Description
Return zero-part count and remaining allowed capacity.
Combinatorial counts depend on whether objects are labeled, order matters, repetitions are permitted and a prefix is already fixed. Local counts, exact integer factors and feasibility bounds answer specific questions and need not enumerate complete objects.
Return zero-part count and remaining allowed capacity.
When to use this tool
Use Composition Zero Part Capacity when checking the stated word, set, multiset or composition convention.
How to use the tool and how it works
- Enter totalParts, nonzeroParts, allowedZeroParts. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read zeroParts, capacityRemaining. Use the output convention below.
Return zero-part count and remaining allowed capacity. Require whole 0 <= nonzeroParts <= totalParts and allowedZeroParts >= 0; zeroParts = total-nonzero, capacityRemaining = allowed-zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| totalParts | Total Parts | Required. Safe integer; minimum 0. |
| nonzeroParts | Nonzero Parts | Required. Safe integer; minimum 0. |
| allowedZeroParts | Allowed Zero Parts | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| zeroParts | Zero Parts | Required. Safe integer. |
| capacityRemaining | Capacity Remaining | Required. Safe integer. |
{
"input": {
"totalParts": 8,
"nonzeroParts": 5,
"allowedZeroParts": 4
},
"output": {
"zeroParts": 3,
"capacityRemaining": 1
}
}Limitations and assumptions
- Negative remaining capacity is reported; supplied counts are not verified against an actual composition.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use complete objects and an appropriate exact counting, ranking or enumeration method when the local contribution is insufficient.
References
Similar or alternative tools
- Integer Composition Zero Part Insertion
Insert a zero into a weak composition.
- Cyclic Composition Part Count
Count positive compositions up to cyclic rotation.