Description
Check completion budget after fixed composition parts.
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.
Check completion budget after fixed composition parts.
When to use this tool
Use Composition Fixedpart Remainder Budget when checking the stated word, set, multiset or composition convention.
How to use the tool and how it works
- Enter total, fixedParts, slots, allowZero. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remaining, feasible, minimumNeeded. Inspect feasible before interpreting the associated values.
Check completion budget after fixed composition parts. Require valid whole total/slots and fixed parts nonnegative or positive according to allowZero; remaining = total-sum(fixed), minimumNeeded is zero or slots, feasible also requires zero remaining when slots zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| total | Total | Required. Safe integer; minimum 0. |
| fixedParts | Fixed Parts | Required. Array of safe integer; maximum items 256. |
| slots | Slots | Required. Safe integer; minimum 0. |
| allowZero | Allow Zero | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remaining | Budget minus use under the stated direction, retaining negative deficits where allowed. | Required. Safe integer. |
| feasible | Whether the stated local constraints hold; this need not establish a valid complete object or procedure. | Required. Boolean. |
| minimumNeeded | Minimum Needed | Required. Safe integer. |
{
"input": {
"total": 10,
"fixedParts": [
3,
2
],
"slots": 2,
"allowZero": false
},
"output": {
"remaining": 5,
"feasible": true,
"minimumNeeded": 2
}
}Limitations and assumptions
- This is a local total budget without per-slot upper limits or enumeration of completions.
- 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
- Composition Part Upper Slack
Return per-part upper-bound slack.
- Combinatorics: Composition Positive Part Shift
Shift positive parts into a weak composition.