2023 Argentinian Programming Tournament (TAP)

14 problems from 2023 Argentinian Programming Tournament (TAP) (contest 104603), difficulty -. 13/14 solutions verified against sample I/O.

14 items

2023 Argentinian Programming Tournament (TAP)

Special | 14 problems | 13/14 verified | Difficulty - | 13m 27s

#	Problem	Time	✓
A	Alfajores	50s	✓
B	Black and white	45s	✓
C	Chromatic	2m 1s	✓
D	Assigning problems	35s	✓
E	Finding progressions	46s	✓
F	Cold day at the beach	43s	✓
G	Great Heights	50s	✓
H	Robotic Skills	1m 18s	✓
I	Regional Integration	1m 10s	✓
J	Jester in danger	48s	✓
K	Kitties	1m 8s	✓
L	Game series	45s	✓
M	Multiple Downloads	1m 1s
N	Lucky Number	47s	✓

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CF 104603N - Lucky Number

We are given a multiset of integers representing cards. Each card has a value, and we want to partition some of these cards into as many disjoint groups as possible. A group is valid if the sum of all values inside it is divisible by 5.

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CF 104603K - Kitties

We are maintaining a dynamic set of axis-aligned rectangles drawn inside a large vertical panel. The panel has fixed width and a fixed total height, and at any moment the user only sees a horizontal window of height equal to the screen height.

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CF 104603M - Multiple Downloads

The solution does not correctly establish the existence of a sequence satisfying Definition R5 while enforcing the prefix constraint.

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CF 104603L - Game series

The task describes a two-match football series between two teams, Archimedians F.C. and Pithgoreans F.C. Each match produces a score for both teams, and the winner of the series is decided by summing goals across both matches.

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CF 104603H - Robotic Skills

We are given an $N times N$ grid where every cell contains a distinct integer from $1$ to $N^2$. A robot moves in straight segments aligned with the grid axes.

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CF 104603J - Jester in danger

We are given an undirected graph with two special nodes: city 1 and city N. These act as fixed endpoints, and we care about how “efficient” a route between them can be.

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CF 104603I - Regional Integration

We are given a collection of geometric regions in the plane, each region being either a disk, a square, or a triangle. All regions are disjoint even on their boundaries, so no two shapes touch. We must choose exactly one square and one triangle.

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CF 104603G - Great Heights

We are given a set of horizontal platforms placed at different heights above the ground. Each platform occupies an interval on the x-axis, and is located at a fixed height. You can think of each platform as a segment floating in 2D space, all parallel to the ground.

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CF 104603F - Cold day at the beach

Two teams take turns throwing discs onto a rectangular beach court. Each throw is a point in a 2D plane, and there is a fixed target point, the “tejin”, somewhere inside the same rectangle. The score is determined entirely by Euclidean distance to this target.

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CF 104603C - Chromatic

We are given many independent pairs of integers $(a, b)$. For each pair, we must decide whether it is possible to construct four positive integers $u, v, x, y$ such that two constraints are satisfied simultaneously. First, $a = u + v$, and both $u$ and $v$ must divide $b$.

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CF 104603E - Finding progressions

We are asked to count how many arithmetic progressions of integers exist that satisfy three constraints simultaneously. Each valid progression is a sequence with a positive common difference, so it strictly increases. Every term must lie inside a fixed interval from L to R.

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CF 104603D - Assigning problems

We are given a fixed structure for a contest: each contest has $K$ difficulty levels, and level $i$ requires exactly $Ci$ problems. Problems are categorized by a minimum usable level: a problem of grade $d$ can only be assigned to levels $d, d+1, dots, K$.

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CF 104603A - Alfajores

We are given a fixed sequence of office groups, where each office has a certain number of employees, and a sequence of trips. On each trip, Seba starts with a box containing a given number of alfajores. He visits offices in order.

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CF 104603B - Black and white

We are given an $N times N$ grid where each cell is either usable (black) or forbidden (white). The task is to place as many horizontal dominoes as possible, where each domino covers exactly two adjacent cells in the same row.