn->ivex; free(pn); } return ivex; } /********************************/ /**** 堆的实现 ****/ /********************************/ queue init_queue() { pnode pn=NULL; queue qu; pn=(pnode)malloc(sizeof(node)); pn->next; pn->ivex=-1; qu.front=qu.rear=pn; return qu; } int empty_queue(queue qu) { if(qu.front==qu.rear) return 1; else return 0; } void en_queue(queue qu, int ivex) { pnode pn=NULL; pn=(pnode)malloc(sizeof(node)); pn->ivex=ivex; pn->next=qu.rear->next; qu.rear=pn; } int de_queue(queue qu) { int ivex=-1; pnode pn=NULL; if(!empty_queue(qu)) { pn=qu.front; qu.front=qu.front->next; ivex=pn->ivex; free(pn); } return ivex; } /********************************/ /**** 图的实现 ****/ /********************************/ int LocateVex(MGraph g, char ch) { int i; for(i=1; i<=g.vexnum; i++) if(ch==g.vexs[i]) return i; return -1; } MGraph Create_UDG() { int i, j, w, p1, p2; char ch1, ch2; MGraph 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].adj=g.arcs[j][i].adj=INFINITY; /* UDG should define i-j and j-i */ printf("Enter %d vex.../n", g.vexnum); for(i=1; i<=g.vexnum; i++) { printf("vex %d: ", i); scanf("%c", &g.vexs[i]); getchar(); } printf("Enter %d arc.../n", g.arcnum); for(i=1; i<=g.arcnum; i++) { printf("arc %d: ", i); scanf("%c %c %d", &ch1, &ch2, &w); getchar(); p1=LocateVex(g, ch1); p2=LocateVex(g, ch2); g.arcs[p1][p2].adj=g.arcs[p2][p1].adj=w; } return g; } int FirstVex(MGraph g, int i) { int k; if(i>=1 && i<=g.vexnum) for(k=1; k<=g.vexnum; k++) if(g.arcs[i][k].adj!=INFINITY) return k; return -1; } int NextVex(MGraph 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].adj!=INFINITY) return k; return -1; } void DFS(MGraph g, int i) { int j; if(!visited[i]) { visited[i]=1; printf("%3c", g.vexs[i]); for(j=FirstVex(g, i); j>=1; j=NextVex(g, i, j)) if(!visited[j]) DFS(g, j); } } void DFS_Graph(MGraph 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); } void DFS2_Graph(MGraph g) { int i, j, k; pstack ps=NULL; ps=init_stack(g.vexnum); 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]) { visited[i]=1; printf("%3c", g.vexs[i]); push_stack(ps, i); k=i; while (!empty_stack(ps)) { for(j=FirstVex(g, k); j>=1; j=NextVex(g, k, j)) { if(!visited[j]) { visited[j]=1; printf("%3c", g.vexs[j]); push_stack(ps, j); /* push all visited ivex */ k=j; /* newer node */ } } k=pop_stack(ps); } } } void BFS_Graph(MGraph g) { int i, j, k; queue qu; qu=init_queue(); 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]) { visited[i]=1; printf("%3c", g.vexs[i]); en_queue(qu, i); while (!empty_queue(qu)) { k=de_queue(qu); for(j=FirstVex(g, k); j>=1; j=NextVex(g, k, j)) if(!visited[j]) { visited[j]=1; printf("%3c", g.vexs[j]); en_queue(qu, j); } } } } /********************************/ /**** 主函数 ****/ /********************************/ int _tmain(int argc, _TCHAR* argv[]) { MGraph g; g=Create_UDG(); printf("/nDFS: "); DFS_Graph(g); /* recursion */ printf("/nDFS: "); DFS2_Graph(g); /* non recursion */ printf("/nBFS: "); BFS_Graph(g); printf("/n"); return 0; }

运行结果：