text: /*-------------------------------------------------------------------------
   *
   * 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) 2001-2015, 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];
  }
  