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
|
/*
Projet d'algorithmique et programmation 2013-2014
(cours de C.Matthieu et J.Stern)
Alex AUVOLAT, Mendes OULAMARA
Implémentation des ensembles d'entiers sous forme de bitsets.
Code sous la juridiction de Mendes OULAMARA.
*/
#include "sets.h"
#include <stdlib.h>
#include <stdio.h>
#include <assert.h>
#define SCOD (unsigned long long)(8*sizeof(unsigned long long))
int nbCells(int n){ //the mathematical ceil function
if(n == (n/SCOD)*SCOD)
return n/SCOD;
else
return n/SCOD+1;
}
int nb_one(unsigned long long x) { //the hamming weight of x
assert(SCOD==64);
//1
x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555); // mask : 0101010101...
//2
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); // mask : 001100110011...
//4
x = (x & 0x0F0F0F0F0F0F0F0F) + ((x >> 4) & 0x0F0F0F0F0F0F0F0F); // mask : 000011110000....
//8
x = (x & 0x00FF00FF00FF00FF) + ((x >> 8) & 0x00FF00FF00FF00FF); // etc.
//16
x = (x & 0x0000FFFF0000FFFF) + ((x >> 16) & 0x0000FFFF0000FFFF);
//32
x = (x & 0x00000000FFFFFFFF) + ((x >> 32) & 0x00000000FFFFFFFF);
return x;
}
int set_size(const set s){
return *(s.size);
}
set empty_set(int n){
assert(n > 0);
set res;
int i;
res.N = n;
res.size = malloc(sizeof(int));
*(res.size) = 0;
int NC = nbCells(n);
res.tab = malloc(SCOD*NC/8);
for(i = 0; i < NC; i++)
res.tab[i] = 0;
return res;
}
set copy_set(const set s){
set res = empty_set(s.N);
*(res.size) = *(s.size);
int NC = nbCells(s.N), i;
for(i = 0; i < NC; i++)
res.tab[i] = s.tab[i];
return res;
}
void delete_set(set a){
free(a.tab);
free(a.size);
}
void set_union_ip(set a, const set b){
if(a.N != b.N){
printf("Union failed : the sets don't have the same size\n");
assert(a.N == b.N);
}
int NC = nbCells(a.N), i;
*(a.size)=0;
for(i = 0; i < NC; i++) {
a.tab[i] = a.tab[i]|b.tab[i];
*(a.size) += nb_one(a.tab[i]);
}
}
void set_inter_ip(set a, const set b){
if(a.N != b.N){
printf("Intersection failed : the sets don't have the same size\n");
assert(a.N == b.N);
}
int NC = nbCells(a.N), i;
*(a.size)=0;
for(i = 0; i < NC; i++){
a.tab[i] = a.tab[i]&b.tab[i];
*(a.size) += nb_one(a.tab[i]);
}
assert((a.N%SCOD == 0) || (a.tab[NC-1]>>(a.N%SCOD)) == 0);
}
void set_diff_ip(set a, const set b){
if(a.N != b.N){
printf("Difference failed : the sets don't have the same size\n");
assert(a.N == b.N);
}
int NC = nbCells(a.N), i;
*(a.size)=0;
for(i = 0; i < NC; i++) {
a.tab[i] = a.tab[i] & (~b.tab[i]);
*(a.size) += nb_one(a.tab[i]);
}
assert((a.N%SCOD == 0) || (a.tab[NC-1]>>(a.N%SCOD)) == 0);
}
bool is_set_empty(const set s){
return (*(s.size) == 0);
}
inline bool set_mem(int x, const set s){
unsigned long long ux = x;
if (!(x < s.N && x >= 0)) {
printf("Invalid argument for set_mem : %d\n", x);
assert(x < s.N && x >= 0);
}
return (s.tab[ux/SCOD]>>(ux%SCOD))&1;
}
int dyadic_val(unsigned long long x){
if(x == 0) {
printf("Infinite valuation\n");
assert(false);
}
int i = 0;
while (((x>>i)&1) == 0) i++;
return i;
}
int elt_of_set(const set s){
int N=nbCells(s.N), i;
for(i=0; i<N; i++)
if(s.tab[i] != 0)
return i*SCOD + dyadic_val(s.tab[i]);
printf("No element in an empty set!\n");
dump_set(s);
assert(false);
}
int elt_of_set_heur(const set s, int h){
int N=nbCells(s.N), i;
if(s.tab[h/SCOD]>>(h%SCOD) !=0)
return h + dyadic_val(s.tab[h/SCOD]>>(h%SCOD)) ;
for(i=0; i<N; i++)
if(s.tab[(i+h/SCOD+1)%N] != 0)
return i*SCOD+dyadic_val(s.tab[(i+h/SCOD+1)%N]);
printf("No element in an empty set!\n");
dump_set(s);
assert(false);
}
void set_add_ip(int x, set s){
unsigned long long ux = x;
if(! set_mem(ux, s)){
s.tab[ux/SCOD] = s.tab[ux/SCOD] | (unsigned long long)(1)<<(ux%SCOD);
*(s.size) = *(s.size)+1;
}
}
void set_remove_ip(int x, set s){
unsigned long long ux = x;
if(set_mem(ux, s) ) {
s.tab[ux/SCOD] = s.tab[ux/SCOD] & (~((unsigned long long)(1)<<(ux%SCOD)));
*(s.size) = *(s.size)-1;
}
}
void dump_set(const set s){
int i=0;
printf("[");
for(i=0; i < s.N; i++)
if(set_mem(i, s))
printf(" %d ", i);
printf("] (%d)\n", *(s.size));
}
set full_set(int n) {
set r = empty_set(n);
*(r.size) = n;
int NC=nbCells(n), i;
for(i=0; i< NC; i++)
r.tab[i]=-1;
r.tab[NC-1] = ( r.tab[NC-1]>>( (SCOD-(n%SCOD))%SCOD ) );
assert((n%SCOD == 0) || (r.tab[NC-1]>>(n%SCOD)) == 0);
return r;
}
|
