Random Indexed Swap Trace

Description

Perform a fixed number of independent uniformly selected ordered distinct-position swaps, retaining index trace; not a uniform final permutation.

A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.

Perform a fixed number of independent uniformly selected ordered distinct-position swaps, retaining index trace; not a uniform final permutation.

When to use this tool

Use this tool to perform a fixed number of independent uniformly selected ordered distinct-position swaps, retaining index trace; not a uniform final permutation.

How to use the tool and how it works

Enter values, swaps, seed using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.trace, result.sourceIndexes, result.values, using the stated boundary, ordering, sign and absence conventions.

Start with identity source indexes. For every requested swap draw a first slot uniformly, then a second uniformly from the other slots; swap their current source indexes and retain the ordered slot pair in trace.^[1]

Input field	Meaning and units	Accepted input
values	Literal string values in original positional order; repeated spellings retain distinct source indexes.	Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units.
swaps	Number of ordered distinct-slot swaps, integer 1–128.	Finite safe integer satisfying the stated bounds.
seed	Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.

Output field	Interpretation
result	Object containing the fields below.
result.seed	Original supplied seed string; injected-source replay additionally requires that source’s state.
result.trace	Sequential swaps or guillotine-cut choices, retaining their stated provenance.
result.sourceIndexes	Output-position-to-original-position map.
result.values	Generated/reordered literal values, preserving the stated positional support.

json

{
  "input": {
    "values": [
      "a",
      "b",
      "c"
    ],
    "swaps": 2,
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "trace": [
        [
          1,
          2
        ],
        [
          2,
          1
        ]
      ],
      "sourceIndexes": [
        0,
        1,
        2
      ],
      "values": [
        "a",
        "b",
        "c"
      ]
    }
  }
}

Limitations and assumptions

At least two values and 1–128 swaps are required. A fixed number of random swaps is not a uniformly sampled final permutation.
A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.

Alternative or Complementary methods

Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.

References

Tool behavior and example: Random Indexed Swap Trace — tool.io

Similar or alternative tools

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