The Hangzhou Normal U Qualification Trials for ZJPSC 2021

12 problems from The Hangzhou Normal U Qualification Trials for ZJPSC 2021 (contest 103462), difficulty -. 12/12 solutions verified against sample I/O.

12 items

The Hangzhou Normal U Qualification Trials for ZJPSC 2021

Special | 12 problems | 12/12 verified | Difficulty - | 10m 6s

#	Problem	Time	✓
A	Array Permutation	44s	✓
B	Baom and Fibonacci	56s	✓
C	Circle Minimal	48s	✓
D	Double Pleasure	46s	✓
E	Eaom and Longzhu	51s	✓
F	Fill the Binary String	48s	✓
G	Guess Strings	1m 1s	✓
H	Hsueh- And Treasure	1m	✓
I	Iaom and Chicken feet	45s	✓
J	Jew Sorting	53s	✓
K	K-Clearing II	41s	✓
L	Little H And Reboot	53s	✓

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CF 103462H - Hsueh- And Treasure

We are standing on an infinite grid starting at the origin. Each test gives a target coordinate, and we must construct a walk that eventually reaches that point. The movement rule is unusual: time is split into phases.

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CF 103462L - Little H And Reboot

We are given a set of rectangular boxes placed somewhere on a large 2D plane. Each box is described by four corner points in counterclockwise order, so every obstacle is a convex quadrilateral with arbitrary orientation, not necessarily axis-aligned.

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CF 103462J - Jew Sorting

We are given an array whose length is exactly a power of two, specifically $2^k$, where $k$ can be as large as 20. Each operation takes the current array and throws away exactly one half of it, either the left half or the right half, and keeps the other half unchanged.

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CF 103462K - K-Clearing II

We are given an integer array and a special value $k$. The process is dynamic: as long as the array still contains at least one element equal to $k$, we repeatedly apply an operation that decreases every positive element of the array by one.

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CF 103462G - Guess Strings

We are interacting with a hidden string of length at most 100. The string uses exactly two distinct lowercase letters, but we are not told which ones. Our only way to learn about it is by asking whether a chosen pattern appears as a contiguous substring of the hidden string.

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CF 103462I - Iaom and Chicken feet

We are given a tree, meaning a connected acyclic graph on $n$ nodes with $n-1$ edges. The task is to count how many distinct subgraphs of a specific shape appear inside this tree.

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CF 103462F - Fill the Binary String

We are given a binary string where some positions are already fixed as 0 or 1, while others are unknown and marked with ?. We are allowed to replace each ? with either 0 or 1, producing a fully binary string.

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CF 103462E - Eaom and Longzhu

We are given a directed or undirected weighted graph of rooms connected by portals. The traveler starts in room 1 and wants to reach room n. Every time he enters a room, he collects exactly one item called a “longzhu”, and each longzhu has one of 7 types.

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CF 103462D - Double Pleasure

We are given a large integer range $[A, B]$, and for each query we must count how many integers inside this range satisfy a special divisibility condition. For a number $x$, we compute the product of its decimal digits. Call this value $P(x)$.

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CF 103462B - Baom and Fibonacci

We are asked to evaluate a double summation over Fibonacci numbers indexed by pairs of integers up to a very large bound.

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CF 103462C - Circle Minimal

We are given a connected undirected graph with exactly one more edge than a tree would have. That means the graph contains exactly one cycle somewhere inside it, while the remaining edges form tree-like attachments to that cycle.

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CF 103462A - Array Permutation

We are building an array of length $n$ using a process that grows it in chunks. Initially the array is empty. At any moment, if the current length is $m$, we choose a number $x$ between $1$ and $n-m$. After choosing $x$, we append the sequence $1, 2, 3, dots, x$ to the array.