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Digit Translation Description: You are given a string of lowercase letters. In one operation, if you can find a substring that is one of the written-out forms of one of the digits from zero to nine (“zero”, “one”, “two”, “three”, “four”, “five”, “six”, “seven”, “eight”, “nine”), you can replace that su...
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Digital Content Protection Description: Dan is working for a digital content protection company, which is responsible for the content protection of blu-ray discs based on a standard called Anti Content Misuse (ACM). The ACM standard works as follows. Assume there are $2^ n$ blu-ray drives/players. We ...
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Digital Speedometer Description: A digital speedometer shows a vehicle’s speed as integer miles per hour. There are occasions when the sensed speed varies between two integer values, such as during cruise control. Using a single threshold to round between adjacent integers often makes the display toggl...
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Digital display Description: There is a suspicion that some officers cheat when reporting exact time of various events. They antedate important documents and gain enormous profit by that. To eliminate such practices, ACM decided to install big digital clock on the wall of each office. Thank to this, ev...
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Digits Description: A googol written out in decimal has $101$ digits. A googolplex has one plus a googol digits. That’s a lot of digits! Given any number $x_{0}$, define a sequence using the following recurrence: Your task is to determine the smallest positive $i$ such that $x_{i} = x_{i-1}$. ## Input Inpu...
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Digits of Unity Description: At the beginning of the school year, the students in the International College of Paper Cutters (ICPC) choose their student IDs. The students can choose any positive integer less than or equal to some maximum number for their IDs, but no two students can choose the same stu...
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Digraphs Description: A digraph is a graph with orientation... oh, sorry, not this time. Let’s stop being nerds for a minute and talk about languages (human languages, not PHP). Digraphs are pairs of characters that represent one phoneme (sound). For example, “ch” in English (as in “church”) is a sing...
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Dihedral Group Description: In mathematics, the dihedral group $D_ n$ is the group of symmetries of a regular $n$-gon. Rotations and reflections are elements of $D_ n$, and in fact all elements of the dihedral group can be expressed as a series of rotations and reflections. Elements of $D_ n$ act o...
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Dim Sum Description: There are $n$ people (labelled $1, \dots , n$ counterclockwise) sitting around a round table, equally spaced. There are $n$ dishes (labelled $1, \dots , n$) on a rotating tray on the table. At the beginning, dish $i$ is right in front of person $i$ ($i=1, \dots ,n$). Pe...
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Dimensional Analysis Description: You are deriving some equations for physics homework and are worried you’ve made some mistakes. To debug them, you will apply dimensional analysis. In dimensional analysis, you remove all magnitudes and units from a set of equations until you are left only with strings...
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Ding Dong Ditch Description: Raunak and his friends want to play a prank on their neighbors by performing the classic "Ding Dong Ditch". They want to individually ring the doorbell of a number of their neighbors and then run away from there. But some neighbors are very dangerous, since they could get v...
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Dinner Description: For several years now, the Nordic Conference on Partitions and Combinatorics, NCPC, has had a growing number of participants. This year the organizing team is expecting an all time high record in the hundreds. Due to the politics of arranging this prestigious event, the conference s...
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Dinner Bet Description: Cesar and Raul like betting and good food, in no particular order. They want to try out a new fancy restaurant and they decided to make a bet – they are going to play a game and the loser pays for dinner. They have a box with $N$ balls. Each ball contains a distinct number betw...
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Dinner Time Description: What a feast! Yams, cranberries, turkey, stuffing, pie. Yum! But the best is the potatoes and gravy. Holiday feasts can also be stressful: people argue about politics and ask too many nosy questions. To complicate things, your family is huge with $10^{18}$ members so it seems ...
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Diplomacy Description: You are a member of the Senate of an ancient empire governed by a mighty dictator. You have joined a bipartisan secret committee of the Senate that is plotting to overthrow the dictator. In order for the plot to succeed, it is crucial that all the states in the empire ultimately...
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Directing Rainfall Description: Porto and the nearby Douro Valley are famous for producing port wine. Wine lovers from all over the world come here to enjoy this sweet wine where it is made. The International Consortium of Port Connoisseurs (ICPC) is organizing tours to the vineyards that are upstream ...
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Directory Management Description: Tired of using existing badly written operating systems, Hieu decided to write a new one. Of course, his new operating system will be awesome, bug-free, fast and easy to use. He has finished most of the work, and now he is asking you to do one last task: Implement a di...
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Dirty Driving Description: Like all other good drivers, you like to curse, swear and honk your horn at your fellow automobile drivers. Today you’re at the rear of a long line, brooding over the others’ inability to keep proper distance to the car in front. But are you really keeping your own distance? ...
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Disastrous Doubling Description: A scientist, E. Collie, is going to do some experiments with bacteria. Right now, she has one bacterium. She already knows that this species of bacteria doubles itself every hour. Hence, after one hour there will be $2$ bacteria. E. Collie will do one experiment every hour...
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Disastrous Downfall Description: There is a heavy rainfall over the Antique Cultural Museum, and the roof has sprung a leak! All the beautiful paintings risk destruction, if it weren’t for one brave night watchman standing in the water’s way – Klunkas Plaskocek. To protect all of the paintings, Klunkas ha...
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Disastrous Downtime Description: You’re investigating what happened when one of your computer systems recently broke down. So far you’ve concluded that the system was overloaded; it looks like it couldn’t handle the hailstorm of incoming requests. Since the incident, you have had ample opportunity to a...
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Disc District Description: You live in the Disc District of Flatland and work for the Nearest Convenient Plot Company (NCPC). Your job is to find the nearest convenient plot of land outside of the Disc District to build on. The Disc District can be described as a disc on a plane with center $(0, 0)$ a...
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Discoveries Description: Jonathan is writing a chess engine and he’s running into issues with discovered checks. Can you help him figure out if a given move made by the white pieces will lead to a discovered check against the opponent? A discovered check is a move that places the opponent in check by ...
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Discrete Logging Description: Given a prime $P$, $2 \le P < 2^{31}$, an integer $B$, $2 \le B < P$, and an integer $N$, $1 \le N < P$, compute the discrete logarithm of $N$, base $B$, modulo $P$. That is, find an integer $L \ge 0$ such that The solution to this problem requires a well know...
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Disgruntled Judge Description: Once upon a time, there was an nwerc judge with a tendency to create slightly too hard problems. As a result, his problems were never solved. As you can image, this made our judge somewhat frustrated. This year, this frustration has culminated, and he has decided that rat...
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Dishonest Lottery Description: You suspect your local lottery of cheating! Some numbers are coming up too often! Each week, the lottery randomly selects five numbers in the range from one to fifty. So, each number should appear about $10\% $ of the time if the numbers are truly chosen randomly. If a n...
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Disposable Switches Description: The data you have gathered consists of the map of the network, as well as the length of each cable. While you do not know the exact time it takes to send a network packet across each cable, you know that it can be calculated as $\ell / v + c$, where * $\ell $ is the ...
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Distance Description: The City of Manhattan is organized as a grid of streets and avenues, with streets running in the North-South direction and avenues running in the East-West direction. Streets are numbered from East to West starting from 1, and avenues are numbered from North to South starting from...
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Distinctive Character Description: The similarity between two characters $A$ and $B$ is calculated as follows: for each feature $f$, if both $A$ and $B$ have feature $f$ or if none of them have feature $f$, the similarity increases by one. Tira does not have a character yet. She would like to create ...
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Distracted Description: Everybody is either married or unmarried. Can you determine if a married person is looking at an unmarried person? ## Input The first line of input consists of two integers: the total number $N$ of people, and the number $L$ of these people who are looking at somebody else. Yo...
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Distributing Ballot Boxes Description: Today, besides SWERC’11, another important event is taking place in Spain which rivals it in importance: General Elections. Every single resident of the country aged 18 or over is asked to vote in order to choose representatives for the Congress of Deputies and th...
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Distributing Levels Description: Rare Candies are one of the scarcest resource in all of Pokemon, for a very good reason. They have the incredibly potent ability to raise a Pokemon’s level by $1$. They were seemingly impossible to mass produce until you stumbled upon a secret item that had never before...
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Distributing Poffins Description: Poffins are one of the most delicious treats that Pokemon love to eat. You want to reward your $N$ Pokemon for their hard work in helping you become the Pokemon Champion, so you decide to buy $M$ poffins and you lay them in a pile for all the Pokemon to take. Each Poke...
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Distributing Seats Description: A particular flights has $n$ passengers. The seats are divided into $r$ rows each containing $c$ seats. Every passenger $i$ is assigned to some particular seat located at row $a_ i$ and column $b_ i$. However, some passengers may be assigned to the same seat. Of cou...
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Div 2, Mul 2, Mul 3 Description: As a third-year student at Hogwarts School of Witchcraft and Wizardry, Harry has to study arithmetic (known as Arithmancy in the wizard world). Today’s Arithmancy lesson revolves around multiplication and division. Thus, for homework, Harry needs to write down $n$ integ...
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Diverse Contest Description: Write what you know! The judges for a certain programming competition have $n$ problems and are trying to prepare a contest using $k$ of them. The judges have tagged each problem with a list of topics needed to solve that problem. To not overly punish teams for not knowing...
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Diverse Cookies Description: Is a world without cookies really worth living in? Alf and Beata do not think so. That’s why they spent the entire weekend baking an enormous amount of cookies. They baked $A$ almond biscuits, $B$ butter cookies and $C$ chocolate macarons. It is now time to eat all these delicious...
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Divide Doughnut Description: This is an interactive problem. Khue and Hanh are obsessed with doughnuts although they are very much overweight. Over the last week, they worked very hard setting up the problems for ICPC Hanoi. To prepare for a long night of coding, they bought a super-large ring-shaped ...
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Divide and Conquer Description: Most people have heard of Julius Caesar, a Roman dictator who lived in the first century BC and who was famous, amongst other things, for defeating enemies by pitting them against each other, thereby preventing them from uniting against him, a strategy known as “Divide a...
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Divide by 100... Description: Dividing two numbers and computing the decimals is an extremely difficult task. Luckily, dividing a number by a “special” number is very easy (at least for us humans)! We will define the set of “special” numbers $S=\{ 10^ K\} $ for all non-negative integers $K$, i.e. $\{ ...
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Divide the Ducks Equally Description: As the benevolent ruler of POland, you want all your citizens to be happy. It is therefore deeply concerning that two children are quarreling. Specifically, they are arguing over $2N$ kodsport-ducks that are scattered across a plane, and the children disagree a...
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Dividing Kingdom Description: The Kingdom of Byteland has $n$ cities, numbered from $1$ to $n$. There are exactly $n-1$ roads in the kingdom, each connects a pair of cities. Using these roads, it is possible to go from any city to any other city. The king of Byteland wants to divide the kingdom into two h...
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Dividing Sequence Description: You are given an integer $N$. Your task is to find the longest sequence of integers $a_1<a_2<\dots < a_ k$, such that $a_ i$ divides $a_{i+1}$ and $1 \le a_ i \le N$ for all $i$. ## Input The input contains one line with integer $N, 1\leq N\leq 1\, 000\, 000$. ## Outpu...
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Divisibility Shortcut Description: There is a well-known shortcut (or “trick”) for determining whether or not a non-negative integer $n$ is divisible by $3$: * Add up the digits in the base-$10$ representation of $n$; call this sum $S_{10}(n)$. * If $S_{10}(n)$ is divisible by $3$, then ...
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Divisible Subsequences Description: Given a sequence of positive integers, count all contiguous subsequences (sometimes called substrings, in contrast to subsequences, which may leave out elements) the sum of which is divisible by a given number. These subsequences may overlap. For example, the sequenc...
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Division Description: Given positive integers $t$, $a$, and $b$ not bigger than $2\, 147\, 483\, 647$, establish whether $(t^ a - 1)/(t^ b -1)$ is an integer with less than $100$ digits. ## Input Each line of input contains a test case $t$, $a$ and $b$. There are at most $100$ lines of input. ## Output For...
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Divisor Counts Description: Given a positive integer $N$, compute the number of divisors for all integers $1 \le i \le N$. ## Input The first line contains the integer $N$ ($1 \le N \le 3\, 000\, 000$). ## Output For each $i$ between $1$ and $N$, output a line with the number of positive diviso...
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Divisor Game Description: RR and Flash are playing a game with a list of numbers that are distinct initially. In this game two players will take alternative turns. In each turn, a player can select a number $X$ in the list and replace it with number $D$ iff $D$ is a divisor of $X$ and $D$ is sm...
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Divisor Shuffle Description: All the positive divisors of two integers $A$ and $B$ were written down together in a list. The numbers on the list were then shuffled around. Can you determine what $A$ and $B$ were, based on the list? ## Input The first line contains an integer $N$ ($1 \le N \le 210...
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Divisors Description: Your task in this problem is to determine the number of divisors of ${n \choose k}$. Just for fun – or do you need any special reason for such a useful computation? ## Input The input consists of several instances, at most $11\, 000$. Each instance consists of a single line ...
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Divisors of a sum Description: You are given a positive integer $n$ and should print the number of positive divisors the sum $1 + 2 + \dots + n$ has. ## Input The first and only line of input contains a positive integer $n \leq 10^{15}$. ## Output Print the number of positive divisors the sum $1 + 2 + ...
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Divljak Description: Nowadays, there are a lot of unusual people. We won’t go into details, but instead focus on a certain type, to us personally the most interesting people. Of course, we’re talking about barbarians! There are a lot of barbarians, but only a few of them are truly important. This stor...
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Divvying Up Description: A solid competitive programming team can rack up a lot of prize money. Knowing how strong your team is, you are certain to win a lot of contests, so you had better sit down now and check that everybody will receive the same fair distribution of winnings. You will participate i...
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Dobra Description: Lea runs into a lot of words in her life. A lot of them she finds unpleasant. To compensate for that she started making up pleasant words. Lea makes up new words by writing a nice looking string of characters on a piece of paper. She than erases a few of the most nasty looking charac...
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Doctor Kattis Description: It is common for cats to have puncture wounds with different severity of infections. To help her local neighbourhood, Doctor Kattis decided to open a clinic! However, there are too many injured cats that come so she needs to prioritise her patients. Given the names of $\text...
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Dodecaphony Description: In the past century, a new style of music composition has emerged. Unlike more traditional methods based on keys and chords, the technique known as dodecaphony focuses on using all twelve notes equally. As a quick reminder, the twelve notes, in ascending order are, The sequenc...
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Dog & Gopher Description: A large field has a dog and a gopher. The dog wants to eat the gopher, while the gopher wants to run to safety through one of several gopher holes dug in the surface of the field. Neither the dog nor the gopher is a math major; however, neither is entirely stupid. The gopher deci...
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Dog Trouble Description: Yraglac is running a daycare service for dogs. He has $N$ dogs and he would like to take them on a walk. However, before he can walk the dogs, he needs to feed them first. Yraglac has $M$ feeding bowls. Because the dogs are very well trained, he can instruct a dog to eat f...
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Doing the Container Shuffle Description: Once the ships reach their destination, their standard-size cargo containers are unloaded from the ship onto stacks on land, from which they are moved to trains or trucks that deliver them to their destination. It turns out that moving containers is expensive, s...
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Domes Description: Saint Basil’s Cathedral is the best-known landmark of Moscow and maybe even of all of Russia. Built under Ivan the Terrible in the $16$th century, the cathedral is known for its colorful domes. No visit to the city is complete without taking a photo of the former church in Red Sq...
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Dominant Strings Description: Given two strings $s_{1}$ and $s_{2}$, we say that $s_{1}$ dominates $s_{2}$ if the (multi)set of characters in $s_{1}$ is a proper superset of the (multi)set of characters in $s_{2}$. For instance, “acmicpc” dominates “camp”, but it does not dominate “chimp” or “macpa...
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Dominating Duos Description: A group of people are standing in a line. Each person has a distinct height. You would like to count the number of unordered pairs of people in the line such that they are taller than everyone in between them in the line. More formally, let $d$ be a sequence of the heights...
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Domine Description: Mirko has a chessboard with $N$ rows and just three columns. Slavica has written an integer on each field. Mirko has $K$ dominoes at his disposal, their dimensions being $2 \times 1$, and has to arrange all of them on the board without overlapping, in a way that each domino cove...
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Domino Description: Mirko received an $N \times N$ table for his birthday, where a non-negative integer is written in each field of the table. Unfortunately, the written numbers are too large for Mirko’s taste, so he will place $K$ dominoes on top of the table that will cover the fields that are to...
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Domino Tiling Description: The aliens want to dominate the whole universe. So it comes as no surprise that their favorite game is played with domino tiles. A domino tile is a tile of size $1 \times 2$ with a digit 0-9 written on each half. Their game board is a rectangular array with a digit 0-9 wr...
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Dominoes 2 Description: Dominoes are lots of fun. Children like to stand the tiles on their side in long lines. When one domino falls, it knocks down the next one, which knocks down the one after that, all the way down the line. However, sometimes a domino fails to knock the next one down. In that case...
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Dominos Description: Dominos are lots of fun. Children like to stand the tiles on their side in long lines. When one domino falls, it knocks down the next one, which knocks down the one after that, all the way down the line. However, sometimes a domino fails to knock the next one down. In that case, we...
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Don't Be Fake Description: DontBeFake is an app where people get a notification at a random point in time, and they have to take a picture of what they are doing right now. You have $N$ friends on DontBeFake. Each friend has a set of intervals of seconds $[L, R]$ when they are available. If they g...
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Don't Fall Down Stairs Description: King Whomp is walking down Whomp Fortress to fight Mario. In order to get down, he must descend down a staircase consisting of $N$ steps. The height of every subsequent step is less than or equal to the step before (so that he can reach Mario at the end of the st...
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Don't Fence Me In Description: Given an orthogonal maze rotated $45$ degrees and drawn with forward and backward slash characters (see below), determine the minimum number of walls that need to be removed to ensure it is possible to escape outside of the maze from every region of the (possibly disconne...
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Don't Hunger Together Description: Ashley and Brandon are designing a survival video game called Don’t Hunger Together. The game works as follows: The game proceeds as a number of turns. Each turn consists of a day followed by a night. Several players have to survive for many turns in the wilderness. They...
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Don't be Perfect Description: Mara hates the word “perfect” - it means there’s nothing left to improve! That’s why she really hates graphs with perfect matchings - surely there’s something that can be done to make them better, so they shouldn’t be called perfect! You are given a randomly generated tre...
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Donations Description: Nicole is a retired wealthy businesswoman who is interested in donating to her favorite charity while maintaining the maximum wealth possible. She currently has $X$ dollars in the bank and would like to donate $Y$ dollars to the charity each year over the next $N$ years. The amou...
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Doodling Description: When thinking about a hard problem a lot of people like to doodle, to create “an unfocused drawing that can help the memory and improve abstract thinking”. The most basic form of doodle is a repetitive pattern covering the whole page. One way to create such a pattern is to take a ...
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Doorman Description: The doorman Bruno at the popular night club Heaven is having a hard time fulfilling his duties. He was told by the owner that when the club is full, the number of women and men let into the club should be roughly the same. When the night club opens, people wanting to enter the club...
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Doors Description: Alex is a circle of radius $R$. Well, life as a circle is not easy. If he were a point, moving around and passing through doors would be effortless. But now he has to carefully inspect the surroundings before making every move. Alex’s is initially at position $(0, y_\infty )$, where $y_...
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Dorm Room Divide Description: Bob and Alice are roommates at the International College of Polygonal Chambers (ICPC). To avoid conflict, they’ve agreed to divide their dorm room in half—as closely as possible. However, the room is shaped so irregularly that they need your help! Each dorm room is a (strictl...
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Dots and Boxes Description: Alice and Bob are playing Dots and Boxes. The game is played on an $N\times N$ square lattice of dots, and they alternate drawing a line segment between horizontally or vertically adjacent dots that haven’t been connected before. Every time a unit square is formed by fou...
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Double Agent Conference Description: Reed Der has finished organizing this year’s Double Agent Conference. The conference consists of a morning event, an afternoon event, and an evening event for local double agents to attend. Reed wants to know how many double agents attended at least one event, so h...
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Double Clique Description: You are given an undirected graph $G$ with $n$ nodes and $m$ edges. The set of vertices is $V$ and the set of edges is $E$. Let the Complement of $G$ be $G’$. The Complement of a graph is a graph with all of the same nodes, but if there’s no edge between nodes $a$ and $b$ in $G$...
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Double Dealing Description: Take a deck of $n$ unique cards. Deal the entire deck out to $k$ players in the usual way: the top card to player $1$, the next to player $2$, the $k^{th}$ to player $k$, the $(k+1)^{st}$ to player $1$, and so on. Then pick up the cards – place player $1$’s cards ...
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Double Deck Description: The rules of the game are simple. You shuffle both decks and place them face up in front of you, so at each point in time you see the top card in each deck. If the top cards are the same you can take them both and get one point. Otherwise you must discard either card. Your goal...
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Double Palindromes Description: You are given a positive integer $n$ and should print the number of positive integers $< n$ which are a palindromes both in base $10$ and base $2$. ## Input The first and only line of input contains a positive integer $n \leq 10^{12}$. ## Output Print the number of posit...
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Double Password Description: A computer at ICPC headquarters is protected by a four-digit password—in order to log in, you normally need to guess the four digits exactly. However, the programmer who implemented the password check left a backdoor in the computer—there is a second four-digit password. If...
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Double Sort Description: Given two integers $n$ and $m$ ($n \le m$), you generate a sequence of $n$ integers as follows: * First, choose $n$ distinct integers between $1$ and $m$, inclusive. * Sort these numbers in non-decreasing order. * Take the difference sequence, which transforms a ...
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Double Up Description: A Double Up game consists of a sequence of $n$ numbers $a_1, \ldots , a_ n$, where each $a_ i$ is a power of two. In one move one can either remove one of the numbers, or merge two identical adjacent numbers into a single number of twice the value. For example, for sequence $4,2,...
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Doubleplusgood Description: In many programming languages, the “plus” symbol (‘+’) has at least two standard meanings: * arithmetic addition * string concatenation arithmetic addition string concatenation Inspired by the old adage, “Variety is the spice of life,” the designers of the Doubleplusgood (D...
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Doubles Horseback Wrestling Description: The Central Asian Audaryspak League (CAAL) maintains a list of all horseback wrestlers and their ratings. From their previous experience with ordinary horseback wrestling, the NGEC has decided that the pairs are best balanced if the ratings of their two riders a...
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Doublets Description: A Doublet is a pair of words that differ in exactly one letter; for example, “booster” and “rooster” or “rooster” and “roaster” or “roaster” and “roasted”. You are given a dictionary of up to $25\, 143$ lower case words, not exceeding $16$ letters each. You are then given a numbe...
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Downpayment Description: Large houses cost a lot of money. Typically, a loan is required in order to finance the investment. The credit institutions provide a plentitude of different mortgage alternatives which come with diferent interest rates. Each alternative has a binding time, during which you may...
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Downsizing Description: Renowned nuclear physicist Adam Szmasczer has found a solution to global overpopulation and scarce resources: shrink everything! More precisely, he has found a way to teleport regions of space (both bounded and unbounded) to a bounded set of points inside a finite spherical cell...
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Draft Time Description: The NFL draft is soon upon us and it is only a few weeks until the best college players will have their dreams come true by joining a professional (American) football team. As always your friend Bubba just won’t stop talking about it. The NFL draft is a process where $N$ NFL teams ...
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Draga Frá Description: Gluggagægir is looking for his friend Atli. Initially, all windows had their curtains drawn. He has already drawn open many window curtains to try to find Atli, but so far without success. He asks you to write a program for him which will tell him how many curtains are remaining....
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Dragon Ball I Description: There is a legendary tale about Dragon Balls on Planet X: if one collects seven Dragon Balls, the Dragon God will show up and help you fulfill your wishes. One day, you are surprised to discover that the tale might possibly be true: you found a Dragon Ball radar at a flea ma...
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Dragon Ball II Description: There used to be a legendary tale about Dragon Balls on Planet X: if one collects seven Dragon Balls, the Dragon God will show up and help you fulfill your wishes. However, ever since a Dragon Ball radar was discovered, which pinpoints the location of each Dragon Ball, collecti...
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Dragon Balls Description: The balls are hidden at unknown locations in a 2D plane and you have been handed a Dragon Radar, designed by Bulma, that you must use to locate them. You can repeatedly fly to arbitrary locations, and the radar will then inform you about the distance to the closest Dragon Ball...
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Dragon Dropped Description: Rarity and Spike are best friends who often spend a lot of time together. Recently, however, Spike’s griffon pen pal Gabby from Griffonstone has come to town to work mail delivery, and he has decided to accompany her in her daily shifts, leaving little time for Rarity. With...
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Dragon Maid Description: Being new to the human world, Tohru realises romantic relationships are complicated, involving the reciprocation of the other party. Not to be deterred, Tohru decides to find a way to win over her master, Kobayashi-san’s heart. With Valentine’s day coming up, its Tohru’s be...
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Draughts Description: Draughts (Or checkers) is a game played by two opponents, on opposite sides of a $10 \times 10$ board. The board squares are painted black and white, as on a classic chessboard. One player controls the dark, and the other the light pieces. The pieces can only occupy the black squa...
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Drawing Circles Description: Alice is drawing circles on a paper with a coordinate system. Each circle is represented by an ordered tuple $(x, y, r)$, where $(x, y)$ is the position of the circle’s center and $r$ is the radius of the circle. Since she does not like two circles to cross each other, ...
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