Multiset Overlap Cardinality
Calculate typed multiset minimum-overlap cardinality including keys absent from one operand; no scalar type coercion.
Description
Calculate typed multiset minimum-overlap cardinality including keys absent from one operand; no scalar type coercion.
Multiset overlap counts shared occurrences rather than only shared distinct values. The smaller multiplicity limits each value's contribution.
When to use this tool
Calculate typed multiset minimum-overlap cardinality including keys absent from one operand; no scalar type coercion.
- Prepare the supplied leftJson, rightJson fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter leftJson, rightJson. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.cardinality. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize leftJson and rightJson as value/count records. For the union of typed JSON keys, sum the smaller left and right count, using zero when absent. Return cardinality.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| leftJson | JSON text, entered as one text field. The decoded structure is illustrated below; it is not a separate file. | Text |
| rightJson | JSON text, entered as one text field. The decoded structure is illustrated below; it is not a separate file. | Text |
For the JSON text fields, the following decoded structures show the example records before they are serialized into input strings. Keep field names, list nesting and value types as shown.
[
{
"field": "leftJson",
"decoded": [
{
"value": "a",
"count": 3
},
{
"value": "b",
"count": 1
}
]
},
{
"field": "rightJson",
"decoded": [
{
"value": "a",
"count": 2
},
{
"value": "c",
"count": 2
}
]
}
]| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.cardinality | The cardinality value under the stated formula or text convention. |
{
"input": {
"leftJson": "[{\"value\":\"a\",\"count\":3},{\"value\":\"b\",\"count\":1}]",
"rightJson": "[{\"value\":\"a\",\"count\":2},{\"value\":\"c\",\"count\":2}]"
},
"output": {
"result": {
"cardinality": 2
}
}
}Limitations and assumptions
- This is minimum intersection cardinality, not distinct-value overlap or an additive total. Scalar value types remain distinct.
- Count records contain a scalar JSON value and an integer count from zero to one million. Duplicate typed values aggregate up to one million per input key and zero aggregates are omitted.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Keep count-table arithmetic separate from occurrence ordering and persistent inventory changes. Choose minimum intersection, maximum union or additive sum explicitly, and retain scalar types when matching values.
References
Similar or alternative tools
- multiplicity union cardinality
Calculate typed multiset maximum-union cardinality including keys absent from one operand; no scalar type coercion.
- Multiset Absolute Multiplicity Difference
Compute typed multiset absolute multiplicity difference from exact scalar identities and nonnegative integer counts; duplicate count rows are summed.