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The Levenshtein distance between two strings is the minimum number of operations needed to transform one string into the other, where an operation may be insertion, deletion or substitution of one character.

-- ---------------------------------------------------------------------------
-- Levenshtein distance

-- from the Artful Common Queries page
-- http://www.artfulsoftware.com/infotree/qrytip.php?id=552
-- ---------------------------------------------------------------------------

-- The Levenshtein distance between two strings is the minimum number of
-- operations needed to transform one string into the other, where an operation
-- may be insertion, deletion or substitution of one character.

CREATE FUNCTION levenshtein( s1 VARCHAR(255), s2 VARCHAR(255) )
  RETURNS INT
  DETERMINISTIC
  BEGIN
    DECLARE s1_len, s2_len, i, j, c, c_temp, cost INT;
    DECLARE s1_char CHAR;
    -- max strlen=255
    DECLARE cv0, cv1 VARBINARY(256);
    SET s1_len = CHAR_LENGTH(s1), s2_len = CHAR_LENGTH(s2), cv1 = 0x00, j = 1, i = 1, c = 0;
    IF s1 = s2 THEN
      RETURN 0;
    ELSEIF s1_len = 0 THEN
      RETURN s2_len;
    ELSEIF s2_len = 0 THEN
      RETURN s1_len;
    ELSE
      WHILE j <= s2_len DO
        SET cv1 = CONCAT(cv1, UNHEX(HEX(j))), j = j + 1;
      END WHILE;
      WHILE i <= s1_len DO
        SET s1_char = SUBSTRING(s1, i, 1), c = i, cv0 = UNHEX(HEX(i)), j = 1;
        WHILE j <= s2_len DO
          SET c = c + 1;
          IF s1_char = SUBSTRING(s2, j, 1) THEN
            SET cost = 0; ELSE SET cost = 1;
          END IF;
          SET c_temp = CONV(HEX(SUBSTRING(cv1, j, 1)), 16, 10) + cost;
          IF c > c_temp THEN SET c = c_temp; END IF;
            SET c_temp = CONV(HEX(SUBSTRING(cv1, j+1, 1)), 16, 10) + 1;
            IF c > c_temp THEN
              SET c = c_temp;
            END IF;
            SET cv0 = CONCAT(cv0, UNHEX(HEX(c))), j = j + 1;
        END WHILE;
        SET cv1 = cv0, i = i + 1;
      END WHILE;
    END IF;
    RETURN c;
  END;

-- Helper function:

CREATE FUNCTION levenshtein_ratio( s1 VARCHAR(255), s2 VARCHAR(255) )
  RETURNS INT
  DETERMINISTIC
  BEGIN
    DECLARE s1_len, s2_len, max_len INT;
    SET s1_len = LENGTH(s1), s2_len = LENGTH(s2);
    IF s1_len > s2_len THEN
      SET max_len = s1_len;
    ELSE
      SET max_len = s2_len;
    END IF;
    RETURN ROUND((1 - LEVENSHTEIN(s1, s2) / max_len) * 100);
  END;