Description
Parse blocksJson as bounded lists of string-member blocks, reject any repeated member across the flattened blocks, and locate left and right.
A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.
Parse blocksJson as bounded lists of string-member blocks, reject any repeated member across the flattened blocks, and locate left and right.
When to use this tool
Use Set Partition Single Pair Coassignment when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.
How to use the tool and how it works
- Enter left, right, blocksJson. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sameBlock, leftBlock, rightBlock. Inspect sameBlock before interpreting the associated values.
Parse blocksJson as bounded lists of string-member blocks, reject any repeated member across the flattened blocks, and locate left and right. Require both present and return their zero-based block indices and sameBlock.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Text; maximum UTF-16 length 8192. |
| right | Right | Required. Text; maximum UTF-16 length 8192. |
| blocksJson | Bounded JSON array of string-member arrays; repeated members are rejected. | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sameBlock | Same Block | Required. Boolean. |
| leftBlock | Left Block | Required. Safe integer. |
| rightBlock | Right Block | Required. Safe integer. |
{
"input": {
"left": "a",
"right": "b",
"blocksJson": "[[\"a\",\"b\"],[\"c\"]]"
},
"output": {
"sameBlock": true,
"leftBlock": 0,
"rightBlock": 0
}
}Limitations and assumptions
- No explicit universe or nonempty-block condition is supplied. The result checks coassignment in the given disjoint blocks, not completeness or validity of a broader partition.
- 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
Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.
References
Similar or alternative tools
- Partition Block Count Change
Compare declared partition block counts without constructing or validating the partitions.
- Partition Block Size Residual
Check cardinality balance of supplied partition block sizes without claiming their disjointness.