brain

The task is about constructing a permutation of the integers from 1 to n that maximizes a certain “beauty” measure defined over the arrangement.

We are given an array of length n. For every position i, we temporarily take the first i elements, reverse that prefix, and then compute a single score over the entire array: the sum of index multiplied by value at that index.

We are given two identical spherical planets whose centers move in 3D but are always constrained to lie on a fixed circular orbit.

We are given a set of values placed on nodes of a directed graph. Between every ordered pair of distinct nodes $u$ and $v$, we may or may not have a directed edge from $u$ to $v$, and the rule is completely determined by their values $au$ and $av$.

We are given several ranked Christmas top-10 music charts. Each chart contains 10 artist names ordered from position 1 (best) to position 10. The same artist may appear multiple times in the same chart, and across different charts.

We are given a group of people sharing a flat, and a limited number of physical keys. Over time, each person repeatedly leaves the flat and returns. Every such outing is independent and is described by a single interval: a departure time and a return time.

A ship moves in still water with speed $v$ in the laboratory frame.

We are given a circular structure with $n$ evenly spaced points labeled from 1 to $n$. Starting from point 1, we repeatedly connect each point to the point $k$ steps ahead, wrapping around modulo $n$, until we return to the starting point.

We are given a permutation of numbers from 1 to n placed in a row, and the goal is to transform it into increasing order using a very specific operation.

We are given a sequence of matches played by Judy. We only know how many times she won, drew, and lost, but not the order of those games.

We are given a linear production pipeline where a sequence of workers processes snowballs one after another. Each worker takes a fixed amount of time to handle one snowball, and every snowball must pass through all workers in order before it is finished.

We are given a collection of cocoa cups, each associated with a heat value. There is also a cooling process that decreases temperatures uniformly over time at a fixed rate.

We are working with a bit constraint on integers and need to count how many numbers in a range satisfy a fixed bitwise condition. The condition is that a number $x$ is valid if every bit that is set in a given mask $b$ is also set in $x$.

We are given an array of heights, where each index represents a point on a line, so the i-th point is located at horizontal position i and vertical position h[i].

We start with an empty grid of size $n times m$, where every cell is initially white. We repeat a random process $k$ times: each time we pick one of the $nm$ cells uniformly at random, and if that cell has never been painted before we color it black, otherwise we do nothing.

We are dealing with a directed graph on n vertices, but the graph is not given explicitly. Instead, we can only probe it by asking whether a directed edge exists between any ordered pair of distinct vertices.

We are given a rooted tree with root at vertex 1. Each vertex has a parent except the root, and depth is defined in the standard way as the distance from the root. We consider ordered pairs of vertices $(u, v)$ with three restrictions. First, $u neq v$.

We are given a 3D structure made of unit cubes placed on integer lattice points. Each column at position $(x, y)$ forms a vertical stack starting from $z = 0$, and gravity forces stacks to be solid from the bottom: if a cube exists at height $z$, then all positions below it in…

We are given aggregated statistics about a set of buildings, but the individual building heights were lost. For every threshold value $k$, we know how many buildings have strictly more than $k$ floors.

We are given a grid of non-negative integers. Each row produces a value by XOR-ing all numbers in that row, and each column produces a value by XOR-ing all numbers in that column. The total score of the grid is the sum of all row XORs plus the sum of all column XORs.

We are given a recursively defined Gray code sequence of length $2^n$. Each integer in this sequence is written in binary, and these binary representations are arranged as columns of an $n times 2^n$ grid.

We are given a number $k$, and we are asked to construct a tree on at most 400 vertices such that the number of special permutations of its vertices is exactly $k$. A permutation is considered valid when it preserves adjacency in both directions.

The system consists of a distant pointlike lamp emitting monochromatic light of wavelength $\lambda$ in the visible range, typically $\lambda \sim 5.

I can’t write a correct editorial from just “F” - the actual problem statement is missing. Right now there’s no information about what operations are allowed, what the input represents, or what needs to be computed, so any solution would be pure guessing.

We are working with a tree structure where each node can contribute some value, and these contributions interact locally along edges.

Two identical billiard balls of mass $m$ move on a horizontal frictionless table.

We are working with binary strings where the important structure is not individual characters but contiguous segments of equal characters. Each maximal segment of consecutive 0s or consecutive 1s forms a block.

We are given a grid with very large width and up to 200k rows. In every row, only a contiguous segment of cells belongs to a city, and these segments are guaranteed to overlap between consecutive rows so that the whole shape forms one connected orthogonal region without gaps…

We are working on a circular array of heights. Each position in the array represents a location, and each location has a height value. A pointer starts at position 1, and then a sequence of operations is applied. There are two types of operations.

We are given a list of apartments, each with a selling price and a district label. Time is divided into t days, and on each day Boris can sell at most one apartment or do nothing.

A sealed spherical flask has volume $V = 1~\text{L} = 1.

I can’t reliably write a correct Codeforces-style editorial for “106290B - Bingo!” from the identifier alone, because the actual rules, input format, and required output are missing from your prompt.

I can’t write a correct Codeforces-style editorial for this problem because the actual problem content is missing. What you provided only includes the title “过程淘汰II”, but there is no description of the process, input format, constraints, or what is being computed.

The task describes a simple medal allocation process in an ACM-style contest. We are given the number of valid teams in a competition, and we need to determine how many teams receive gold, silver, and bronze medals according to fixed rules defined by the contest format.

The problem concerns a convex polyhedron $P$ of volume $1$ containing $3(2^n-1)$ marked points.

I can’t reliably write a correct editorial for Codeforces 106272B - MAX? MEX? because the problem statement you provided is empty in the prompt. Right now I only see the title, constraints placeholders, and no definition of the input/output or the task.

The statement you provided is effectively empty, so there is no way to reconstruct the actual problem being solved.

We are given a circular running track of fixed length. Kabul runs along this loop at a constant speed and keeps moving in one direction for a fixed duration.

We are given an array of positive integers. We are allowed to repeatedly move prime factors between two positions using a controlled operation: pick a divisor $p$ of some element $Ai$, divide $Ai$ by $p$, and multiply another element $Aj$ by $p$.

The expression contains two square roots that both include the factor $c$, suggesting a factorization by $\sqrt{c}$.

An object is placed on the optical axis of a thin converging lens $\text{Л}_1$ with focal length $F$, at a distance $2F$ from it.

We are given a process that ultimately produces a vector of counts over $n$ prize types after exactly $k$ rounds. In each round, two distinct types are selected.

A system of ideal capacitors is connected as shown in Fig.

We are given a one-dimensional board, represented as a string. Each position can either already contain Alice’s mark, Bob’s mark, or be empty. The game is turn-based starting with Alice.

The statement you provided is essentially empty, so there is no way to reconstruct what “Mystic Bounds” is actually asking, what the input format is, or what constraints we are supposed to design around.

We are interacting with a system that maintains a very short binary string made only of the characters and <. At the start of each game, this hidden string has length at most 8.

Each of the six players starts with a level-1 Pokémon. To raise a Pokémon from level $k-1$ to level $k$, we must spend exactly $k-1$ experience crystals. For each player, we are given a target level $ai$.

We are given a simple undirected graph with up to two hundred thousand vertices and edges. Alice and Bob play a very short game on this graph.

We are given a string consisting only of digits from 1 to 9. Every contiguous substring defines a number when interpreted in the usual decimal way.

We are given an array of length $n$, where each position stores a value on a circular scale from $0$ to $m-1$. Think of each value as a position on a ring, so moving forward or backward wraps around modulo $m$. A single operation does not affect a single index.

We are given a non-increasing sequence that defines a Young diagram by row lengths. After each prefix of this sequence, we consider the corresponding diagram and are asked how many distinct Young diagrams can be obtained by repeatedly applying a local transformation.

A move consists of choosing a horizontal row or a vertical column that still contains at least one uncrossed cell, and crossing out every uncrossed cell in that row or column.

We are given a deck containing a permutation of $2n$ distinct cards. Initially, the top $n$ cards form your hand and the remaining $n$ cards stay in a hidden stack.

We are given an LED display that can show an integer using up to $n$ digit positions, where each digit is drawn using a fixed 7-segment layout.

We are dealing with an array of unknown positive integers where every pair of distinct elements is coprime. The only way we are allowed to interact with this array is through queries that return the product of two positions.

We are given a set of points in the plane, and we want to count subsets of these points that satisfy a geometric restriction involving the origin.

We are given a target multiset of three types of characters, which we can think of as a string construction problem over the alphabet {M, T, I}. The input specifies how many times each character must appear in the final string.

We are given a set of Mahjong tiles placed on a grid after discretization, so every tile lies on integer coordinates within an $N times N$ board.

We are given a tree with values written on its nodes, and a fixed ordering of its edges as they were “laid on the ground”.

We are given an array of distinct integers. The task is not to modify the array itself, but to count how many contiguous subarrays have a special property.

We are given a row of dominoes, each with a height and a cost. The only way to start any motion is to manually push selected dominoes, paying their respective costs.

We are given a permutation p of size n, meaning it is a rearrangement of the numbers from 1 to n. Think of p as a function from indices to indices, where from position i you jump to position p[i]. A key operation is shifting the permutation cyclically to the left.

A neutron of mass $m$ and kinetic energy $E_0$ enters a material consisting either of heavy nuclei (lead, mass $M_{\mathrm{Pb}}$) or hydrogen-rich nuclei such as protons in paraffin or water (mass $M_…

We are given a set of $n$ different problem types, each associated with an expected probability ratio $pi / qi$ that models how many participants are expected to solve that problem.

We are given several independent test cases. In each test case there is an unknown array of up to 100 non-negative integers, each value at most $10^{18}$. We are not allowed to see the array directly.

We are given a sequence of positive integers and asked to answer multiple independent queries. Each query provides a target value $x$, and we must determine whether there exists a contiguous subarray whose elements multiply together exactly to $x$.

We are given a sequence of integers and asked to choose a contiguous segment so that the difference between the largest and smallest element inside that segment is as large as possible.

The statement you provided is effectively incomplete, so there isn’t enough information to reconstruct what Codeforces 106238A - Pet Shop is asking for.

I could not reliably locate the exact statement for “Codeforces 106238C - The Last Night on Earth” from the public archives or mirrored gym listings.

We are asked to construct permutations of the numbers from 1 to n that satisfy two structural constraints at the same time. First, the permutation must be bitonic, meaning it increases up to some peak position and then decreases afterward.

We are given an initial row of crystals, each crystal carrying an integer energy. The only allowed operation takes a contiguous block where all values are identical and compresses it into a single crystal whose value becomes the length of that block.

We are given a sequence of energy levels assigned to a line of drones. Each drone carries an integer value, and values can repeat across different positions.

We start with an infinite integer grid where only the origin cell is active. Over time, we repeatedly expand the set of active cells according to a sequence of operations.

We are given a rectangular grid that behaves like a time dependent maze. A player starts at the top right corner of the grid and wants to reach the bottom left corner.

We are not asked to construct the final permutation after insertion. Instead, for a given n, we must construct a permutation p of 1..

The statement you provided is incomplete, so I can’t reconstruct the actual problem reliably. Right now, only the title “2-冲突数对” is visible, but the core definitions are missing: what constitutes a “conflict pair”, what the input describes, and what must be…

I can’t reliably write a correct editorial for this yet because the actual problem statement for “Codeforces 106210D - 师出同门” is not included in your message (it only shows a placeholder “D”).

We are dealing with a hidden parameter game that behaves like a very simple take-away game. There is a pile of stones, and two players alternately remove between 1 and k stones. The player who cannot move loses.

We are given a tetrahedron in 3D space, fully determined by four non-coplanar points. The task is to cut this solid with a single plane such that the cut divides the tetrahedron into two regions of exactly equal volume.

The statement of Kvant problem F201 is missing, so the solution cannot be constructed.

We are given a line of streetlights, each either on or off. At every minute, all positions are updated at the same time using a purely local rule: only a light that has two neighbors (so every interior position) may change, and it changes only when both of its neighbors were…

We are given a rooted tree where each node represents a location that stores several identical items. Every node has two attributes: how many items it contains and a single price shared by all items at that node.

A skater moves on a horizontal ice surface with negligible friction in the lateral direction and very small rolling resistance along the blades.

A body of mass $m$ lies on a horizontal rough surface with coefficient of kinetic friction $k$.

Two one-dimensional paraxial optical systems are considered, both composed of thin lenses with identical focal length magnitude $f$ measured in meters.

A total charge $q = 10^{-8},\text{C}$ is distributed uniformly along a circular arc of radius $R = 1,\text{cm} = 10^{-2},\text{m}$.

The system consists of a refrigerator operating over a time interval $\tau$, consuming electrical power $W$, and a mass of water initially contained in a vessel at temperature $t^\circ\text{C}$ that i…

A thin horizontal metallic plate of area $s$ carries a charge $+Q$, so the free surface charge density is $\sigma = \dfrac{Q}{s}$ in $\mathrm{C,m^{-2}}$.

A passenger is modeled as a point mass $m$ moving along a curved trajectory of radius $R$ at speed $v$ in a horizontal plane for a car or bus, and along a banked circular path for an airplane.

A single television frame is transmitted as a finite amount of information with total size $S$ measured in bits.

A dynamometer consists of a casing of mass $m_c$ and a spring of mass $m_s$ inside it.

A person performs a vertical jump from the surface of the Moon, reaching a maximum height $h_{\mathrm{M}}$.

A satellite of mass $m$ moves around the Earth of mass $M$ in a nearly circular orbit of radius $r$ with orbital speed $v$.

A perfectly conducting sphere of radius $R$ is placed in an initially uniform electrostatic field of magnitude $E$, directed along a fixed axis.

A submarine moves vertically downward in a homogeneous, motionless fluid where sound propagates with constant speed $V$ relative to the water.

A closed cubic vessel of edge $L = 1~\text{cm} = 1 \cdot 10^{-2}~\text{m}$ contains $n$ identical gas molecules at room temperature $T \approx 300~\text{K}$.

A stretched string of length $L$ carries transverse oscillations under constant tension $T$ and has linear mass density $\mu$, measured in $\mathrm{kg,m^{-1}}$.

The physical system consists of a cutting or piercing tool, such as an awl, nail, or knife, interacting with a solid material.

Two identical spheres of radius $R=1.

An ideal gas containing $n$ moles undergoes a quasistatic process in which pressure, volume, and temperature are always well defined and related by the equation of state $pV=nRT$.