Winter Cup 5.0 Online Mirror Contest

14 problems from Winter Cup 5.0 Online Mirror Contest (contest 105018), difficulty -. 12/14 solutions verified against sample I/O.

14 items

Winter Cup 5.0 Online Mirror Contest

Special | 14 problems | 12/14 verified | Difficulty - | 11m 33s

#	Problem	Time	✓
A	Antiprefix Function	52s	✓
B	GCD LCM SUM	50s	✓
C	Rooks	56s	✓
D	Casino I	1m 2s	✓
E	Casino II	1m 7s	✓
F	Expected Runtime	1m 4s	✓
G	Find The Array	56s	✓
H	Balance The sequence	47s	✓
I	Hall of Faces	42s	✓
J	Multiplicative Array	30s
K	Splitting Game	46s	✓
L	Good Transformations	54s	✓
M	Colour the Banners	22s
N	The Volcano And the Dragon Egg	45s	✓

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CF 105018N - The Volcano And the Dragon Egg

The problem describes a volcanic pit represented as an $n times m$ grid where each cell stores how much higher that point is compared to the magma level at time zero. Cells with value zero are already at magma level, meaning they are submerged immediately.

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CF 105018L - Good Transformations

We are given an integer $m$ and a linear transformation on integer grid points of the form $$T(i, j) = (a i + b j,; c i + d j),$$ where $a, b, c, d$ are integers in the range $[0, m-1]$. The plane is also partitioned into $m times m$ blocks.

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CF 105018M - Colour the Banners

Codeforces 105018M: Colour the Banners

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CF 105018K - Splitting Game

We are given a multiset of positive integers, stored as an array. Two players alternate turns, starting with the first player.

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CF 105018J - Multiplicative Array

We are given an array indexed from 1 to n with a special multiplicative structure, but that structure is not what we directly compute with. Instead, the process repeatedly transforms the array using divisor aggregation.

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CF 105018G - Find The Array

We are asked to construct any integer array such that its prefix sums and suffix sums satisfy four extremal conditions simultaneously. For a chosen array, consider the running prefix sum sequence that starts from zero and accumulates elements from left to right.

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CF 105018H - Balance The sequence

We are given a string that consists only of opening and closing brackets. The string is guaranteed to be “balanced” in the classical sense, meaning it can be turned into a valid arithmetic expression if we insert plus signs and ones between characters.

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CF 105018I - Hall of Faces

We are given a circular arrangement of labeled faces. Each position contains a string label describing the face, and exactly one position is marked with the label "Jaqen", which represents the current position of the traveler.

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CF 105018F - Expected Runtime

We start with a number R = 1 and repeatedly multiply it by uniformly random integers from 0 to n-1. After each multiplication we check whether the current value is divisible by n.

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CF 105018E - Casino II

We are given a long sequence of real numbers between 0 and 1, and a fixed number of rounds $k$. We traverse the sequence from left to right exactly once, and we cut it into $k$ consecutive parts.

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CF 105018D - Casino I

We are playing a repeated interactive betting game against a dealer. In each round, both sides build a score starting from zero by repeatedly drawing random values uniformly from the interval $[0,1]$. On your turn you decide whether to draw another random value or stop.

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CF 105018C - Rooks

We are given an $n times n$ grid and several rooks placed on distinct cells. A rook controls every cell in its row and every cell in its column. A cell is considered “safe” only if no rook shares its row or column. The operation allowed is removing rooks from the board.

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CF 105018A - Antiprefix Function

We are given a binary string and asked to compute, for every prefix ending at position i, how well that prefix can be matched by a previous prefix of the string under a very strict rule. For a fixed position i, we try all possible lengths j from 0 up to i-1.

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CF 105018B - GCD LCM SUM

We are trying to construct two positive integers $a$ and $b$, with $a le b$, under a very specific arithmetic constraint involving their greatest common divisor and least common multiple.