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1 | /* |
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2 | * dsf.c: some functions to handle a disjoint set forest, |
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3 | * which is a data structure useful in any solver which has to |
4 | * worry about avoiding closed loops. |
5 | */ |
6 | |
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7 | #include <assert.h> |
8 | #include <string.h> |
9 | |
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10 | #include "puzzles.h" |
11 | |
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12 | /*void print_dsf(int *dsf, int size) |
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13 | { |
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14 | int *printed_elements = snewn(size, int); |
15 | int *equal_elements = snewn(size, int); |
16 | int *inverse_elements = snewn(size, int); |
17 | int printed_count = 0, equal_count, inverse_count; |
18 | int i, n, inverse; |
19 | |
20 | memset(printed_elements, -1, sizeof(int) * size); |
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21 | |
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22 | while (1) { |
23 | equal_count = 0; |
24 | inverse_count = 0; |
25 | for (i = 0; i < size; ++i) { |
26 | if (!memchr(printed_elements, i, sizeof(int) * size)) |
27 | break; |
28 | } |
29 | if (i == size) |
30 | goto done; |
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31 | |
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32 | i = dsf_canonify(dsf, i); |
33 | |
34 | for (n = 0; n < size; ++n) { |
35 | if (edsf_canonify(dsf, n, &inverse) == i) { |
36 | if (inverse) |
37 | inverse_elements[inverse_count++] = n; |
38 | else |
39 | equal_elements[equal_count++] = n; |
40 | } |
41 | } |
42 | |
43 | for (n = 0; n < equal_count; ++n) { |
44 | fprintf(stderr, "%d ", equal_elements[n]); |
45 | printed_elements[printed_count++] = equal_elements[n]; |
46 | } |
47 | if (inverse_count) { |
48 | fprintf(stderr, "!= "); |
49 | for (n = 0; n < inverse_count; ++n) { |
50 | fprintf(stderr, "%d ", inverse_elements[n]); |
51 | printed_elements[printed_count++] = inverse_elements[n]; |
52 | } |
53 | } |
54 | fprintf(stderr, "\n"); |
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55 | } |
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56 | done: |
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57 | |
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58 | sfree(printed_elements); |
59 | sfree(equal_elements); |
60 | sfree(inverse_elements); |
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61 | }*/ |
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62 | |
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63 | void dsf_init(int *dsf, int size) |
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64 | { |
65 | int i; |
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66 | |
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67 | for (i = 0; i < size; i++) dsf[i] = 6; |
68 | /* Bottom bit of each element of this array stores whether that |
69 | * element is opposite to its parent, which starts off as |
70 | * false. Second bit of each element stores whether that element |
71 | * is the root of its tree or not. If it's not the root, the |
72 | * remaining 30 bits are the parent, otherwise the remaining 30 |
73 | * bits are the number of elements in the tree. */ |
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74 | } |
75 | |
76 | int *snew_dsf(int size) |
77 | { |
78 | int *ret; |
79 | |
80 | ret = snewn(size, int); |
81 | dsf_init(ret, size); |
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82 | |
83 | /*print_dsf(ret, size); */ |
84 | |
85 | return ret; |
86 | } |
87 | |
88 | int dsf_canonify(int *dsf, int index) |
89 | { |
90 | return edsf_canonify(dsf, index, NULL); |
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91 | } |
92 | |
93 | void dsf_merge(int *dsf, int v1, int v2) |
94 | { |
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95 | edsf_merge(dsf, v1, v2, FALSE); |
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96 | } |
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97 | |
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98 | int dsf_size(int *dsf, int index) { |
99 | return dsf[dsf_canonify(dsf, index)] >> 2; |
100 | } |
101 | |
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102 | int edsf_canonify(int *dsf, int index, int *inverse_return) |
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103 | { |
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104 | int start_index = index, canonical_index; |
105 | int inverse = 0; |
106 | |
107 | /* fprintf(stderr, "dsf = %p\n", dsf); */ |
108 | /* fprintf(stderr, "Canonify %2d\n", index); */ |
109 | |
110 | assert(index >= 0); |
111 | |
112 | /* Find the index of the canonical element of the 'equivalence class' of |
113 | * which start_index is a member, and figure out whether start_index is the |
114 | * same as or inverse to that. */ |
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115 | while ((dsf[index] & 2) == 0) { |
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116 | inverse ^= (dsf[index] & 1); |
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117 | index = dsf[index] >> 2; |
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118 | /* fprintf(stderr, "index = %2d, ", index); */ |
119 | /* fprintf(stderr, "inverse = %d\n", inverse); */ |
120 | } |
121 | canonical_index = index; |
122 | |
123 | if (inverse_return) |
124 | *inverse_return = inverse; |
125 | |
126 | /* Update every member of this 'equivalence class' to point directly at the |
127 | * canonical member. */ |
128 | index = start_index; |
129 | while (index != canonical_index) { |
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130 | int nextindex = dsf[index] >> 2; |
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131 | int nextinverse = inverse ^ (dsf[index] & 1); |
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132 | dsf[index] = (canonical_index << 2) | inverse; |
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133 | inverse = nextinverse; |
134 | index = nextindex; |
135 | } |
136 | |
137 | assert(inverse == 0); |
138 | |
139 | /* fprintf(stderr, "Return %2d\n", index); */ |
140 | |
141 | return index; |
142 | } |
143 | |
144 | void edsf_merge(int *dsf, int v1, int v2, int inverse) |
145 | { |
146 | int i1, i2; |
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147 | |
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148 | /* fprintf(stderr, "dsf = %p\n", dsf); */ |
149 | /* fprintf(stderr, "Merge [%2d,%2d], %d\n", v1, v2, inverse); */ |
150 | |
151 | v1 = edsf_canonify(dsf, v1, &i1); |
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152 | assert(dsf[v1] & 2); |
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153 | inverse ^= i1; |
154 | v2 = edsf_canonify(dsf, v2, &i2); |
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155 | assert(dsf[v2] & 2); |
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156 | inverse ^= i2; |
157 | |
158 | /* fprintf(stderr, "Doing [%2d,%2d], %d\n", v1, v2, inverse); */ |
159 | |
160 | if (v1 == v2) |
161 | assert(!inverse); |
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162 | else { |
163 | assert(inverse == 0 || inverse == 1); |
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164 | /* |
165 | * We always make the smaller of v1 and v2 the new canonical |
166 | * element. This ensures that the canonical element of any |
167 | * class in this structure is always the first element in |
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168 | * it. 'Keen' depends critically on this property. |
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169 | * |
170 | * (Jonas Koelker previously had this code choosing which |
171 | * way round to connect the trees by examining the sizes of |
172 | * the classes being merged, so that the root of the |
173 | * larger-sized class became the new root. This gives better |
174 | * asymptotic performance, but I've changed it to do it this |
175 | * way because I like having a deterministic canonical |
176 | * element.) |
177 | */ |
178 | if (v1 > v2) { |
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179 | int v3 = v1; |
180 | v1 = v2; |
181 | v2 = v3; |
182 | } |
183 | dsf[v1] += (dsf[v2] >> 2) << 2; |
184 | dsf[v2] = (v1 << 2) | !!inverse; |
185 | } |
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186 | |
187 | v2 = edsf_canonify(dsf, v2, &i2); |
188 | assert(v2 == v1); |
189 | assert(i2 == inverse); |
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190 | |
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191 | /* fprintf(stderr, "dsf[%2d] = %2d\n", v2, dsf[v2]); */ |
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192 | } |