$min (aggregation)

Result Type

$min compares input data following the BSON Comparison order to determine the appropriate output type. When the input data contains multiple data types, the $min output type is the lowest in the comparison order.

Null or Missing Values

If some, but not all, documents for the $min operation have either a null value for the field or are missing the field, the $min operator only considers the non-null and the non-missing values for the field.

If all documents for the $min operation have null value for the field or are missing the field, the $min operator returns null for the minimum value.

Array Operand

In the $group and $setWindowFields stages, if the expression resolves to an array, $min does not traverse the array and compares the array as a whole.

In the other supported stages:

• With a single expression as its operand, if the expression resolves to an array, $min traverses into the array to operate on the numeric elements of the array to return a single value.
• With a list of expressions as its operand, if any of the expressions resolves to an array, $min does not traverse into the array but instead treats the array as a non-numeric value.

Use in $group Stage

Consider a sales collection with the following documents:

db.sales.insertMany( [
   { _id : 1, "item" : "abc", "price" : 10, "quantity" : 2, "date" : ISODate("2014-01-01T08:00:00Z") },
   { _id : 2, "item" : "jkl", "price" : 20, "quantity" : 1, "date" : ISODate("2014-02-03T09:00:00Z") },
   { _id : 3, "item" : "xyz", "price" : 5, "quantity" : 5, "date" : ISODate("2014-02-03T09:05:00Z") },
   { _id : 4, "item" : "abc", "price" : 10, "quantity" : 10, "date" : ISODate("2014-02-15T08:00:00Z") },
   { _id : 5, "item" : "xyz", "price" : 5, "quantity" : 10, "date" : ISODate("2014-02-15T09:05:00Z") }
] )

Grouping the documents by the item field, the following operation uses the $min accumulator to compute the minimum amount and minimum quantity for each grouping.

db.sales.aggregate(
   [
     {
       $group:
         {
           _id: "$item",
           minQuantity: { $min: "$quantity" }
         }
     }
   ]
)

The operation returns the following results:

{ "_id" : "xyz", "minQuantity" : 5 }
{ "_id" : "jkl", "minQuantity" : 1 }
{ "_id" : "abc", "minQuantity" : 2 }

Use in $project Stage

A collection students contains the following documents:

db.students.insertMany( [
   { _id: 1, "quizzes": [ 10, 6, 7 ], "labs": [ 5, 8 ], "final": 80, "midterm": 75 },
   { _id: 2, "quizzes": [ 9, 10 ], "labs": [ 8, 8 ], "final": 95, "midterm": 80 },
   { _id: 3, "quizzes": [ 4, 5, 5 ], "labs": [ 6, 5 ], "final": 78, "midterm": 70 }
] )

The following example uses the $min in the $project stage to calculate the minimum quiz scores, the minimum lab scores, and the minimum of the final and the midterm:

db.students.aggregate([
   { $project: { quizMin: { $min: "$quizzes"}, labMin: { $min: "$labs" }, examMin: { $min: [ "$final", "$midterm" ] } } }
])

The operation results in the following documents:

{ "_id" : 1, "quizMin" : 6, "labMin" : 5, "examMin" : 75 }
{ "_id" : 2, "quizMin" : 9, "labMin" : 8, "examMin" : 80 }
{ "_id" : 3, "quizMin" : 4, "labMin" : 5, "examMin" : 70 }

Use in $setWindowFields Stage

Create a cakeSales collection that contains cake sales in the states of California (CA) and Washington (WA):

db.cakeSales.insertMany( [
   { _id: 0, type: "chocolate", orderDate: new Date("2020-05-18T14:10:30Z"),
     state: "CA", price: 13, quantity: 120 },
   { _id: 1, type: "chocolate", orderDate: new Date("2021-03-20T11:30:05Z"),
     state: "WA", price: 14, quantity: 140 },
   { _id: 2, type: "vanilla", orderDate: new Date("2021-01-11T06:31:15Z"),
     state: "CA", price: 12, quantity: 145 },
   { _id: 3, type: "vanilla", orderDate: new Date("2020-02-08T13:13:23Z"),
     state: "WA", price: 13, quantity: 104 },
   { _id: 4, type: "strawberry", orderDate: new Date("2019-05-18T16:09:01Z"),
     state: "CA", price: 41, quantity: 162 },
   { _id: 5, type: "strawberry", orderDate: new Date("2019-01-08T06:12:03Z"),
     state: "WA", price: 43, quantity: 134 }
] )

This example uses $min in the $setWindowFields stage to output the minimum quantity of cake sales for each state:

db.cakeSales.aggregate( [
   {
      $setWindowFields: {
         partitionBy: "$state",
         sortBy: { orderDate: 1 },
         output: {
            minimumQuantityForState: {
               $min: "$quantity",
               window: {
                  documents: [ "unbounded", "current" ]
               }
            }
         }
      }
   }
] )

In the example:

• partitionBy: "$state" partitions the documents in the collection by state. There are partitions for CA and WA.
• sortBy: { orderDate: 1 } sorts the documents in each partition by orderDate in ascending order (1), so the earliest orderDate is first.

• output sets the minimumQuantityForState field to the minimum quantity value using $min that is run in a documents window.

  The window contains documents between an unbounded lower limit and the current document in the output. This means $min returns the minimum quantity for the documents between the beginning of the partition and the current document.

In this output, the minimum quantity for CA and WA is shown in the minimumQuantityForState field:

{ "_id" : 4, "type" : "strawberry", "orderDate" : ISODate("2019-05-18T16:09:01Z"),
  "state" : "CA", "price" : 41, "quantity" : 162, "minimumQuantityForState" : 162 }
{ "_id" : 0, "type" : "chocolate", "orderDate" : ISODate("2020-05-18T14:10:30Z"),
  "state" : "CA", "price" : 13, "quantity" : 120, "minimumQuantityForState" : 120 }
{ "_id" : 2, "type" : "vanilla", "orderDate" : ISODate("2021-01-11T06:31:15Z"),
  "state" : "CA", "price" : 12, "quantity" : 145, "minimumQuantityForState" : 120 }
{ "_id" : 5, "type" : "strawberry", "orderDate" : ISODate("2019-01-08T06:12:03Z"),
  "state" : "WA", "price" : 43, "quantity" : 134, "minimumQuantityForState" : 134 }
{ "_id" : 3, "type" : "vanilla", "orderDate" : ISODate("2020-02-08T13:13:23Z"),
  "state" : "WA", "price" : 13, "quantity" : 104, "minimumQuantityForState" : 104 }
{ "_id" : 1, "type" : "chocolate", "orderDate" : ISODate("2021-03-20T11:30:05Z"),
  "state" : "WA", "price" : 14, "quantity" : 140, "minimumQuantityForState" : 104 }