| 1 | /* |
| 2 | * dsf.c: some functions to handle a disjoint set forest, |
| 3 | * which is a data structure useful in any solver which has to |
| 4 | * worry about avoiding closed loops. |
| 5 | */ |
| 6 | |
| 7 | #include <assert.h> |
| 8 | #include <string.h> |
| 9 | |
| 10 | #include "puzzles.h" |
| 11 | |
| 12 | /*void print_dsf(int *dsf, int size) |
| 13 | { |
| 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); |
| 21 | |
| 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; |
| 31 | |
| 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"); |
| 55 | } |
| 56 | done: |
| 57 | |
| 58 | sfree(printed_elements); |
| 59 | sfree(equal_elements); |
| 60 | sfree(inverse_elements); |
| 61 | }*/ |
| 62 | |
| 63 | void dsf_init(int *dsf, int size) |
| 64 | { |
| 65 | int i; |
| 66 | |
| 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. */ |
| 74 | } |
| 75 | |
| 76 | int *snew_dsf(int size) |
| 77 | { |
| 78 | int *ret; |
| 79 | |
| 80 | ret = snewn(size, int); |
| 81 | dsf_init(ret, size); |
| 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); |
| 91 | } |
| 92 | |
| 93 | void dsf_merge(int *dsf, int v1, int v2) |
| 94 | { |
| 95 | edsf_merge(dsf, v1, v2, FALSE); |
| 96 | } |
| 97 | |
| 98 | int dsf_size(int *dsf, int index) { |
| 99 | return dsf[dsf_canonify(dsf, index)] >> 2; |
| 100 | } |
| 101 | |
| 102 | int edsf_canonify(int *dsf, int index, int *inverse_return) |
| 103 | { |
| 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. */ |
| 115 | while ((dsf[index] & 2) == 0) { |
| 116 | inverse ^= (dsf[index] & 1); |
| 117 | index = dsf[index] >> 2; |
| 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) { |
| 130 | int nextindex = dsf[index] >> 2; |
| 131 | int nextinverse = inverse ^ (dsf[index] & 1); |
| 132 | dsf[index] = (canonical_index << 2) | inverse; |
| 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; |
| 147 | |
| 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); |
| 152 | assert(dsf[v1] & 2); |
| 153 | inverse ^= i1; |
| 154 | v2 = edsf_canonify(dsf, v2, &i2); |
| 155 | assert(dsf[v2] & 2); |
| 156 | inverse ^= i2; |
| 157 | |
| 158 | /* fprintf(stderr, "Doing [%2d,%2d], %d\n", v1, v2, inverse); */ |
| 159 | |
| 160 | if (v1 == v2) |
| 161 | assert(!inverse); |
| 162 | else { |
| 163 | assert(inverse == 0 || inverse == 1); |
| 164 | if ((dsf[v2] >> 2) > (dsf[v1] >> 2)) { |
| 165 | int v3 = v1; |
| 166 | v1 = v2; |
| 167 | v2 = v3; |
| 168 | } |
| 169 | dsf[v1] += (dsf[v2] >> 2) << 2; |
| 170 | dsf[v2] = (v1 << 2) | !!inverse; |
| 171 | } |
| 172 | |
| 173 | v2 = edsf_canonify(dsf, v2, &i2); |
| 174 | assert(v2 == v1); |
| 175 | assert(i2 == inverse); |
| 176 | |
| 177 | /* fprintf(stderr, "dsf[%2d] = %2d\n", v2, dsf[v2]); */ |
| 178 | } |