Coding and AI classes in Penarth

The Met Office publishes monthly records for its historic station in Bute Park, Cardiff, about 6 km north of Penarth's town centre, going back to September 1977. The learner takes the average daily maximum temperature for each month, keeps the 48 complete calendar years from 1978 to 2025, and averages the twelve months of each year. The coolest year by this measure was 1979 at 13.03 °C and the warmest 2022 at 16.36 °C. A few dozen monthly values are marked by the Met Office as estimated, and the page treats the averages as our own calculation, not an official statistic.

The question is the longest increasing subsequence: pick years in time order, skipping as many as you like, so that each picked year is warmer than the one picked before it. The longest run of years rising one after another without a gap is only 5, from 1986 to 1990. Allow gaps and the chain gets far longer. The learner finds a chain of 16: 1979, 1985, 1987, 1991, 1992, 1994, 1998, 2000, 2002, 2004, 2005, 2006, 2014, 2020, 2023 and 2025, each warmer than the last.

Brute force really is hopeless. The learner times it on the first 20 years, which already means 1,048,575 selections and 0.8 seconds on our laptop; each extra year doubles the work, so all 48 years would take roughly seven years of computing. Dynamic programming works year by year, asking for each one: what is the longest chain that ends here? Patience sorting deals the temperatures into piles like the card game, always placing a card on the leftmost pile whose top card is warmer, and the number of piles at the end is the answer. Dynamic programming and patience sorting both give 16, and on the first 12, 16 and 20 years, where brute force can finish, all three agree.

Is 16 a lot? The learner shuffles the 48 values into random order 10,000 times and finds the longest chain in each. Shuffled years give chains of 10.9 on average, and only 10 of the 10,000 shuffles reached 16. So the real order of the years produces a much longer rising chain than chance usually does. The project stops at that statement. It does not try to explain why, which would need far more than one weather station and one algorithm.

For a teenager in Penarth, knowing why one algorithm finishes and another never will lets them judge AI-written code instead of trusting it, and that judgement is learned by writing algorithms. The longer argument is in why algorithms are still worth learning in 2026.