Description
Deduplicate universe and return members absent from covered as missing, with gap equal to that missing count.
A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.
Deduplicate universe and return members absent from covered as missing, with gap equal to that missing count.
When to use this tool
Use Finite Set Prefix Cover Count Gap when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.
How to use the tool and how it works
- Enter universe, covered. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read missing, gap. Use the output convention below.
Deduplicate universe and return members absent from covered as missing, with gap equal to that missing count.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| universe | Universe | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| covered | Covered | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| missing | Missing | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| gap | Gap | Required. Safe integer. |
{
"input": {
"universe": [
"a",
"b",
"c"
],
"covered": [
"a",
"c"
]
},
"output": {
"missing": [
"b"
],
"gap": 1
}
}Limitations and assumptions
- Despite prefix in the tool name, this is exact membership, not string-prefix matching. Extra covered items are ignored and duplicates cannot increase coverage.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.
References
Similar or alternative tools
- Family Union Support Count
Count union membership from explicit member/family incidences, ignoring duplicate incidences.
- Finite Set Complement Cardinality Pair
Deduplicate universe and members, require members inside the universe, and return complement in universe order plus memberCount and complementCount.