1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
|
/**
* This program is free software: you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3 of the
* License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see
* <http://www.gnu.org/licenses/>.
*
* (c) Vincenzo Nicosia 2009-2017 -- <v.nicosia@qmul.ac.uk>
*
* This file is part of NetBunch, a package for complex network
* analysis and modelling. For more information please visit:
*
* http://www.complex-networks.net/
*
* If you use this software, please add a reference to
*
* V. Latora, V. Nicosia, G. Russo
* "Complex Networks: Principles, Methods and Applications"
* Cambridge University Press (2017)
* ISBN: 9781107103184
*
***********************************************************************
*
* This program finds the minimum/maximum spanning tree of a graph
* given as input, using the Kruskal's algorithm
*
*
* References:
*
* [1] J. B. Kruskal. "On the shortest spanning subtree of a graph and
* the traveling sales-man problem". P. Am. Math. Soc. 7 (1956),
* 48-48.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dset.h"
#include "gen_heap.h"
#include "utils.h"
#include "edge_w_funs.h"
void usage(int argc, char *argv[]){
printf("********************************************************************\n"
"** **\n"
"** -*- kruskal -*- **\n"
"** **\n"
"** Find the minimum/maximum spanning tree of a weighted graph **\n"
"** 'graph_in' provided as input. **\n"
"** **\n"
"** The input file 'graph_in' is a weighted edge-list: **\n"
"** **\n"
"** I_1 J_1 W_1 **\n"
"** I_2 J_2 W_2 **\n"
"** I_3 J_3 W_3 **\n"
"** ... ... **\n"
"** I_K J_K W_K **\n"
"** **\n"
"** The program computes by default the minimum spanning tree **\n"
"** of 'graph_in', unless the second parameter 'MAX' is **\n"
"** specified. **\n"
"** **\n"
"** The program prints on STDOUT the weighted edge-list of the **\n"
"** minimum/maximum spanning tree of 'graph_in'. **\n"
"** **\n"
"** If 'graph_in' is an unweighted graph, the program prints **\n"
"** on output one of the spanning trees of the graph. **\n"
"** **\n"
"********************************************************************\n"
" This is Free Software - You can use and distribute it under \n"
" the terms of the GNU General Public License, version 3 or later\n\n"
" Please visit http://www.complex-networks.net for more information\n\n"
" (c) Vincenzo Nicosia 2009-2017 (v.nicosia@qmul.ac.uk)\n"
"********************************************************************\n\n"
);
printf("Usage: %s <graph_in> [MAX]\n", argv[0]);
}
void kruskal(gen_heap_t *h, unsigned int N){
dset_t *nodes, set1, set2;
edge_w_t *elem;
unsigned int i;
nodes = malloc(N * sizeof(dset_t));
for(i=0; i<N; i++){
nodes[i] = NULL;
dset_makeset(nodes + i);
}
while(! gen_heap_delete(h, (void**)(&elem))){
/* get the next edge */
set1 = dset_find(nodes[elem->i]);
set2 = dset_find(nodes[elem->j]);
/* if i and j do not belong to the same disjoint set...*/
if (set1 != set2){
/* ... the edge (i,j) belongs to the spanning tree, */
/* so we print it...*/
print_elem_edge_w(elem);
/* ...then merge the two sets... */
dset_union(nodes[elem->i], nodes[elem->j]);
}
free(elem);
}
/* We now destroy all the disjoint sets... */
for (i=0;i<N;i++){
dset_destroy(nodes[i]);
}
free(nodes);
}
void load_edges_into_heap(FILE *filein, gen_heap_t *h){
char buff[256];
char *ptr;
edge_w_t *elem;
while(fgets(buff, 256, filein)){
if (buff[0] == '#')
continue;
elem = malloc(sizeof(edge_w_t));
ptr = strtok(buff, " "); /* read the first node */
VALID_PTR_OR_EXIT(ptr, 7);
elem->i = atoi(ptr);
ptr = strtok(NULL, " "); /* read the second node */
VALID_PTR_OR_EXIT(ptr, 7);
elem->j = atoi(ptr);
ptr = strtok(NULL, " "); /* read the weight */
if (!ptr)
/* if no weight is specified, assume it is set to 1.0 */
elem->w = 1.0;
else
elem->w = atof(ptr);
/* put the edge in the heap */
gen_heap_insert(h, elem);
}
}
int count_num_lines(FILE *filein){
int i, ch ;
i = 0;
while ((ch = fgetc(filein)) != EOF){
if (ch == '\n')
i ++;
}
rewind(filein);
return i;
}
int main(int argc, char *argv[]){
gen_heap_t *h;
unsigned int N;
FILE *filein;
char htype;
gen_heap_func_t *funs;
if(argc < 2){
usage(argc, argv);
exit(1);
}
htype = MIN_HEAP;
if (argc > 2 && !my_strcasecmp(argv[2], "MAX")){
htype = MAX_HEAP;
}
/* Initialisation of functions for gen_heap*/
funs = malloc(sizeof(gen_heap_func_t));
(*funs).compare = compare_edge_w;
(*funs).alloc_vector = alloc_vector_edge_w;
(*funs).dealloc_vector = dealloc_vector_edge_w;
(*funs).dealloc_elem = dealloc_elem_edge_w;
(*funs).print_elem = print_elem_edge_w;
filein = openfile_or_exit(argv[1], "r", 2);
N = count_num_lines(filein);
h = gen_heap_init(N, htype, funs);
load_edges_into_heap(filein, h);
fclose(filein);
kruskal(h, N);
gen_heap_destroy(h);
free(funs);
}
|
