最小生成ツリーアルゴリズムC言語コード例
MST.h
#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
#include "mst.h"
#include
#include
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
", g.edgelist[e]->A->data, g.edgelist[e]->B->data, g.edgelist[e]->w);
e++;
}
printf("------------------------------------------------------
");
kruskal(&g, X);
e = 0;
while (e < (g.nodeLen-1))
{
printf("%c-%c %d
", 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
", g->edgelist[e]->A->data, g->edgelist[e]->B->data, g->edgelist[e]->w);
e++;
}
printf("------------------------------------------------------
");
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;
}
このアルゴリズムを実現するにあたって,テストの重要性を実感した.プログラムのコンパイルに成功したのはほんの一部で、繰り返しのテストを経てから発表しなければならない.