Random Beam Search Pruning Challenge Generator

Description

Grow a bounded scored tree and delegate beam traces, comparing the result with exhaustive best paths at the same depth to expose pruning losses.

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.

Grow a bounded scored tree and delegate beam traces, comparing the result with exhaustive best paths at the same depth to expose pruning losses.

When to use this tool

Use this generator to create reproducible beam search pruning challenge 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 branchingFactor, treeDepth, searchDepth, width, minimumScore, maximumScore 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, beam, comparison, convention. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw a complete scored tree and run beam search to searchDepth. Exhaustively enumerate all paths to that same depth, compare cumulative scores, and return the optimality gap and whether the beam score matches the exhaustive best.^[1]

Delegated operations used for this result: beam search. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
branchingFactor	Branching Factor	Required. Safe integer; minimum 2; maximum 4.
treeDepth	Tree Depth	Required. Safe integer; minimum 1; maximum 5.
searchDepth	Search Depth	Required. Safe integer; minimum 1; maximum 5.
width	Width	Required. Safe integer; minimum 1; maximum 16.
minimumScore	Minimum Score	Required. Safe integer.
maximumScore	Maximum Score	Required. Safe integer.
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 Object; no unknown keys.; minimum items 3; maximum items 341.
nodes[].label	Supplied display label.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
nodes[].parent	Parent	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64. or Null.
nodes[].depth	Depth	Required. Safe integer; minimum 0; maximum 5.
nodes[].score	Score	Required. Safe integer.
beam	Beam	Required. Object; no unknown keys.
beam.bestPath	Best Path	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 6.
beam.bestScore	Best Score	Required. Finite number.
beam.levels	Levels	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 5.
beam.levels[].kept	Kept	Required. Array of Text.; minimum items 1; maximum items 16.
beam.levels[].pruned	Pruned	Required. Array of Text.; minimum items 0; maximum items 64.
comparison	Comparison	Required. Object; no unknown keys.
comparison.depth	Depth	Required. Safe integer; minimum 1; maximum 5.
comparison.exhaustivePathCount	Exhaustive Path Count	Required. Safe integer; minimum 2; maximum 256.
comparison.exhaustiveBestPath	Exhaustive Best Path	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 1; maximum items 6.
comparison.exhaustiveBestScore	Exhaustive Best Score	Required. Finite number.
comparison.gap	Gap	Required. Finite number.
comparison.beamIsOptimal	Beam Is Optimal	Required. Boolean.
convention	Convention	Required. Text.
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": {
    "branchingFactor": 2,
    "treeDepth": 2,
    "searchDepth": 2,
    "width": 1,
    "minimumScore": -5,
    "maximumScore": 5,
    "seed": 42
  },
  "output": {
    "nodes": [
      {
        "label": "n000",
        "parent": null,
        "depth": 0,
        "score": 0
      },
      {
        "label": "n001",
        "parent": "n000",
        "depth": 1,
        "score": 1
      },
      {
        "label": "n002",
        "parent": "n001",
        "depth": 2,
        "score": -1
      },
      {
        "label": "n003",
        "parent": "n001",
        "depth": 2,
        "score": 4
      },
      {
        "label": "n004",
        "parent": "n000",
        "depth": 1,
        "score": 2
      },
      {
        "label": "n005",
        "parent": "n004",
        "depth": 2,
        "score": -4
      },
      {
        "label": "n006",
        "parent": "n004",
        "depth": 2,
        "score": 0
      }
    ],
    "beam": {
      "bestPath": [
        "n000",
        "n004",
        "n006"
      ],
      "bestScore": 2,
      "levels": [
        {
          "kept": [
            "n000 > n004"
          ],
          "pruned": [
            "n000 > n001"
          ]
        },
        {
          "kept": [
            "n000 > n004 > n006"
          ],
          "pruned": [
            "n000 > n004 > n005"
          ]
        }
      ]
    },
    "comparison": {
      "depth": 2,
      "exhaustivePathCount": 4,
      "exhaustiveBestPath": [
        "n000",
        "n001",
        "n003"
      ],
      "exhaustiveBestScore": 5,
      "gap": 3,
      "beamIsOptimal": false
    },
    "convention": "Scores are cumulative node increments from a zero-score root. Compare paths at the same depth; ties use the core's ascending path-label convention. Beam pruning may discard the exhaustive optimum.",
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The root contributes zero and other scores are node increments. Narrow beams can discard the optimum. Equal-score paths follow the stated label convention; the tree and arithmetic budgets bound exhaustive comparison.
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 Beam Search Pruning Challenge Generator — tool.io
Calculation or validation: search/beam-search — tool.io

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