Description
Uniformly sample bounded positive chunk-length compositions of an explicit total with fixed chunk count using exact completion-count unranking; infeasible support rejects.
A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.
Uniformly sample bounded positive chunk-length compositions of an explicit total with fixed chunk count using exact completion-count unranking; infeasible support rejects.
When to use this tool
Use this tool to uniformly sample bounded positive chunk-length compositions of an explicit total with fixed chunk count using exact completion-count unranking; infeasible support rejects.
How to use the tool and how it works
- Enter length, chunks, minimum, maximum, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.lengths, result.cuts, result.support, using the stated boundary, ordering, sign and absence conventions.
Count bounded positive chunk-length completions with memoized exact integer arithmetic. Draw a uniform support rank, then choose each next length according to the number of completions it leaves. Return lengths, cumulative internal cuts and exact support.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Explicit integer source/sequence length under the bounds stated above. | Finite safe integer satisfying the stated bounds. |
| chunks | Exact number of positive chunks, integer 0–128. | Finite safe integer satisfying the stated bounds. |
| minimum | Inclusive positive run/chunk-length lower bound, integer 1–128. | Finite safe integer satisfying the stated bounds. |
| maximum | Inclusive positive run/chunk-length upper bound, integer 1–128. It must be at least minimum; a reflecting walk requires it to be strictly greater. | Finite safe integer satisfying the stated bounds. |
| seed | Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.seed | Original supplied seed string; injected-source replay additionally requires that source’s state. |
| result.lengths | Ordered positive chunk lengths summing to the requested length. |
| result.cuts | Cumulative internal chunk boundaries, excluding zero and final total. |
| result.support | Exact finite support count as decimal text. |
{
"input": {
"length": 6,
"chunks": 3,
"minimum": 1,
"maximum": 3,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"lengths": [
2,
3,
1
],
"cuts": [
2,
5
],
"support": "7"
}
}
}Limitations and assumptions
- length and chunk count are 0–128; minimum/maximum are ordered 1–128. A zero-completion model rejects; complete valid length compositions are the sampling support.
- A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.
Alternative or Complementary methods
Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.
References
Similar or alternative tools
- Random Cyclic List Cut
Choose one of N cyclic list cut positions, preserving order and original position mapping; empty lists reject.
- Random Guillotine Rectangle Cut Trace
At each step choose a uniform splittable current rectangle, then a uniform legal axis and integer interior cut; local-choice process, not uniform over final partitions.