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404 lines
12 KiB
C
404 lines
12 KiB
C
/*
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* levenshtein.c
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*
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* Functions for "fuzzy" comparison of strings
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*
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* Joe Conway <mail@joeconway.com>
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*
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* Copyright (c) 2001-2013, PostgreSQL Global Development Group
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* ALL RIGHTS RESERVED;
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*
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* levenshtein()
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* -------------
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* Written based on a description of the algorithm by Michael Gilleland
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* found at http://www.merriampark.com/ld.htm
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* Also looked at levenshtein.c in the PHP 4.0.6 distribution for
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* inspiration.
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* Configurable penalty costs extension is introduced by Volkan
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* YAZICI <volkan.yazici@gmail.com>.
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*/
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/*
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* External declarations for exported functions
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*/
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#ifdef LEVENSHTEIN_LESS_EQUAL
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static int levenshtein_less_equal_internal(text *s, text *t,
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int ins_c, int del_c, int sub_c, int max_d);
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#else
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static int levenshtein_internal(text *s, text *t,
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int ins_c, int del_c, int sub_c);
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#endif
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#define MAX_LEVENSHTEIN_STRLEN 255
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/*
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* Calculates Levenshtein distance metric between supplied strings. Generally
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* (1, 1, 1) penalty costs suffices for common cases, but your mileage may
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* vary.
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*
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* One way to compute Levenshtein distance is to incrementally construct
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* an (m+1)x(n+1) matrix where cell (i, j) represents the minimum number
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* of operations required to transform the first i characters of s into
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* the first j characters of t. The last column of the final row is the
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* answer.
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*
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* We use that algorithm here with some modification. In lieu of holding
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* the entire array in memory at once, we'll just use two arrays of size
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* m+1 for storing accumulated values. At each step one array represents
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* the "previous" row and one is the "current" row of the notional large
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* array.
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*
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* If max_d >= 0, we only need to provide an accurate answer when that answer
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* is less than or equal to the bound. From any cell in the matrix, there is
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* theoretical "minimum residual distance" from that cell to the last column
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* of the final row. This minimum residual distance is zero when the
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* untransformed portions of the strings are of equal length (because we might
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* get lucky and find all the remaining characters matching) and is otherwise
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* based on the minimum number of insertions or deletions needed to make them
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* equal length. The residual distance grows as we move toward the upper
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* right or lower left corners of the matrix. When the max_d bound is
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* usefully tight, we can use this property to avoid computing the entirety
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* of each row; instead, we maintain a start_column and stop_column that
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* identify the portion of the matrix close to the diagonal which can still
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* affect the final answer.
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*/
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static int
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#ifdef LEVENSHTEIN_LESS_EQUAL
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levenshtein_less_equal_internal(text *s, text *t,
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int ins_c, int del_c, int sub_c, int max_d)
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#else
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levenshtein_internal(text *s, text *t,
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int ins_c, int del_c, int sub_c)
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#endif
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{
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int m,
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n,
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s_bytes,
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t_bytes;
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int *prev;
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int *curr;
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int *s_char_len = NULL;
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int i,
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j;
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const char *s_data;
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const char *t_data;
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const char *y;
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/*
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* For levenshtein_less_equal_internal, we have real variables called
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* start_column and stop_column; otherwise it's just short-hand for 0 and
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* m.
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*/
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#ifdef LEVENSHTEIN_LESS_EQUAL
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int start_column,
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stop_column;
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#undef START_COLUMN
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#undef STOP_COLUMN
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#define START_COLUMN start_column
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#define STOP_COLUMN stop_column
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#else
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#undef START_COLUMN
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#undef STOP_COLUMN
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#define START_COLUMN 0
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#define STOP_COLUMN m
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#endif
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/* Extract a pointer to the actual character data. */
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s_data = VARDATA_ANY(s);
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t_data = VARDATA_ANY(t);
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/* Determine length of each string in bytes and characters. */
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s_bytes = VARSIZE_ANY_EXHDR(s);
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t_bytes = VARSIZE_ANY_EXHDR(t);
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m = pg_mbstrlen_with_len(s_data, s_bytes);
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n = pg_mbstrlen_with_len(t_data, t_bytes);
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/*
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* We can transform an empty s into t with n insertions, or a non-empty t
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* into an empty s with m deletions.
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*/
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if (!m)
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return n * ins_c;
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if (!n)
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return m * del_c;
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/*
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* For security concerns, restrict excessive CPU+RAM usage. (This
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* implementation uses O(m) memory and has O(mn) complexity.)
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*/
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if (m > MAX_LEVENSHTEIN_STRLEN ||
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n > MAX_LEVENSHTEIN_STRLEN)
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ereport(ERROR,
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(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
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errmsg("argument exceeds the maximum length of %d bytes",
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MAX_LEVENSHTEIN_STRLEN)));
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#ifdef LEVENSHTEIN_LESS_EQUAL
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/* Initialize start and stop columns. */
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start_column = 0;
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stop_column = m + 1;
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/*
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* If max_d >= 0, determine whether the bound is impossibly tight. If so,
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* return max_d + 1 immediately. Otherwise, determine whether it's tight
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* enough to limit the computation we must perform. If so, figure out
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* initial stop column.
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*/
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if (max_d >= 0)
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{
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int min_theo_d; /* Theoretical minimum distance. */
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int max_theo_d; /* Theoretical maximum distance. */
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int net_inserts = n - m;
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min_theo_d = net_inserts < 0 ?
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-net_inserts * del_c : net_inserts * ins_c;
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if (min_theo_d > max_d)
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return max_d + 1;
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if (ins_c + del_c < sub_c)
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sub_c = ins_c + del_c;
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max_theo_d = min_theo_d + sub_c * Min(m, n);
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if (max_d >= max_theo_d)
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max_d = -1;
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else if (ins_c + del_c > 0)
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{
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/*
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* Figure out how much of the first row of the notional matrix we
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* need to fill in. If the string is growing, the theoretical
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* minimum distance already incorporates the cost of deleting the
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* number of characters necessary to make the two strings equal in
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* length. Each additional deletion forces another insertion, so
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* the best-case total cost increases by ins_c + del_c. If the
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* string is shrinking, the minimum theoretical cost assumes no
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* excess deletions; that is, we're starting no further right than
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* column n - m. If we do start further right, the best-case
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* total cost increases by ins_c + del_c for each move right.
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*/
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int slack_d = max_d - min_theo_d;
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int best_column = net_inserts < 0 ? -net_inserts : 0;
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stop_column = best_column + (slack_d / (ins_c + del_c)) + 1;
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if (stop_column > m)
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stop_column = m + 1;
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}
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}
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#endif
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/*
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* In order to avoid calling pg_mblen() repeatedly on each character in s,
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* we cache all the lengths before starting the main loop -- but if all
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* the characters in both strings are single byte, then we skip this and
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* use a fast-path in the main loop. If only one string contains
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* multi-byte characters, we still build the array, so that the fast-path
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* needn't deal with the case where the array hasn't been initialized.
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*/
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if (m != s_bytes || n != t_bytes)
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{
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int i;
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const char *cp = s_data;
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s_char_len = (int *) palloc((m + 1) * sizeof(int));
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for (i = 0; i < m; ++i)
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{
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s_char_len[i] = pg_mblen(cp);
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cp += s_char_len[i];
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}
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s_char_len[i] = 0;
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}
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/* One more cell for initialization column and row. */
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++m;
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++n;
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/* Previous and current rows of notional array. */
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prev = (int *) palloc(2 * m * sizeof(int));
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curr = prev + m;
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/*
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* To transform the first i characters of s into the first 0 characters of
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* t, we must perform i deletions.
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*/
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for (i = START_COLUMN; i < STOP_COLUMN; i++)
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prev[i] = i * del_c;
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/* Loop through rows of the notional array */
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for (y = t_data, j = 1; j < n; j++)
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{
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int *temp;
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const char *x = s_data;
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int y_char_len = n != t_bytes + 1 ? pg_mblen(y) : 1;
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#ifdef LEVENSHTEIN_LESS_EQUAL
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/*
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* In the best case, values percolate down the diagonal unchanged, so
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* we must increment stop_column unless it's already on the right end
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* of the array. The inner loop will read prev[stop_column], so we
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* have to initialize it even though it shouldn't affect the result.
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*/
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if (stop_column < m)
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{
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prev[stop_column] = max_d + 1;
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++stop_column;
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}
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/*
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* The main loop fills in curr, but curr[0] needs a special case: to
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* transform the first 0 characters of s into the first j characters
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* of t, we must perform j insertions. However, if start_column > 0,
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* this special case does not apply.
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*/
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if (start_column == 0)
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{
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curr[0] = j * ins_c;
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i = 1;
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}
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else
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i = start_column;
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#else
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curr[0] = j * ins_c;
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i = 1;
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#endif
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/*
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* This inner loop is critical to performance, so we include a
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* fast-path to handle the (fairly common) case where no multibyte
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* characters are in the mix. The fast-path is entitled to assume
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* that if s_char_len is not initialized then BOTH strings contain
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* only single-byte characters.
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*/
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if (s_char_len != NULL)
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{
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for (; i < STOP_COLUMN; i++)
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{
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int ins;
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int del;
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int sub;
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int x_char_len = s_char_len[i - 1];
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/*
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* Calculate costs for insertion, deletion, and substitution.
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*
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* When calculating cost for substitution, we compare the last
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* character of each possibly-multibyte character first,
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* because that's enough to rule out most mis-matches. If we
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* get past that test, then we compare the lengths and the
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* remaining bytes.
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*/
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ins = prev[i] + ins_c;
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del = curr[i - 1] + del_c;
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if (x[x_char_len - 1] == y[y_char_len - 1]
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&& x_char_len == y_char_len &&
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(x_char_len == 1 || rest_of_char_same(x, y, x_char_len)))
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sub = prev[i - 1];
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else
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sub = prev[i - 1] + sub_c;
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/* Take the one with minimum cost. */
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curr[i] = Min(ins, del);
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curr[i] = Min(curr[i], sub);
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/* Point to next character. */
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x += x_char_len;
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}
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}
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else
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{
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for (; i < STOP_COLUMN; i++)
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{
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int ins;
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int del;
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int sub;
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/* Calculate costs for insertion, deletion, and substitution. */
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ins = prev[i] + ins_c;
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del = curr[i - 1] + del_c;
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sub = prev[i - 1] + ((*x == *y) ? 0 : sub_c);
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/* Take the one with minimum cost. */
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curr[i] = Min(ins, del);
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curr[i] = Min(curr[i], sub);
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/* Point to next character. */
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x++;
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}
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}
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/* Swap current row with previous row. */
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temp = curr;
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curr = prev;
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prev = temp;
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/* Point to next character. */
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y += y_char_len;
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#ifdef LEVENSHTEIN_LESS_EQUAL
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/*
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* This chunk of code represents a significant performance hit if used
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* in the case where there is no max_d bound. This is probably not
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* because the max_d >= 0 test itself is expensive, but rather because
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* the possibility of needing to execute this code prevents tight
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* optimization of the loop as a whole.
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*/
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if (max_d >= 0)
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{
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/*
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* The "zero point" is the column of the current row where the
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* remaining portions of the strings are of equal length. There
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* are (n - 1) characters in the target string, of which j have
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* been transformed. There are (m - 1) characters in the source
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* string, so we want to find the value for zp where (n - 1) - j =
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* (m - 1) - zp.
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*/
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int zp = j - (n - m);
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/* Check whether the stop column can slide left. */
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while (stop_column > 0)
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{
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int ii = stop_column - 1;
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int net_inserts = ii - zp;
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if (prev[ii] + (net_inserts > 0 ? net_inserts * ins_c :
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-net_inserts * del_c) <= max_d)
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break;
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stop_column--;
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}
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/* Check whether the start column can slide right. */
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while (start_column < stop_column)
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{
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int net_inserts = start_column - zp;
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if (prev[start_column] +
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(net_inserts > 0 ? net_inserts * ins_c :
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-net_inserts * del_c) <= max_d)
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break;
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/*
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* We'll never again update these values, so we must make sure
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* there's nothing here that could confuse any future
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* iteration of the outer loop.
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*/
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prev[start_column] = max_d + 1;
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curr[start_column] = max_d + 1;
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if (start_column != 0)
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s_data += (s_char_len != NULL) ? s_char_len[start_column - 1] : 1;
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start_column++;
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}
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/* If they cross, we're going to exceed the bound. */
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if (start_column >= stop_column)
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return max_d + 1;
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}
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#endif
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}
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/*
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* Because the final value was swapped from the previous row to the
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* current row, that's where we'll find it.
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*/
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return prev[m - 1];
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}
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