Huazhong University of Science of Technology Freshmen Cup 2023

14 problems from Huazhong University of Science of Technology Freshmen Cup 2023 (contest 104728), difficulty -. 8/14 solutions verified against sample I/O.

14 items

Huazhong University of Science of Technology Freshmen Cup 2023

Special | 14 problems | 8/14 verified | Difficulty - | 20m

#	Problem	Time	✓
A	\u7b80\u5355\u7684\u52a0\u6cd5\u4e58\u6cd5\u8ba1\u7b97\u9898	1m 17s	✓
B	\u9006 KMP	1m 18s	✓
C	\u6392\u5217\u6392\u5e8f\u95ee\u9898	1m 8s	✓
D	\u7f51\u683c\u67d3\u8272	1m	✓
E	\u5e8f\u5217\u914d\u5bf9	2m 8s
F	\u65b0\u53d6\u6a21\u8fd0\u7b97	1m 35s
G	\u5e7f\u4e49\u7ebf\u6bb5\u6811	1m 38s	✓
H	\u72ed\u4e49\u7ebf\u6bb5\u6811	1m 39s
I	Fujisaki \u8ba8\u538c\u6570\u5b66	1m 3s	✓
J	\u57fa\u56e0\u7f16\u8f91	1m 44s
K	\u4e0d\u5b9a\u9879\u9009\u62e9\u9898	1m 16s	✓
L	Azur Lane	54s
M	\u8fd1\u4f3c\u9012\u589e\u5e8f\u5217	2m 21s
N	A+B problem	59s	✓

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CF 104728M - 近似递增序列

We are counting sequences of positive integers where the product of all elements is at most a given limit, and the sequence is “almost increasing” in the sense that along the sequence there is at most one position where the monotonic increase condition fails.

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CF 104728L - Azur Lane

We are given the final state of a sequence of loot boxes after several days of operations. Each day, some multiset of boxes was obtained, then internally sorted in non-increasing order of rarity, and appended to the existing sequence.

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CF 104728E - 序列配对

We are given a sequence of length $n$, initially all zeros. Alongside this sequence comes a list of $n$ pairing operations, each operation connects two indices $l$ and $r$.

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CF 104728J - 基因编辑

We are given a collection of DNA strings, each over the alphabet {A, C, G, T}. From any ordered pair of strings, we are allowed to form a new string by taking a prefix of the first string and concatenating it with a suffix of the second string.

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CF 104728H - 狭义线段树

We are given a fixed rooted binary tree with $2n-1$ nodes and $n$ leaves. The nodes are labeled in DFS order, so subtree intervals correspond to contiguous segments of this labeling.

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CF 104728G - 广义线段树

We are given a rooted binary tree with exactly $2n-1$ nodes. The leaves correspond one-to-one with positions of an array $a$, and every internal node represents a contiguous interval formed by merging its left and right children.

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CF 104728F - 新取模运算

We are given a prime number $p$, and many queries. Each query provides a huge integer $n$, and we need to evaluate a custom operation on $n!$.

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CF 104728B - 逆 KMP

We are given a length-n array of constraints. For each position i, a value a[i] tells us that the first a[i] characters of the final sequence must match a block of length a[i] ending at position i. In other words, for every i, the segment s[1..

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CF 104728D - 网格染色

We are given an $n times n$ grid of unit squares. The grid edges are initially uncolored. Two players alternate turns, with Walk Alone starting first. On each move, a player chooses any currently uncolored edge and colors it in their own color.

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CF 104728N - A+B problem

Each input consists of two single uppercase letters, and each letter represents a number in base 26 where A corresponds to 0, B to 1, and so on up to Z as 25.

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CF 104728K - 不定项选择题

We are dealing with a situation where there are $n$ distinct options, and the correct answer is some unknown non-empty subset of these options. Initially, no option is selected.

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CF 104728I - Fujisaki 讨厌数学

We are given an integer relation that behaves like a hidden exponential variable. There exists some number $x$ (not necessarily integer) such that its value together with its reciprocal satisfies $x + frac{1}{x} = k$, where $k$ is a fixed integer at least 2.

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CF 104728A - 简单的加法乘法计算题

We start with a value x = 0 and want to reach a target value y. We are allowed two types of operations. The first type adds any integer from 1 to n to the current value. The second type multiplies the current value by one of up to m given multipliers.

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CF 104728C - 排列排序问题

We are given a permutation of the numbers from 1 to n, and we want to transform it into the sorted sequence 1, 2, 3, ..., n using a special kind of restructuring operation.