/**
02. * 定义基本数据结构
03. * @author 小宇
04. */
05.
06.public class MGraph
07.{
08. //当边edges[i][j]不存在时,用null表示其值
09. public static final int NULL = 1000;
10. static final int MAXV = 100;
11. //边集
12. int[][] edges = new int[this.MAXV][this.MAXV];
13. //顶点数，和边数
14. int n,e;
15.}
/**
02. * 该结构用于克鲁斯卡尔算法
03. * @author 小宇
04. */
05.public class EStruct implements Comparable<EStruct>
06.{
07. int begin;
08. int end;
09. int weight;
10. //用于给List<EStruct>排序,实现接口comparable方法
11. public int compareTo(EStruct e)
12. {
13. return this.weight - e.weight;
14. }
15.
16.}
/**
02. * 生成邻接矩阵并输出
03. * @author 小宇
04. *
05. */
06.
07.public class CreateGraph {
08. public void createMat(MGraph g, int A[][], int n)
09. {
10. int i, j;
11. g.n = n;
12. g.e = 0;
13. for(i = 0; i < n; i++)
14. for(j = 0; j < n; j++)
15. {
16. g.edges[i][j] = A[i][j];
17. if(g.edges[i][j] != 1000)
18. g.e++;
19. }
20. }
21. //---------------------------------------------------
22. public void DispMat(MGraph g)
23. {
24. int i, j;
25. for(i = 0; i < g.n; i++)
26. {
27. for(j = 0; j < g.n; j++)
28. if(g.edges[i][j] == g.NULL)
29. System.out.print("-" + " ");
30. else
31. System.out.print(g.edges[i][j] + " ");
32. System.out.println();
33. }
34. }
35.
36.}
import java.util.ArrayList;
02.import java.util.Collections;
03.import java.util.List;
04./**
05. * 核心算法
06. * 用prim算法及克鲁斯卡尔算法求解最小生成树
07. * @author 小宇
08. *
09. */
10.public class MinimalSpanningTree {
11.
12. static final int INF = 32767;
13.
14. private List<EStruct> eArray = new ArrayList<EStruct>();
15.
16. //--------------------------------Prim算法--------------------------------
17. public void Prim(MGraph g, int v)
18. {
19. int[] lowcost = new int[g.n];
20. int min;
21. int[] closest = new int[g.n];
22. int i,j,k = 0;
23. for(i = 0; i < g.n; i++)
24. {
25. lowcost[i] = g.edges[v][i];
26. closest[i] = v;
27. }
28. for(i = 1; i < g.n; i++)
29. {
30. min = INF;
31. for(j = 0; j < g.n; j++)
32. if(lowcost[j] != 0 && lowcost[j] < min)
33. {
34. min = lowcost[j];
35. k = j;
36. }
37. System.out.println( "边" + closest[k] + "," + k + "权值" + min);
38. lowcost[closest[k]] = 0;
39. lowcost[k] = 0;
40. for(j = 0; j < g.n; j++)
41. if(g.edges[k][j] != 0 && g.edges[k][j] < lowcost[j])
42. {
43. lowcost[j] = g.edges[k][j];
44. closest[j] = k;
45. }
46. }
47. }
48. //---------------------克鲁斯卡尔算法-----------------------------------------------
49. public void getEStruct(MGraph mgraph)
50. {
51. /**
52. * 用EStruct结构保存每条边
53. * 最后存于EStruct数组
54. * 然后用java类库提供方法排序
55. */
56. for(int i = 0;i < mgraph.n; i++)
57. {
58. for(int j = 0; j < mgraph.n; j++)
59. {
60. //由于是无向图
61. if(j < i)
62. {
63. //如果begin：i ， end: j ,的边存在
64. if(mgraph.edges[i][j] != mgraph.NULL)
65. {
66. //创建EStruct保存该边信息并加入List:eArray
67. EStruct estruct = new EStruct();
68. estruct.begin = i;
69. estruct.end = j;
70. estruct.weight = mgraph.edges[i][j];
71. eArray.add(estruct);
72. }
73. }
74. }
75. }
76. //用java类库提供方法排序
77. Collections.sort(eArray);
78. }
79.
80. //查找连线顶点的尾部下标
81. public int find(int[] p,int f)
82. {
83. while(p[f] != 0)
84. f = p[f];
85. return f;
86. }
87.
88. public void Kruskal(MGraph mgraph)
89. {
90. int i, n, m;
91. //parent数组用于判断数组边集是否形成环路
92. int[] parent = new int[eArray.size()];
93. //初始化数组为零
94. for(i = 0; i < eArray.size(); i++)
95. parent[i] = 0;
96. //循环生成最小生成树，最小生成树的边数为图的（顶点数 - 1）
97. for(i = 0; i < mgraph.n - 1; i++)
98. {
99. n = find(parent, eArray.get(i).begin);
100. m = find(parent,eArray.get(i).end);
101. //如果n不等于m说明此边与现有生成树没有形成环路
102. if(n != m)
103. {
104. //将此边的表尾节点放入下标为起点的parent中
105. //表明此顶点已在生成树集合中
106. parent[n] = m;
107. System.out.println(eArray.get(i).begin + "," + eArray.get(i).end + " 权：" + eArray.get(i).weight);
108. }
109. }
110. }
111.}
/**
02. * 测试代码
03. * 生成邻接矩阵->prim->kruskal
04. * @author 小宇
05. *
06. */
07.
08.public class Test
09.{
10. public static void main(String[] args)
11. {
12. MGraph mgraph = new MGraph();
13.
14. int[][] array = new int[6][6];
15. for(int i = 0;i < 6; i++)
16. for(int j = 0;j < 6; j++)
17. array[i][j] = mgraph.NULL;
18. array[0][1] = 6;
19. array[1][0] = 6;
20. array[0][3] = 5;
21. array[3][0] = 5;
22. array[0][2] = 1;
23. array[2][0] = 1;
24. array[1][2] = 5;
25. array[2][1] = 5;
26. array[2][3] = 5;
27. array[3][2] = 5;
28. array[1][4] = 3;
29. array[4][1] = 3;
30. array[4][2] = 6;
31. array[2][4] = 6;
32. array[2][5] = 4;
33. array[5][2] = 4;
34. array[4][5] = 6;
35. array[5][4] = 6;
36. array[3][5] = 2;
37. array[5][3] = 2;
38.
39.
40. CreateGraph myGraph = new CreateGraph();
41.
42. System.out.println("创建邻接矩阵:");
43. myGraph.createMat(mgraph,array, 6);
44. myGraph.DispMat(mgraph);
45.
46. System.out.println("Prim算法生成最小生成树:");
47. MinimalSpanningTree mst = new MinimalSpanningTree();
48. mst.Prim(mgraph, 0);
49.
50. mst.getEStruct(mgraph);
51. mst.Kruskal(mgraph);
52. }
53.}
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