Description
Generate union and connectivity queries with path-compressed disjoint-set snapshots, explicit redundant unions and per-step connected-components cross-checks; endpoint sampling permits self operations.
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 union and connectivity queries with path-compressed disjoint-set snapshots, explicit redundant unions and per-step connected-components cross-checks; endpoint sampling permits self operations.
When to use this tool
Use this generator to create reproducible union find connectivity trace 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 nodeCount, operations, eventCount 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 events, finalComponents. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw union/query operations and endpoint indexes, maintain path-compressed disjoint sets and merge toward the smaller representative. After every event, derive component labels and cross-check them against delegated connected components on the accumulated edges.1
Delegated operations used for this result: connected components. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodeCount | Node Count | Required. Safe integer; minimum 1; maximum 16. |
| operations | Operations | Required. Array of Text; one of "union", "query".; minimum items 1; maximum items 2. |
| eventCount | Event Count | Required. Safe integer; minimum 1; maximum 64. |
| 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 |
|---|---|---|
| events | Events | Required. Array of Object; no unknown keys.; minimum items 0; maximum items 64. |
| events[].kind | Kind | Required. Text; one of "union", "query". |
| events[].a | A | Required. Safe integer; minimum 0; maximum 15. |
| events[].b | B | Required. Safe integer; minimum 0; maximum 15. |
| events[].connected | Connected | Required. Boolean. |
| events[].redundantUnion | Redundant Union | Required. Boolean. |
| events[].components | Component loading vectors in component order, each aligned with the original feature columns. | Required. Array of Safe integer; minimum 0; maximum 15.; minimum items 0; maximum items 16. |
| finalComponents | Final Components | Required. Array of Safe integer; minimum 0; maximum 15.; minimum items 0; maximum items 16. |
| 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.
{
"input": {
"nodeCount": 3,
"operations": [
"union",
"query"
],
"eventCount": 3,
"seed": 42
},
"output": {
"events": [
{
"kind": "query",
"a": 1,
"b": 2,
"connected": false,
"redundantUnion": false,
"components": [
0,
1,
2
]
},
{
"kind": "query",
"a": 0,
"b": 1,
"connected": false,
"redundantUnion": false,
"components": [
0,
1,
2
]
},
{
"kind": "union",
"a": 1,
"b": 2,
"connected": true,
"redundantUnion": false,
"components": [
0,
1,
1
]
}
],
"finalComponents": [
0,
1,
1
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Endpoint sampling permits self operations and redundant unions. Snapshots describe this finite operation sequence; they do not simulate a distributed union-find protocol or establish an amortized performance benchmark.
- 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
Similar or alternative tools
- Random Graph Articulation Point Exercise Generator
Construct candidate cut-vertex exercises and verify each vertex removal using connected-component counts, with bounded optional chords.
- Random Graph Bridge Cut Exercise Generator
Construct a recursive connected graph with optional chords and label candidate/all-edge removals by delegated component changes.