# Compute String Difference: Minimize Inserts/Deletes

• 0rthodontist
In summary, the individual is looking for an efficient method to compute the difference between two strings, A and B, where B is a modified version of A with operations of string deletion and insertion. They mention the Levenshtein distance as a potential solution, but they would prefer to specify the operations in a more specific way. The individual considers implementing a custom version of the "diff" command in Unix and suggests using the longest common substring algorithm to generate the operations. They also mention the need for an algorithm that is efficient in terms of time and bandwidth. However, they later discover that there is already a function in Python, specifically in the difflib library, that can perform this task effectively.
0rthodontist
I have a need to compute a "difference" between two strings A and B. The idea is that B is similar to A, except it has had operations of string deletion and string insertion performed on it. An operation of deletion transforms a string xyz into a string xz (x, y, z being strings) and an operation of insertion transforms a string xz into a string xyz.

What I want is an input of A and B, where A is fairly similar to B, and an output which is a series of deletion and insertion operations that transforms A into B. Hopefully this will be a shortest series, but reasonably close is good enough.

Any idea where I should look for information on this before I try to hack something up?

edit: actually I hadn't really done enough looking, 10 more seconds of time brings me to the Levenshtein distance. Though this isn't exactly what I want since I'd rather be able to say "insert the string 'abcdxyzqrstuvqwertyz' at character position 900" than have to give that as 20 different character insertions.

edit2: Perhaps I'm basically looking to implement a custom version of unix's "diff" that goes character-by-character and not line-by-line. Unless "diff" works by treating lines as single symbols, in which case that's not what I need.

edit3: I could be more specific on the criterion I want for "shortest series of insertions and deletions." What I mean is roughly, let an insertion be denoted by a string +n,k,[s1..sk] where n is a number indicating the position of the first character to be inserted, k is the number of characters that follow, and s1..sk are the characters to be inserted. Similarly a deletion can be denoted by a string -n,k where k is the # of characters after position n to be deleted. I want to roughly minimize the total length of the descriptions of all insertions and deletions required to transform A into B. To simplify the problem, you could similarly assume that the cost of an insertion is p + L where L is the length of the inserted string, and p is a small "penalty" constant, and the cost of a deletion is p.

Last edited:
Further thought: I could use the longest common substring algorithm as in the diff algorithm to generate the character-by-character operations to transform one string into the other. Then I could treat the operations as the set of all removals followed by the set of all additions, and unify adjacent single-character operations to create contiguous stretches that are summarized by multi-character operations. Then I could look for "islands" in the contiguous stretches of removals--short sequences between two removals--and replace these by a longer removal and then an addition. Letting r denote removed characters and k denote characters that are in both A and B, if the sequence goes like
rrrrrkkrrrrrrkkrrrr
which would be represented by two removals, then I could shorten this to
rrrrrrrrrrrrrrrrrrr followed by the insertion of kkkk, at a cost of 2p + 4 instead of 3p.

Also, the standard diff algorithm takes like the square of the string lengths to run (actually I haven't verified that but I believe it to be true), but it would be great if I had a diff-like algorithm that takes nearly linear time when the strings are nearly the same.

The purpose of all this is to conserve bandwidth, sending differences instead of entire files when a low-bandwidth computer requests updates of a file from a server.

Well, fortuitously, Python happens to have a function that does almost precisely what I need, and Python is the language I have been working in. The difflib library and the SequenceMatcher class do it all.

Last edited:

## 1. What is the purpose of computing string difference and minimizing inserts/deletes?

The purpose of computing string difference and minimizing inserts/deletes is to determine the minimum number of changes needed to transform one string into another. This can be useful in various applications such as spell checkers, data compression, and bioinformatics.

## 2. How is string difference calculated?

String difference is typically calculated using algorithms such as Levenshtein distance or dynamic programming. These algorithms compare two strings and determine the minimum number of edits (insertions, deletions, or substitutions) needed to transform one string into the other.

## 3. Can string difference be negative?

No, string difference cannot be negative. It represents the absolute value of the minimum number of edits needed to transform one string into another. Therefore, it is always a non-negative integer.

## 4. How does minimizing inserts/deletes affect the final result?

Minimizing inserts/deletes can reduce the overall string difference and result in a more efficient transformation between two strings. This can also make the algorithm more accurate, as it takes into account the cost of inserting or deleting characters.

## 5. Is computing string difference and minimizing inserts/deletes a solved problem?

Yes, this problem is considered to be solved as there are well-established algorithms and techniques for calculating string difference and minimizing inserts/deletes. However, new approaches and optimizations may still be developed to improve the efficiency and accuracy of these algorithms.

• Engineering and Comp Sci Homework Help
Replies
10
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
20
Views
5K
• Quantum Physics
Replies
4
Views
1K
• Programming and Computer Science
Replies
5
Views
2K
• General Math
Replies
6
Views
1K
• General Math
Replies
4
Views
909
• Special and General Relativity
Replies
75
Views
4K
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• General Math
Replies
6
Views
7K