Description
Construct a permutation with an exact sampled feasible inversion count using sequential constrained Lehmer digits and retain its sorted answer; sampling is not uniform over permutations.
A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.
Construct a permutation with an exact sampled feasible inversion count using sequential constrained Lehmer digits and retain its sorted answer; sampling is not uniform over permutations.
When to use this tool
Use this generator to create reproducible sorting inversion 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 size, minimumInversions, maximumInversions 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 permutation, lehmerDigits, inversionCount, sortedAnswer. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw a target inversion count and construct a permutation of 1 through size using feasible Lehmer digits that reserve enough inversions for the remaining suffix. Recount inversions directly and return the sorted answer and construction digits.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| size | Size | Required. Safe integer; minimum 2; maximum 32. |
| minimumInversions | Minimum Inversions | Required. Safe integer; minimum 0; maximum 496. |
| maximumInversions | Maximum Inversions | Required. Safe integer; minimum 0; maximum 496. |
| 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 |
|---|---|---|
| permutation | Permutation | Required. Array of Safe integer; minimum 1; maximum 32.; minimum items 0; maximum items 32. |
| lehmerDigits | Lehmer Digits | Required. Array of Safe integer; minimum 0; maximum 31.; minimum items 0; maximum items 32. |
| inversionCount | Inversion Count | Required. Safe integer; minimum 0; maximum 496. |
| sortedAnswer | Sorted Answer | Required. Array of Safe integer; minimum 1; maximum 32.; minimum items 0; maximum items 32. |
| 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": {
"size": 4,
"minimumInversions": 3,
"maximumInversions": 3,
"seed": 42
},
"output": {
"permutation": [
2,
4,
1,
3
],
"lehmerDigits": [
1,
2,
0,
0
],
"inversionCount": 3,
"sortedAnswer": [
1,
2,
3,
4
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The target cannot exceed size*(size-1)/2. Construction guarantees the chosen count, not uniform sampling over all permutations or all permutations with that count.
- 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
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