Kruskal adds edges in ascending weight order whenever they join different components..
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 | #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <limits.h> #include <errno.h> // Kruskal Minimum Spanning Tree in C // // PURPOSE // Kruskal adds edges in ascending weight order whenever they join different components. // // METHOD // Sort edge indices by weight using a stable bottom-up merge. Use union by size and path // halving to accept edges joining different roots. Stop after n-1 accepted edges. // // COMPLEXITY // O(E log E + V) time and O(V+E) auxiliary space. // // CONTRACT // n>=1, parallel edge arrays have m entries and valid vertex IDs. Weights nonnegative; total // fits signed 32-bit. Returns -1 for a disconnected graph. // Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex // counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers. // Sorted order, correct tree topology, and caller-owned data-structure invariants are // preconditions; checking them on every query would change query complexity. // Scalar and shape checks are included. Value-range checks are included where needed to // prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000 // workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python // uses arbitrary precision. Native allocation failures propagate. In-place outputs may be // partly updated after arithmetic failure. These are single-threaded, in-memory // implementations. // // LANGUAGE DETAILS // C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors // return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result. // Input/output arrays must not alias. No variable-length stack arrays. // // EXAMPLE // Expected return: 6. // Run: gcc -std=c99 -O2 example.c -o example && ./example // Tests for this exact source artifact run before publication. The accompanying source // archive includes unit cases, runtime results, and source hashes. static int alg_min(int a, int b) { return a < b ? a : b; } static int alg_max(int a, int b) { return a > b ? a : b; } static int alg_checked(int64_t v, int *error) { if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; } return (int)v; } static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); } static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); } static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); } int kruskal(const int *from_vertex, size_t from_vertex_length, const int *to_vertex, size_t to_vertex_length, const int *weight, size_t weight_length, int n) { int alg_error = 0; int alg_result = INT_MIN; errno = 0; int *order = NULL; int *buffer = NULL; int *parent = NULL; int *size = NULL; if (from_vertex_length > 1000000 || (from_vertex_length && !from_vertex)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (to_vertex_length > 1000000 || (to_vertex_length && !to_vertex)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (weight_length > 1000000 || (weight_length && !weight)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } int m = (int)from_vertex_length; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((m >= 0) && (m <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((int)from_vertex_length == m))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((int)to_vertex_length == m))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((int)weight_length == m))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!((n >= 1))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } for (int alg_i = 0; alg_i < (int)from_vertex_length; alg_i++) { int alg_value = from_vertex[alg_i]; if (!(((alg_value >= 0) && (alg_value < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } for (int alg_i = 0; alg_i < (int)to_vertex_length; alg_i++) { int alg_value = to_vertex[alg_i]; if (!(((alg_value >= 0) && (alg_value < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } { int alg_length = alg_add(m, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } order = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*order)); if (!order) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; } } { int alg_length = alg_add(m, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } buffer = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*buffer)); if (!buffer) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; } } { int alg_length = n; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } parent = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*parent)); if (!parent) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; } } { int alg_length = n; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } size = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*size)); if (!size) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; } } int i = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int j = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int k = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int width = 1; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int left = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int mid = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int right = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int edge = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int u = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int v = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int temp = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int accepted = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int total = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (i < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; order[i] = i; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } i = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } while (1) { int alg_condition = (width < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; left = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (left < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; mid = alg_min(alg_add(left, width, &alg_error), m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } right = alg_min(alg_add(left, alg_mul(2, width, &alg_error), &alg_error), m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } i = left; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } j = mid; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } k = left; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (k < right); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; int alg_condition_1 = ((i < mid) && ((j >= right) || (weight[order[i]] <= weight[order[j]]))); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_1) { buffer[k] = order[i]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } i = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } else { buffer[k] = order[j]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } j = alg_add(j, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } k = alg_add(k, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } left = alg_add(left, alg_mul(2, width, &alg_error), &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } i = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (i < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; order[i] = buffer[i]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } i = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } width = alg_mul(width, 2, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } i = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (i < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; parent[i] = i; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } size[i] = 1; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } i = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } while (1) { int alg_condition = ((edge < m) && (accepted < alg_sub(n, 1, &alg_error))); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; u = from_vertex[order[edge]]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = to_vertex[order[edge]]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (parent[u] != u); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; parent[u] = parent[parent[u]]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } u = parent[u]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } while (1) { int alg_condition = (parent[v] != v); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; parent[v] = parent[parent[v]]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = parent[v]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } int alg_condition_2 = (u != v); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_2) { int alg_condition_3 = (size[u] < size[v]); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_3) { temp = u; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } u = v; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = temp; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } parent[v] = u; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } size[u] = alg_add(size[u], size[v], &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } accepted = alg_add(accepted, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } total = alg_add(total, weight[order[edge]], &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } edge = alg_add(edge, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } int alg_condition_4 = (accepted != alg_sub(n, 1, &alg_error)); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_4) { alg_result = alg_sub(0, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; } alg_result = total; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; alg_cleanup: free(order); free(buffer); free(parent); free(size); return alg_result; } int main(void) { int from_vertex[] = {0, 1, 0}; int to_vertex[] = {1, 2, 2}; int weight[] = {4, 2, 10}; int n = 3; int result = kruskal(from_vertex, 3, to_vertex, 3, weight, 3, n); printf("%d\n", result); if (errno) { perror("algorithm"); return 1; } return 0; } |
