Full cycle

<h2 id="example-1-in-cc">Example 1 (in C/C++)</h2>
<p>Given a random number seed that is greater or equal to zero, a total sample size greater than 1, and an increment <a href="/facts/Coprime_integers/bnCxCXxs">coprime</a> 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.
</p>
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;
}

<h2 id="example-1-in-python">Example 1 (in Python)</h2>
# 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))

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Linear_congruential_generator/E4PyJQ5U">Linear congruential generator</a></li>
<li><a href="/facts/Xorshift/N6cr5Tfw">Xorshift</a></li></ul>

Full cycle open-in-new

Full cycle