Index Permutation Validator

Audit a proposed zero-based index permutation with invalid positions, duplicates and missing indexes; malformed evidence is reported rather than accepted.

Description

Audit a proposed zero-based index permutation with invalid positions, duplicates and missing indexes; malformed evidence is reported rather than accepted.

A proposed index permutation can have out-of-range values, repeats and missing indexes. An audit reports all three without requiring a valid permutation first.

When to use this tool

Audit a proposed zero-based index permutation with invalid positions, duplicates and missing indexes; malformed evidence is reported rather than accepted.

Prepare the supplied permutation 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 permutation. 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.valid, result.invalid, result.duplicates, result.missing. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

For length n, list positions whose values are not safe integers in [0,n), group duplicate values with occurrence indexes and list missing indexes. valid requires no invalid positions and no duplicates.^[1]

Input field	Meaning and representation	Accepted input
permutation	permutation.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.valid	Flag for valid under the exact condition described above.
result.invalid	The invalid list in the ordering and representation described above.
result.duplicates	The duplicates list in the ordering and representation described above.
result.missing	The missing list in the ordering and representation described above.

json

{
  "input": {
    "permutation": [
      0,
      0,
      3
    ]
  },
  "output": {
    "result": {
      "valid": false,
      "invalid": [
        2
      ],
      "duplicates": [
        {
          "key": "0",
          "indexes": [
            0,
            1
          ]
        }
      ],
      "missing": [
        1,
        2
      ]
    }
  }
}

Limitations and assumptions

All inputs still must be finite numbers. Duplicate-group keys are string spellings, and an empty list is a valid permutation.
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

Tool behavior and example: Index Permutation Validator — tool.io

Similar or alternative tools

Index Permutation Composition
Compose index permutations by applying first then second to each index; composition convention is explicit and operand lengths must agree.
Index Permutation Cycle Table
Decompose an index permutation into disjoint cycles, including fixed points and starting each cycle at its smallest unseen index.