Description
Check a lattice word's remaining symbol budget.
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 a lattice word's remaining symbol budget.
When to use this tool
Use Lattice Word Symbol Budget when checking the stated word, set, multiset or composition convention.
How to use the tool and how it works
- Enter available, used. 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 remaining, feasible. Inspect feasible before interpreting the associated values.
Check a lattice word's remaining symbol budget. Require aligned nonnegative available/used arrays; remaining = available-used per position, feasible means every remainder >= 0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| available | Available | Required. Array of safe integer; maximum items 256. |
| used | Used | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remaining | Budget minus use under the stated direction, retaining negative deficits where allowed. | 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": {
"available": [
3,
2
],
"used": [
2,
1
]
},
"output": {
"remaining": [
1,
1
],
"feasible": true
}
}Limitations and assumptions
- Negative deficits are reported, not rejected; no prefix ordering constraint or actual word content is validated.
- 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
- Word Prefix Symbol Deficit
Return symbol deficits of a supplied word prefix.
- Multiset Word Adjacent Equality Count
Count equal adjacent symbols in a supplied word.