Mongodb what is the cost of array queries?

As far as I can tell, find queries in mongodb involving an array appear very expensive. Take as example the queries given in: https://docs.mongodb.com/manual/tutorial/query-array-of-documents/ db.inventory.insertMany( [ { item: "journal", instock: [ { warehouse: "A", qty: 5 }, { warehouse: "C", qty: 15 } ] }, { item: "notebook", instock: [ { warehouse: "C", qty: 5 } ] }, { item: "paper", instock: [ { warehouse: "A", qty: 60 }, { warehouse: "B", qty: 15 } ] }, { item: "planner", instock: [ { warehouse: "A", qty: 40 }, { warehouse: "B", qty: 5 } ] }, { item: "postcard", instock: [ { warehouse: "B", qty: 15 }, { warehouse: "C", qty: 35 } ] } ]); And find query: db.inventory.find( { "instock": { warehouse: "A" } } ) The above example can be described as simple as "Find all records connected to warehouse A". But what is the cost of the find query (big o)? Are there any indexing optimizations going on here, or is it basically an exhaustive search with a cost of O(N*K), where N is the number of inventory records, and K is the number of elements in the instock array of each record? and if so, are there any ways of optimizing this to minimize cost, by say indexing?