Description
Count alternations in an explicitly supplied two-label run-length encoding, preserving empty-stream status.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Count alternations in an explicitly supplied two-label run-length encoding, preserving empty-stream status.
When to use this tool
Use Run Boundary Alternation Parity when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter runLengths. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read boundaries, parity, lastMatchesFirst. Inspect lastMatchesFirst before interpreting the associated values.
Return boundaries=max(0,runLengths.length-1), its parity, and lastMatchesFirst for a nonempty odd number of runs. Require positive integer run lengths.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| runLengths | Run Lengths | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| boundaries | Boundaries | Required. Safe integer. |
| parity | Parity | Required. Safe integer. |
| lastMatchesFirst | Last Matches First | Required. Boolean. |
{
"input": {
"runLengths": [
2,
3,
1
]
},
"output": {
"boundaries": 2,
"parity": 0,
"lastMatchesFirst": true
}
}Limitations and assumptions
- Only run count affects these outputs. Alternation of successive run labels is assumed rather than checked, and an empty list has lastMatchesFirst false.
- 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
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Sequence: Lucas Pair Parity Label
Report adjacent canonical Lucas-number parities using L0=2,L1=1 and the period-three parity recurrence; no value enumeration.
- Periodic Sample Phase Boundary Token
Return phase as nonnegative index modulo positive integer period, cycle=floor(index/period), and boundary when phase is zero.