Random Dag Longest Path Exercise Generator

Description

Generate bounded weighted DAGs with a guaranteed forward chain, retained topological order and independently replayable longest-path relaxations.

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 bounded weighted DAGs with a guaranteed forward chain, retained topological order and independently replayable longest-path relaxations.

When to use this tool

Use this generator to create reproducible dag longest path exercise 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, extraEdgeProbability, minimumWeight, maximumWeight 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 edges, order, distances, path, relaxations. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Plant an ascending input-order chain, optionally add further forward edges, and draw integer weights. Process a delegated topological order, accepting strictly improving longest-path relaxations from the first node and retaining distances, a final-node path, and relaxation evidence.^[1]

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

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 2; maximum items 16.
extraEdgeProbability	Extra Edge Probability	Required. Finite number; minimum 0; maximum 1.
minimumWeight	Minimum Weight	Required. Safe integer.
maximumWeight	Maximum Weight	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
edges	Edges	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 120.
edges[].source	Source	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
edges[].target	Target	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
edges[].weight	Weight	Required. Safe integer.
order	Order	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 16.
distances	Distances	Required. Array of Safe integer.; minimum items 2; maximum items 16.
path	Path	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 64.; minimum items 2; maximum items 16.
relaxations	Relaxations	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 120.
relaxations[].source	Source	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
relaxations[].target	Target	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
relaxations[].previous	Previous	Required. Safe integer. or Null.
relaxations[].candidate	Candidate	Required. Safe integer.
relaxations[].accepted	Accepted	Required. Boolean.
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"
    ],
    "extraEdgeProbability": 0,
    "minimumWeight": 1,
    "maximumWeight": 3,
    "seed": 42
  },
  "output": {
    "edges": [
      {
        "source": "a",
        "target": "b",
        "weight": 2
      },
      {
        "source": "b",
        "target": "c",
        "weight": 2
      }
    ],
    "order": [
      "a",
      "b",
      "c"
    ],
    "distances": [
      0,
      2,
      4
    ],
    "path": [
      "a",
      "b",
      "c"
    ],
    "relaxations": [
      {
        "source": "a",
        "target": "b",
        "previous": null,
        "candidate": 2,
        "accepted": true
      },
      {
        "source": "b",
        "target": "c",
        "previous": null,
        "candidate": 4,
        "accepted": true
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The mandatory chain makes all nodes reachable. Equal-length candidates keep the existing path. Distances must remain safe integers and this applies to a DAG, not arbitrary graphs with cycles.
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 Dag Longest Path Exercise Generator — tool.io
Calculation or validation: graph/topological-sort — tool.io

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