A Linear List Diff Algorithm

When building modern web applications, it's common for data to be represented as lists. Updating these lists efficiently can be a challenging problem, especially when the updates are complex or frequent. One solution to this problem is to use a list diff algorithm, which calculates the differences between two versions of a list and executes the minimum number of operations required to transform one version into the other.

There are several popular list diff algorithms, including Myers diff algorithm and Hunt-McIlroy diff algorithm. However, both of these algorithms have time complexity of O(N^2), which makes them inefficient for large lists. In this article, we will introduce a linear list diff algorithm that has a time complexity of O(N).

The Linear List Diff Algorithm

The linear list diff algorithm is based on the observation that the differences between two versions of a list can be expressed as a series of insertions or deletions of consecutive elements. By identifying these segments of consecutive elements, we can perform the necessary operations in a linear fashion, without having to compare every element in the list.

The algorithm works by first computing the longest common subsequence (LCS) of the two input lists. The LCS represents the elements that appear in both lists in the same order. We can then identify the segments of elements that are not part of the LCS, which are the elements that must be inserted or deleted.

To identify these segments, we use a dynamic programming approach. We initialize a table of size (M+1)x(N+1), where M and N are the lengths of the two input lists. Each cell in the table contains two values: the length of the LCS up to that point, and a flag indicating whether the last element in the subsequence came from the first or second list. We then iterate over the cells of the table, filling in the LCS length and flag values using the following rules:

If the current elements of the two lists are equal, we increment the LCS length and set the flag to indicate that the element came from both lists.
Otherwise, we take the max of the LCS lengths in the adjacent cells and copy the corresponding flag value.

Once we have computed the LCS table, we can use it to identify the segments of elements that are not part of the LCS. We do this by starting at the bottom right corner of the table and tracing back through the flags, identifying each segment of elements that corresponds to a change (insertion or deletion).

Example Code

Here's an example implementation of the linear list diff algorithm in JavaScript:

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This implementation returns an array of changes that need to be made to transform the first input list into the second input list. Each change is represented as an object with a type property (either "insert" or "delete"), an index property indicating the position in the original list where the change should be made, and an optional item property containing the item to be inserted (only present for "insert" changes).

Conclusion

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