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Coding
codecontest
Write Python code to solve the task. You are given three integers k, pa and pb. You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability pa / (pa + pb), add 'a' to the end of the sequence. Otherwise (with probability pb / ...
Step 1: The problem asks us to use a given algorithm to construct a sequence until there are at least k subsequences that form 'ab' and then calculate the expected number of times 'ab' appears in the sequence. Step 2: We need to determine the probability of getting 'ab' as a subsequence. Step 3: We can use dynamic p...
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Coding
codecontest
Write Python code to solve the task. Jiva is a self driven car and is out on its very first drive. It aims to earn some revenue by serving as taxi driver. It starts its journey from a point and travels in a line for 100 Km. It picks and drops passenger on the way,but can accommodate a maximum of M passengers at once. ...
Step 1: The problem requires us to calculate the total revenue earned by Jiva during its journey. Step 2: We need to apply fare and discounts at different times based on the number of passengers present. Step 3: To solve the problem, we need to iterate through the kilometers of the journey. Step 4: At each kilomet...
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Coding
codecontest
Write Python code to solve the task. Jiva is a self driven car and is out on its very first drive. It aims to earn some revenue by serving as taxi driver. It starts its journey from a point and travels in a line for 100 Km. It picks and drops passenger on the way,but can accommodate a maximum of M passengers at once. ...
Step 1: The given problem is to implement a revenue calculation mechanism for a taxi journey in terms of the number of passenger pick-ups and drop-offs. Step 2: We need to keep track of the discount calculations for each part of the journey, evaluate the revenue, and report if the taxi was full at any point. Step 3: ...
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Coding
codecontest
Write Python code to solve the task. You are given two integers x and y (it is guaranteed that x > y). You may choose any prime integer p and subtract it any number of times from x. Is it possible to make x equal to y? Recall that a prime number is a positive integer that has exactly two positive divisors: 1 and this ...
Step 1: The problem requires us to determine if it is possible to choose a prime number p and subtract it any number of times from x to make it equal to y. Step 2: Given that x > y, we can simply subtract y from x to get the difference m. Step 3: If the difference m is not equal to 1, we always choose the prime numb...
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Coding
codecontest
Write Python code to solve the task. You are given two integers x and y (it is guaranteed that x > y). You may choose any prime integer p and subtract it any number of times from x. Is it possible to make x equal to y? Recall that a prime number is a positive integer that has exactly two positive divisors: 1 and this ...
Step 1: To solve this problem, we need to iterate through each test case and check if it is possible to choose a prime number p and subtract it any number of times from x so that x becomes equal to y. Step 2: We can determine if it is possible by calculating the absolute difference between x and y. If the difference ...
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Coding
codecontest
Write Python code to solve the task. Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high. At the beginning of the first experiment there ...
Step 1: The problem involves simulating the growth of bacteria in a test tube based on certain parameters. Step 2: We can start by understanding the growth rule for the bacteria and how it affects the number of bacteria over time. Step 3: The first part of the provided code seems to handle a special case when k is e...
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Coding
codecontest
Write Python code to solve the task. Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high. At the beginning of the first experiment there ...
Step 1: The given problem involves the growth of bacteria in a test tube over time, with the presence of abnormalities affecting the number of bacteria. Step 2: We need to understand the rules governing the growth of bacteria based on given parameters k and b, as well as the time n needed to grow z bacteria in the fi...
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Coding
codecontest
Write Python code to solve the task. Two pirates Polycarpus and Vasily play a very interesting game. They have n chests with coins, the chests are numbered with integers from 1 to n. Chest number i has ai coins. Polycarpus and Vasily move in turns. Polycarpus moves first. During a move a player is allowed to choose a...
Step 1: The problem can be approached by making the player move in turns and taking coins from chests based on certain conditions. We can define a function to determine the minimum number of moves needed to finish the game, taking into account the number of coins in each chest and the conditions of the game. Step 2: ...
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Coding
codecontest
Write Python code to solve the task. Two pirates Polycarpus and Vasily play a very interesting game. They have n chests with coins, the chests are numbered with integers from 1 to n. Chest number i has ai coins. Polycarpus and Vasily move in turns. Polycarpus moves first. During a move a player is allowed to choose a...
Step 1: To solve this problem, we need to determine the minimum number of moves required for the game to finish. Step 2: We can approach this problem using a recursive function to simulate the moves made by the players. Step 3: The input consists of the number of chests with coins and the initial number of coins in...
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Coding
codecontest
Write Python code to solve the task. Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not. Two integers x, y are written on the blackboard. It is allowed to erase one of them and ...
Step 1: To solve this problem, we need to determine the minimum number of operations to make the given pair of integers m-perfect. Step 2: We can use conditional statements to check if the initial pair of integers is already m-perfect, negative, or neither. Step 3: Then, we can use a while loop to perform the replac...
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Coding
codecontest
Write Python code to solve the task. Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not. Two integers x, y are written on the blackboard. It is allowed to erase one of them and ...
Step 1: To solve this problem, we need to consider the conditions for when the pair of integers is m-perfect and when it is not. Step 2: We also need to consider the minimum number of operations required to transform the given pair to the m-perfect state. Step 3: We can start by checking the initial state of the pai...
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Coding
codecontest
Write Python code to solve the task. We'll call a set of positive integers a beautiful if the following condition fulfills: for any prime p, if <image>, then <image>. In other words, if one number from the set is divisible by prime p, then at least half of numbers from the set is divisible by p. Your task is to find a...
Step 1: We need to find a beautiful set of positive integers based on the given condition. Step 2: The size of the set is determined by the input integer k. Step 3: We can start by initializing a set with 1, and then apply the conditions for each prime number to add integers that satisfy the beautiful set condition....
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Coding
codecontest
Write Python code to solve the task. We'll call a set of positive integers a beautiful if the following condition fulfills: for any prime p, if <image>, then <image>. In other words, if one number from the set is divisible by prime p, then at least half of numbers from the set is divisible by p. Your task is to find a...
Step 1: To solve this problem, we need to find a set of positive integers that fulfills the condition of being a beautiful set. Step 2: The condition states that for any prime number p, if one number from the set is divisible by p, then at least half of the numbers from the set should be divisible by p. Step 3: We c...
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Coding
codecontest
Write Python code to solve the task. Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options: ...
Step 1: To solve this problem, we need to iterate through the sequence of integers representing each day and keep track of Vasya's activities to find the minimum possible number of days on which he will have a rest. Step 2: We can start by initializing a variable to store the number of days on which Vasya will have a...
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Coding
codecontest
Write Python code to solve the task. Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options: ...
Step 1: To solve this problem, we need to iterate through each day of Vasya's vacation and determine if he will have a rest. Step 2: We need to consider the restrictions that Vasya has in terms of consecutive days of the same activity. Step 3: We'll use a counter to keep track of the number of rest days and update i...
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Coding
codecontest
Write Python code to solve the task. Vasya plays The Elder Trolls III: Morrowindows. He has a huge list of items in the inventory, however, there is no limits on the size of things. Vasya does not know the total amount of items but he is sure that are not more than x and not less than 2 items in his inventory. A new pa...
Step 1: This problem requires us to determine the fewest number of modes needed to uniquely determine the number of items in Vasya's inventory. Step 2: We start by checking if there are particular conditions that allow a quick decision to be made or if it is impossible to determine the number of items. Step 3: We a...
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Coding
codecontest
Write Python code to solve the task. Vasya plays The Elder Trolls III: Morrowindows. He has a huge list of items in the inventory, however, there is no limits on the size of things. Vasya does not know the total amount of items but he is sure that are not more than x and not less than 2 items in his inventory. A new pa...
Step 1: This problem involves determining the minimum number of modes required for Vasya to uniquely determine the number of items in his inventory. Step 2: We need to consider the inputs provided and how Vasya can utilize the inventory view modes to find the required number of items. Step 3: Based on the given info...
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Coding
codecontest
Write Python code to solve the task. A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97. Alice is given a sequence of n composite numbe...
Step 1: To solve this problem, we need to identify a way to color the composite numbers such that the greatest common divisor (GCD) of any two elements with the same color is greater than 1. Step 2: We can iterate through the sequence of composite numbers and assign colors based on the factors of each number. Step 3:...
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Coding
codecontest
Write Python code to solve the task. A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97. Alice is given a sequence of n composite numbe...
Step 1: The problem asks us to color a sequence of composite numbers with a maximum of 11 colors so that no elements with the same color are coprime. Step 2: To solve this problem, we need to implement a function to check if a number is prime, then use this function to find the prime factors of each number in the seq...
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4f345c771b28f0ba43520702189e7db363cf9ff0c50b67def9b9dba45d35a5b3
Coding
codecontest
Write Python code to solve the task. Polycarp is in really serious trouble — his house is on fire! It's time to save the most valuable items. Polycarp estimated that it would take ti seconds to save i-th item. In addition, for each item, he estimated the value of di — the moment after which the item i will be completel...
Step 1: The problem requires us to save the maximum possible total value of items in Polycarp's house Step 2: We need to consider the time required to save each item, the time after which the item will burn, and the value of each item. Step 3: To maximize the total value of saved items, we need to find a set of item...
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cdffae75d1e6585536ad085e64518fd20a33c06aa046db3ee5f7913ee107fd98
Coding
codecontest
Write Python code to solve the task. Polycarp is in really serious trouble — his house is on fire! It's time to save the most valuable items. Polycarp estimated that it would take ti seconds to save i-th item. In addition, for each item, he estimated the value of di — the moment after which the item i will be completel...
Step 1: The problem is asking us to find the maximum possible total value of the set of saved items. We must save the items one after another, and Polycarp saves the items based on the time needed to save the item, ti. We need to consider the deadline after which the item will burn completely and the value of each ite...
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cdffae75d1e6585536ad085e64518fd20a33c06aa046db3ee5f7913ee107fd98
Coding
codecontest
Write Python code to solve the task. A dice is a cube, its faces contain distinct integers from 1 to 6 as black points. The sum of numbers at the opposite dice faces always equals 7. Please note that there are only two dice (these dices are mirror of each other) that satisfy the given constraints (both of them are show...
Step 1: To solve this problem, we need to determine whether it is possible to uniquely identify the numbers on the faces of all the dice in the tower based on the information given by Bob. Step 2: We can start by parsing the input to get the number of dice in the tower, the number Bob sees at the top of the tower, an...
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1a1e4b65ee26fc4ce3e634863ac0df1b2d664d4836b47dfa769eb67879cb5d34
Coding
codecontest
Write Python code to solve the task. A dice is a cube, its faces contain distinct integers from 1 to 6 as black points. The sum of numbers at the opposite dice faces always equals 7. Please note that there are only two dice (these dices are mirror of each other) that satisfy the given constraints (both of them are show...
Step 1: To solve this problem, we need to check whether it is possible to uniquely identify the numbers on the faces of all the dice in the tower based on Bob's observations. Step 2: We will start by iterating through the dice in the tower and using set operations to calculate the possible numbers on the remaining fa...
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1a1e4b65ee26fc4ce3e634863ac0df1b2d664d4836b47dfa769eb67879cb5d34
Coding
codecontest
Write Python code to solve the task. Dima and Anya love playing different games. Now Dima has imagined a new game that he wants to play with Anya. Dima writes n pairs of integers on a piece of paper (li, ri) (1 ≤ li < ri ≤ p). Then players take turns. On his turn the player can do the following actions: 1. choose t...
Step 1: The problem requires determining the number of ways Dima can write n pairs of integers to make sure that Anya wins the game, given the constraints. Step 2: Dima has to write out the pairs of integers such that Anya wins, and the number of ways to do it needs to be calculated and printed after dividing by 1000...
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Coding
codecontest
Write Python code to solve the task. Dima and Anya love playing different games. Now Dima has imagined a new game that he wants to play with Anya. Dima writes n pairs of integers on a piece of paper (li, ri) (1 ≤ li < ri ≤ p). Then players take turns. On his turn the player can do the following actions: 1. choose t...
Step 1: The problem describes a game that involves choosing pairs of numbers and replacing them according to certain conditions. Step 2: To solve this problem, we need to calculate the number of ways Dima can write out n pairs of integers (li, ri) such that the first player wins using optimal strategies. Step 3: The...
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f679fce7fdd2e53339f8acc70c935cc7413de1d2d02a234bfd7fbbbc96baf325
Coding
codecontest
Write Python code to solve the task. There is a new TV game on BerTV. In this game two players get a number A consisting of 2n digits. Before each turn players determine who will make the next move. Each player should make exactly n moves. On it's turn i-th player takes the leftmost digit of A and appends it to his or ...
Step 1: The problem requires finding the sequence of moves of Homer and Marge that gives them the maximum possible total prize. This involves making decisions about which player takes the leftmost digit of the number A and appends it to their number. The goal is to maximize the total prize by making strategic moves. ...
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62203e140af4e500d8ca4b1ee9858fcbb081f8ab68f0fb7fa369c89189a12f6a
Coding
codecontest
Write Python code to solve the task. There is a new TV game on BerTV. In this game two players get a number A consisting of 2n digits. Before each turn players determine who will make the next move. Each player should make exactly n moves. On it's turn i-th player takes the leftmost digit of A and appends it to his or ...
Step 1: To solve this problem, we need to maximize the total prize for both players by determining the sequence of moves that results in the highest total prize. Step 2: We can use dynamic programming to solve this problem. We'll create a 2D array to store the maximum total prize for each state of the game, and then ...
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62203e140af4e500d8ca4b1ee9858fcbb081f8ab68f0fb7fa369c89189a12f6a
Coding
codecontest
Write Python code to solve the task. Inna loves sweets very much. She has n closed present boxes lines up in a row in front of her. Each of these boxes contains either a candy (Dima's work) or nothing (Sereja's work). Let's assume that the boxes are numbered from 1 to n, from left to right. As the boxes are closed, In...
Step 1: To solve this problem, we need to simulate the process of Inna asking Dima questions about the candy in the boxes. We also need to calculate the minimum number of operations needed to make the answer to each question positive. This involves checking the candies in certain positions and adding or removing candi...
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72257170058c24299cb7701222674f4217c140945f2ddc642c1de793c6e4ff29
Coding
codecontest
Write Python code to solve the task. Inna loves sweets very much. She has n closed present boxes lines up in a row in front of her. Each of these boxes contains either a candy (Dima's work) or nothing (Sereja's work). Let's assume that the boxes are numbered from 1 to n, from left to right. As the boxes are closed, In...
Step 1: The problem requires us to calculate the minimum number of operations required to make the answer to each question positive. We can start by reading the input values and processing the data to determine the minimum number of actions required. Step 2: We will calculate the number of candies in two distinct int...
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72257170058c24299cb7701222674f4217c140945f2ddc642c1de793c6e4ff29
Coding
codecontest
Write Python code to solve the task. Notice that the memory limit is non-standard. Recently Arthur and Sasha have studied correct bracket sequences. Arthur understood this topic perfectly and become so amazed about correct bracket sequences, so he even got himself a favorite correct bracket sequence of length 2n. Unli...
Step 1: The problem requires us to restore a favorite correct bracket sequence given the approximate distances from the opening brackets to the corresponding closing ones. Step 2: We can use a stack-based approach to restore the correct bracket sequence using the given distances. Step 3: We need to track the positio...
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Coding
codecontest
Write Python code to solve the task. Notice that the memory limit is non-standard. Recently Arthur and Sasha have studied correct bracket sequences. Arthur understood this topic perfectly and become so amazed about correct bracket sequences, so he even got himself a favorite correct bracket sequence of length 2n. Unli...
Step 1: This problem involves restoring a correct bracket sequence given some information about the distances of opening and closing brackets. Step 2: We need to iterate over the given segments for each opening bracket and determine the corresponding closing bracket based on the given distance segments. Step 3: We s...
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46bcba31388bf9e3f93f87e008b4914ca9a45fb8664e7fc5a783abaf37e670f0
Coding
codecontest
Write Python code to solve the task. One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior. We will call person a a subordinates of another ...
Step 1: To solve this problem, we need to find the maximum possible efficiency of the workgroup that can be formed under the given conditions. Step 2: We can start by parsing the input to extract information about each employee. We can store the information in a data structure to keep track of each employee's relatio...
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409febbe75cc9949980e32c5d9e1d1578157a106bdc14aa1ec3037dabf266e30
Coding
codecontest
Write Python code to solve the task. One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior. We will call person a a subordinates of another ...
Step 1: The problem involves processing a hierarchical structure with efficiencies associated with each employee. Step 2: We need to traverse the hierarchy and compute the maximum possible efficiency of the workgroup based on the given condition. Step 3: A dynamic programming approach might be effective for processi...
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409febbe75cc9949980e32c5d9e1d1578157a106bdc14aa1ec3037dabf266e30
Coding
codecontest
Write Python code to solve the task. For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4. You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D? Constraints ...
Step 1: The problem is asking to calculate the number of positive integers N such that the reverse of N (without leading zeros) is N + D. Step 2: To solve this problem, we can use a recursive approach to calculate the number of valid N. We need to traverse through various combinations of the digits of N and check if ...
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Coding
codecontest
Write Python code to solve the task. For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4. You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D? Constraints ...
Step 1: To solve this problem, we need to determine the number of positive integers N that satisfy the given condition. Step 2: We can start by defining a recursive function, f, that takes three parameters: d, x, and y. Step 3: We can then calculate the number of positive integers N that satisfy the given condition ...
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51b1a08f2454f83cd385d7e363d38d2ca95b0012b350be372783805bbe99764a
Coding
codecontest
Write Python code to solve the task. Little Vasya's uncle is a postman. The post offices are located on one circular road. Besides, each post office has its own gas station located next to it. Petya's uncle works as follows: in the morning he should leave the house and go to some post office. In the office he receives ...
Step 1: The problem describes a scenario where Vasya's uncle needs to travel in a high-tech car around a circular road to visit post offices located on the road. The car consumes gasoline according to the distance traveled and needs refueling at the post offices. We are tasked with determining which post offices the u...
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Coding
codecontest
Write Python code to solve the task. Little Vasya's uncle is a postman. The post offices are located on one circular road. Besides, each post office has its own gas station located next to it. Petya's uncle works as follows: in the morning he should leave the house and go to some post office. In the office he receives ...
Step 1: The problem describes a scenario where the postman must start from a post office, travel a circular road, and return to the starting post office while refueling at each post office along the way. It also mentions that the sum of all gas amounts at each station is equal to the sum of the distances between the p...
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30a47ea7188e5b6f06e30e797a2d42bad70b9115afb7a17e9aecd33930b0ce9b
Coding
codecontest
Write Python code to solve the task. A new innovative ticketing systems for public transport is introduced in Bytesburg. Now there is a single travel card for all transport. To make a trip a passenger scan his card and then he is charged according to the fare. The fare is constructed in the following manner. There are...
Step 1: To solve this problem, we need to consider the minimum total cost of tickets to cover all trips. Step 2: We can iterate through the trips and for each trip, calculate the minimum total cost using the given ticket types. Step 3: We need to keep track of the minimum total cost for each trip and the total sum ...
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2dc4e69f5ba799b896df7acca0164ed0d4079c0b7b7d1bbadc2ff7de1e43c03c
Coding
codecontest
Write Python code to solve the task. A new innovative ticketing systems for public transport is introduced in Bytesburg. Now there is a single travel card for all transport. To make a trip a passenger scan his card and then he is charged according to the fare. The fare is constructed in the following manner. There are...
Step 1: The problem presents a ticketing system based on a series of trips taken by a passenger, with associated charges based on different fare types for one trip, 90 minutes, and one day (1440 minutes). Step 2: Our task is to write a program to calculate the sum the passenger is charged after each trip. Step 3: We...
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2dc4e69f5ba799b896df7acca0164ed0d4079c0b7b7d1bbadc2ff7de1e43c03c
Coding
codecontest
Write Python code to solve the task. Our hero - Maga is going to make a new contest for making the best teams. He is really excited about it. There will be S students in the contest. First N students in the final standings will be awarded. He has a list( favourite students list ) what contains the best students in in...
Step 1: The problem asks us to calculate the probability that at least K of Maga's favorite students will be awarded. Step 2: To solve this problem, we can use a combination calculation to compute the probability based on the number of favorite students, total students, and awarded students. Step 3: We'll need to ca...
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6e058da0ca941328f58ed88573ac2274e3fd3d0c260544131d289b7f74bea039
Coding
codecontest
Write Python code to solve the task. Our hero - Maga is going to make a new contest for making the best teams. He is really excited about it. There will be S students in the contest. First N students in the final standings will be awarded. He has a list( favourite students list ) what contains the best students in in...
Step 1: This problem asks us to calculate the probability that a certain number of students from a list of favorite students will win an award in a contest. Step 2: We are given the number of total students, the number of students who will be awarded, the number of favorite students, and the minimum number of favorit...
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6e058da0ca941328f58ed88573ac2274e3fd3d0c260544131d289b7f74bea039
Coding
codecontest
Write Python code to solve the task. Recently Watson learned the concept of coprime numbers and now he wonders given an array A1, A2 . . . AN what is the size of the largest subset of the array such that the each pair of elements in the subset is coprime. Watson asks Sherlock for help and in turn Sherlock needs you. ...
Step 1: To solve this problem, we need to find the size of the largest subset of the array such that each pair of elements in the subset is coprime. Step 2: We can start by defining a function to check if a number is prime, and another function to calculate the greatest common divisor (GCD) of two numbers. Step 3: W...
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6b4c1448c5b56321b7520d61ddad95a7b8bb30ceb4d0f3508eb0a272908b0efe
Coding
codecontest
Write Python code to solve the task. Recently Watson learned the concept of coprime numbers and now he wonders given an array A1, A2 . . . AN what is the size of the largest subset of the array such that the each pair of elements in the subset is coprime. Watson asks Sherlock for help and in turn Sherlock needs you. ...
Step 1: The problem is asking for the size of the largest subset of the array such that each pair of elements in the subset is coprime. Step 2: We can start by defining a function to check if a number is prime and use it to find all prime numbers in the given range. Step 3: Then we can define a function to count the...
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6b4c1448c5b56321b7520d61ddad95a7b8bb30ceb4d0f3508eb0a272908b0efe
Coding
codecontest
Write Python code to solve the task. Aizuwakamatsu City is known as the "City of History". About 400 years ago, the skeleton of the castle town was created by Gamo Ujisato, but after that, it became the central city of the Aizu clan 230,000 stones, whose ancestor was Hoshina Masayuki, the half-brother of Tokugawa's thi...
Step 1: The problem requires us to determine the minimum number of lanterns needed to light the streets connecting historic sites in Aizuwakamatsu City. Step 2: We are given the number of historic sites, the number of streets, and the distance between the historic sites. Step 3: We can use the Kruskal's algorithm to...
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Coding
codecontest
Write Python code to solve the task. Aizuwakamatsu City is known as the "City of History". About 400 years ago, the skeleton of the castle town was created by Gamo Ujisato, but after that, it became the central city of the Aizu clan 230,000 stones, whose ancestor was Hoshina Masayuki, the half-brother of Tokugawa's thi...
Step 1: The problem involves modeling the streets connecting historic sites and finding the minimum number of lanterns required on these streets. We need to minimize the number of lanterns while ensuring that all historic sites can be reached by following the streets decorated with lanterns. Step 2: To solve this pro...
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68b369fab67ee07eab210a9b9f1ca8397c583b25b15f11d2f8b246cd2e29cf64
Coding
codecontest
Write Python code to solve the task. Let f_{x} = c^{2x-6} ⋅ f_{x-1} ⋅ f_{x-2} ⋅ f_{x-3} for x ≥ 4. You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7). Input The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 ≤ n ≤ 10^{18}, 1 ≤ f_{1}, f_{2}, f_{3}, c ≤ 10^{9}). Output...
Step 1: The problem involves calculating a sequence based on a given recurrence relation and then finding the value of the sequence modulo a large number. Step 2: The solution uses matrix exponentiation to efficiently calculate f_n. Step 3: We can start by understanding the structure of the recursive relation and ho...
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824ebd4052cc976fc66db119c2116ae9be409fd8b52790ab0b7111e5da57fdf8
Coding
codecontest
Write Python code to solve the task. Let f_{x} = c^{2x-6} ⋅ f_{x-1} ⋅ f_{x-2} ⋅ f_{x-3} for x ≥ 4. You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7). Input The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 ≤ n ≤ 10^{18}, 1 ≤ f_{1}, f_{2}, f_{3}, c ≤ 10^{9}). Output...
Step 1: The problem requires the calculation of the value of a sequence defined by a recursive function with given initial values and a constant 'c'. Step 2: To solve the problem, we need to understand the recursive nature of the sequence, which is defined by the function f_x = c^(2x-6) * f_{x-1} * f_{x-2} * f_{x-3} ...
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824ebd4052cc976fc66db119c2116ae9be409fd8b52790ab0b7111e5da57fdf8
Coding
codecontest
Write Python code to solve the task. With the motto "Creating your own path," a shrine created a fortune-telling fortune with its own hands. Ask the person who draws the lottery to throw six stones first, then the line segment connecting the first and second of the thrown stones, the line segment connecting the third a...
Step 1: The problem statement requires us to calculate the area of a triangle formed by three line segments and determine the corresponding fortune based on the calculated area. Step 2: We can use mathematical principles to calculate the area of the triangle formed by the line segments. To do this, we'll first determ...
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77a06109a1938faacb0af386c5e6185121650cbfe34a85f6cbd74f4439586f83
Coding
codecontest
Write Python code to solve the task. With the motto "Creating your own path," a shrine created a fortune-telling fortune with its own hands. Ask the person who draws the lottery to throw six stones first, then the line segment connecting the first and second of the thrown stones, the line segment connecting the third a...
Step 1: The program should read the coordinates of the endpoints of three line segments and determine if they form a triangle. Step 2: If the points form a triangle, the program should calculate the area of the triangle and use the area to map it to a fortune. Step 3: The calculation of the triangle area and mapping...
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77a06109a1938faacb0af386c5e6185121650cbfe34a85f6cbd74f4439586f83
Coding
codecontest
Write Python code to solve the task. Miyako came to the flea kingdom with a ukulele. She became good friends with local flea residents and played beautiful music for them every day. In return, the fleas made a bigger ukulele for her: it has n strings, and each string has (10^{18} + 1) frets numerated from 0 to 10^{18}...
Step 1: The problem requires us to process multiple queries to determine the number of distinct pitches on a ukulele for a given range of frets. Step 2: We should start by understanding the ukulele's tuning and how to calculate the number of distinct pitches based on the fret range. Step 3: We also need to consider ...
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5fb62528bff18809ccd531ea526de73056fc5aa6c6c84095596dd76461bce1a6
Coding
codecontest
Write Python code to solve the task. Miyako came to the flea kingdom with a ukulele. She became good friends with local flea residents and played beautiful music for them every day. In return, the fleas made a bigger ukulele for her: it has n strings, and each string has (10^{18} + 1) frets numerated from 0 to 10^{18}...
Step 1: The given problem involves processing data from input to output. Step 2: We need to parse the inputs, process the queries, and calculate the number of different pitches within the specified fret range. Step 3: We can create a function to binary search for the number of different pitches using a given fret r...
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5fb62528bff18809ccd531ea526de73056fc5aa6c6c84095596dd76461bce1a6
Coding
codecontest
Write Python code to solve the task. You are given n - 1 integers a_2, ..., a_n and a tree with n vertices rooted at vertex 1. The leaves are all at the same distance d from the root. Recall that a tree is a connected undirected graph without cycles. The distance between two vertices is the number of edges on the sim...
Step 1: The problem requires maximizing the number of points gained after d moves by moving the red coin to any child of r and the blue coin to any vertex b'. The distance between the two vertices must be the same after d moves. The problem includes reading input, computing vertex distances, and selecting vertices to ...
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9097de2673f9bcd15770850c8dbafeb801e7e92b68a4ece7436bae454a885e68
Coding
codecontest
Write Python code to solve the task. You are given n - 1 integers a_2, ..., a_n and a tree with n vertices rooted at vertex 1. The leaves are all at the same distance d from the root. Recall that a tree is a connected undirected graph without cycles. The distance between two vertices is the number of edges on the sim...
Step 1: This problem involves optimizing the placement of red and blue coins on the vertices of a tree to maximize the points gained after d moves. Step 2: We can parse the input for each test case and represent the tree as an adjacency list. Step 3: Then, we can use dynamic programming to iterate through the tree ...
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9097de2673f9bcd15770850c8dbafeb801e7e92b68a4ece7436bae454a885e68
Coding
codecontest
Write Python code to solve the task. You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1, b2, ..., bk (1 ≤ b1 < b2 < ... < bk ≤ n) in such a way that the value of <image> is maximized. Chosen sequence can be empty. Print the maximum possible ...
Step 1: The problem requires finding the maximum possible value of a sum modulo m for a given array of integers. Step 2: We need to calculate all possible subsequence sums for the array and then find the maximum value of the subsequence sum modulo m. Step 3: To achieve this, we first calculate all the subsequence su...
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b8791309d449571771df5e99abdbf34ece386398008c97113d96b2c72e69d166
Coding
codecontest
Write Python code to solve the task. You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1, b2, ..., bk (1 ≤ b1 < b2 < ... < bk ≤ n) in such a way that the value of <image> is maximized. Chosen sequence can be empty. Print the maximum possible ...
Step 1: The problem requires finding the maximum value of a defined function based on input. Step 2: We have to find a sequence of indices that maximizes the value of the function. The chosen sequence can be empty. Step 3: We can approach this problem by iterating through all possible subsequences of the given arra...
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b8791309d449571771df5e99abdbf34ece386398008c97113d96b2c72e69d166
Coding
codecontest
Write Python code to solve the task. Petya loves volleyball very much. One day he was running late for a volleyball match. Petya hasn't bought his own car yet, that's why he had to take a taxi. The city has n junctions, some of which are connected by two-way roads. The length of each road is defined by some positive in...
Step 1: The problem involves finding the minimum cost for Petya to travel from one junction to another using taxis. Step 2: This is a routing problem, similar to Dijkstra's algorithm, where we need to find the shortest path and associated costs among connected junctions. Step 3: We can use Dijkstra's algorithm to fi...
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7b76abbff0e2653b55a842dd66e60cbada688760bf70fdb2b7a2e021adfa0960
Coding
codecontest
Write Python code to solve the task. Petya loves volleyball very much. One day he was running late for a volleyball match. Petya hasn't bought his own car yet, that's why he had to take a taxi. The city has n junctions, some of which are connected by two-way roads. The length of each road is defined by some positive in...
Step 1: The problem requires determining the minimum cost for Petya to travel from the initial junction to the volleyball stadium. Step 2: We can use Dijkstra's algorithm to find the minimum cost path to reach the destination junction. Step 3: The roads in the city and the taxi driver's maximum distance and cost are...
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7b76abbff0e2653b55a842dd66e60cbada688760bf70fdb2b7a2e021adfa0960
Coding
codecontest
Write Python code to solve the task. Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate s...
Step 1: The problem requires finding the minimum time the train would need to deliver all the candies based on different starting stations. Step 2: We'll need to determine the candy delivery time from each station, given the distribution of the candies. Step 3: We can refer to the input and output examples to unders...
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340e87dc7ed61df4d7a4941cf8b1efd378675426f0a6b34395e9b23cdbe77549
Coding
codecontest
Write Python code to solve the task. Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate s...
Step 1: The problem is asking us to calculate the minimum time needed for a train to deliver all candies if it starts from each station. Step 2: To solve this problem, we can store the number of candies and their minimum distance from each station, who has candies, to their destinations. Step 3: We then calculate th...
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340e87dc7ed61df4d7a4941cf8b1efd378675426f0a6b34395e9b23cdbe77549
Coding
codecontest
Write Python code to solve the task. You've been in love with Coronavirus-chan for a long time, but you didn't know where she lived until now. And just now you found out that she lives in a faraway place called Naha. You immediately decided to take a vacation and visit Coronavirus-chan. Your vacation lasts exactly x ...
Step 1: The goal of this problem is to maximize the number of hugs that can be received during a vacation period by visiting Coronavirus-chan on the best days. Step 2: To do this, we need a plan to determine the maximum number of hugs based on the structure of Naha's calendar and the specific number of days that can ...
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ebe0bf704b818a8d44845df8752644c8aeabae80a86fff88a3c66e2996059bf2
Coding
codecontest
Write Python code to solve the task. You've been in love with Coronavirus-chan for a long time, but you didn't know where she lived until now. And just now you found out that she lives in a faraway place called Naha. You immediately decided to take a vacation and visit Coronavirus-chan. Your vacation lasts exactly x ...
Step 1: This problem requires calculating the number of hugs you can get from Coronavirus-chan during a vacation. Step 2: We can achieve this by first calculating the cumulative number of days in each month and the cumulative hugs until each month. Step 3: Then, we can use binary search to find the optimal number of...
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ebe0bf704b818a8d44845df8752644c8aeabae80a86fff88a3c66e2996059bf2
Coding
codecontest
Write Python code to solve the task. Gerald has n younger brothers and their number happens to be even. One day he bought n2 candy bags. One bag has one candy, one bag has two candies, one bag has three candies and so on. In fact, for each integer k from 1 to n2 he has exactly one bag with k candies. Help him give n ...
Step 1: To solve this problem, we need to distribute the bags of candies to Gerald's brothers in a way that ensures each brother receives the same number of candies. Step 2: The number of candies in the bags is from 1 to n^2, and there are n brothers. Since n is specified to be even, we will ensure an equal number of...
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6e5aa85b69131472387f6db02ff3e43958fce48e829a189a606438c2a7651f79
Coding
codecontest
Write Python code to solve the task. Gerald has n younger brothers and their number happens to be even. One day he bought n2 candy bags. One bag has one candy, one bag has two candies, one bag has three candies and so on. In fact, for each integer k from 1 to n2 he has exactly one bag with k candies. Help him give n ...
Step 1: To solve this problem, we need to distribute the candy bags such that all brothers have the same number of candies. Step 2: We can start by iterating through each brother and then assigning distinct bags of candies such as to ensure that each brother gets a unique set of bags. Step 3: We also need to ensure ...
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6e5aa85b69131472387f6db02ff3e43958fce48e829a189a606438c2a7651f79
Coding
codecontest
Write Python code to solve the task. Monocarp has drawn a tree (an undirected connected acyclic graph) and then has given each vertex an index. All indices are distinct numbers from 1 to n. For every edge e of this tree, Monocarp has written two numbers: the maximum indices of the vertices of the two components formed ...
Step 1: The problem seems to involve constructing a tree based on given pairs of numbers and checking if the tree can produce the given list of pairs. Step 2: We need to first determine if a tree can be constructed from the given list of pairs and if so, find the edges of the tree. Step 3: We'll need to keep track...
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d55ece6be5cf032d016b8d13a08e319e225b633a76cfeb86f7a853af8aff7374
Coding
codecontest
Write Python code to solve the task. Monocarp has drawn a tree (an undirected connected acyclic graph) and then has given each vertex an index. All indices are distinct numbers from 1 to n. For every edge e of this tree, Monocarp has written two numbers: the maximum indices of the vertices of the two components formed ...
Step 1: The problem seems to require the construction of a valid tree based on the given list of pairs of numbers. The tree should produce the same pairs as given in the input file. Step 2: We can start by reading the input and processing the given list of pairs to check if a tree that can produce the list exists. St...
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d55ece6be5cf032d016b8d13a08e319e225b633a76cfeb86f7a853af8aff7374
Coding
codecontest
Write Python code to solve the task. Hag is a very talented person. He has always had an artist inside him but his father forced him to study mechanical engineering. Yesterday he spent all of his time cutting a giant piece of wood trying to make it look like a goose. Anyway, his dad found out that he was doing arts ra...
Step 1: The task requires understanding input parameters, such as the number of vertices for the strictly convex polygon, and the number of queries, and the descriptions of the wooden polygon. To start, the code initializes x, y coordinates and calculates the Centroid. This part of the code will help us to calculate ...
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72dda79c0ff7c93b832c9eca7b789d31518561445a33d2835eb9858aec3aa820
Coding
codecontest
Write Python code to solve the task. Hag is a very talented person. He has always had an artist inside him but his father forced him to study mechanical engineering. Yesterday he spent all of his time cutting a giant piece of wood trying to make it look like a goose. Anyway, his dad found out that he was doing arts ra...
Step 1: The problem requires performing queries on a polygon to manipulate its rotation and obtaining vertex coordinates. Step 2: We need to calculate the centroid of the polygon to use as a reference point and then apply the transformations and rotations based on the input queries. Step 3: When processing the quer...
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Coding
codecontest
Write Python code to solve the task. Zibi is a competitive programming coach. There are n competitors who want to be prepared well. The training contests are quite unusual – there are two people in a team, two problems, and each competitor will code exactly one of them. Of course, people in one team will code different...
Step 1: The problem describes a scenario where teams of two are created to solve two problems. The participants have different scores for the two problems, and the goal is to minimize the sum of the scores for each participant. Additionally, there are some pairs of people who don't like to cooperate, and they won't be...
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Coding
codecontest
Write Python code to solve the task. Zibi is a competitive programming coach. There are n competitors who want to be prepared well. The training contests are quite unusual – there are two people in a team, two problems, and each competitor will code exactly one of them. Of course, people in one team will code different...
Step 1: This is a complex problem involving combinatorics and optimization. The main task is to calculate the score of each participant given their preferences and restrictions. Step 2: To solve this problem, we can use a greedy approach to optimize the assignments of the problems such that the score of each particip...
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Coding
codecontest
Write Python code to solve the task. Alice is playing a game with her good friend, Marisa. There are n boxes arranged in a line, numbered with integers from 1 to n from left to right. Marisa will hide a doll in one of the boxes. Then Alice will have m chances to guess where the doll is. If Alice will correctly guess t...
Step 1: The problem wants to calculate the number of scenarios in which Marisa is able to win the game if she puts the doll in a certain box and performs tricks after each guess by Alice. Step 2: To solve this, we need to simulate the process of moving the doll based on the guesses made by Alice. Step 3: We can keep...
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Coding
codecontest
Write Python code to solve the task. Alice is playing a game with her good friend, Marisa. There are n boxes arranged in a line, numbered with integers from 1 to n from left to right. Marisa will hide a doll in one of the boxes. Then Alice will have m chances to guess where the doll is. If Alice will correctly guess t...
Step 1: The problem is to calculate the number of scenarios in which Marisa can win the game based on where she puts the doll at the beginning and the end of the game. Step 2: We need to consider the game order and the number of scenarios based on the sequence of guesses made by Alice. Step 3: To solve this problem,...
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83e257f03646cca0ca2a905b1bcafe06f5a3a068310d52b129d6c8e7c4bc1b4c
Coding
codecontest
Write Python code to solve the task. You are given a directed graph G which can contain loops (edges from a vertex to itself). Multi-edges are absent in G which means that for all ordered pairs (u, v) exists at most one edge from u to v. Vertices are numbered from 1 to n. A path from u to v is a sequence of edges such...
Step 1: The problem involves finding the number of paths from vertex 1 to each vertex v in a directed graph. Step 2: We can use the concept of strongly connected components (SCCs) to solve this problem. Step 3: To do this, we can first find all the SCCs in the graph and then use dynamic programming to calculate the ...
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Coding
codecontest
Write Python code to solve the task. You are given a directed graph G which can contain loops (edges from a vertex to itself). Multi-edges are absent in G which means that for all ordered pairs (u, v) exists at most one edge from u to v. Vertices are numbered from 1 to n. A path from u to v is a sequence of edges such...
Step 1: The problem requires us to create a function that calculates the number of paths from vertex 1 to each of the other vertices in the graph. Step 2: To do this, we can use a depth-first search algorithm to visit the vertices and determine the path counts from vertex 1 to each vertex. Step 3: We'll start by cr...
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Coding
codecontest
Write Python code to solve the task. Manao's friends often send him new songs. He never listens to them right away. Instead, he compiles them into a playlist. When he feels that his mind is open to new music, he opens the playlist and starts to listen to the songs. Of course, there are some songs that Manao doesn't pa...
Step 1: The problem requires us to calculate the maximum expected listening time over all permutations of songs. Step 2: To solve this problem, the main logic involves going through all possible orders of songs in the playlist and calculating the expected listening time for each order. Step 3: One way to solve this...
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Coding
codecontest
Write Python code to solve the task. Manao's friends often send him new songs. He never listens to them right away. Instead, he compiles them into a playlist. When he feels that his mind is open to new music, he opens the playlist and starts to listen to the songs. Of course, there are some songs that Manao doesn't pa...
Step 1: The given problem deals with finding the maximum expected listening time over all permutations of songs in the playlist. Step 2: We need to calculate the expected value of the listening time for each permutation and find the maximum among them. Step 3: To do this, we will iterate through all permutations of ...
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Coding
codecontest
Write Python code to solve the task. Barney lives in country USC (United States of Charzeh). USC has n cities numbered from 1 through n and n - 1 roads between them. Cities and roads of USC form a rooted tree (Barney's not sure why it is rooted). Root of the tree is the city number 1. Thus if one will start his journey...
Step 1: The problem requires us to find the expected value of starting_time for each city i in USC. This suggests that we need to find the average starting time for each city based on the DFS algorithm provided. Step 2: We can start by parsing the input to represent the tree using a list of children for each city. St...
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Coding
codecontest
Write Python code to solve the task. Barney lives in country USC (United States of Charzeh). USC has n cities numbered from 1 through n and n - 1 roads between them. Cities and roads of USC form a rooted tree (Barney's not sure why it is rooted). Root of the tree is the city number 1. Thus if one will start his journey...
Step 1: The problem asks to find the expected value of the starting time for each city in the rooted tree. The DFS algorithm is used to run the depth first search starting from the root. It uses a pseudo code to achieve this. The expected value of the starting time for each city is calculated based on the number of ti...
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946143fde969588f593eebc5f66aeb6f469367510b2691f145c79c00605444f5
Coding
codecontest
Write Python code to solve the task. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik solved the task immediately. Can you? You are given a set of digits, your task is to find...
Step 1: This problem solving task requires understanding the rules of divisibility by 2, 3, and 5. Step 2: We need to find the maximum integer that can be made from the given set of digits while adhering to the divisibility conditions. Step 3: The input integer n specifies the number of digits in the set, and the se...
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Coding
codecontest
Write Python code to solve the task. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik solved the task immediately. Can you? You are given a set of digits, your task is to find...
Step 1: To solve this problem, we first need to understand the constraints and requirements for building the maximum integer from the given set of digits. Step 2: We also need to consider the divisibility requirement by 2, 3, and 5, as well as the rule against leading zeroes. Step 3: We can start by parsing the inpu...
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Coding
codecontest
Write Python code to solve the task. You have a rooted tree consisting of n vertices. Let's number them with integers from 1 to n inclusive. The root of the tree is the vertex 1. For each i > 1 direct parent of the vertex i is pi. We say that vertex i is child for its direct parent pi. You have initially painted all t...
Step 1: The problem is asking us to determine the number of distinct possible colorings of the vertices of the tree and find its remainder of division by 1000000007 (109 + 7). Step 2: We can iteratively perform the painting operation using recursion, keeping track of the count of different colorings using dynamic pro...
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Coding
codecontest
Write Python code to solve the task. You have a rooted tree consisting of n vertices. Let's number them with integers from 1 to n inclusive. The root of the tree is the vertex 1. For each i > 1 direct parent of the vertex i is pi. We say that vertex i is child for its direct parent pi. You have initially painted all t...
Step 1: The problem can be approached by defining a function to calculate the number of distinct possible colorings of the vertices of the given tree. We need to have a recursive approach that tracks the colorings of the vertices based on certain probabilities. The final result will be the number of distinct possible ...
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Coding
codecontest
Write Python code to solve the task. A mad scientist Dr.Jubal has made a competitive programming task. Try to solve it! You are given integers n,k. Construct a grid A with size n × n consisting of integers 0 and 1. The very important condition should be satisfied: the sum of all elements in the grid is exactly k. In o...
Step 1: The problem requires us to create a grid of size n x n consisting of integers 0 and 1 such that the sum of all the elements in the grid is equal to k, and the value f(A) is minimized. Step 2: To solve this, we can calculate the minimal value of f(A) by dividing k by n to get the average value per row, then di...
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Coding
codecontest
Write Python code to solve the task. A mad scientist Dr.Jubal has made a competitive programming task. Try to solve it! You are given integers n,k. Construct a grid A with size n × n consisting of integers 0 and 1. The very important condition should be satisfied: the sum of all elements in the grid is exactly k. In o...
Step 1: The problem requires constructing a grid of size n x n consisting of 0 and 1 such that the sum of all elements in the grid is exactly k. Step 2: We need to calculate the minimum possible value of f(A) for each test case. The function f(A) is defined as (max(R)-min(R))^2 + (max(C)-min(C))^2, where R_i are row ...
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3c6646cf1dcc16e9d17031fc3c8dca157ed7ba146885a84bc0f84eaecb26082b
Coding
codecontest
Write Python code to solve the task. You play a computer game. Your character stands on some level of a multilevel ice cave. In order to move on forward, you need to descend one level lower and the only way to do this is to fall through the ice. The level of the cave where you are is a rectangular square grid of n row...
Step 1: The problem mentions that the player can move to cells that are side-adjacent, and the ice on a cell becomes cracked if the character fails to move to the cell or the character moves away from this cell. This suggests that we will need to implement a depth-first search (DFS) algorithm to determine if it's poss...
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9dd56c377a252e7e730ce7f50585d8247fad7fb8a320053b230d086ecc4f5840
Coding
codecontest
Write Python code to solve the task. You play a computer game. Your character stands on some level of a multilevel ice cave. In order to move on forward, you need to descend one level lower and the only way to do this is to fall through the ice. The level of the cave where you are is a rectangular square grid of n row...
Step 1: The problem involves finding a path from the starting cell to the destination cell while navigating through the cave. We can use depth-first search (DFS) to traverse the cave and find the destination cell. Step 2: The DFS algorithm will involve moving to adjacent cells until the destination is reached. We als...
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9dd56c377a252e7e730ce7f50585d8247fad7fb8a320053b230d086ecc4f5840
Coding
codecontest
Write Python code to solve the task. Alook was composing magical spells for his mage master. The mage was good at spellcasting but since spell design requires intricate mathematics, this task was given to Alook who had the gift of numbers. The power contained in a spell is a function of its lexicographical structure, ...
Step 1: The problem requires finding the number of phonetically different spells the mage casts, given the length of the spells in terms of phonemes. To solve this problem, we need to use a mathematical formula to find the number of different phonetic variations for each spell length. We can use the concept of Fibonac...
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86b582539a5726be89f3fbef226a59cb9c6a993b253ce7212af6b46952ad1476
Coding
codecontest
Write Python code to solve the task. Alook was composing magical spells for his mage master. The mage was good at spellcasting but since spell design requires intricate mathematics, this task was given to Alook who had the gift of numbers. The power contained in a spell is a function of its lexicographical structure, ...
Step 1: We need to calculate the number of phonetically different spells the mage can cast for a given length of phonemes. Step 2: We need to understand the relationship between lexicographical structures and phonetic variations to determine the number of different spells. Step 3: The output is expected to be large,...
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86b582539a5726be89f3fbef226a59cb9c6a993b253ce7212af6b46952ad1476
Coding
codecontest
Write Python code to solve the task. <image> This figure shows railway tracks for reshuffling cars. The rail tracks end in the bottom and the top-left rail track is used for the entrace and the top-right rail track is used for the exit. Ten cars, which have numbers from 1 to 10 respectively, use the rail tracks. We ...
Step 1: To solve this problem, we need to simulate the movement of the cars on the railway tracks represented by the given sequence. Step 2: We can use a stack data structure to keep track of the cars on the railway tracks. Step 3: When a car enters, we push it onto the stack. When a car exits, we pop the top car fr...
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a2b89630ab171bee4bdf69ed66298d4cd969d9e72fd4d013f4dbb4fd7ee8de76
Coding
codecontest
Write Python code to solve the task. <image> This figure shows railway tracks for reshuffling cars. The rail tracks end in the bottom and the top-left rail track is used for the entrace and the top-right rail track is used for the exit. Ten cars, which have numbers from 1 to 10 respectively, use the rail tracks. We ...
Step 1: To solve this problem, we need to simulate the comings and goings of cars on the railway tracks based on the input sequence. Step 2: We can use a stack to keep track of the cars on the tracks. Each time we encounter a car number, we push it onto the stack. When we encounter a 0, we pop a car number from the s...
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a2b89630ab171bee4bdf69ed66298d4cd969d9e72fd4d013f4dbb4fd7ee8de76
Coding
codecontest
Write Python code to solve the task. Every superhero has been given a power value by the Felicity Committee. The avengers crew wants to maximize the average power of the superheroes in their team by performing certain operations. Initially, there are n superheroes in avengers team having powers a_1, a_2, …, a_n, respe...
Step 1: The problem requires maximizing the average power of the Avengers team by performing operations on the superhero powers. Step 2: To achieve maximum average power, we need to consider removing superheroes from the team or increasing the power of a superhero within the constraints of maximum operations. Step 3:...
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3f1138b3f722a5160cdd85a2717f37c554873b242656fdb8b4b5aa89cc497822
Coding
codecontest
Write Python code to solve the task. Every superhero has been given a power value by the Felicity Committee. The avengers crew wants to maximize the average power of the superheroes in their team by performing certain operations. Initially, there are n superheroes in avengers team having powers a_1, a_2, …, a_n, respe...
Step 1: To solve this problem, we will devise a strategy to maximize the average power of the superheroes. This strategy will involve removing a superhero from the team or increasing the power of a superhero. We should aim to remove superheroes with lower power and increase the power of the remaining superheroes to ma...
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3f1138b3f722a5160cdd85a2717f37c554873b242656fdb8b4b5aa89cc497822
Coding
codecontest
Write Python code to solve the task. This problem is split into two tasks. In this task, you are required to find the maximum possible answer. In the task Village (Minimum) you are required to find the minimum possible answer. Each task is worth 50 points. There are N houses in a certain village. A single villager liv...
Step 1: This problem involves finding an optimal assignment of new houses for the villagers so that the total length of the shortest paths between the old and new houses is maximized. Step 2: We can start by parsing the input to represent the village as a graph, where the houses are nodes and the roads are edges. Ste...
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f8932f065e3c60f6f833aa65a780633abb521683cdabd51bb5c0f94030de64f8
Coding
codecontest
Write Python code to solve the task. This problem is split into two tasks. In this task, you are required to find the maximum possible answer. In the task Village (Minimum) you are required to find the minimum possible answer. Each task is worth 50 points. There are N houses in a certain village. A single villager liv...
Step 1: The first task of the problem is to find the largest possible total length in kilometers of the shortest paths between the old and the new houses for all villagers. Step 2: The second task is to find an example assignment of the new houses to the villagers. Step 3: To solve the problem, we need to implement ...
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f8932f065e3c60f6f833aa65a780633abb521683cdabd51bb5c0f94030de64f8
Coding
codecontest
Write Python code to solve the task. There are n + 2 towns located on a coordinate line, numbered from 0 to n + 1. The i-th town is located at the point i. You build a radio tower in each of the towns 1, 2, ..., n with probability 1/2 (these events are independent). After that, you want to set the signal power on each...
Step 1: The given problem involves building towers in designated towns and calculating the probability that a proper signal power allocation can be achieved according to the given constraints. The problem seems to involve dynamic programming, probability calculations, and modular arithmetic. Step 2: We need to analyz...
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c657987f4194274f62a65256d663178d5015c6808f2d6ea3bd101c5c33c73288
Coding
codecontest
Write Python code to solve the task. There are n + 2 towns located on a coordinate line, numbered from 0 to n + 1. The i-th town is located at the point i. You build a radio tower in each of the towns 1, 2, ..., n with probability 1/2 (these events are independent). After that, you want to set the signal power on each...
Step 1: The problem requires calculating the probability that after building the towers, there will be a way to set signal powers to meet all constraints. To approach this problem, we can use dynamic programming to calculate the probability. We can initialize a dynamic programming array to store the probabilities. We...
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c657987f4194274f62a65256d663178d5015c6808f2d6ea3bd101c5c33c73288
Coding
codecontest
Write Python code to solve the task. It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For example, he can hit the ball di...
Step 1: The problem requires us to calculate the point on the wall to which Robo-Wallace should kick the ball so that it bounces off the wall and goes straight to the goal. Step 2: To do this, we first need to calculate the point based on various inputs such as the coordinates of the goal, wall, and ball, as well as ...
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6eead3888dd8336799cbe72e4ff6bc2561d27fed5f8f7061ae27765a3e7f1a20
Coding
codecontest
Write Python code to solve the task. It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For example, he can hit the ball di...
Step 1: The problem requires determining the spot on the wall to which Robo-Wallace should kick the ball so that it bounces once and only once off the wall and goes straight to the goal. Step 2: We can calculate the abscissa of the point of aiming using a given formula based on the y-coordinates and coordinates of th...
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6eead3888dd8336799cbe72e4ff6bc2561d27fed5f8f7061ae27765a3e7f1a20
Coding
codecontest
Write Python code to solve the task. The research center Q has developed a new multi-core processor. The processor consists of n cores and has k cells of cache memory. Consider the work of this processor. At each cycle each core of the processor gets one instruction: either do nothing, or the number of the memory cell...
Step 1: The problem necessitates processing instructions for multiple cores across numerous cycles, simulating an environment where there might be conflicts causing deadlock. Step 2: We are given m cycles and k memory cells, and given instructions on what each core should do each cycle. Step 3: For each core, we nee...
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a9218cba681880755a29d32d915980c6de5ed285cdb603a62d0120eb5d00b1d0
Coding
codecontest
Write Python code to solve the task. The research center Q has developed a new multi-core processor. The processor consists of n cores and has k cells of cache memory. Consider the work of this processor. At each cycle each core of the processor gets one instruction: either do nothing, or the number of the memory cell...
Step 1: We need to simulate the processor for a given set of instructions and track the cores to resolve conflicts and detect deadlocks. Step 2: I will implement a program to simulate the processor for m cycles. Step 3: For each cycle, I will define for each core the number of the cycle during which it will become l...
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a9218cba681880755a29d32d915980c6de5ed285cdb603a62d0120eb5d00b1d0
Coding
codecontest
Write Python code to solve the task. Devu is a renowned classical singer. He is invited to many big functions/festivals. Recently he was invited to "All World Classical Singing Festival". Other than Devu, comedian Churu was also invited. Devu has provided organizers a list of the songs and required time for singing th...
Step 1: The problem requires us to find an optimal schedule for a music event featuring Devu and Churu, while following certain conditions. Step 2: We need to calculate the total time taken by Devu to sing the songs and the total number of jokes Churu can crack. Step 3: Then we should compare the total time taken b...
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