Multi Key Order Witness
Compare two numeric multi-key tuples with per-key ascending/descending directions, exposing the first decisive key rather than coercing ties.
Description
Compare two numeric multi-key tuples with per-key ascending/descending directions, exposing the first decisive key rather than coercing ties.
A multi-key comparison stops at its first differing key, with per-key ascending or descending direction.
When to use this tool
Compare two numeric multi-key tuples with per-key ascending/descending directions, exposing the first decisive key rather than coercing ties.
- Prepare the supplied left, right, directions 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 left, right, directions. 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.decisiveKey, result.order. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require equal list lengths and directions each +1 or -1. Return the first unequal zero-based key index and the sign of left minus right multiplied by its direction. Equal tuples give null and zero.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| left | left. | List of finite numbers; at most 128 entries |
| right | right. | List of finite numbers; at most 128 entries |
| directions | directions. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.decisiveKey | The decisive key value under the stated formula or text convention. |
| result.order | Comparison result under the exact convention above; -1 means left before right, 0 equal, +1 after. |
{
"input": {
"left": [
1,
3
],
"right": [
1,
2
],
"directions": [
1,
-1
]
},
"output": {
"result": {
"decisiveKey": 1,
"order": -1
}
}
}Limitations and assumptions
- No key extraction, locale collation or tolerance is applied. Large finite subtraction can overflow to infinity internally, but its sign is still used.
- 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 the tie policy and whether you need values, original indexes, sorted positions or one-based ranks. Use a complete sort verifier when a local stability or adjacent-comparison check is insufficient.
References
Similar or alternative tools
- Lexicographic Tuple Order Check
Check finite numeric tuples in lexicographic order, with shorter matching prefixes before longer tuples and explicit adjacent failure witnesses.
- Rank Order Agreement Pairs
Classify numeric rank-order pair agreement and disagreement while retaining all pairs tied in either observation; not a normalized correlation coefficient.