Random Forest Component Size Set Generator

Description

Generate an acyclic forest with caller-selected component sizes, shuffled node membership and verified degree/connectivity labels.

A graph uses vertices and edges to represent relationships. Direction, duplicate handling, indexing, and traversal order affect its interpretation; returning a constructed graph together with a witness or calculated answer helps verify an algorithm.

Generate an acyclic forest with caller-selected component sizes, shuffled node membership and verified degree/connectivity labels.

When to use this tool

Use this generator to create reproducible forest component size set 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 nodes, sizes 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 nodes, edges, componentLabels, sizes, degrees, componentCount. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Require component sizes to sum to the distinct node count, shuffle nodes into those groups, and construct an ordered recursive tree inside each group. Return aligned component labels, degrees, and independently checked component and edge counts.^[1]

Input field	Meaning and units	Accepted input
nodes	Nodes	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 32.
sizes	Sizes	Required. Array of Safe integer; minimum 1; maximum 32.; minimum items 1; maximum items 32.
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
nodes	Nodes	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 32.
edges	Edges	Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 2.; minimum items 0; maximum items 31.
componentLabels	Component Labels	Required. Array of Safe integer.; minimum items 1; maximum items 32.
sizes	Sizes	Required. Array of Safe integer.; minimum items 1; maximum items 32.
degrees	Degrees	Required. Array of Safe integer.; minimum items 1; maximum items 32.
componentCount	Component Count	Required. Safe integer.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer 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": {
    "nodes": [
      "a",
      "b",
      "c"
    ],
    "sizes": [
      2,
      1
    ],
    "seed": 42
  },
  "output": {
    "nodes": [
      "c",
      "a",
      "b"
    ],
    "edges": [
      [
        "c",
        "a"
      ]
    ],
    "componentLabels": [
      0,
      0,
      1
    ],
    "sizes": [
      2,
      1
    ],
    "degrees": [
      1,
      1,
      0
    ],
    "componentCount": 2,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Each component is a tree, including isolated vertices for size one. The result is not uniform over all forests with the requested component sizes, and labels align with the returned shuffled node order.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
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 Forest Component Size Set Generator — tool.io

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