Description
For distinct keys aligned with nonnegative integer counts and capacities, return each capacity-minus-count slack and allWithinCapacity when every slack is nonnegative.
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.
For distinct keys aligned with nonnegative integer counts and capacities, return each capacity-minus-count slack and allWithinCapacity when every slack is nonnegative.
When to use this tool
Use Multiset Key Capacity Slack 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 keys, counts, capacities. 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 slacks, allWithinCapacity. Inspect allWithinCapacity before interpreting the associated values.
For distinct keys aligned with nonnegative integer counts and capacities, return each capacity-minus-count slack and allWithinCapacity when every slack is nonnegative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| keys | Keys | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| counts | Counts | Required. Array of safe integer; minimum 0; maximum items 256. |
| capacities | Capacities | Required. Array of safe integer; minimum 0; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slacks | Slacks | Required. Array of safe integer; maximum items 256. |
| allWithinCapacity | All Within Capacity | Required. Boolean. |
{
"input": {
"keys": [
"a",
"b"
],
"counts": [
2,
5
],
"capacities": [
3,
4
]
},
"output": {
"slacks": [
1,
-1
],
"allWithinCapacity": false
}
}Limitations and assumptions
- Negative slacks are valid outputs. The tool does not change counts, resolve duplicate keys, or verify that capacities represent a real storage or allocation constraint.
- 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
- Multiset Quotient Remainder One Key
Use exact BigInt quotient and remainder to divide nonnegative integer multiplicity by positive integer divisor, returning bounded numeric outputs.
- Multiset Subtraction Truncated One Key
Return count=max(0,first-second) and deficit=max(0,second-first) for nonnegative integer multiplicities.