Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed to turn one token sequence into another..
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 | #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <limits.h> #include <errno.h> // Levenshtein Edit Distance in C // // PURPOSE // Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed // to turn one token sequence into another. // // METHOD // Retain one row and the previous diagonal. Equal tokens keep the diagonal distance. // Different tokens add one to the cheapest deletion, insertion, or substitution. // // COMPLEXITY // O(nm) time and O(min(n,m)) auxiliary space. The public function automatically orients the // shorter input as its work row. // // CONTRACT // Inputs are integer tokens. For text, tokenize consistently before calling; Unicode // normalization and grapheme rules are separate concerns. Returns distance only. // 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 edit_distance(const int *a, size_t a_length, const int *b, size_t b_length) { int alg_error = 0; int alg_result = INT_MIN; errno = 0; int *dp = NULL; if (a_length > 1000000 || (a_length && !a)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (b_length > 1000000 || (b_length && !b)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } int n = (int)a_length; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int m = (int)b_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)a_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; } if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!(((int)b_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 < m) return edit_distance(b, b_length, a, a_length); { 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; } dp = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*dp)); if (!dp) { 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 diagonal = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int old = 0; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (j <= m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; dp[j] = 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; } } while (1) { int alg_condition = (i < n); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; diagonal = dp[0]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } dp[0] = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } j = 1; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } while (1) { int alg_condition = (j <= m); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (!alg_condition) break; old = dp[j]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } int alg_condition_1 = (a[i] == b[alg_sub(j, 1, &alg_error)]); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } if (alg_condition_1) { dp[j] = diagonal; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } else { dp[j] = alg_add(1, alg_min(dp[j], alg_min(dp[alg_sub(j, 1, &alg_error)], diagonal)), &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } diagonal = old; 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; } } i = alg_add(i, 1, &alg_error); if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } } alg_result = dp[m]; if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; } goto alg_cleanup; alg_cleanup: free(dp); return alg_result; } int main(void) { int a[] = {1, 2, 3}; int b[] = {1, 4, 3, 5}; int result = edit_distance(a, 3, b, 4); printf("%d\n", result); if (errno) { perror("algorithm"); return 1; } return 0; } |
