How to Query a database values which exceeds the memory limit without any filters. Is there a way we can just type the first 3 characters and the respective values should be fetched?
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Yes, there is a way.
You could check for the length of that text and return a empty data subset if the text has less than 3 characters.
You would want to have a paging limit applied to the search results, especially when they might possibly return so many that it throws an error due to the memory limit.