[kilotaras]

Story time.

Back in university I was taking part in programming competition. I don't remember the exact details of a problem, but it was expected to be solved as a dynamic problem with dp[n][n] as an answer, n < 1000. But, wrangling some numbers around one could show that dp[n][n] = dp[n-1][n-1] + 1/n, and the answer was just the sum of first N elements of harmonic series. Unluckily for us the intended solution had worse precision and our solution failed.

[HarryHirsch]

They didn't take into account that floats come with an estimated uncertainty, and that values that are the same within the limits of experimental error are identical? That's a really badly set problem!

[kilotaras]

I think it that particular case they just didn't do error analysis.

The task was to output answer with `10^-6` precision, which they solution didn't achieve. Funnily enough the number of other teams went the "correct" route and passed (as they were doing additions in same order as original solution).