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title: "Full cycle" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["pseudorandom-number-generators", "articles-with-example-python-(programming-language)-code"] description: "Behavior used in pseudorandom number generation" topic_path: "general/pseudorandom-number-generators" source: "https://en.wikipedia.org/wiki/Full_cycle" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Behavior used in pseudorandom number generation ::

In a pseudorandom number generator (PRNG), a full cycle or full period is the behavior of a PRNG over its set of valid states. In particular, a PRNG is said to have a full cycle if, for any valid seed state, the PRNG traverses every valid state before returning to the seed state, i.e., the period is equal to the cardinality of the state space.

The restrictions on the parameters of a PRNG for it to possess a full cycle are known only for certain types of PRNGs, such as linear congruential generators and linear-feedback shift registers. There is no general method to determine whether a PRNG algorithm is full-cycle short of exhausting the state space, which may be exponentially large compared to the size of the algorithm's internal state.

Example 1 (in C/C++)

Given a random number seed that is greater or equal to zero, a total sample size greater than 1, and an increment coprime to the total sample size, a full cycle can be generated with the following logic. Each nonnegative number smaller than the sample size occurs exactly once.

::code[lang=cpp] unsigned int seed = 0; unsigned int sample_size = 3000; unsigned int generated_number = seed % sample_size; unsigned int increment = 7;

for (unsigned int iterator = 0; iterator < sample_size; ++iterator) { generated_number = (generated_number + increment) % sample_size; } ::

Example 1 (in Python)

::code[lang=python]

Generator that goes through a full cycle

def cycle(seed: int, sample_size: int, increment: int): nb = seed for i in range(sample_size): nb = (nb + increment) % sample_size yield nb

Example values

seed = 17 sample_size = 100 increment = 13

Print all the numbers

print(list(cycle(seed, sample_size, increment)))

Verify that all numbers were generated correctly

assert set(cycle(seed, sample_size, increment)) == set(range(sample_size)) ::

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::