ColdFusion Levenshtein Distance: String comparison and highlighting
Posted by
Brad Wood
Jul 29, 2008 22:01:00 UTC
This is a fun project I put out there a while back. I recently went through and optimized the performance a bit so I could officially blog it. It is an implementation of the Levenshtein Distance Algorithm in CFScript that I based off of a C# version written by Siderite Zackwehdex. Finding the "distance" between two strings is a means of comparing two strings to see how similar they both are. This can be done by finding the Longest Common String or LCS. It is as much a brain bender as it can be occasionally useful.The basic gist of the concept is this: Iterate over two strings making a note of how many characters were inserted, deleted, or transposed from one string to the other. When a difference is found, "bookmark" where you are and start looking ahead in each string to see if the strings are going to start matching up again down the line. How far down the line you look is controlled by in an input called maxOffset. The LCS is the number of characters between the two strings which were identical. The "distance" of the two strings is simply the average string length minus the longest common string. The similarity of the two strings can be expressed as a percentage given 1 minus the strings' distance divided the length of the longest string. Enough theory-- let's look at an example:
I love to go ride my go-kart. (29 chars)
I love to ride my go-cart outside. (34 chars)
There are 25 characters in the two strings that are identical. This is our LCS.
String 1 is 4 characters different than string 2, and string 2 has 9 characters different than string 1.
So on average, we will say 6.5 characters would need to be changed to make the strings identical. This is our distance. (4 + 9 = 13 / 2 = 6.5)
Divide that distance by the length of our longest string and we can come to the conclusion that the strings are an 81% match. (1 - (6.5 / 34) = .8088 = 81%) Here's another example:
I love to ride my go-cart outside. (34 chars)
- There is a deletion of the word "go "
- There is a substitution of "c" for "k" in go-cart
- There is an addition of the word "outside"
There are 25 characters in the two strings that are identical. This is our LCS.
String 1 is 4 characters different than string 2, and string 2 has 9 characters different than string 1.
So on average, we will say 6.5 characters would need to be changed to make the strings identical. This is our distance. (4 + 9 = 13 / 2 = 6.5)
Divide that distance by the length of our longest string and we can come to the conclusion that the strings are an 81% match. (1 - (6.5 / 34) = .8088 = 81%) Here's another example:
The rain in Spain stays mainly on the plains The rain in Spain stays mainly on the plains The rain in Spain stays mainly on the plains Lorum Ipsum, yadda yadda. Lorum Ipsum, yadda yadda. La La La La Luke, I am your father. |
The rain in Madrid stays totally on the plains The rain in Spain stays mainly on the plains The rain in Barcelona stays entirely in the air Lorum Ipsum, Yabba dabba doo. Whatcha eatin? Nutin' Honey. Da Da Da Duke, I am your father. |
- Roughly 67 characters are different between the two strings.
- The Longest Common String (LCS) is 180.
- The strings are a 73% match.
- If both strings are empty, I short circuit and return a 0 for distance and LCS. Similarity is 100%.
- If either string is empty, I short circuit and return the length of the non-empty string as the distance. The LCS and similarity is 0.
- To better detect differences at the start of the string I check the first three characters. That way a matching first letter wouldn't be confused in two strings like "top hat" and "the hat"
- When looking ahead in the strings trying to reconcile a difference I search for the distance of the maxOffset until I find THREE contiguous matching characters. This is to try and eliminate false positives.
- My function will highlight the differences between the strings by wrapping the deviations in the HTML tag of your choice. Default is <span style="background: yellow;"></span>
[code] <cfscript> /* StringSimilarity Brad Wood [email protected] May 2007 Code adopted from Siderite Zackwehdex's Blog http://siderite.blogspot.com/2007/04/super-fast-and-accurate-string-distance.html Parameters: s1: First string to be compared s2: Second string to be compared maxOffset: Average number of characters that s1 will deviate from s2 at any given point. This is used to control how far ahead the function looks to try and find the end of a peice of inserted text. Play with it to suit. */ function stringSimilarity(s1,s2,maxOffset) { var c = 0; var offset1 = 0; var offset2 = 0; var lcs = 0; // These two strings will contain the "highlighted" version var _s1 = createObject("java","java.lang.StringBuffer").init(javacast("int",len(s1)*3)); var _s2 = createObject("java","java.lang.StringBuffer").init(javacast("int",len(s2)*3)); // These chaactes will surround differences in the strings // (Inserted into _s1 and _s2) var h1 = "<span style=""background: yellow;"">"; var h2 = "</span>"; var return_struct = structNew(); // If both strings are empty if (not len(trim(s1)) and not len(trim(s2))) { return_struct.lcs = 0; return_struct.similarity = 1; return_struct.distance = 0; return_struct.s1 = ""; return_struct.s2 = ""; return return_struct; } // If s2 is empty, but s1 isn't if (len(trim(s1)) and not len(trim(s2))) { return_struct.lcs = 0; return_struct.similarity = 0; return_struct.distance = len(s1); return_struct.s1 = h1 & s1 & h2; return_struct.s2 = ""; return return_struct; } // If s1 is empty, but s2 isn't else if (len(trim(s2)) and not len(trim(s1))) { return_struct.lcs = 0; return_struct.similarity = 0; return_struct.distance = len(s2); return_struct.s1 = ""; return_struct.s2 = h1 & s2 & h2; return return_struct; } // Examine the strings, one character at a time, anding at the shortest string // The offset adjusts for extra characters in either string. while ((c + offset1 lt len(s1)) and (c + offset2 lt len(s2))) { // Pull the next charactes out of s1 anbd s2 next_s1 = mid(s1,c + offset1+1,iif(not c,3,1)); // First time through check the first three next_s2 = mid(s2,c + offset2+1,iif(not c,3,1)); // First time through check the first three // If they are equal if (compare(next_s1,next_s2) eq 0) { // Our longeset Common String just got one bigger lcs = lcs + 1; // Append the characters onto the "highlighted" version _s1.append(left(next_s1,1)); _s2.append(left(next_s2,1)); } // The next two charactes did not match // Now we will go into a sub-loop while we attempt to // find our place again. We will only search as long as // our maxOffset allows us to. else { // Don't reset the offsets, just back them up so you // have a point of reference old_offset1 = offset1; old_offset2 = offset2; _s1_deviation = ""; _s2_deviation = ""; // Loop for as long as allowed by our offset // to see if we can match up again for (i = 0; i lt maxOffset; i=i+1) { next_s1 = mid(s1,c + offset1 + i+1,3); // Increments each time through. len_next_s1 = len(next_s1); bookmarked_s1 = mid(s1,c + offset1+1,3); // stays the same next_s2 = mid(s2,c + offset2 + i+1,3); // Increments each time through. len_next_s2 = len(next_s2); bookmarked_s2 = mid(s2,c + offset2+1,3); // stays the same // If we reached the end of both of the strings if(not len_next_s1 and not len_next_s2) { // Quit break; } // These variables keep track of how far we have deviated in the // string while trying to find our match again. _s1_deviation = _s1_deviation & left(next_s1,1); _s2_deviation = _s2_deviation & left(next_s2,1); // It looks like s1 has a match down the line which fits // where we left off in s2 if (compare(next_s1,bookmarked_s2) eq 0) { // s1 is now offset THIS far from s2 offset1 = offset1+i; // Our longeset Common String just got bigger lcs = lcs + 1; // Now that we match again, break to the main loop break; } // It looks like s2 has a match down the line which fits // where we left off in s1 if (compare(next_s2,bookmarked_s1) eq 0) { // s2 is now offset THIS far from s1 offset2 = offset2+i; // Our longeset Common String just got bigger lcs = lcs + 1; // Now that we match again, break to the main loop break; } } //This is the number of inserted characters were found added_offset1 = offset1 - old_offset1; added_offset2 = offset2 - old_offset2; // We reached our maxoffset and couldn't match up the strings if(added_offset1 eq 0 and added_offset2 eq 0) { _s1.append(h1 & left(_s1_deviation,added_offset1+1) & h2); _s2.append(h1 & left(_s2_deviation,added_offset2+1) & h2); } // s2 had extra characters else if(added_offset1 eq 0 and added_offset2 gt 0) { _s1.append(left(_s1_deviation,1)); _s2.append(h1 & left(_s2_deviation,added_offset2) & h2 & right(_s2_deviation,1)); } // s1 had extra characters else if(added_offset1 gt 0 and added_offset2 eq 0) { _s1.append(h1 & left(_s1_deviation,added_offset1) & h2 & right(_s1_deviation,1)); _s2.append(left(_s2_deviation,1)); } } c=c+1; } // Anything left at the end of s1 is extra if(c + offset1 lt len(s1)) { _s1.append(h1 & right(s1,len(s1)-(c + offset1)) & h2); } // Anything left at the end of s2 is extra if(c + offset2 lt len(s2)) { _s2.append(h1 & right(s2,len(s2)-(c + offset2)) & h2); } // Distance is the average string length minus the longest common string distance = (len(s1) + len(s2))/2 - lcs; // Whcih string was longest? maxLen = iif(len(s1) gt len(s2),de(len(s1)),de(len(s2))); // Similarity is the distance divided by the max length similarity = iif(maxLen eq 0,1,1-(distance/maxLen)); // Return what we found. return_struct.lcs = lcs; return_struct.similarity = similarity; return_struct.distance = distance; return_struct.s1 = _s1.toString(); // "highlighted" version return_struct.s2 = _s2.toString(); // "highlighted" version return return_struct; } </cfscript> [/code]
[code]<cfset string1 = "The rain in Spain stays mainly on the plains The rain in Spain stays mainly on the plains The rain in Spain stays mainly on the plains Lorum Ipsum, yadda yadda. Lorum Ipsum, yadda yadda. La La La La Luke, I am your father."> <cfset string2 = "The rain in Madrid stays totally on the plains The rain in Spain stays mainly on the plains The rain in Barcelona stays entirely in the air Lorum Ipsum, Yabba dabba doo. Whatcha eatin? Nutin' Honey. Da Da Da Duke, I am your father."> <cfset comparison_result = stringSimilarity(string1,string2,10)> <cfoutput> Roughly #comparison_result.distance# characters are different between the two strings.<br> The strings are a #numberformat(comparison_result.similarity*100)#% match.<br> The Longest Common String is #comparison_result.lcs#.<br> <br> <table border="1" cellpadding="10" cellspacing="0"> <tr> <td> #replacenocase(comparison_result.s1,chr(10),"<br>","all")# </td> <td> #replacenocase(comparison_result.s2,chr(10),"<br>","all")# </td> <tr> </table> </cfoutput>[/code]
Tags: ColdFusion, Technology
Adrian Lynch
Excellent work!
I was about to add a feature to a project that needs to tell the user that two pieces of text aren't different enough (for SEO purposes) and this looks like it'll work a treat.
Many thanks.
Brad Wood
Glad it's useful to you!
Micah
Thanks this worked perfectly and was very useful.
George Jempty
You know there is a Java implementation of the Levenshtein algorithm under StringUtils in the Jakarta Commons lang package that you ought to be able to access directly from ColdFusion? That being said, I'm very interested in how you did your highlighting, and almost wish I was using ColdFusion instead of JSP so I could just use yours ;)
Topper
Legend! You just saved me a monkey load of work. I need to correct an error in some software that has led to a database being out of touch with another reference database - don't ask about the bad DB design.
If this works, I'll owe you a cupcake!
Brad Wood
@Topper: I hope it helps you. I like chocolate :)
Seriously though, if you need to compare two databases, Redgate software makes some very kick butt tools for that. They will show you line by line comparisons of stored procs and stuff, but when it comes to the differences in data I think it just tells you they aren't the same.
Hal Helms
Very nice work, Brad. I was all set to dive into this when I found your blog post. Thanks much!
Siderite
Hey, after a year I actually find this post :) Thanks for linking my blog and for using my algorithm! Your explanations are so much cooler and visually nice than mine. Good job!
Andy Bellenie
Hey, Nice script! .. .but you need to var the return_stuct too. / Andy www.cfwheels.org
Brad Wood
Good call, Andy.
I updated the post and the download.
Kerr
Hey guys, I know I'm late to the game here, though wanted to extend my thanks. I was looking for a ColdFusion implementation of string comparison highlighting, and Brad's solution works great! I did add a couple function arguments for the highlighting markup used, but other than that the original function was left untouched.
HP
Hi, Anyone knows how to compare two strings, then returns the diff. For example: s1 = 'GIT-04 (INT) AMT DR' s2 = 'GIT-04 (INT)' it will returns 'AMT DR' I spent hours using Javascript and Coldfusion, but there is no luck. Any advise, anyone?
Nebu
Great post. One comment: 177 distance = (len(s1) + len(s2))/2 - lcs; 178 // Whcih string was longest? 179 maxLen = iif(len(s1) gt len(s2),de(len(s1)),de(len(s2))); 180 // Similarity is the distance divided by the max length 181 similarity = iif(maxLen eq 0,1,1-(distance/maxLen)); Should/could be 177 var distance = (len(s1) + len(s2))/2 - lcs; 178 // Whcih string was longest? 179 var maxLen = iif(len(s1) gt len(s2),de(len(s1)),de(len(s2))); 180 // Similarity is the distance divided by the max length 181 var similarity = iif(maxLen eq 0,1,1-(distance/maxLen));
You might also be interested in http://cfdiff.googlecode.com/ . Keep up the good work.
Aiming Xu
The script is great to compare char by char. Is there a script to highlight whole word if one char is different?
Valeriy Nenov
I needed this function to be in Cso I converted the code from the original CF but am getting index out of bounds error. Attached is the code. Can someone please try this out in Cand help me figure out why it is crashing. Perhaps my manual conversion is not adequate.
Val
Brad Wood
@Valeriy: Sorry, I'm not much of a Cguru, but one thing to keep in mind is that ColdFusion uses 1-based arrays instead of 0-based arrays. In other words, an array with only 1 item in it is accessed as myArray[1].
Siderite
Lol! The original code was C#. You are converting something back. Although it would make an interesting analysis of how Cto CF to Cchanges code.
Sam
Wonderful. Thanks!