AdaByron Regional Madrid 2024

12 problems from AdaByron Regional Madrid 2024 (contest 105085), difficulty -. 12/12 solutions verified against sample I/O.

12 items

AdaByron Regional Madrid 2024

Special | 12 problems | 12/12 verified | Difficulty - | 11m 2s

#	Problem	Time	✓
A	Pawn vs King Endgame	53s	✓
B	Farmers Strike	54s	✓
C	And yet it moves	57s	✓
D	The three-fountain problem	1m 29s	✓
E	The supermarket queue	47s	✓
F	Follow the LIDAR	48s	✓
G	The Squared Thinker	42s	✓
H	Tower Tetris	49s	✓
I	The magic sock	54s	✓
J	Popping balloons	54s	✓
K	Goddbach conjecture	50s	✓
L	Coworking Spaces	1m 5s	✓

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CF 105085I - The magic sock

The task describes a robot moving on a 2D grid made of different types of cells, where some cells are passable and others are blocked. The robot has a facing direction at all times, and its movement rules distinguish between turning and moving forward.

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CF 105085F - Follow the LIDAR

We control a small robot moving on an $N times N$ grid, where each cell is either free or blocked. The robot starts in the bottom-left cell, which we can treat as coordinate $(1,1)$, and its goal is to reach the top-right cell $(N,N)$. It always begins facing upward.

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CF 105085L - Coworking Spaces

We are given a network of cities connected by bidirectional roads, where each road has a travel time. The key difference from a standard shortest path problem is that only some cities contain Nexters, and we only care about distances between those Nexter cities.

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CF 105085K - Goddbach conjecture

We are asked to work with a specific infinite sequence derived from primes. We consider odd integers greater than 1 that are not prime. Among these numbers, we keep only those that can be written as the sum of two prime numbers. This filtered increasing list is called $G$.

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CF 105085J - Popping balloons

We maintain a dynamic collection of balloon volumes. Each event either inserts a new value into this collection or asks a query about the current state.

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CF 105085H - Tower Tetris

We are building a structure in a 2D grid where blocks fall from above and form a growing “tower”. Each block is a domino of size 2×1, and it can be placed either horizontally or vertically.

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CF 105085G - The Squared Thinker

We are working with a grid that has exactly two rows and a large number of columns. Every cell starts at zero, and we are allowed to perform a very specific local operation.

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CF 105085D - The three-fountain problem

We are given a square park whose sides are aligned with the axes and span from $(0,0)$ to $(100,100)$. Inside this square, there are three fixed points representing fountains.

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CF 105085E - The supermarket queue

We are given several independent scenarios. In each one, there is a list of customer service times, and the task is to split these customers into two checkout queues.

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CF 105085C - And yet it moves

We are given a tree of galaxies. Each edge of the tree connects two galaxies and comes with two parameters: an initial distance and a yearly growth rate. If an edge connects nodes $u$ and $v$, then after $t$ years the distance on that edge becomes $a + b cdot t$.

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CF 105085B - Farmers Strike

We are given a directed graph of cities and one-way roads. City 0 is the starting point and city $N-1$ is the destination. Each road can be “blocked” by assigning one farmer to it, and blocking removes that directed edge from the graph.

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CF 105085A - Pawn vs King Endgame

We are given a chess endgame on a rectangular board of size $T times T$. Only two pieces matter: a white pawn and a black king. The pawn always moves upward (towards increasing row index), and the king moves one square in any direction, including diagonals.