其他分享
首页 > 其他分享> > 数据结构【图】—024最小生成树

数据结构【图】—024最小生成树

作者:互联网

/*****************************普里姆(Prim)算法***************************/

 

/*
此为无向图
Prim算法思想很简单,依托临接矩阵
就是从顶点0开始,依次比较起始点到下一个点的最短路径,并将其更新
然后以新的点为起始点,再找到该点能够到达的下一个最短路径,
直到所有点都遍历完为止!
*/

根据程序,最小线段生成如下:

 

 1 #include "000库函数.h"
 2 
 3 #define MAXVEX 20
 4 #define INFINITY 65535//视为无穷大
 5 
 6 //临接矩阵的数据结构
 7 struct MGraph {
 8     int arc[MAXVEX][MAXVEX];
 9     int numVertexes, numEdges;
10 };
11 
12 //初始化临接矩阵
13 MGraph *CreateMGraph(MGraph *G) {
14     G->numEdges = 15;
15     G->numVertexes = 9;
16 
17     for (int i = 0; i < G->numVertexes; i++)/* 初始化图 */
18     {
19         for (int j = 0; j < G->numVertexes; j++)
20         {
21             if (i == j)
22                 G->arc[i][j] = 0;
23             else
24                 G->arc[i][j] = G->arc[j][i] = INFINITY;
25         }
26     }
27 
28     G->arc[0][1] = 10;
29     G->arc[0][5] = 11;
30     G->arc[1][2] = 18;
31     G->arc[1][8] = 12;
32     G->arc[1][6] = 16;
33     G->arc[2][8] = 8;
34     G->arc[2][3] = 22;
35     G->arc[3][8] = 21;
36     G->arc[3][6] = 24;
37     G->arc[3][7] = 16;
38     G->arc[3][4] = 20;
39     G->arc[4][7] = 7;
40     G->arc[4][5] = 26;
41     G->arc[5][6] = 17;
42     G->arc[6][7] = 19;
43 
44     for (int i = 0; i < G->numVertexes; i++)
45     {
46         for (int j = i; j < G->numVertexes; j++)
47         {
48             G->arc[j][i] = G->arc[i][j];
49         }
50     }
51     return G;
52 }
53 
54 //使用Prim算法生成最小树
55 void MiniSpanTree_Prim(MGraph *G) {
56     int min, i, j, k;
57     int adjvex[MAXVEX];//保存相关顶点的下标
58     int lowcost[MAXVEX]; // 保存相关顶点间边的权值
59     lowcost[0] = 0;//将v0顶点加入进来
60     adjvex[0] = 0;//初始化第一个顶点为0
61     for (int i = 1; i < G->numVertexes; ++i) {
62         lowcost[i] = G->arc[0][i];//先将v0能到其他点的距离记录下来
63         adjvex[i] = 0;//即到达每个点的起始点都为0点
64     }
65 
66     for (int i = 1; i < G->numVertexes; ++i) {
67         min = INFINITY;//将最短路径设为无穷
68         j = 1; k = 0;
69         while (j < G->numVertexes) {
70             if (lowcost[j] != 0 && lowcost[j] < min) {//找到点0到下一个距离最短的值
71                 min = lowcost[j];//
72                 k = j;//记住最小值的点
73             }
74             ++j;
75         }
76 
77         printf("(%d, %d)\n", adjvex[k], k);
78         lowcost[k] = 0;//重新以点k为起始点,然后继续寻找下一个最短路径
79         for (j = 1; j < G->numVertexes; ++j) {
80             if (lowcost[j] != 0 && G->arc[k][j] < lowcost[j]) {//找到下一个最短路劲
81                 lowcost[j] = G->arc[k][j];
82                 adjvex[j] = k;
83             }
84         }
85 
86     }
87 }
88 
89 int T025(void){
90     MGraph *G;
91     G = new MGraph;//初始化图
92     G = CreateMGraph(G);
93     MiniSpanTree_Prim(G);
94 
95     return 0;
96 
97 }

  

 

/************************克鲁斯卡尔(Kruskal)******************/

根据权值大小,生成权值表,然后根据权值表进行探索路径

 

 

 

  1 #include "000库函数.h"
  2 
  3 #define MAXVEX 20
  4 #define INFINITY 65535//视为无穷大
  5 
  6 //临接矩阵的数据结构
  7 struct MGraph {
  8     int arc[MAXVEX][MAXVEX];
  9     int numVertexes, numEdges;
 10 };
 11 
 12 //初始化临接矩阵
 13 MGraph *CreateMGraph(MGraph *G) {
 14     G->numEdges = 15;
 15     G->numVertexes = 9;
 16 
 17     for (int i = 0; i < G->numVertexes; i++)/* 初始化图 */
 18     {
 19         for (int j = 0; j < G->numVertexes; j++)
 20         {
 21             if (i == j)
 22                 G->arc[i][j] = 0;
 23             else
 24                 G->arc[i][j] = G->arc[j][i] = INFINITY;
 25         }
 26     }
 27 
 28     G->arc[0][1] = 10;
 29     G->arc[0][5] = 11;
 30     G->arc[1][2] = 18;
 31     G->arc[1][8] = 12;
 32     G->arc[1][6] = 16;
 33     G->arc[2][8] = 8;
 34     G->arc[2][3] = 22;
 35     G->arc[3][8] = 21;
 36     G->arc[3][6] = 24;
 37     G->arc[3][7] = 16;
 38     G->arc[3][4] = 20;
 39     G->arc[4][7] = 7;
 40     G->arc[4][5] = 26;
 41     G->arc[5][6] = 17;
 42     G->arc[6][7] = 19;
 43 
 44     for (int i = 0; i < G->numVertexes; i++)
 45     {
 46         for (int j = i; j < G->numVertexes; j++)
 47         {
 48             G->arc[j][i] = G->arc[i][j];
 49         }
 50     }
 51     return G;
 52 }
 53 
 54 //寻找下一个顶点位置
 55 int Find(vector<int>parent, int v) {
 56     while (parent[v] > 0)v = parent[v];
 57     return v;
 58 }
 59 
 60 
 61 //使用MiniSpanTree_Kruskal生成最小树
 62 void MiniSpanTree_Kruskal(MGraph *G) {
 63     int n, m;
 64     int k = 0;
 65     vector<int> Parent(MAXVEX, 0);//定义一个数组,用来判断是否形成了环路
 66     int Edge[MAXVEX][3];//权值表,存放起始点、终止点、权值
 67     //构建权值表
 68     for (int i = 0; i < G->numVertexes; ++i) {
 69         for (int j = i + 1; j < G->numVertexes; ++j) {
 70             if (G->arc[i][j] < INFINITY) {
 71                 Edge[k][0] = i;
 72                 Edge[k][1] = j;
 73                 Edge[k][2] = G->arc[i][j];
 74                 k++;
 75             }
 76         }
 77     }
 78     //进行排序
 79     for (int i = 0; i < k; ++i) {
 80         int min = Edge[i][2];
 81         for (int j = i + 1; j < k; ++j) {
 82             if (min > Edge[j][2]) {
 83                 min = Edge[j][2];
 84                 for (int t = 0; t < 3; ++t) {
 85                     int temp;
 86                     temp = Edge[i][t];
 87                     Edge[i][t] = Edge[j][t];
 88                     Edge[j][t] = temp;
 89                 }
 90             }
 91         }
 92     }
 93 
 94 
 95     /*************************算法的核心*****************************/
 96 
 97 
 98 
 99 
100     int adjvex[MAXVEX];//保存相关顶点的下标
101     int lowcost[MAXVEX]; // 保存相关顶点间边的权值
102     lowcost[0] = 0;//将v0顶点加入进来
103     adjvex[0] = 0;//初始化第一个顶点为0
104     for (int i = 1; i < G->numVertexes; ++i) {
105         lowcost[i] = G->arc[0][i];//先将v0能到其他点的距离记录下来
106         adjvex[i] = 0;//即到达每个点的起始点都为0点
107     }
108 
109     for (int i = 0; i < k; ++i) {//循环每一个权值矩阵
110         n = Find(Parent, Edge[i][0]);
111         m = Find(Parent, Edge[i][1]);
112         if (n != m) {//不会形成环,可以使用
113             Parent[n] = m;
114             cout << Edge[i][0] << "," << Edge[i][1] << endl;
115         }
116     }
117 }
118 
119     
120 
121 int T026(void) {
122     MGraph *G;
123     G = new MGraph;//初始化图
124     G = CreateMGraph(G);
125     MiniSpanTree_Kruskal(G);
126 
127     return 0;
128 
129 }

 

标签:int,++,最小,024,arc,lowcost,numVertexes,Edge,数据结构
来源: https://www.cnblogs.com/zzw1024/p/10581682.html