Description
Sample uniformly over order-preserving queue-identity interleavings by choosing next queue proportional to remaining item count; unequal queue lengths are not equal-weight queues.
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.
Sample uniformly over order-preserving queue-identity interleavings by choosing next queue proportional to remaining item count; unequal queue lengths are not equal-weight queues.
When to use this tool
Use this tool to sample uniformly over order-preserving queue-identity interleavings by choosing next queue proportional to remaining item count; unequal queue lengths are not equal-weight queues.
How to use the tool and how it works
- Enter queuesJson, seed using the definitions below. Serialize JSON text fields in the decoded shape shown below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.output, using the stated boundary, ordering, sign and absence conventions.
Maintain each queue’s next position. At each step choose a queue with probability proportional to its remaining item count, emit that next item and advance only that queue. Return queue/position/value provenance for every item.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| queuesJson | JSON array of string queues; the flattened nonempty sequence must have at most 128 entries. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| 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. |
These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.
{
"queuesJson": [
[
"a",
"b"
],
[
"c"
]
]
}| 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.output | Interleaved queue records retaining queue, original position and value. |
{
"input": {
"queuesJson": "[[\"a\",\"b\"],[\"c\"]]",
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"output": [
{
"queue": 0,
"position": 0,
"value": "a"
},
{
"queue": 1,
"position": 0,
"value": "c"
},
{
"queue": 0,
"position": 1,
"value": "b"
}
]
}
}
}Limitations and assumptions
- The nonempty flattened bank must contain at most 128 positions. Sampling is uniform over labeled order-preserving interleavings, not independent equal-probability queue choices.
- 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
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