What Is the Next Best Ingredient to Add?

I am building a program that allows users to optimize their grocery shopping so they can make the most recipes using the fewest ingredients.

One of the features of this program is a function I’m calling the “NEXT BEST INGREDIENT” or NBI. For example, if you already have salt, oil, and rosemary, what NBI will unlock the most additional recipes?

Let’s say the answer is beef. If you buy beef, you’ll be able to create more new recipes than if you bought any other ingredient.

After buying beef, what is the NEXT BEST INGREDIENT one should add after that? And so on.

The feature will allow a user to enter any number of starting ingredients (including zero). So someone could start with 0, 3, or even 50 ingredients. What should they add next?

I’m using a database of recipes (about 500K recipes in all) to compile results.

I can map out the individuals steps for writing out a specific algorithm. But I need help writing a more generic algorithm.

Here’s a specific algorithm:

A user enters in 3 ingredients A, B, and C

1. 
   

   Isolate all 4-ingredient recipes that use use A+B+C + BLANK. Note the BLANK with highest frequency.

   
   


2. 
   

   Isolate all 3-ingredient recipes that use A+B + BLANK… A+C + BLANK… B+C + BLANK. Note the BLANK with highest frequency.

   
   


3. 
   

   Isolate all 2-ingredient recipes that use A + BLANK….B + BLANK…C+ BLANK. Note the BLANK with highest frequency.

   
   


4. 
   

   Isolate all 1-ingredient recipes that simply use BLANK. Note the BLANK with highest frequency.

   
   


5. 
   

   Calculate the BLANK with the highest TOTAL frequency. This is the NEXT BEST INGREDIENT.

   
   

But I need a way to write a more generic algorithm for when a user enters N number of ingredients (anything from 0 ingredients to 100).

I can write out the rules in plain English – but my programmer needs a way to write a generic rule using coding logic.

Here it is in plain English.

When user searches N ingredients (including zero), instantly ignore any recipes that require N+2 ingredients or more. And then isolate ALL remaining recipes that use ALL, SOME, or NONE of those ingredients such that there is 1 (and only 1) vacant slot for an “unsearched” ingredient.

Tally up the frequency of all “unsearched” ingredients. Whichever “unsearched” ingredient has the highest frequency becomes the NEXT BEST INGREDIENT.

The goal is to make this search feature accurate (or as accurate as my database is) and fast. A few ingredients is easy. But when looking at 10+ ingredients, it may slow down a bit.

Any thoughts?