Prim grows a minimum spanning tree by choosing the cheapest edge that connects an unvisited vertex to the current tree.
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 | #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <limits.h> #include <errno.h> // Prim Minimum Spanning Tree in C // // PURPOSE // Prim grows a minimum spanning tree by choosing the cheapest edge that connects an // unvisited vertex to the current tree. The cut property justifies each greedy choice. // // METHOD // Keep the cheapest connection cost for every unvisited vertex. Select the cheapest one, add // its cost, and update neighbors. If no finite connection remains before all vertices are // added, the graph is disconnected. // // COMPLEXITY // O(n squared) time and O(n) auxiliary space for a dense adjacency matrix. // // CONTRACT // n >= 1; symmetric flattened matrix for an undirected graph. -1 means absent, weights are // nonnegative and < 1,000,000,000. Total must fit. Returns MST weight or -1 if disconnected. // 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 prim_mst(const int *graph, size_t graph_length, int n) { int alg_error = 0; int alg_result = INT_MIN; errno = 0; int *cost = NULL; int *used = NULL; if (graph_length > 1000000 || (graph_length && !graph)) { errno = EINVAL; 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 (!(((int)graph_length == alg_mul(n, n, &alg_error)))) { 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)graph_length; alg_i++) { int alg_value = graph[alg_i]; if (!(((alg_value >= alg_sub(0, 1, &alg_error)) && (alg_value < 1000000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; 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; } cost = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*cost)); if (!cost) { 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; } used = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*used)); if (!used) { 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 v = 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 best = 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 < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; cost[i] = 1000000000; 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; } } cost[0] = 0; 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; u = alg_sub(0, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } best = 1000000000; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (v < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; int alg_condition_1 = ((used[v] == 0) && (cost[v] < best)); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_1) { best = cost[v]; 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 = alg_add(v, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } int alg_condition_2 = (u == alg_sub(0, 1, &alg_error)); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_2) { alg_result = alg_sub(0, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; } used[u] = 1; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } total = alg_add(total, cost[u], &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (v < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; int alg_condition_3 = (graph[alg_add(alg_mul(u, n, &alg_error), v, &alg_error)] >= 0); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_3) { cost[v] = alg_min(cost[v], graph[alg_add(alg_mul(u, n, &alg_error), v, &alg_error)]); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } v = alg_add(v, 1, &alg_error); 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; } } alg_result = total; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; alg_cleanup: free(cost); free(used); return alg_result; } int main(void) { int graph[] = {0, 4, 10, 4, 0, 2, 10, 2, 0}; int n = 3; int result = prim_mst(graph, 9, n); printf("%d\n", result); if (errno) { perror("algorithm"); return 1; } return 0; } |
