/src/backend/utils/adt/levenshtein.c
C | 401 lines | 188 code | 37 blank | 176 comment | 41 complexity | 25d11d86e8ec21e161ad332fa78457a8 MD5 | raw file
- /*-------------------------------------------------------------------------
- *
- * levenshtein.c
- * Levenshtein distance implementation.
- *
- * Original author: Joe Conway <mail@joeconway.com>
- *
- * This file is included by varlena.c twice, to provide matching code for (1)
- * Levenshtein distance with custom costings, and (2) Levenshtein distance with
- * custom costings and a "max" value above which exact distances are not
- * interesting. Before the inclusion, we rely on the presence of the inline
- * function rest_of_char_same().
- *
- * Written based on a description of the algorithm by Michael Gilleland found
- * at http://www.merriampark.com/ld.htm. Also looked at levenshtein.c in the
- * PHP 4.0.6 distribution for inspiration. Configurable penalty costs
- * extension is introduced by Volkan YAZICI <volkan.yazici@gmail.com.
- *
- * Copyright (c) 2001-2016, PostgreSQL Global Development Group
- *
- * IDENTIFICATION
- * src/backend/utils/adt/levenshtein.c
- *
- *-------------------------------------------------------------------------
- */
- #define MAX_LEVENSHTEIN_STRLEN 255
- /*
- * Calculates Levenshtein distance metric between supplied strings, which are
- * not necessarily null-terminated.
- *
- * source: source string, of length slen bytes.
- * target: target string, of length tlen bytes.
- * ins_c, del_c, sub_c: costs to charge for character insertion, deletion,
- * and substitution respectively; (1, 1, 1) costs suffice for common
- * cases, but your mileage may vary.
- * max_d: if provided and >= 0, maximum distance we care about; see below.
- * trusted: caller is trusted and need not obey MAX_LEVENSHTEIN_STRLEN.
- *
- * One way to compute Levenshtein distance is to incrementally construct
- * an (m+1)x(n+1) matrix where cell (i, j) represents the minimum number
- * of operations required to transform the first i characters of s into
- * the first j characters of t. The last column of the final row is the
- * answer.
- *
- * We use that algorithm here with some modification. In lieu of holding
- * the entire array in memory at once, we'll just use two arrays of size
- * m+1 for storing accumulated values. At each step one array represents
- * the "previous" row and one is the "current" row of the notional large
- * array.
- *
- * If max_d >= 0, we only need to provide an accurate answer when that answer
- * is less than or equal to max_d. From any cell in the matrix, there is
- * theoretical "minimum residual distance" from that cell to the last column
- * of the final row. This minimum residual distance is zero when the
- * untransformed portions of the strings are of equal length (because we might
- * get lucky and find all the remaining characters matching) and is otherwise
- * based on the minimum number of insertions or deletions needed to make them
- * equal length. The residual distance grows as we move toward the upper
- * right or lower left corners of the matrix. When the max_d bound is
- * usefully tight, we can use this property to avoid computing the entirety
- * of each row; instead, we maintain a start_column and stop_column that
- * identify the portion of the matrix close to the diagonal which can still
- * affect the final answer.
- */
- int
- #ifdef LEVENSHTEIN_LESS_EQUAL
- varstr_levenshtein_less_equal(const char *source, int slen,
- const char *target, int tlen,
- int ins_c, int del_c, int sub_c,
- int max_d, bool trusted)
- #else
- varstr_levenshtein(const char *source, int slen,
- const char *target, int tlen,
- int ins_c, int del_c, int sub_c,
- bool trusted)
- #endif
- {
- int m,
- n;
- int *prev;
- int *curr;
- int *s_char_len = NULL;
- int i,
- j;
- const char *y;
- /*
- * For varstr_levenshtein_less_equal, we have real variables called
- * start_column and stop_column; otherwise it's just short-hand for 0 and
- * m.
- */
- #ifdef LEVENSHTEIN_LESS_EQUAL
- int start_column,
- stop_column;
- #undef START_COLUMN
- #undef STOP_COLUMN
- #define START_COLUMN start_column
- #define STOP_COLUMN stop_column
- #else
- #undef START_COLUMN
- #undef STOP_COLUMN
- #define START_COLUMN 0
- #define STOP_COLUMN m
- #endif
- /* Convert string lengths (in bytes) to lengths in characters */
- m = pg_mbstrlen_with_len(source, slen);
- n = pg_mbstrlen_with_len(target, tlen);
- /*
- * We can transform an empty s into t with n insertions, or a non-empty t
- * into an empty s with m deletions.
- */
- if (!m)
- return n * ins_c;
- if (!n)
- return m * del_c;
- /*
- * For security concerns, restrict excessive CPU+RAM usage. (This
- * implementation uses O(m) memory and has O(mn) complexity.) If
- * "trusted" is true, caller is responsible for not making excessive
- * requests, typically by using a small max_d along with strings that are
- * bounded, though not necessarily to MAX_LEVENSHTEIN_STRLEN exactly.
- */
- if (!trusted &&
- (m > MAX_LEVENSHTEIN_STRLEN ||
- n > MAX_LEVENSHTEIN_STRLEN))
- ereport(ERROR,
- (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
- errmsg("levenshtein argument exceeds maximum length of %d characters",
- MAX_LEVENSHTEIN_STRLEN)));
- #ifdef LEVENSHTEIN_LESS_EQUAL
- /* Initialize start and stop columns. */
- start_column = 0;
- stop_column = m + 1;
- /*
- * If max_d >= 0, determine whether the bound is impossibly tight. If so,
- * return max_d + 1 immediately. Otherwise, determine whether it's tight
- * enough to limit the computation we must perform. If so, figure out
- * initial stop column.
- */
- if (max_d >= 0)
- {
- int min_theo_d; /* Theoretical minimum distance. */
- int max_theo_d; /* Theoretical maximum distance. */
- int net_inserts = n - m;
- min_theo_d = net_inserts < 0 ?
- -net_inserts * del_c : net_inserts * ins_c;
- if (min_theo_d > max_d)
- return max_d + 1;
- if (ins_c + del_c < sub_c)
- sub_c = ins_c + del_c;
- max_theo_d = min_theo_d + sub_c * Min(m, n);
- if (max_d >= max_theo_d)
- max_d = -1;
- else if (ins_c + del_c > 0)
- {
- /*
- * Figure out how much of the first row of the notional matrix we
- * need to fill in. If the string is growing, the theoretical
- * minimum distance already incorporates the cost of deleting the
- * number of characters necessary to make the two strings equal in
- * length. Each additional deletion forces another insertion, so
- * the best-case total cost increases by ins_c + del_c. If the
- * string is shrinking, the minimum theoretical cost assumes no
- * excess deletions; that is, we're starting no further right than
- * column n - m. If we do start further right, the best-case
- * total cost increases by ins_c + del_c for each move right.
- */
- int slack_d = max_d - min_theo_d;
- int best_column = net_inserts < 0 ? -net_inserts : 0;
- stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
- if (stop_column > m)
- stop_column = m + 1;
- }
- }
- #endif
- /*
- * In order to avoid calling pg_mblen() repeatedly on each character in s,
- * we cache all the lengths before starting the main loop -- but if all
- * the characters in both strings are single byte, then we skip this and
- * use a fast-path in the main loop. If only one string contains
- * multi-byte characters, we still build the array, so that the fast-path
- * needn't deal with the case where the array hasn't been initialized.
- */
- if (m != slen || n != tlen)
- {
- int i;
- const char *cp = source;
- s_char_len = (int *) palloc((m + 1) * sizeof(int));
- for (i = 0; i < m; ++i)
- {
- s_char_len[i] = pg_mblen(cp);
- cp += s_char_len[i];
- }
- s_char_len[i] = 0;
- }
- /* One more cell for initialization column and row. */
- ++m;
- ++n;
- /* Previous and current rows of notional array. */
- prev = (int *) palloc(2 * m * sizeof(int));
- curr = prev + m;
- /*
- * To transform the first i characters of s into the first 0 characters of
- * t, we must perform i deletions.
- */
- for (i = START_COLUMN; i < STOP_COLUMN; i++)
- prev[i] = i * del_c;
- /* Loop through rows of the notional array */
- for (y = target, j = 1; j < n; j++)
- {
- int *temp;
- const char *x = source;
- int y_char_len = n != tlen + 1 ? pg_mblen(y) : 1;
- #ifdef LEVENSHTEIN_LESS_EQUAL
- /*
- * In the best case, values percolate down the diagonal unchanged, so
- * we must increment stop_column unless it's already on the right end
- * of the array. The inner loop will read prev[stop_column], so we
- * have to initialize it even though it shouldn't affect the result.
- */
- if (stop_column < m)
- {
- prev[stop_column] = max_d + 1;
- ++stop_column;
- }
- /*
- * The main loop fills in curr, but curr[0] needs a special case: to
- * transform the first 0 characters of s into the first j characters
- * of t, we must perform j insertions. However, if start_column > 0,
- * this special case does not apply.
- */
- if (start_column == 0)
- {
- curr[0] = j * ins_c;
- i = 1;
- }
- else
- i = start_column;
- #else
- curr[0] = j * ins_c;
- i = 1;
- #endif
- /*
- * This inner loop is critical to performance, so we include a
- * fast-path to handle the (fairly common) case where no multibyte
- * characters are in the mix. The fast-path is entitled to assume
- * that if s_char_len is not initialized then BOTH strings contain
- * only single-byte characters.
- */
- if (s_char_len != NULL)
- {
- for (; i < STOP_COLUMN; i++)
- {
- int ins;
- int del;
- int sub;
- int x_char_len = s_char_len[i - 1];
- /*
- * Calculate costs for insertion, deletion, and substitution.
- *
- * When calculating cost for substitution, we compare the last
- * character of each possibly-multibyte character first,
- * because that's enough to rule out most mis-matches. If we
- * get past that test, then we compare the lengths and the
- * remaining bytes.
- */
- ins = prev[i] + ins_c;
- del = curr[i - 1] + del_c;
- if (x[x_char_len - 1] == y[y_char_len - 1]
- && x_char_len == y_char_len &&
- (x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
- sub = prev[i - 1];
- else
- sub = prev[i - 1] + sub_c;
- /* Take the one with minimum cost. */
- curr[i] = Min(ins, del);
- curr[i] = Min(curr[i], sub);
- /* Point to next character. */
- x += x_char_len;
- }
- }
- else
- {
- for (; i < STOP_COLUMN; i++)
- {
- int ins;
- int del;
- int sub;
- /* Calculate costs for insertion, deletion, and substitution. */
- ins = prev[i] + ins_c;
- del = curr[i - 1] + del_c;
- sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
- /* Take the one with minimum cost. */
- curr[i] = Min(ins, del);
- curr[i] = Min(curr[i], sub);
- /* Point to next character. */
- x++;
- }
- }
- /* Swap current row with previous row. */
- temp = curr;
- curr = prev;
- prev = temp;
- /* Point to next character. */
- y += y_char_len;
- #ifdef LEVENSHTEIN_LESS_EQUAL
- /*
- * This chunk of code represents a significant performance hit if used
- * in the case where there is no max_d bound. This is probably not
- * because the max_d >= 0 test itself is expensive, but rather because
- * the possibility of needing to execute this code prevents tight
- * optimization of the loop as a whole.
- */
- if (max_d >= 0)
- {
- /*
- * The "zero point" is the column of the current row where the
- * remaining portions of the strings are of equal length. There
- * are (n - 1) characters in the target string, of which j have
- * been transformed. There are (m - 1) characters in the source
- * string, so we want to find the value for zp where (n - 1) - j =
- * (m - 1) - zp.
- */
- int zp = j - (n - m);
- /* Check whether the stop column can slide left. */
- while (stop_column > 0)
- {
- int ii = stop_column - 1;
- int net_inserts = ii - zp;
- if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
- -net_inserts * del_c) <= max_d)
- break;
- stop_column--;
- }
- /* Check whether the start column can slide right. */
- while (start_column < stop_column)
- {
- int net_inserts = start_column - zp;
- if (prev[start_column] +
- (net_inserts > 0 ? net_inserts * ins_c :
- -net_inserts * del_c) <= max_d)
- break;
- /*
- * We'll never again update these values, so we must make sure
- * there's nothing here that could confuse any future
- * iteration of the outer loop.
- */
- prev[start_column] = max_d + 1;
- curr[start_column] = max_d + 1;
- if (start_column != 0)
- source += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
- start_column++;
- }
- /* If they cross, we're going to exceed the bound. */
- if (start_column >= stop_column)
- return max_d + 1;
- }
- #endif
- }
- /*
- * Because the final value was swapped from the previous row to the
- * current row, that's where we'll find it.
- */
- return prev[m - 1];
- }