Phil Factor takes a look at using JSON to perform memoization:
For the SQL Server developer, matrices are probably most valuable for solving more complex string-searching problems, using Dynamic Programming. Once you get into the mindset of this sort of technique, a number of seemingly-intractable problems become easier. Here are fifty common data structure problems that can be solved using Dynamic programming. Until SQL Server 2017, these were hard to do in SQL because of the lack of support for this style of programming. Memoization, one of the principles behind the technique is easy to do in SQL but it is very tricky to convert existing procedural algorithms to use table variables. It is usually easier and quicker to use strings as pseudo-variables as I did with Edit Distance and the Levenshtein algorithm, the longest common subsequence, and the Longest Common Substring. The problem with doing this is that the code to fetch the array values can be very difficult to decypher or debug. JSON can do it very easily with path array references.
The results aren’t fantastic but the code is easier at least.