Find documents whose array field contain some subsets in MongoDB - arrays

Question

The "users" collection has documents with an array field.
Example documents:
{
"_id" :1001,
"properties" : ["A", "B", "C", "D", "E", "F", "G", "H", "I"]
}
{
"_id" : 1002,
"properties" : ["1", "2", "3", "4", "5", "6", "7", "8", "9", "10"]
}
How can I build a query to get the documents which follow the next condition?
Get only the documents that have the properties:
[ "3" AND ("A" OR "1") AND ("B" OR "2") ]
or in other way:
"3" AND "A" AND "B"
OR
"3" AND "A" AND "2"
OR
"3" AND "1" AND "B"
OR
"3" AND "1" AND "2"
In the previous example, the query has to result only the document:
{
"_id" : 1002,
"properties" : ["1", "2", "3", "4", "5", "6", "7", "8", "9", "10"]
}
The collection has 4 million documents. The document array "properties" field has average length of 15 elements. The query I am looking for must have a good performance in this quite a big collection.

Answer 1

Stephan's answer is ok. Other ways to achieve the result using $in and $all operators:
db.users.find(
{
$and:[
{"properties":"3"},
{"properties" : {$in: ["A", "1"]}},
{"properties" : {$in: ["B", "2"]}}
]
}
);
(translation of your first description of the subset)
And
db.users.find(
{
$or: [
{"properties" : {$all: ["3", "A", "B"]}},
{"properties" : {$all: ["3", "A", "2"]}},
{"properties" : {$all: ["3", "1", "B"]}},
{"properties" : {$all: ["3", "1", "2"]}}
]
}
);
(translation of your second description of the subset)
I'm afraid I can't tell which one will ensure the best performance. I hope that you have and index on properties.
You may try the queries on a smaller collection with explain to see the execution plan

Answer 2

try this:
db.users.find(
{
$or: [
{$and: [{ "properties": "3" }, { "properties": "A" }, { "properties": "B" }]},
{$and: [{ "properties": "3" }, { "properties": "A" }, { "properties": "2" }]},
{$and: [{ "properties": "3" }, { "properties": "1" }, { "properties": "B" }]},
{$and: [{ "properties": "3" }, { "properties": "1" }, { "properties": "2" }]}
]
}
);
or
db.users.find(
{
$and: [
{"properties": "3" },
{$or: [ { "properties": "A" }, { "properties": "1" } ]},
{$or: [ { "properties": "B" }, { "properties": "2" } ]}
]
}
);