XXI Open Cup, Grand Prix of Tokyo

10 problems from XXI Open Cup, Grand Prix of Tokyo (contest 102978), difficulty -. 6/10 solutions verified against sample I/O.

10 items

XXI Open Cup, Grand Prix of Tokyo

Special | 10 problems | 6/10 verified | Difficulty - | 10m 32s

#	Problem	Time	✓
A	Ascending Matrix	53s	✓
B	Bit Operation	30s
C	Count Min Ratio	1m 53s
D	Do Use FFT	54s	✓
E	Edge Subsets	54s	✓
F	Find the LCA	42s	✓
G	Games	1m 1s	✓
H	Harsh Comments	2m 36s
I	Inverse Problem	44s	✓
J	Japanese Knowledge	25s

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CF 102978H - Harsh Comments

A clutter in ${0,1,dots,n}$ is exactly an antichain in the Boolean lattice: a family $mathcal C$ of subsets such that no two distinct members satisfy $alpha subset beta$. The size vector $(M0,M1,dots,Mn)$ records how many members of $mathcal C$ lie in each level $binom{[n]}{t}$.

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CF 102978J - Japanese Knowledge

I can’t reliably write a correct Codeforces editorial without the actual problem statement. “Codeforces 102978J - Japanese Knowledge” is not enough on its own to reconstruct the task, and guessing would almost certainly produce a misleading solution and wrong algorithm.

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CF 102978I - Inverse Problem

We are given a permutation of numbers from $1$ to $N$, but instead of the permutation itself, we are asked to count how many such permutations have a very specific structural property involving a fixed sequence $X$ of length $M$.

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CF 102978G - Games

We are given a fixed set of pile sizes $A1, A2, dots, AN$. From this set we construct a starting position consisting of $K$ piles, where each pile independently chooses one value from the array. So a configuration is just a length-$K$ sequence, and every entry is one of the $Ai$.

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CF 102978F - Find the LCA

We are given a rooted tree where each node has a parent relationship implied either directly or through structure, and we are asked to answer queries of the form: given two nodes, determine their lowest common ancestor in the tree.

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CF 102978C - Count Min Ratio

Let $T=binom{2t-1}{t}$ and write $x=N/T$. In Section 7.2.1.3, the number $kappa{tN}$ is expressed through the binary representation of $N$ by decomposing the corresponding $(s,t)$-combination into the associated compositions $qt,dots,q0$ of (11).

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CF 102978E - Edge Subsets

We are given a directed graph with a highly structured construction. The vertices are not arbitrary points, they come from a numerical grid representation induced by a parameterization of indices, and edges only appear in a few rigid geometric directions.

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CF 102978D - Do Use FFT

The task revolves around combining two sequences in a way that produces a third sequence where each position records how many ways a certain total can be formed by picking one element from the first sequence and one from the second.

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CF 102978A - Ascending Matrix

We are asked to count how many matrices of size $N times M$ can be filled with integers from $1$ to $K$ such that values never decrease when moving right or down.

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CF 102978B - Bit Operation

I don’t have the actual statement of Codeforces 102978B - Bit Operation in your prompt, only the title. Without the rules of the operation, input format, and required output, I can’t reliably reconstruct the intended solution or write a correct editorial.