Chapter 7(图)

1.Prim算法生成最小生成树

//Prim算法生成最小生成树
void MiniSpanTree_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.numVertexes;i++)
	{
		lowcost[i] = G.arc[0][i];
		adjvex[i] = 0;
	}
	for(i = 1;i < G.numVertexes;i++)
	{
		min = INFINITY;

		j = 1;k = 0;
		while(j < G.numVertexes)
		{
			if(lowcost[j] != 0 && lowcost[j] < min)
			{
				min = lowcost[j];
				k = j;
			}
			j++;
		}

		printf("(%d,%d)",adjvex[k],k);
		lowcost[k] = 0;
		for(j = i;j < G.numVertexes;j++)
		{
			if(lowcost[j]!=0 && G.arc[k][j] < lowcost[j])
			{
				lowcost[j] = G.arc[k][j];
				adjvex[j] = k;
			}
		}
	}
}

42

 

1

//Prim算法生成最小生成树

2

void MiniSpanTree_Prim(MGraph G)

3

{

4

    int min,i,j,k;

5

    int adjvex[MAXVEX];

6

    int lowcost[MAXVEX];

7

    lowcost[0] = 0;

8

9

10

    adjvex[0] = 0;

11

    for(i = 1;i < G.numVertexes;i++)

12

    {

13

        lowcost[i] = G.arc[0][i];

14

        adjvex[i] = 0;

15

    }

16

    for(i = 1;i < G.numVertexes;i++)

17

    {

18

        min = INFINITY;

19

20

        j = 1;k = 0;

21

        while(j < G.numVertexes)

22

        {

23

            if(lowcost[j] != 0 && lowcost[j] < min)

24

            {

25

                min = lowcost[j];

26

                k = j;

27

            }

28

            j++;

29

        }

30

31

        printf("(%d,%d)",adjvex[k],k);

32

        lowcost[k] = 0;

33

        for(j = i;j < G.numVertexes;j++)

34

        {

35

            if(lowcost[j]!=0 && G.arc[k][j] < lowcost[j])

36

            {

37

                lowcost[j] = G.arc[k][j];

38

                adjvex[j] = k;

39

            }

40

        }

41

    }

42

}

2.克鲁斯卡尔（Kruskal）算法

//Kruskal算法生成最小生成树
void MiniSpanTree_Kruskal(MGraph G)
{
	int i,n,m;
	Edge edges[MAXEDGE];
	int parentp[MAXVEX];

	//省略将邻接矩阵转化为边集数组edges并按权由小到大排序的代码
	for(i = 0; i < G.numEdges;i++)
	{
		parent[i] = 0;
	}
	for(i = o;i < G.numEdges;i++)
	{
		n = Find(parent,edges[i].begin);
		m = Find(parent,edges[i].end);
		if(n != m)
		{
			parent[n] = m;
			printf("(%d,%d) %d ",edges[i].begin,edges[i].end,edges[i].weight);

		}
	}
}

int Find(int *parent,int f)
{
	while(parent[f] > 0)
	{
		f = parent[f];
	}
	return f;
}

34

 

1

//Kruskal算法生成最小生成树

2

void MiniSpanTree_Kruskal(MGraph G)

3

{

4

    int i,n,m;

5

    Edge edges[MAXEDGE];

6

    int parentp[MAXVEX];

7

8

    //省略将邻接矩阵转化为边集数组edges并按权由小到大排序的代码

9

    for(i = 0; i < G.numEdges;i++)

10

    {

11

        parent[i] = 0;

12

    }

13

    for(i = o;i < G.numEdges;i++)

14

    {

15

        n = Find(parent,edges[i].begin);

16

        m = Find(parent,edges[i].end);

17

        if(n != m)

18

        {

19

            parent[n] = m;

20

            printf("(%d,%d) %d ",edges[i].begin,edges[i].end,edges[i].weight);

21

22

        }

23

    }

24

}

25

26

27

int Find(int *parent,int f)

28

{

29

    while(parent[f] > 0)

30

    {

31

        f = parent[f];

32

    }

33

    return f;

34

}

3.迪杰斯特拉（Dijkstra）算法

//迪杰斯特拉（Dijkstra）算法
#define MAXVEX 9
#define INFINITY 65535

typedef int Patharc[MAXVEX];
typedef int ShortPathTable[MAXVEX];

void ShortestPath_Dijkstra(MGraph G,INT V0,Patharc *P,ShortPathTable *D)
{
	int v,w,k,min;
	int final[MAXVEX];
	for(v = 0;v < G.numVertexes;v++)
	{
		final[v] = 0;
		(*D)[v] = G.arc[v0][v];
		(*P)[v] = 0;
	}
	(*D)[v0] = 0;
	final[vo] = 1;

	for(v = 1;v < G.numVertexes;w++)
	{
		min = INFINITY;
		for(w = 0;w < G.numVertexes;w++)
		{
			if(!final[w] && (*D)[w] < min)
			{
				k = w;
				min = (*D)[w];
			}
		}

		final[k] = 1;
		for(w = 0;w < G.numVertexes;w++)
		{
			if(!final[w] && (min+G.arc[k][w])< (*D)[w])
			{
				(*D)[w] = min + G.arc[k][w];
				(*P)[w] = k;
			}
		}
	}
}

44

 

1

//迪杰斯特拉（Dijkstra）算法

2

#define MAXVEX 9

3

#define INFINITY 65535

4

5

typedef int Patharc[MAXVEX];

6

typedef int ShortPathTable[MAXVEX];

7

8

9

void ShortestPath_Dijkstra(MGraph G,INT V0,Patharc *P,ShortPathTable *D)

10

{

11

    int v,w,k,min;

12

    int final[MAXVEX];

13

    for(v = 0;v < G.numVertexes;v++)

14

    {

15

        final[v] = 0;

16

        (*D)[v] = G.arc[v0][v];

17

        (*P)[v] = 0;

18

    }

19

    (*D)[v0] = 0;

20

    final[vo] = 1;

21

22

    for(v = 1;v < G.numVertexes;w++)

23

    {

24

        min = INFINITY;

25

        for(w = 0;w < G.numVertexes;w++)

26

        {

27

            if(!final[w] && (*D)[w] < min)

28

            {

29

                k = w;

30

                min = (*D)[w];

31

            }

32

        }

33

34

        final[k] = 1;

35

        for(w = 0;w < G.numVertexes;w++)

36

        {

37

            if(!final[w] && (min+G.arc[k][w])< (*D)[w])

38

            {

39

                (*D)[w] = min + G.arc[k][w];

40

                (*P)[w] = k;

41

            }

42

        }

43

    }

44

}

4.弗洛伊德（Floyd算法）

//弗洛伊德（Floyd算法）
typedef int PathMatirx[MAXVEX][MAXVEX];
typedef int ShortPathTable[MAXVEX][MAXVEX];

void ShortestPath_Floyd(MGraph G,Pathmatirx *P,ShortPathTable *D)
{
	int v,w,k;
	for(v = 0;v < G.numVertexes; ++v)
	{
		for(w = 0;w < G.numVertexes;++w)
		{
			(*D)[v][w] = G.matirx[v][w]；
			(*P)[v][w] = w;
		}
	}

	for(k = 0;k < G.numVertexes;++k)
	{
		for(v = 0;v < G.numVertexes;++v)
		{
			for(w = 0;w < G.numVertexes;++w)
			{
				if((*D)[v][w] > (*D)[v][k]+(*D)[k][w])
				{
					(*D)[v][w] = (*D)[v][w]+(*D)[k][w];
					(*P)[v][w] = (*P)[v][k];
				}
			}
		}
	}
}

//最短路径显示代码段
for(v = 0;v < Q.numVertexes;++v)
{
	for(w = v+1;w < G.numVertexes;w++)
	{
		printf("v%d-v%d weight: %d ",v,w,D[v][w]);
		k = P[v][w];
		printf(" path: %d",v);

		while(k != w)
		{
			printf(" -> %d",k);
			k = P[k][w];
		}
		printf(" -> %d\n",w);
	}
	printf("\n");
}

x

 

1

//弗洛伊德（Floyd算法）

2

typedef int PathMatirx[MAXVEX][MAXVEX];

3

typedef int ShortPathTable[MAXVEX][MAXVEX];

4

5

void ShortestPath_Floyd(MGraph G,Pathmatirx *P,ShortPathTable *D)

6

{

7

    int v,w,k;

8

    for(v = 0;v < G.numVertexes; ++v)

9

    {

10

        for(w = 0;w < G.numVertexes;++w)

11

        {

12

            (*D)[v][w] = G.matirx[v][w]；

13

            (*P)[v][w] = w;

14

        }

15

    }

16

17

    for(k = 0;k < G.numVertexes;++k)

18

    {

19

        for(v = 0;v < G.numVertexes;++v)

20

        {

21

            for(w = 0;w < G.numVertexes;++w)

22

            {

23

                if((*D)[v][w] > (*D)[v][k]+(*D)[k][w])

24

                {

25

                    (*D)[v][w] = (*D)[v][w]+(*D)[k][w];

26

                    (*P)[v][w] = (*P)[v][k];

27

                }

28

            }

29

        }

30

    }

31

}

32

33

34

35

//最短路径显示代码段

36

for(v = 0;v < Q.numVertexes;++v)

37

{

38

    for(w = v+1;w < G.numVertexes;w++)

39

    {

40

        printf("v%d-v%d weight: %d ",v,w,D[v][w]);

41

        k = P[v][w];

42

        printf(" path: %d",v);

43

44

        while(k != w)

45

        {

46

            printf(" -> %d",k);

47

            k = P[k][w];

48

        }

49

        printf(" -> %d\n",w);

50

    }

51

    printf("\n");

52

}

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