Permutation Unrestricted Swap Distance
Compute minimum unrestricted swap distance between two index permutations from relative cycle count; adjacent-swap distance is different.
Description
Compute minimum unrestricted swap distance between two index permutations from relative cycle count; adjacent-swap distance is different.
Arbitrary-transposition distance between permutations differs from adjacent-swap distance. Cycle structure determines the former.
When to use this tool
Compute minimum unrestricted swap distance between two index permutations from relative cycle count; adjacent-swap distance is different.
- Prepare the supplied first, second 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 first, second. 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.distance. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate equal-size permutations, map each first value to its position in second and return size minus the number of cycles of that relative permutation.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| first | first. | List of finite numbers; at most 128 entries |
| second | second. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.distance | The distance value under the stated formula or text convention. |
{
"input": {
"first": [
0,
1,
2
],
"second": [
2,
0,
1
]
},
"output": {
"result": {
"distance": 2
}
}
}Limitations and assumptions
- Each swap can exchange any two positions. The tool returns a distance, without a swap sequence or item-label interpretation.
- Except in the diagnostic validator, a permutation must contain each integer from zero through length minus one exactly once. Lists contain at most 128 entries.
- 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
Keep the index-to-image convention and composition direction explicit. A rank, cycle table, reorder-index list and inverse map encode different operations even when their entries are all integers.
References
Similar or alternative tools
- Index Permutation Cycle Table
Decompose an index permutation into disjoint cycles, including fixed points and starting each cycle at its smallest unseen index.
- Permutation Adjacent Swap Distance
Compute the minimum adjacent-swap distance between two index permutations by relative inversion count; no arbitrary value sorting.