Random Negative Pair Sampler Generator

Description

Sample uniformly among supplied-item pairs after positive and self exclusions, with explicit endpoint ordering, replacement, and conditional weights.

Sampling selects from a supplied population under rules for replacement, grouping, or eligibility. Draw probabilities, inclusion probabilities, and repeat counts describe different aspects of selection; a reproducible sample is not automatically representative of a real population.

Sample uniformly among supplied-item pairs after positive and self exclusions, with explicit endpoint ordering, replacement, and conditional weights.

When to use this tool

Use this generator to create reproducible negative pair sampler cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply itemIds, positives, convention, allowSelfPairs, count, replacement in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read pairs, eligiblePairCount, excludedPairCount. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Enumerate ordered or unordered item pairs with the chosen self-pair rule, subtract supplied positives, and sample from the remaining pool. Return each draw's conditional probability and eligible/excluded counts, removing selected pairs when replacement is disabled.^[1]

Delegated operations used for this result: cartesian product; difference. Their calculation or parsing conventions apply to the corresponding result fields.^{[2, 3]}

Input field	Meaning and units	Accepted input
itemIds	Item Ids	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 128.; minimum items 0; maximum items 128.
positives	Positives	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 16384.
positives[].first	First	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
positives[].second	Second	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
convention	Unordered pairs use the supplied item order as their canonical endpoint order.	Required. Text; one of "ordered", "unordered".
allowSelfPairs	Allow Self Pairs	Required. Boolean.
count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 0; maximum 4096.
replacement	Replacement	Required. Boolean.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
pairs	Pairs	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 4096.
pairs[].first	First	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
pairs[].second	Second	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
pairs[].conditionalProbability	Conditional Probability	Required. Finite number; minimum 0; maximum 1.
eligiblePairCount	Eligible Pair Count	Required. Safe integer; minimum 0.
excludedPairCount	Distinct positive pairs removed from the convention's space after the self-pair policy; repeated or self-disallowed positives do not add exclusions.	Required. Safe integer; minimum 0.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "itemIds": [
      "A",
      "B",
      "C"
    ],
    "positives": [
      {
        "first": "A",
        "second": "B"
      }
    ],
    "convention": "unordered",
    "allowSelfPairs": false,
    "count": 2,
    "replacement": false,
    "seed": 42
  },
  "output": {
    "pairs": [
      {
        "first": "B",
        "second": "C",
        "conditionalProbability": 0.5
      },
      {
        "first": "A",
        "second": "C",
        "conditionalProbability": 1
      }
    ],
    "eligiblePairCount": 2,
    "excludedPairCount": 1,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Negative means absent from the supplied positives, not a verified negative relationship. For unordered pairs orientation is canonicalized. Without replacement changes conditional draw probability as the pool shrinks.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Negative Pair Sampler Generator — tool.io
Calculation or validation: list/cartesian-product — tool.io
Calculation or validation: set/difference — tool.io

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