Bit String Circular One Runs
Inventory circular one-bit runs with modular starting positions and lengths; all-ones has one full-cycle run and empty/all-zero strings have none.
Description
Inventory circular one-bit runs with modular starting positions and lengths; all-ones has one full-cycle run and empty/all-zero strings have none.
In a circular bitstring, a run of ones can cross the end-to-start boundary. A linear run table would split that run.
When to use this tool
Inventory circular one-bit runs with modular starting positions and lengths; all-ones has one full-cycle run and empty/all-zero strings have none.
- Prepare the supplied bits fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter bits. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.runs. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Find each one preceded cyclically by zero and count its run length modulo the string length. An all-ones nonempty string is one run starting at zero; no ones gives an empty list.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| bits | bits. | Binary text containing only 0 and 1; at most 128 characters |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.runs | The runs list in the ordering and representation described above. |
{
"input": {
"bits": "110001"
},
"output": {
"result": {
"runs": [
{
"start": 5,
"length": 3
}
]
}
}
}Limitations and assumptions
- Runs use start plus length rather than half-open end coordinates because they can wrap. No padding or rotation normalization is applied.
- Every bitstring is at most 128 characters and contains only literal zero and one.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Choose a packed-integer or textual-bit representation deliberately before combining operations. Preserve the documented index direction, width and exclusive boundaries; do not substitute a rank query for select.
References
Similar or alternative tools
- Bit String One Run Table
Inventory maximal half-open 1-bit runs in a bounded linear string; no circular merging or compression.
- Bit String Rank One Query
Count 1 bits in the half-open prefix before an explicit endpoint; rank excludes the endpoint position itself.