Description
Generate a connected signed-integer-weight graph, delegate tree selection to the existing Kruskal calculation, and sum the selected weights exactly instead of inheriting its display rounding.
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 a connected signed-integer-weight graph, delegate tree selection to the existing Kruskal calculation, and sum the selected weights exactly instead of inheriting its display rounding.
When to use this tool
Use this generator to create reproducible minimum spanning tree test case 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, edgeCount, 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 nodes, edges, componentCount, treeEdges, totalWeight. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Construct a connected simple undirected weighted graph, delegate its minimum spanning tree, and independently sum selected edge weights using exact integers before converting to a safe numeric total.1
Delegated operations used for this result: minimum spanning tree. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodeCount | Number of vertices, labeled 0 through nodeCount - 1. | Required. Safe integer; minimum 2; maximum 32. |
| edgeCount | Exact number of generated edges; feasibility is checked against the selected construction. | Required. Safe integer; minimum 0; maximum 496. |
| minimumWeight | Safe-integer edge weight in caller-selected consistent units; the inclusive sampling range must also have a safe-integer width. | Required. Safe integer. |
| maximumWeight | Safe-integer edge weight in caller-selected consistent units; the inclusive sampling range must also have a safe-integer width. | 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 Safe integer; minimum 0.; maximum items 32. |
| edges | Edges | Required. Array of Array of Safe integer.; minimum items 3; maximum items 3.; maximum items 496. |
| componentCount | Component Count | Required. Safe integer; exactly 1. |
| 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". |
| treeEdges | Tree Edges | Required. Array of Text.; maximum items 31. |
| totalWeight | Total Weight | Required. Safe integer. |
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": 5,
"edgeCount": 6,
"minimumWeight": 2,
"maximumWeight": 30,
"seed": 42
},
"output": {
"nodes": [
0,
1,
2,
3,
4
],
"edges": [
[
0,
1,
10
],
[
0,
3,
7
],
[
0,
4,
16
],
[
1,
3,
21
],
[
2,
3,
19
],
[
2,
4,
2
]
],
"componentCount": 1,
"randomness": {
"seed": 42,
"source": "seed"
},
"treeEdges": [
"2|4",
"0|3",
"0|1",
"0|4"
],
"totalWeight": 35
}
}Limitations and assumptions
- Equal weights can admit several minimum trees. Nodes use numeric IDs in the instance and string IDs in delegated tree edges; construction is synthetic and not uniform over all connected graphs.
- 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
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