Problem 43592. Sample from random roulette

Created by Jakub Rysanek

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Given a list of values and their probabilities sample 10,000 values.
Example:
x = [1 2 3 4 5];
prob = [0.2 0.1 0.4 0.1 0.2]
Note that sum(prob)=1. Function output should look like this:
output = [1 4 3 1 4 1 2 3 1 1 1 ... 3 4 2] % a vector of length 10,000
All vectors are meant to be row vectors.

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Last Solution submitted on Nov 14, 2024

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Peng Liu on 23 Oct 2016

Completely irrelevant test suite.

Jakub Rysanek on 23 Oct 2016

How would you test random output? : )

Peng Liu on 23 Oct 2016

One possible way is to compute the empirical distribution based on a large number of random samples, and then compare the empirical distribution with the true distribution (up to a specified tolerance). Taking integer samples as an example, x = histcounts(data, [unique(data) Inf], 'Normalization','probability') returns the empirical probability of data.

Jakub Rysanek on 23 Oct 2016

That is exactly how the code validation is done (it mimics the central limit theorem), except I set the admissible variance sufficiently large in case someone ends up as outlier. Anyway, I changed it a little today so that "deterministic" solution does not get accepted any more...

Peng Liu on 23 Oct 2016

Your test is very weak. It does not fully reflect the random sampling procedure.

Peng Liu on 23 Oct 2016

See my new solution which takes advantage of the weakness of your test suite. It is essentially "deterministic", but it passes your test.

David Verrelli on 20 Nov 2017

Hi, Jakub. One more fairly simple check you could add would be to ensure that the result of diff( output ) does not produce mostly zeros. .... BTW, you do not need to put all checks inside one assert command. Indeed, it may be helpful for players to know which assertion is tripping them up, with the addition of text error messages. —DIV

David Verrelli on 21 Nov 2017

To be fair, Jakub, it is certainly a lot of work to set up a robust Test Suite for this problem. It is not possible to make a perfect Test Suite that will stop all cheating, so the plan would be just to make cheating difficult in comparison to a genuine solution. BTW, the leeway you allow on the sums (±50%) seems too generous. According to https://www.mathworks.com/matlabcentral/cody/problems/43592-sample-from-random-roulette/solutions/1351272 it seems ±2% would be about right, or perhaps ±5% if you still want to be extremely conservative / very generous.

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Problem 43592. Sample from random roulette

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Problem 43592. Sample from random roulette

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