最小生成树算法C语言代码实例

在贪婪算法这一章提到了最小生成树的一些算法，首先是Kruskal算法，实现如下：

MST.h

代码如下:

#ifndef H_MST
#define H_MST

#define NODE node *
#define G graph *
#define MST edge **

/* the undirect graph start */
typedef struct _node {
 char data;
 int flag;
 struct _node *parent;
} node;

typedef struct _edge {
 node *A;
 node *B;
 int w;
} edge;

typedef struct _graph {
 node **nodelist;
 int nodeLen;
 edge **edgelist;
 int edgeLen;
} graph;

/* the undirect graph end */

int kruskal(G , edge *[]);

int makeset(NODE);

int find(NODE , NODE);

int merge(NODE , NODE);

int comp(const void *, const void *);

#endif

MST.c

代码如下:

#include "mst.h"
#include <stdlib.h>
#include <stdio.h>

int main(int argc, char *argv[])
{
 /* Construct the undirect connected graph */
 graph g;
 g.nodeLen = 6;
 g.edgeLen = 10;

node node_a, node_b, node_c, node_d, node_e, node_f;
 edge edge_1, edge_2, edge_3, edge_4, edge_5, edge_6, edge_7, edge_8, edge_9, edge_10;

node_a.data = 'a';
 node_a.flag = 0;
 node_a.parent = (node *)malloc(sizeof(node));
 node_b.data = 'b';
 node_b.flag = 0;
 node_b.parent = (node *)malloc(sizeof(node));
 node_c.data = 'c';
 node_c.flag = 0;
 node_c.parent = (node *)malloc(sizeof(node));
 node_d.data = 'd';
 node_d.flag = 0;
 node_d.parent = (node *)malloc(sizeof(node));
 node_e.data = 'e';
 node_e.flag = 0;
 node_e.parent = (node *)malloc(sizeof(node));
 node_f.data = 'f';
 node_f.flag = 0;
 node_f.parent = (node *)malloc(sizeof(node));

edge_1.A = &node_a;
 edge_1.B = &node_b;
 edge_1.w = 5;

edge_2.A = &node_a;
 edge_2.B = &node_c;
 edge_2.w = 6;

edge_3.A = &node_a;
 edge_3.B = &node_d;
 edge_3.w = 4;

edge_4.A = &node_b;
 edge_4.B = &node_c;
 edge_4.w = 1;

edge_5.A = &node_b;
 edge_5.B = &node_d;
 edge_5.w = 2;

edge_6.A = &node_c;
 edge_6.B = &node_d;
 edge_6.w = 2;

edge_7.A = &node_c;
 edge_7.B = &node_e;
 edge_7.w = 5;

edge_8.A = &node_c;
 edge_8.B = &node_f;
 edge_8.w = 3;

edge_9.A = &node_d;
 edge_9.B = &node_f;
 edge_9.w = 4;

edge_10.A = &node_e;
 edge_10.B = &node_f;
 edge_10.w = 4;

node **nodelist;
 nodelist = (node **)malloc(sizeof(node *) * g.nodeLen);
 edge **edgelist;
 edgelist = (edge **)malloc(sizeof(edge *) * g.edgeLen);

nodelist[0] = &node_a;
 nodelist[1] = &node_b;
 nodelist[2] = &node_c;
 nodelist[3] = &node_d;
 nodelist[4] = &node_e;
 nodelist[5] = &node_f;

edgelist[0] = &edge_1;
 edgelist[1] = &edge_2;
 edgelist[2] = &edge_3;
 edgelist[3] = &edge_4;
 edgelist[4] = &edge_5;
 edgelist[5] = &edge_6;
 edgelist[6] = &edge_7;
 edgelist[7] = &edge_8;
 edgelist[8] = &edge_9;
 edgelist[9] = &edge_10;

g.nodelist = nodelist;
 g.edgelist = edgelist;

edge *X[g.nodeLen-1];

int e = 0;
 while (e < g.edgeLen)
 {
  printf("%c-%c %d\n", g.edgelist[e]->A->data, g.edgelist[e]->B->data, g.edgelist[e]->w);
  e++;
 }

printf("------------------------------------------------------\n");

kruskal(&g, X);

e = 0;
 while (e < (g.nodeLen-1))
 {
  printf("%c-%c %d\n", X[e]->A->data, X[e]->B->data, X[e]->w);
  e++;
 }
}

int kruskal(G g, edge *pX[])
{
 int i, j;

/* Initially every disjoint set have one node */
 for (i = 0; i < g->nodeLen; i++)
  makeset(g->nodelist[i]);

/* sort the edgelist */
 qsort(g->edgelist, g->edgeLen, sizeof(edge *), comp);

int e = 0;
 while (e < g->edgeLen)
 {
  printf("%c-%c %d\n", g->edgelist[e]->A->data, g->edgelist[e]->B->data, g->edgelist[e]->w);
  e++;
 }

printf("------------------------------------------------------\n");

node da, db;
 da.parent = (node *)malloc(sizeof(node));
 db.parent = (node *)malloc(sizeof(node));

for (j = 0; j < g->edgeLen; j++)
 {
  find(g->edgelist[j]->A, &da);
  find(g->edgelist[j]->B, &db);

if (da.data != db.data)
  {
   merge(g->edgelist[j]->A, g->edgelist[j]->B);
   *pX++ = g->edgelist[j];
  }
 }
}

int makeset(NODE n)
{
 n->parent = n;
}

int find(NODE n, NODE ds)
{
 if (n->parent == n)
 {
  ds->data = n->data;
  ds->flag = 1;
  ds->parent = n->parent;
 }

if (n->parent != n)
  find(n->parent, ds);
}

int merge(NODE da, NODE db)
{
 if (da->flag)
  db->parent = da;
 else
  da->parent = db;
}

int comp(const void *ea, const void *eb)
{
 if ((*(edge **)ea)->w > (*(edge **)eb)->w) return 1;
 else if ((*(edge **)ea)->w == (*(edge **)eb)->w ) return 0;
 else return -1;
}

在实现这个算法的时候，真正体会到了测试的重要性。程序能成功编译只是完成了一小部分，必须经过反复的测试才能发布。