Bellman-Ford permits negative edge weights and detects negative cycles reachable from the source.
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 | #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <limits.h> #include <errno.h> // Bellman Ford Shortest Path in C // // PURPOSE // Bellman-Ford permits negative edge weights and detects negative cycles reachable from the // source. Repeated edge relaxation finds progressively longer optimal paths. // // METHOD // Relax every edge up to n-1 times, stopping early if nothing changes. Perform one extra // pass to detect a reachable negative cycle. Guard unreachable endpoints before adding // weights. // // COMPLEXITY // O(VE) time and O(V) auxiliary space. // // CONTRACT // Edge arrays from_vertex, to_vertex, weight each have m entries; n >= 1. Finite distances // and all relaxed sums stay strictly between -1,000,000,000 and 1,000,000,000. Returns // distance, INF if unreachable, or -INF for any reachable negative cycle (even if it cannot // reach target). // 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: 2. // 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 bellman_ford(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 source, int target) { int alg_error = 0; int alg_result = INT_MIN; errno = 0; int *distance = 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) && (source >= 0) && (source < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((target >= 0) && (target < 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)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 = 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; } distance = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*distance)); if (!distance) { 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 edge = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int iteration = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int changed = 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; } while (1) { int alg_condition = (i < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; distance[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; } } distance[source] = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (iteration < alg_sub(n, 1, &alg_error)); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; changed = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } edge = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (edge < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; u = from_vertex[edge]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = to_vertex[edge]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int alg_condition_1 = ((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge], &alg_error) < distance[v])); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_1) { distance[v] = alg_add(distance[u], weight[edge], &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } changed = 1; 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_2 = (changed == 0); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_2) { break; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } iteration = alg_add(iteration, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } edge = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (edge < m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; u = from_vertex[edge]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } v = to_vertex[edge]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int alg_condition_3 = ((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge], &alg_error) < distance[v])); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_3) { alg_result = alg_sub(0, 1000000000, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; } edge = alg_add(edge, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } alg_result = distance[target]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; alg_cleanup: free(distance); return alg_result; } int main(void) { int from_vertex[] = {0, 1, 0}; int to_vertex[] = {1, 2, 2}; int weight[] = {4, -2, 9}; int n = 3; int source = 0; int target = 2; int result = bellman_ford(from_vertex, 3, to_vertex, 3, weight, 3, n, source, target); printf("%d\n", result); if (errno) { perror("algorithm"); return 1; } return 0; } |
