As 2024 nears its end, let’s share the problems we enjoyed the most this year so far! Drop the problem name, link and what made it special (optional).
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
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2044F - Easy Demon Problem Quite an interesting problem, looked really hard but had an easy mathematical solution (Do give it a try if you haven't).
Would you mind giving some hints about it?
Think about how you could decompose the query that you have been given into parts that you can correlate with the orignal input.
Try factoring
Indeed, this is one of the best questions I came across this year.
1933E. Xor-Grid Problem It demonstrates the magical nature of XOR operations, completing the missing rows and columns in an array.
1919D — 01 Tree Everything fits so nicely together!
1878F - Vasilije Loves Number Theory
2029C - New Rating Although dp is easier to think here, the bin search solution is really satisfying.
1843E — Tracking Segments binary search on the prefix sum!
https://mirror.codeforces.com/contest/1931/problem/F It was such a nice thing to use cycle detection in a statement like this.
Universal Cup 3.11 O - New School Term
I enjoyed being trolled by this problem. The final observation is so natural, yet so invisible. As far as I know, some LGMs were also trolled.
Can you share the observation? My idea is a bit ugly.
I have a straightforward $$$O(n^2 \sqrt n \log n / w + m)$$$ solution. Try adding edges to a graph in decreasing order of index. Check if it is possible to add the current edge to the graph, such that it remains bipartite. If the current edge will destroy this property, then skip it.
Let the value of the component be abs((number of nodes in the first group) — (number of nodes in the second group)). You want to find if you can have a sum of 0 by multiplying some of the values of the components by $$$-1$$$. There are at most $$$n - 1$$$ edges that can merge two components. For each of these edges, you run a DP.
If the edge is wrong, it connects nodes of the same color. So you can merge the two components anyway.
I feel so stupid now ;-; Thanks!
1977D - XORificator never seen this trick before and thought it was unsolvable before seeing the tutorial
https://mirror.codeforces.com/problemset/problem/2042/E
ARC171E — Rookhopper's Tour
The setting feels very chaotic to me initially, but after thinking it though, it turns out there exist an elegant way to analysis the problem model very simply to make it solvable. It's just... astonishing!
https://mirror.codeforces.com/contest/1991/problem/H
D. YEET!
Not because I'm the author , but because the non-randomized solution is really satisfying and cool !
For Problems I solved , hmm
B. Shohag Loves Strings is cool.
D. Harder Problem is indeed a nice "harder" trolling problem .
https://mirror.codeforces.com/contest/321/problem/C
My 1st and only centroid decomposition AC
I don't know about best problem, but worst problem of the year is definitely problem C in APIO, the problem sucks A LOT
All of the median related problems which appeared in late 2024