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Traveling Salesman Description: ## Input Each test case consists of a line containing $c$, the number of countries ($4 \le c \le 6000$), followed by $c$ lines containing the integers $n\; x_1\; y_1\; z_1\; \dots \; x_ n\; y_ n\; z_ n$, describing (in order) the $n$ corners of a closed polygon ...
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Travelling Caterpillar Description: Lilith is a hungry caterpillar! From her vantage point at the root of a tree, she has identified some leaves she wishes to munch before returning to the root. She wants to finish munching all of them as quickly as possible so that she will grow into a plump, buttery ...
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Travelling Delivery Person Description: Frederic Edward Xavier runs a very successful delivery company called FredEX. He’s been looking at driving records lately, and is not happy with the costs of delivery. He has made the following estimations: * Driving from one intersection to the neighboring one ...
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Travelling Salesperson 2D Description: ## Input Your program should take as input a single TSP instance. It will be run several times, once for every test case. The time limit is per test case. The first line of standard input contains an integer $1 \le N \le 1000$, the number of points. The followin...
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Tray Bien Description: André Claude Marzipan is the head chef at the French restaurant Le Chaud Chien. He owns a vast number of baking trays, which come in two sizes: $1$ foot by $1$ foot, and $1$ foot by $2$ feet. He stores them along $3$-foot deep shelves of various lengths. For example, on a shelf t...
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Treasure Diving Description: Legends often tell of great treasures. But you rarely get the chance to actually stumble upon those treasures. Most of them are lost in the sea, or hidden below mountains. But as you learned from one of your biggest idols, treasures do belong into a museum. And now you have...
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Treasure Hunt Description: You are a treasure hunter searching for gold in the wild. Luckily you got a map of the area from a black marketeer. The map clearly shows where a box of gold is along with the surrounding terrain. Of course, you want to head to the treasure as fast as possible. However, the t...
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Treasure Hunt Description: Jill has created a new smartphone game that leads players to find a treasure. The app uses the phone’s GPS to determine the player’s location. The app then tells the player the direction in which to go on a route to find the treasure. When the player reaches some specific loc...
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Treasure Map Description: You have come into possession of a pirate map that gives a series of steps to get from your landing place on a desert isle to the spot marked $X$ where the treasure is located. Each step consists of a compass heading and a number of paces. After spending most of your savings ...
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Treasure Spotting Description: For Timmy’s birthday his parents threw him a pirate themed party! A treasure is buried in the yard and now it is up to Timmy and his pirate crew to find it. Help the pirates find the treasure by letting them know who can see where the treasure is buried. To make the game...
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Tree Canopy Graphs Description: You are conducting a study on the health of Calgary’s trees. Your assistant has spent $17$ years collecting data for your study, and now it’s finally time to utilize it! You would like to figure out how healthy the trees are by analyzing how large the canopy of each tree...
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Tree Hopping Description: You are given a tree and a permutation of its vertices. It can be proven that for any tree and any pair of source/destination nodes, there is some permutation of the nodes where the first node is the source, the last node is the destination, and the distance between each pair ...
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Tree Hugging Description: Once, two trees forgot their place and started to grow into each other. One of the trees grew from the left, and the other from the right. On $n$ points, they collided. Numbering the points $1, 2, \dots , n$ from left to right, the left tree ended up connecting all of the...
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Tree Insertion Description: All modern banks employ information systems to process their data. The amount of data is enormous. Imagine all the transactions, payments, e-banking, web services, etc. Therefore, advanced data structures must be used to store the data and allow to access them very quickly. ...
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Tree Number Generator Description: One day Young Anna comes up with a whimsical idea of using a tree to create a number generator. The generator is created with a modulus $m$ and an internal tree of $n$ nodes numbered from $1$ to $n$. Each tree node is assigned a single digit between $0$ to $9$...
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Tree Shopping Description: Andy is going holiday shopping and needs to buy several Christmas trees. At the store, there is a row of Christmas trees of various heights. Andy is only allowed to buy trees that are next to each other, i.e. trees that are contiguous within the row. He also wants to make sur...
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Treehouses Description: In a rainforest there are $n$ treehouses high in the forest canopy on different trees (numbered from $1$ to $n$). The $i$-th tree’s location is at $(x_ i, y_ i)$. The first $e$ of them in the list are close enough to neighboring open land around the rainforest so that transp...
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Treequivalence Description: The following grammar describes a textual notation for a tree with (not necessarily unique) vertex labels: ``` tree ::= label tree ::= label ( subtrees ) subtrees ::= tree subtrees ::= subtrees , tree label ::= A | B | C | ... | Z ``` That is, the representation of a tree ...
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Trending Topic Description: Imagine you are in the hiring process for a company whose principal activity is the analysis of information in the Web. One of the tests consists in writing a program for maintaining up to date a set of trending topics. You will be hired depending on the efficiency of your s...
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Trezor Description: Mirko decided to open a new business—bank vaults. A branch of the bank can be visualized in a plane, vaults being points in the plane. Mirko’s branch contains exactly $L\cdot (A+1+B)$ vaults, so that each point with integer coordinates inside the rectangle with corners $(1, -A)$ and...
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Tri Description: Little Mirko wrote into his math notebook an equation containing three positive integers, the equals sign and one of the four basic arithmetic operations (addition, subtraction, multiplication and division). During another class, his friend Slavko erased the equals sign and the operat...
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Tri Tiling Description: In how many ways can you tile a $3\times n$ rectangle with $2\times 1$ dominoes? Here is a sample tiling of a $3\times 12$ rectangle. Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer $0 \leq n \leq 30$. For ...
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Triangle Area Description: Per-Magnus managed to solve his addition homework thanks to you, but now he is unfortunately posed with an even greater problem. He has been given a triangular cake by his mother, and wonders what the area of it is. It turns out Per-Magnus forgot the formula for computing it...
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Triangle Containment Description: You recently discovered there is treasure buried on your farm land. A lot of treasure! You quickly decide to put a fence around the land. Alas, you have but a single fence post! You will have to drive to town to get more fencing material. But you can’t just leave the ...
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Triangle Cuts Description: Figure 1 Figure 2 Disallowed Pattern Figure 3 Figure 4 A computer science professor was watching his young daughter use scissors to cut large triangular pieces of paper that were green on one side and white on the other. She always kept the white side of the paper up, ...
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Triangle Drama Description: It’s the year 3035, and you are Chief Relationship Officer on the Pluto colonization mission, currently en route to the beigeish not-planet. Your task is to make sure that there is no excessive amount of relationship drama during the 10 year long trip. The biggest source of ...
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Triangle Ornaments Description: Write a program that computes the minimum required length for the rod, given a list of triangles! ## Input The input consists of a single test case. The first line contains one integer $N$ ($0 < N \le 100$), denoting the number of triangles. The next $N$ lines each con...
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Triangle Text Description: Write a program which will read lines of text and print the text in a triangle. In particular, no line begins or ends with a space. There is exactly one space between words on the same line if they are part of the same sentence. There are exactly two spaces following a perio...
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Triangle To Hexagon Description: Given a triangle $ABC$ with incenter (center of its inscribed circle) $I$, and circumscribed circle $O$, let $M$, $N$ and $P$ be the second points of intersection of the lines through $A$ and $I$, $B$ and $I$ resp. $C$ and $I$ with the circle $O$. Let $E$ and $...
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Triangle Trees Description: A triangle tree is an undirected graph in which every cycle contains exactly three edges. Recall that a cycle is a sequence of at least $3$ distinct vertices $v_1, v_2, \ldots , v_ k$ such that there is an edge between $v_ i$ and $v_{i+1}$ for $i=1,\dots ,k-1$ and there is a...
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Triangle Trilemma Description: You’re interested in writing a program to classify triangles. Triangles can be classified according to their internal angles. If one of the internal angles is exactly 90 degrees, then that triangle is known as a "right" triangle. If one of the internal angles is greater t...
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Triangles Description: You got a very strange gift for your birthday: two triangles in the three-dimensional space. Each triangle consists of three infinitely thin segments, and each segment stays straight no matter how hard you press it. Now, you actually wanted to get just one triangle, so you try to...
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Triangles Description: Alice has once again devised a game for Bob. She would first scatter seeds all over the kitchen floor. Then, Bob will have to kneel down and trace out triangles with his finger. For each triangle Bob traces out, Alice gives him a number of cookies equal to the square of the area of ...
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Triangles Description: For your trip to Beijing, you have brought plenty of puzzle books, many of them containing challenges like the following: how many triangles can be found in Figure 1? While these puzzles keep your interest for a while, you quickly get bored with them and instead start thinking about...
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Triangles of a Square Description: Ashley has given Brandon a square of side $2024$. She also has drawn a single line segment that connects two different sides of the square. Brandon wants to draw some additional line segments such that it is possible to decompose the square into a set of disjoint tri...
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Triangular Clouds Description: Garry is looking at the sky. Such a beautiful day! He notices that the clouds are particularly beautiful today, and wishes to record the current state of the sky. He has no camera, so he begins writing down coordinate points. Fortunately for Garry, the current cloud cover...
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Triangular Collection Description: Call a set of positive integers triangular if it has size at least three and, for all triples of distinct integers from the set, a triangle with those three integers as side lengths can be constructed. Given a set of positive integers, compute the number of its trian...
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Triangular Logs Description: The local forest has a lot of trees! Each tree is located at integer coordinates and has an integer height. Cutting down any tree gives you a log with a length equal to its height. You want to obtain three triangular logs (that is, three logs that form a non-degenerate tria...
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Trick Shot Description: Your game development studio, Ad Hoc Entertainment, is currently working on a billiards-based app they’re calling Pool Shark. Players face a sequence of increasingly devious pool puzzles in which they need to carefully position and aim a single billiards shot to sink multiple po...
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Trick and Treat Description: During Halloween, kids come by your house to request candy. If you can not give them any, they will become angry and throw toilet paper at your house! This year, you have already scouted the neighbourhood and know that kids will come to your house in groups of $A_1, A_2, \...
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Trick or Treat Description: Johnny and his friends have decided to spend Halloween night doing the usual candy collection from the households of their village. As the village is too big for a single group to collect the candy from all houses sequentially, Johnny and his friends have decided to split up...
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Tricky Factoring Description: Ms. Alice was working on making some factoring homework for her students last week, where the students get questions in the form of $ax^2+bx+c$, and must rewrite the expression in the form $(dx+ e)(fx + g)$, where $a,b,c,d,e,f,g$ are integers. However, last night the ZomBs...
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Tricky Triangulation Description: Amy is trying to find a stronghold by using Eyes of Ender. When thrown, Eyes of Ender fly in the direction of the closest stronghold. However, since Eyes of Ender have a chance of breaking when thrown, Amy wants to limit the number of throws she makes. So, she attempts...
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Triforce Description: Link (the famous green-hatted hero from the Legend of Zelda series), was really bored after yet again having saved the day. As he was relaxing in the sun at Lake Hylia, he noticed he could make really nice patterns in the sand, and then walk around in them. One of these patterns h...
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Trik Description: Jealous of Mirko’s position as head of the village, Borko stormed into his tent and tried to demonstrate Mirko’s incompetence for leadership with a trick. Borko puts three opaque cups onto the table next to each other (opening facing down) and a small ball under the leftmost cup. He ...
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Trimming Convex Polygons Description: You are the proud owner of a beautiful convex polygon! But university is expensive, so you decide to sell your polygon to support your studies. The market value, in dollars, for a polygon is exactly twice its area. But there is an illegal black market for individua...
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Triolingo Push Description: Trio from Triolingo wants to remind you to take your daily programming lessons! To make sure you actually will complete your lesson every day, Trio sends you several notifications according to the following increasing pattern: On the first day, Trio sends $1$ notification. On ...
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Trip Odometer Description: A trip odometer can be used to record the distance driven on a single trip. You are very diligent: at the start of each trip you reset the trip odometer to read $0$ and at the end of each trip you write down the distance travelled. Thus, you maintain a list of distances (in kilo...
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Trip Planning Description: Lars is planning to do a backpacking tour by train throughout $N$ cities in Europe. He has a list of train lines numbered from $1$ to $M$ that each goes back and forth between some pair of cities, no two between the same pair. He wants to visit the cities in the order $1$, $2...
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TripTik Description: Have you ever been on a long road journey? AAA (the American Automobile Association) has a tool for long road trips. It’s called a TripTik, and it follows the highways, showing points of interest. You are building a TripTik app, which allows users to see what’s on their route. It ...
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Triple Sevens Description: Eddy is overseeing construction of some new slot machines. His slot machines consist of three wheels, each of which can show one of several different digits. When activated, each wheel shows a random digit. The goal is for all wheels to be able to show the digit $7$. A slot ...
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Triple Texting Description: Julia enjoys talking to her grandma, playing with legos, and inventing two-player card games where she has a winning strategy. Recently however, she has not been able to talk to her grandma in person because of some kind of “pandemonium”. Instead, they have resorted to texti...
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Triplet-Free Queens Description: The $n$-queens problem is popular among computer science students. Its task is to place a maximum number of queens on an $n\times n$ chessboard so that no two queens attack each other. Two queens attack each other if they share a row, column, or diagonal. One day Zapra...
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Trojke Description: Mirko and Slavko are playing a new game, “Trojke” (Triplets, in English). First they use a chalk to draw an $N \times N$ square grid on the road. Then they write letters into some of the squares. No letter is written more than once in the grid. The game consists of trying to find three...
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Troll Hunt Description: Apprehensive of its imminent decapitation, the troll fled, and did not have the decency to even leave a forwarding address. Being a troll, it was clear that the troll was hiding under some other stone bridge than the one it had used for its shady business practice, but which? Th...
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True/False Worksheet Description: Bob is completing a true/false worksheet, consisting of a list of $n$ problems where each answer is either “true” or “false”. The problems are numbered from $1$ to $n$. They are too hard for Bob, so the TA, Alice, has given Bob $m$ hints. For each hint $i$, Alice g...
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Truls' Troubles Description: Truls and Henry are playing table tennis against each other. Both Truls and Henry strongly dislike math. More than anything, they hate calculating how many points each of them has during the game. To simplify scoring, they have come up with their own solution: Instead of ...
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Tug of War Description: A tug of war is to be arranged at the local office picnic. For the tug of war, the picnickers must be divided into two teams. Each person must be on one team or the other; the number of people on the two teams must not differ by more than $1$; the total weight of the people ...
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Tunnelling the Earth Description: For example, travelling from Waterloo to Cairo requires a distance of $9\, 293\, 521$ metres following the great circle route around the earth, but only $8\, 491\, 188$ metres following the straight line through the earth. For this problem, assume that the earth i...
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Turbo Description: Frane has been given the task of sorting an array of numbers. The array consists of $N$ integers, each between $1$ and $N$ (inclusive), with each of those appearing exactly once in the array. Frane has come up with the following sorting algorithm which operates in $N$ phases, and nam...
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Turn It Up! Description: Your volume control is at a comfortable $7$ – not too high, not too low. Your friends entirely disagree, and frequently request you turn it up or turn it down, often in a somewhat inappropriate tone of voice. Ever aiming to please, you try to accomodate their requests and incr...
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Turning Red Description: Mei’s parents have spent the last year remodeling their house, but their lighting system is quite complex! Each room in the house has an LED light, which can be set to red, green, or blue, as seen in Figure 1. Throughout the house are various buttons which are each connected t...
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Turning Trominos Description: The $L$-tromino is composed of three unit squares arranged as shown in part A of the illustration to the right. The $L$-tromino is also an example of a rep-tile because four $L$-trominos can be arranged to make a replica of itself that is twice as tall and twice as wide, a...
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Turtle Master Description: Robot Turtles is one of Theta’s favorite games. In this game, kindergarteners learn how to “code” by creating programs that move a turtle from a starting field to a diamond. Robot Turtles is reportedly the most successful game funded by the Kickstarter incubator. In the actu...
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Tvær Vikur Description: ‘Alright boys, where we dropping in?’ can be heard from Benni’s headphones. He groans and tries to focus on the task at hand. Benni is competing in the game ‘Two weeks’. On the sideline sits Arnar who’s paying close attention. Arnar is quite into betting and knows no better feel...
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Twenty Four, Again Description: Yes, we know $\ldots $ we’ve used Challenge $24$ before for contest problems. In case you’ve never heard of Challenge $24$ (or have a very short memory) the object of the game is to take $4$ given numbers (the base values) and determine if there is a way to p...
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Two Charts Become One Description: When businesses feel that they are a little bloated and in need of restructuring, they call in the well-known reorganization consultant Don Sizing. One of the first things Don asks for is a chart showing the hierarchy of departments in the business, i.e., which depart...
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Two Knights' Poem Description: Two chess knights have decided to collaborate on writing short, one-line poems. They have obtained the use of a laptop to type their poetry. The laptop keyboard is composed of 4 rows of 10 keys. 30 of these are symbol keys, 4 are Shift keys, and 6 are Space keys. ``` +-----+...
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Two-Class Binary Neural Network for Handwritten Digits Description: The objective of this problem is to train a Binary Neural Network to classify images. The training occurs on your own computer, and you should submit a program which simply outputs the trained weights. The images are of handwritten digits...
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Two-sum Description: Per-Magnus is trying to add two integers, but he never learned how to. Write a program to help him with this most difficult task! ## Input The input consists of a single line with two integers $0 \le a \le 1\, 000$ and $0 \le b \le 1\, 000$. ## Output Output a single integer, ...
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Tycho Description: The planetary exploration vehicle Tycho VIII needs to get back to the home base after collecting mineral samples. Tycho travels in a straight line from position $0$ to the home base at position $b$. While moving, it advances at a slow but steady pace of $1$ unit per second. Every...
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Type Charts Description: You are playing the game Nudgémon, a common element of which is Nudgémon battles. In a battle, you and your opponent each start by sending out a Nudgémon of your choice, and then take turns attacking the opposing Nudgémon. Each attack has a type (an integer between $1$ and $n$), a...
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Typo Description: It is now far into the future and human civilization is ancient history. Archaeologists from a distant planet have recently discovered Earth. Among many other things, they want to decipher the English language. They have collected many printed documents to form a dictionary, but are ...
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Typo Squatting Description: After Coding Cup grew to over $100\, 000$ participants, our website codingcup.se faced a new problem. Spammers started to register domain names that were deceptively similar to ours, differing in just a single letter (such as codingcap.se). Unsuspecting participants some...
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Tónlistarlisti Description: Atli is very disorganized and only has one playlist of songs to listen to. All songs he likes go into the top of the list, and when he listens to music he starts with the top song and listens to them in order. If he has listened to them all, he starts anew from the top. For...
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Töflur Description: You really like playing games with your friend. You are currently playing a game where each player is given $n$ tiles with numbers on them. Each player then places the tiles down such that they form a sequence. Let $a_ j$ denote the number on the $j$-th tile in the sequence, for...
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Tölfræði Description: Murray Christianson was one of the most accomplished Scottish mathematicians of the 20th century but he was mostly known for his work in combinatorics and statistics. Among his more known work is Christianson’s theorem which revolves around permutations and permutation patterns. D...
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Tölvunarfræðingar telja Description: Computer scientists count a bit different from normal people. Most people start counting at $1$, then go to $2$, and after that $3$ follows and so forth. But the first number according to computer scientists is $0$. Therefore the second number is $1$ and the $1\, 337$-t...
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Tölvuíhlutir Description: Magni is purchasing a new desktop computer, which raises the important question of which components to buy to put into it. He of course doesn’t have infinite money, so the tricky thing is to get the best possible performance for the money he can spend. In the real world differ...
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Töskupökkun Description: New autumn, new airline. There’s construction work going on at Keflavík so the new airline “Pow!” can make room for themselves. Part of this process is laying out new belts where the luggage goes through a scanning gate that takes images of what is inside the bags. When purcha...
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Töskuröðun Description: As usual, Atli is travelling to yet another contest and has luggage with him. Rather than travelling light, he takes a near empty case with him so he can shop cheaply abroad. Often this results in him having to stand and wait for his luggage at the drop off when he is at his des...
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UTF-8 Description: Unicode is an international standard for encoding characters that was designed to overcome the limitations of older text encoding standards like ASCII. The main deficiency of ASCII and similar systems is that they represent only a very limited number of characters (primarily the char...
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Ultimate Binary Watch Description: The Ultimate Binary Watch is a maker project that uses small LEDs to display time on a watch face. The display uses four columns of four LEDs each, with each column representing one digit of the current time in hours and minutes. Time is displayed in $24$-hour for...
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Ultimate Pipe Game Description: Pipe games are interesting and hard puzzle games. In these games, our mission is to connect the pipes to make the water flow in the pipeline from a source to a destination, without leaking out. Today we are playing a new generation of pipe game, the Ultimate Pipe Game. ...
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Ultra-QuickSort Description: In this problem, you have to analyze a particular sorting algorithm. The algorithm processes a sequence of $n$ distinct integers by swapping two adjacent sequence elements until the sequence is sorted in ascending order. For the input sequence ``` 9 1 0 5 4 , ``` Ultra-QuickS...
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Umbral Decoding Description: You are planning a clever attack against a new encryption algorithm. To succeed, you need to find the key, which is a pair of integers $(p, q)$. We can think of the key as a point on a two-dimensional integer lattice whose location is unknown. However, you know that $(p...
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Umferð Description: Traffic jams are a major problem in larger cities like Njú Jork and Síattúl, especially during rush hour. In a traffic jam there are many cars with very little spacing between them, and they are not moving particularly fast. To simplify things we will assume that traffic is divided ...
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Umm Code Description: The current programming club president, Norbit, gives speeches at the weekly club meetings. Casual viewers are underwhelmed with the quality of Norbit’s elocution. Specifically, Norbit often hesitates during his speeches with interjections like “umm.” You, however, are no casual ...
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Un-bear-able Zoo Description: Given an integer $n$, and $n$ lines describing animals, output in alphabetical order the animals Dr. Back has in his zoo, followed by their count. ## Input The input will contain multiple test cases, up to $5$. Each test case contains a line containing a single integ...
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UnDetected Description: The Department of Defense has been designing autonomous robots that can infiltrate war zones and other hostile places in order to carry out missions. Now they want to test their latest design, the Penetrator1700, and they’ve hired you to help design the test environment. The te...
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Unbalanced Parentheses Description: Barry and Bruce are twin brothers. Bruce likes keeping his parenthetical sequences balanced. Barry would like to mess with Bruce by performing some operations on the sequence. Each operation is one of the following: * Change a single ‘(’ to a ‘)’ in the sequence. * Cha...
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Uncrossed Knight's Tour Description: A well-known puzzle is to “tour” all the squares of an $8 \times 8$ chessboard using a knight, which is a piece that can move only by jumping one square in one direction and two squares in an orthogonal direction. The knight must visit every square of the chessb...
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Undead or Alive Description: Now that zombies have learned to use SMS messaging, it is imperative to develop software for detecting zombies over text. After many long months of study, the top scientists have figured out how to do it. The key observation is that humans only use smiley faces, represented...
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Undrabarn Description: Jón and his wife, Gunna, just had their first child. Her name is Marta Elísabet, and to no one’s surprise, she is as smart as her parents. Her first word was the first $100$ digits of $\pi $, she knows all programming languages and just solved chess. Even though it may seem impossibl...
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Undratré Description: Unnur has an interest in plants. She waters all her plants once a day. Most of the plants are rather normal, but one of her trees is especially odd and unique. That’s Unnur’s wondertree. The wondertree is originally just a branch sticking out of the ground, but that branch is ofte...
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Unequalled Consumption Description: The ACM is only able to make a small number $n$ of different types of candy, but while limited in imagination, it is virtually limitless in resources, so it is able to produce as many as it wants of each type of candy. Furthermore, the candy types have different weig...
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Unicycle Counting Description: Going to circus college is not as fun as you were led to believe. You are juggling so many classes. Trapeze class is sometimes up, sometimes down. There’s a lot of tension in your high-wire class. And you’ve seen that lion taming can be cat-astrophic. The one pleasure yo...
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Unicyclic Count Description: A unicyclic graph is a graph with exactly one cycle. A spanning subgraph of a graph $G$ is a subgraph that has one component and includes all the vertices of $G$. Given a simple graph $G$, count the number of spanning unicyclic subgraphs. The illustration below ...
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Uniform Subtrees Description: Define a Uniform tree as one in which all of the nodes at a given level (i.e. distance from the root) have the same degree (i.e. number of children). Since all of the nodes at a given level have the same number of children, a uniform tree can be represented as simply a lis...
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Uniform Variation Description: The Alpine Community Performance Center (ACPC) is doing a promotional photoshoot at a ski resort. To create a sense of balance and inclusion in the photos, the ACPC has decided that the colour of the people’s gear must fit certain criteria. Each person has four pieces of gea...
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