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Aspen Avenue Description: ## Input The input file starts with a positive even integer $N$ between $4$ and $2\, 000$ (inclusive), giving the total number of trees in the avenue. The next line contains two integers $L$ and $W$, where $1 \le L \le 10\, 000$ is the length of the road, in meters, and $...
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Assassins Description: Assassins generally lay careful plans before executing them, including planning multiple attempts to dispose of the same target, with the second attempt being a backup in case the first attempt fails, the third attempt being a secondary backup, and so on. Using their great annihi...
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Assembly Line Description: The last worker in a production line at the factory of Automated Composed Machinery is worried. She knows that her job hangs in the balance unless her productivity increases. Her work consists of assembling a set of pieces in a given sequence, but the time spent on assembling...
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Assigning Workstations Description: Penelope is very lazy and hates unlocking machines for the arriving researchers. She can unlock the machines remotely from her desk, but does not feel that this menial task matches her qualifications. Should she decide to ignore the security guidelines she could simp...
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Assistant Ranking Description: The online retailer Amagoogsoftbook currently offers $N$ different so-called “home assistants”, which it wants to recommend to its customers. For this recommendation, they wish to rank all the assistants. The quality of this ranking is not very important – multiple as...
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Association for Computing Machinery Description: ACM (Association for Computing Machinery) organizes the International Collegiate Programming Contest (ICPC) worldwide every year. In the ICPC, a team of three students is presented with a problem set that contains $N$ problems1 of varying types and diff...
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Association for Control Over Minds Description: You are the boss of ACM (Association for Control over Minds), an upstanding company with a single goal of world domination. Yesterday, you woke up, and saw that the weather was clear, and the birds were singing. “Another day, another world domination pla...
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Association for Convex Main Office Description: You are the boss of ACM (Association for Convex Main Office), an upstanding company with a single goal of world domination. Today, you have decided to move your main office from Helsinki to Singapore. You have purchased a square-shaped land in Singapore,...
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Association for Cool Machineries (Part 1) Description: You are the boss of ACM (Association for Cool Machineries), an upstanding company with a single goal of world domination. Like all other world domination oriented villains, you dream of having a gigantic evil robot doing evil deeds. I mean, is the...
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Association for Cool Machineries (Part 2) Description: In order to understand this problem, you need to read the “Association for Cool Machineries (Part 1)” problem. You are the boss of ACM (Association for Cool Machineries), an upstanding company with a single goal of world domination. Today, after ...
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Association for the Country of Mububa Description: You are the boss of ACM (Association for the Country of Mububa), an upstanding company with a single goal of world domination. Today, you have conquered the unnamed country of Mububa (how an unnamed country has a name is, of course, outside the scope ...
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Association of Camera Makers Description: ACM (Association of Camera Makers) is a company that produces amazing surveillance cameras. Each camera can produce a live panoramic video feed, giving you a 360-degree view of the surroundings. However, they also have a certain visual range $R$, beyond which t...
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Association of Cats and Magical Lights Description: Rar the Cat$^($™$^)$ is the founder of ACM (Association of Cats and Magical Lights). This is the story of the founding of ACM. It is the second half of the year again and Rar the Cat$^($™$^)$ is looking forward to Christmas. When people think of Christma...
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Association of Computer Maintenance Description: In order to keep up with the rapid technological advancements, Mr. Panda needs to backup all the data on his computer to allow him to do a full upgrade of his computer. Since the upgrade will take some time, he will peruse the services of the company ACM...
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Association of Myths Description: Arnar is playing his favourite video game Association of Myths. He’s playing a character by the name of Lumen. Lumen has a special ability where she can shoot a laser beam across the entire map killing all enemies it hits. The only drawback is that the beam is rather ...
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Associative Exponents Description: The Association for Curtailing Parentheses in Computations is having some trouble. Some members learned in class that $a^{b^ c} = a^{(b^ c)}$, but others insist that ${a^ b}^ c = {(a^ b)}^ c$. You are trying to keep the peace by assuring them that it works either ...
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Asteroid Avoidance Description: The legendary starship of Flatland, Rectalateral, needs to escape from a star which is about to go supernova by teleporting away. Unfortunately, the possible teleport destinations are in the middle of an asteroid field. Luckily, you have a map of the asteroid field with ...
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Asteroid Mining Description: Shofa is working on her new spacefaring game, No Person’s Star. The star systems in the game are procedurally generated, and contain stars, planets and asteroids. The asteroids are only used to mine minerals, and consist of multiple mineral veins. Players can only mine one ...
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Asteroid Rangers Description: The year is 2112 and humankind has conquered the solar system. The Space Ranger Corps have set up bases on any hunk of rock that is even remotely inhabitable. Your job as a member of the Asteroid Communications Ministry is to make sure that all of the Space Ranger asteroid...
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Asteroids Description: The year is 2115. The asteroid communication relay system was set up a decade ago by the Asteroid Communication Ministry. It is running fine except for one small problem – there are too many asteroids! The smaller ones not only keep interfering with the signals from the relay sta...
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Astro Description: Ivica and Marica are attending astronomy classes and are observing two unusual stars. They noted the time when each of them flashed. They further noticed that each of the stars flashes periodically, at regular intervals, and now they are wondering: on what day, at what hour will the ...
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Astrological Sign Description: Harry Potter and his friends are now fourth-year students at Hogwarts School of Witchcraft and Wizardry. This year, one of their subjects is Astrology. To become a successful wizard, Astrology is crucial, as it allows one to predict future events or gain insights into peo...
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Astronomer Description: The astronomer has a passion for stargazing. In particular, he gets immense pleasure out of gazing at $k$ stars simultaneously through his telescope. Building a telescope with radius $r$ costs $t\cdot r$ kroner. A newly built telescope will point exactly at the origin $(...
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Atlantis Description: You may have heard of the lost city of Atlantis. As legend goes, Atlantis was a city of great wealth and power. Then the Gods became displeased with Atlantis and sank it into the ocean. What you may not have heard is the story of Demetrios, the only person in Atlantis with a ship ...
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Atlögur Description: Guðmundur is a Ph.D. student at an Icelandic university, where he studies history. He has a burning interest in duels and the ways of knights of past times. In the middle ages, and the ages before them, battles between knights were common. His research revolves around these knights...
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Atomic Energy Description: Although an atom is composed of various parts, for the purposes of this method only the number of neutrons in the atom is relevant1. In the method, a laser charge is fired at the atom, which then releases energy in a process formally called explodification. Exactly how th...
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Attendance Description: It is the first day of school at Liking University, or “Lku” for short. Lku administration is very strict with attendance, especially on the first day. In order to verify everyone’s attendance, the Lku’s principal has made an attendance list. He then asked to all students to sta...
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Attendance Description: Taking attendance in your class is a tedious task. You call out the names of students one at a time in alphabetical order. If the student is present, they respond by saying “Present!” before you call the next name. This is such a boring task that you sometimes zone out and don’t ke...
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Austan Atlantshafs Description: Many cities and other institutions have a tendency to raise statues of various kinds to garner attention. In this context larger statues are of course preferable, as a larger statue garners more attention. It is even better when the statue is the largest in a large area ...
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Auto Completion Description: The auto completion algorithm works based on a pre-defined dictionary of $n$ words. Suppose the search box contains the text $w$. When the user presses the tab key $i$ times in a row, the algorithm finds the $i$-th lexicographically smallest word from the dictionary tha...
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Auto-Coin-o-Matic Description: It’s finally here! The day you unveil your new invention, the Auto-Coin-o-Matic! You watch with glee and anxiety as people insert their card into the machine, type in the amount they want, and get exact change out with the fewest number of coins. But was it actually the ...
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Automatic Trading Description: A brokerage firm is interested in detecting automatic trading. They believe that a particular algorithm repeats itself; that is, it makes the same sequence of trades at a later time. The firm has identified a set of 26 key stocks that they believe are likely to be traded ...
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Autori Description: Great scientific discoveries are often named by the last names of scientists that made them. For example, the most popular asymmetric cryptography system, RSA was discovered by Rivest, Shamir and Adleman. Another notable example is the Knuth-Morris-Pratt algorithm, named by Knuth, M...
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Av(1324) Description: Five problems ready, and already Arnar and Atli are running out of ideas. In desperation they start asking other members of the faculty at RU what problems they should pose for their students, and after a bit of searching they end up talking to Henning. He says that “Pattern avoid...
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Avalanche Description: After Joshua saw through Alexander’s attempts to fake pictures of snowflakes1, Alexander has become vengeful and obsessed with snow. He has come up with an evil master plan which could be the end of Joshua, where the first step is to invite him on a skiing trip. Together, they a...
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Average Character Description: Have you ever wondered what the average ASCII character of any given string is? No? Never? Really? Well, is it a character in the string or something else? Would you do this calculation by hand with an ASCII table? Probably not! All modern programming languages include f...
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Average Rank Description: The National Weekly Escape Room Challenge (NWERC) is a long-running competition held in Eindhoven. Every week a new escape room is presented, and anyone who completes it in their first attempt gains one point. At the end of each week, competitors are ranked by the total numbe...
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Average Spanning Tree Description: Victor works at a company dealing with trees. Unlike most such companies, the one Victor works at does not cut them down. Instead, they create new trees from graphs. For example, some customers might give them a graph and ask for the minimum spanning tree, while other...
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Average Speed Description: You have bought a car in order to drive from Waterloo to a big city. The odometer on their car is broken, so you cannot measure distance. But the speedometer and cruise control both work, so the car can maintain a constant speed which can be adjusted from time to time in resp...
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Average Substring Value Description: Let $s$ be a nonempty string consisting entirely of $\textrm{base-}10$ digits (0–9). If the length of $s$ is $n,$ number the digits $1, 2, 3, \ldots , n$ from left to right, and for $1 \leq i \leq j \leq n,$ let $s[i,j]$ denote the substring consisting of the di...
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Avion Description: Mirko and Slavko are USKOK agents tracking the movements of an unnamed corrupt government official. Anonymous sources have tipped them about his upcoming escape attempt. They now know he plans to use his diplomatic liaisons to try and hitch a ride on a CIA blimp leaving from Severin ...
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Avogadro Description: Luka is slacking again during chemistry class, while the teacher is explaining Avogadro’s law. Luka first drew a table consisting of $3$ rows and $N$ columns. Then he wrote the numbers $1$ to $N$ into the first row in arbitrary order, each number appearing exactly once. In the other ...
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Avoiding Airports Description: David is currently at the airport in country $1$, and the current time is $0$, and he would like to travel country $n$. He does not care about the total amount of time needed to travel, but he really hates waiting in the airport. If he waits $t$ seconds in an airport,...
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Avoiding Asteroids Description: You escaped the planet, but enemy starfighters are right behind you! To make things worse, in between you and the safety of your base is an asteroid field. The starfighters would never follow you into the asteroids, but unfortunately you used all your fuel in the escape,...
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Avoiding the Abyss Description: You are standing on a point with integer coordinates $(x_s, y_s)$. You want to walk to the point with integer coordinates $(x_t, y_t)$. To do this, you can walk along a sequence of line segments. But there is a swimming pool in your way. The swimming pool is an axis alig...
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Avoiding the Apocalypse Description: You and the rest of your team are stuck in a town during the zombie apocalypse of 2020. You all might be infected with the virus and hence you will have to find your way to one of the medical facilities to get a cure before you also become zombies. Because you are s...
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Avoidland Description: Avoidland is a puzzle played on an $n \times n$ board with $n$ pawns. The pawns are initially placed on the squares of the board, at most one pawn per square. The goal is to move the pawns so that they “avoid” each other—there cannot be a row or a column with more than one pawn. ...
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Awkward Party Description: Martin has invited everyone he knows to celebrate his 535th birthday, and a whopping $n$ people from all over the world have accepted the invitation. When deciding the seating arrangement, Martin’s mother Margarethe have decided that all the guests should be seated with maxi...
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Aww Man Description: You need a total of $T$ different rare materials that can only be found in the deepest caves of the rarest biome at very specific times of the year. The materials are very important to you, so you want to make sure that nothing bad happens. Thus, you want to make a plan. For e...
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Azulejos Description: Your task is to find an ordering of the tiles in each row that satisfies these constraints, or determine that no such ordering exists. ## Input The first line of input contains an integer $n$ ($1 \leq n \leq 5\cdot 10^5$), the number of tiles in each row. The next four lines con...
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B Road Band Description: All the residents of the rural community of Axes Point live on one of two parallel streets separated by a band of green park land. Recently, the local board of supervisors received a grant to (finally) bring wireless service to the town. The grant provides enough money for them...
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BAAS Description: BAAS Inc. (Build Airplanes As-a-Service) has grand plans to build lots of airplanes. Naturally, the airplane construction process consists of multiple steps, each of which may take some time. Some steps can take more time to complete than others, e.g. attaching a plane wing may take l...
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BASIC Interpreter Description: The BASIC computer programming language has been popular for many years, and there have been dozens of ‘dialects’ of the language. It’s considered a high-level language and is typically interpreted (rather than compiled). For this problem, write an interpreter for a restr...
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Babelfish Description: You have just moved from Waterloo to a big city. The people here speak an incomprehensible dialect of a foreign language. Fortunately, you have a dictionary to help you understand them. ## Input Input consists of up to $100\, 000$ dictionary entries, followed by a blank line, ...
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Baby Bites Description: Unfortunately, talking while having a mouthful sometimes causes Arild to mumble incomprehensibly, making it hard to know how far he has counted. Sometimes you even suspect he loses his count! You decide to write a program to determine whether Arild’s counting makes sense or not....
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Baby Names Description: Kattis is having a baby! O.o. However, she does not know what to name her baby. Thankfully, her friends have many ideas, giving suggestions for both genders. Given $\textbf{N}$ distinct baby name suggestions (each babyName string consists of only UPPERCASE alphabet characters o...
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Baby Panda Description: Alex is taking care of a baby panda who seems to be unusually sniffly. Every day, the baby panda may sneeze out zero or one slime(s) into its enclosure; every night, all slimes present in the enclosure split, so that the number of slimes doubles overnight. Alex places the baby p...
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Babylonian Numbers Description: More than $4\, 000$ years ago, the ancient Babylonians used a numerical system that is well known for being the first positional numerical system. In such a system, a non-negative integer is represented by a sequence of digits such that the value of a digit depends both ...
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Bachelor's Thesis Description: For SoCCat’s Final Year Project, SoCCat will write a thesis studying the behaviour of a particular operation: the cat-split. Initially, suppose SoCCat has an array of $n$ integers $a_1, a_2, \ldots , a_ n$, and an integer $k$ ($1 \leq k \leq n$). In one cat-split operati...
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Bachet's Game Description: ## Input The input consists of a number of lines (between $1$ and $100$, inclusive). Each line describes one game by a sequence of positive numbers. The first number is $n \leq 1\, 000\, 000$ the number of stones on the table; the second number is $m \leq 10$ giving the ...
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Backpack Buddies Description: The prudent Mr. Day and adventurous Dr. Knight have decided to be backpack buddies and go trekking in the gorgeous Norwegian mountains. Of course they will use the trails marked by the Norwegian Trekking Association (DNT), like any sane trekkers would; such trails all star...
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Backspace Description: Right before Forritunarkeppni Framhaldsskólanna started, Bjarki decided to update his computer. He didn’t notice anything off until he started writing code in his favourite editor Bim (Bjarki IMproved). Usually when he uses this editor and presses backspace one letter to the left...
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Bacon, Eggs, and Spam Description: You are a short-order cook in a local diner. Each day, a series of customers enter your diner and order a list of items from the menu. You not only prepare their orders, but you also make a list of who ordered what. At the end of the day, you like to reflect back on w...
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Bad Packing Description: We have a knapsack of integral capacity and some objects of assorted integral sizes. We attempt to fill the knapsack up, but unfortunately, we are really bad at it, so we end up wasting a lot of space that can’t be further filled by any of the remaining objects. In fact, we are...
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Bag of Tiles Description: You and your friend are playing a game involving chance, and you are interested in the odds of winning the game. The game proceeds as follows: * Your friend chooses $m$ tiles, each labeled with a positive integer. He shows them to you, and puts them in a bag. He then ...
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Baggage Description: An airline has two flights leaving at about the same time from ICPCity, one to city B and one to city A. The airline also has $n$ counters where passengers check their baggage. At each counter there is a pair of identical baggage bins, one for city B and one for city A. Just b...
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Bakice Description: When it comes to trams, a lot of people are civilized individuals who know how to behave in one. However, there are always those few who upon spotting a place to sit will run towards it in supersonic speeds. If they spot more than one place, they always try the closest one first. P...
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Bakterije Description: Luka is bored in chemistry class yet again. This time, he’s playing with intelligent bacteria. He has arranged his $K$ bacteria on a rectangular board divided in $N$ rows, labelled with numbers from $1$ to $N$ starting from the top, and $M$ columns, labelled with numbers ...
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Balanced Cut Description: Professor Anna van Lier is preparing to give a lecture on balanced binary search trees. Recall that these are binary trees with two properties: * Balanced tree: For every node, the height of its left subtree and the height of its right subtree differ by at most $1$. F...
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Balanced Diet Description: Appreciating the time savings, product consistency and nutritional value of prepared foods, you have decided to eat all your meals from cans. You have a shopping bag full of cans, enough for the next two meals. You want to finish the entire contents of all of these cans withi...
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Balanced Diet Description: Every day, Danny buys one sweet from the candy store and eats it. The store has $m$ types of sweets, numbered from $1$ to $m$. Danny knows that a balanced diet is important and is applying this concept to his sweet purchasing. To each sweet type $i$, he has assigned a target ...
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Balanced Tree Path Description: You are given a tree where each node is annotated with a character from ()[]{}. A path is a sequence of one or more nodes where no node is repeated and every pair of adjacent nodes is connected with an edge. A path is balanced if the characters at each node, when concate...
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Balancing Art Description: Pete Tencious is a world-renowned artist who specializes in mobiles. The San Francisco Museum of Art is currently displaying a collection of his artwork entitled Balance I, Balance II, Balance III, …, you get the idea. Each of these works contains two or more spheres with wir...
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Balatro Description: You’re given some cards arranged in a row. Each card has a value, and is one of two types: add, or multiply. Compute the score for a row of cards as follows: Initially, the score is zero. Then, process the cards from left to right. If it is an add card, increase the score by the card...
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Ball Description: There is a school dance scheduled tomorrow and $n$ students will attend. The students are numbered from $1$ to $n$. The students are registered in pairs and the list of attendees is $\frac{n}{2} + 1$ lines long. Each number also appears once in the list. But that doesn’t add up! S...
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Ball Bearings Description: The Swedish company SKF makes ball bearings. As explained by Britannica Online, a ball bearing is “one of the two types of rolling, or anti friction, bearings (the other is the roller bearing). Its function is to connect two machine members that move relative to one another...
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Ball Colors Description: Baby Timmy has a pool of balls that he plays with. The pool is made up of balls with $n$ different colors with a certain number of each color. Baby Timmy finds it interesting to order these balls in a line given certain conditions he made. Timmy has two conditions when playing ...
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Ball Tricks Description: RB is a basketball coach and he has several teams of exceptionally skilled basketball players, who dominate basketball leagues all over the world. Why are RB’s players so good? The reason is that each of them has already mastered exactly one ball trick – either the Triple Spin...
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Ball of Whacks Description: Danny has a new toy called Ball of Whacks. It’s a rhombic triacontahedron (which we all know is a thirty sided polyhedron) made of small pyramid-shaped pieces which look like the following: When all $30$ pieces are all put together, they form the object shown in Figure 2a. ...
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Balls and Bins Description: In the balls and bins game, you toss balls into bins and try to earn some prize money. In front of you are $N$ bins. Each turn, you throw a ball into one of the bins. Unfortunately your aim is not so precise; maybe it is because the bins are so far away. So, in each turn th...
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Balls and Needles Description: Joana Vasconcelos is a Portuguese artist who uses everyday objects in her creations, like electric irons or plastic cutlery. She is an inspiration to Ana, who wants to make ceiling hanging sculptures with straight knitting needles and balls of wool. For safety reasons, th...
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Baloni Description: There are $N$ balloons floating in the air in a large room, lined up from left to right. Young Perica likes to play with arrows and practice his hunting abilities. He shoots an arrow from the left to the right side of the room from an arbitrary height he chooses. The arrow moves...
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Banana Problem Description: Gon is playing the game ‘Greedy Monkeys’. The game is setup as follows: * There are $N$ ladders, numbered from $1$ to $N$. Each ladder has height $H$, and has $H + 1$ steps at height $0, 1 \ldots , H$. Let $(\ell , h)$ represent the step at ...
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Bandit Raids Description: Three rival gangs of bandits, the Marauders, the Attackers, and the Plunderers, are fighting one another for a limited supply of gold. Each gang has one member for each piece of gold collectively owned by the gang. Every night one gang will raid the hideout of another gang to ...
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Banjo Description: Having mastered the classic games Banjo-Kazooie and Banjo-Tooie, Bob has moved on to playing their secretly-released sequel, Banjo-Threeie. The game can be modelled with a 2-dimensional coordinate system. The player’s objective is simply to walk from one point to another as the t...
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Bank Queue Description: However, there are too many people and only one counter is open which can serve one person per minute. Greedy as Oliver is, he would like to select some people in the queue, so that the total amount of cash stored by these people is as big as possible and that money then can wor...
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Bannorð Description: ## Input The first line of the input contains a non-empty string $S$. The string $S$ contains lower case letters of the English alphabet and none of which is repeated. The next line of the input contains the string $M$. The string $M$ contains only lower case letters and space...
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Bar Classification Description: You are taking a course on machine learning at your university, and as homework you have been tasked with writing a program that can tell vertical bars from horizontal bars in images. To generate some training data, you use the following method. First, take an $N \times ...
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Bar Code Description: Bar Code is a puzzle game invented by Thinh Van Duc Lai in 2017 that was first published in the New York Times. Bar Code is played on a square grid consisting of $n \times n$ unit squares with $(n+1) \times (n+1)$ grid points. For a given specification, the puzzle requires the ...
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Bar Shelf Description: Organ pipes, the von Trapp children, staircases—oh, how Quark loves these things. For they are neatly arranged ascending order, the very signal of cleanliness, structure, civilisation. Quark is your fellow bartender at Meson, the longest bar in the galaxy. Were it up to Quark...
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Barcelona Description: Arnar, Benni and Unnar were at the airport in Barcelona on their way to a competitive programming training camp. When the plane had landed they exited and went to the baggage claim. When they arrived there was no baggage on the conveyor belts. After a few minutes the baggage star...
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Barcode Description: To prepare for ACM-ICPC 2017 in Saigon, the host univeristy – Ho Chi Minh city University of Education (HCMUE) – decided to print barcodes on the participants’ t-shirts. The barcode requirement needs to be simple to reduce the cost but still show some scientific style. HCMUE decide...
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Bard Description: Every evening villagers in a small village gather around a big fire and sing songs. A prominent member of the community is the bard. Every evening, if the bard is present, he sings a brand new song that no villager has heard before, and no other song is sung that night. In the event ...
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Barica Description: Barica is an unusual frog. She lives in a pond where $N$ plants float on the surface of the water. The plants are numbered $1$ through $N$. When viewing from above, the location of each plant is given by a pair of coordinates. What makes Barica unusual is her fear of jumping diagona...
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Barking Up The Wrong Tree Description: Your dog Spot is let loose in the park. Well, relatively loose – he is tied to a post with a leash, limiting his movements. Spread around the park are various squeaky toys and other dog paraphernalia, which Spot happily goes after when he sees them. When he gets t...
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Base-2 Palindromes Description: A positive integer $N$ is a base-$b$ palindrome if the base-$b$ representation of $N$ (with no leading zeros) is a palindrome, i.e. reads the same way in either direction. For instance, $7$ (base $10$) is a palindrome in any base greater than or equal to $8$. It ...
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Baseball Court Description: After lengthy meetings on the subject, the NCPC jury has decided that getting the contestants’ blood pumping would result in better contests. Thus they figured it would be a good idea to compete for bragging rights in some kind of sport prior to the programming contest. For ...
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Based Porridge Description: Computer science students, like kindergarteners, care a lot about fair outcomes: irregardless of whether this is achieved through helping the low or keeping down the high. You are hosting a sittning in Basen for $N$ students. There are K kinds of porridge and you have pr...
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Basic Basis Description: You are given a sequence of $n$ bit strings $b_1, b_2, \ldots , b_ n$, each with $k \times 4$ bits. You are also given another sequence of $m$ bit strings $a_1, a_2, \ldots , a_ m$, each also with $k \times 4$ bits. Let $f(x)$ denote the minimum index $i$ such that it is ...
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Basic Programming 1 Description: You think you can code? This problem will test you on various basic programming techniques. You are given two integers $N$ and $t$; and then an array $A$ of $N$ integers ($0$-based indexing). Based on the value of $t$, you will perform an action on $A$. $t$ Action...
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