Description
Check bounded composition parts against supplied caps.
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 bounded composition parts against supplied caps.
When to use this tool
Use Bounded Composition Cap Slack when checking the stated word, set, multiset or composition convention.
How to use the tool and how it works
- Enter parts, caps. 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, feasible. Inspect feasible before interpreting the associated values.
Check bounded composition parts against supplied caps. Require aligned nonnegative whole arrays; slacks = caps-parts, feasible means all slacks nonnegative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parts | Parts | Required. Array of safe integer; maximum items 256. |
| caps | Caps | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slacks | Slacks | Required. Array of safe integer; maximum items 256. |
| feasible | Whether the stated local constraints hold; this need not establish a valid complete object or procedure. | Required. Boolean. |
{
"input": {
"parts": [
2,
4
],
"caps": [
3,
3
]
},
"output": {
"slacks": [
1,
-1
],
"feasible": false
}
}Limitations and assumptions
- No fixed-total requirement is checked; feasible refers only to these component bounds.
- 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.
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.
- Composition Fixedpart Remainder Budget
Check completion budget after fixed composition parts.