CCF CAT 2024

10 problems from CCF CAT 2024 (contest 105267), difficulty -. 10/10 solutions verified against sample I/O.

10 items

CCF CAT 2024

Special | 10 problems | 10/10 verified | Difficulty - | 10m 21s

#	Problem	Rating	Tags	Accepted	Time	✓
A	2026\u7f8e\u52a0\u58a8\u4e16\u754c\u676f				1m 12s	✓
B	Stop! High School Maths Please No More				58s	✓
C	Diamond				1m 17s	✓
D	A xor B problem				1m 7s	✓
E	Rolling for the Destination				56s	✓
F	\u9759\u6d41\u7684\u8def\u5f84				1m 4s	✓
G	Candidate Master of Both (VI)				53s	✓
H	Duel on the Chessboard				57s	✓
I	\u9ec4\u91d1\u6811				1m 6s	✓
J	\u7b80\u5355\u7684\u6307\u6570\u8fd0\u7b97				51s	✓

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CF 105267C - Diamond

We are given a set of points in the plane and need to count how many distinct selections of five points can form a very specific geometric configuration called a “diamond”. A valid diamond is not just any 5-tuple.

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CF 105267D - A xor B problem

We are working in a very unusual “programming model” where we do not directly compute expressions like XOR, but instead manipulate 32-bit variables through a small instruction set.

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CF 105267J - 简单的指数运算

We are given two numbers: a positive integer $N$ and a prime $P$. The task is to compute a double sum over all ordered pairs $(i, j)$ where both indices run from $1$ to $N$.

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CF 105267I - 黄金树

We are given a rooted tree where every node starts with an initial positive integer value. Time evolves in discrete steps, and each node carries a value that changes every day according to a local rule involving its parent. At day zero, each node i has a value a[i].

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CF 105267H - Duel on the Chessboard

We are given a small grid with obstacles and two special cells containing pieces A and B. Initially these two pieces occupy adjacent cells.

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CF 105267G - Candidate Master of Both (VI)

We are given an array of length $n$, and for every pair of indices $(l, r)$ with $l le r$, we define a value that depends on whether the greatest common divisor of the two endpoints equals a chosen parameter $k$.

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CF 105267F - 静流的路径

We are given a number $N$ that is fully described by its prime factorization. Every prime $pi$ appears with the same exponent $m$, so $N = p1^m p2^m cdots pk^m$.

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CF 105267E - Rolling for the Destination

We start at position zero on an infinite number line and repeatedly roll a fair four-sided die, which produces one of the values 1, 2, 3, or 4 with equal probability. After each roll we move forward by the rolled amount.

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CF 105267A - 2026美加墨世界杯

We are simulating the final round of a four-team football group. Three matches are already known: China has already played two matches against Thailand, and now only the last round remains, consisting of China versus Korea and Thailand versus Singapore.

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CF 105267B - Stop! High School Maths Please No More

We are given an array of positive integers and we are allowed to overwrite elements arbitrarily. Each overwrite picks an index and assigns it any positive integer value. The goal is to transform the array into a geometric progression whose common ratio is a positive integer.