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Coding | codecontest | Write Python code to solve the task.
Creatnx has n mirrors, numbered from 1 to n. Every day, Creatnx asks exactly one mirror "Am I beautiful?". The i-th mirror will tell Creatnx that he is beautiful with probability (p_i)/(100) for all 1 ≤ i ≤ n.
Creatnx asks the mirrors one by one, starting from the 1-st mirror. Ever... | Step 1: To solve this problem, we need to calculate the expected number of days until Creatnx becomes happy based on the given probabilities for each mirror.
Step 2: We can use the concept of expected value to calculate this. The expected value is the weighted average of all possible values, where the weight assigned... | 020a153896302f1b0f7b49d3e0010bb0992318f6d9a46fb8bbe210e84287a183_1_1 | 60445319412361e1afbfc33bfee1fb56cbf1acea2accf404e1afb1730c805fd6 |
Coding | codecontest | Write Python code to solve the task.
A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder.
You are given two integers x and y. Find the number of special pairs (a,b) such that 1≤ a ≤ x and 1 ≤ b ≤ y... | Step 1: To solve this problem, we need to find the number of special pairs (a,b) such that 1 ≤ a ≤ x and 1 ≤ b ≤ y.
Step 2: We can use a loop to iterate through possible values of a and b and check if the pair is special based on the given condition.
Step 3: For each test case, we'll calculate the number of special... | 0fcb1611cced24a28d3557654714a79a77fd6d45f25c75ffda4f439338625c58_1_1 | 37d2f13059f6fdeadda96fd7495ef800421d966705ee7827b48f348785f83d97 |
Coding | codecontest | Write Python code to solve the task.
A pair of positive integers (a,b) is called special if ⌊ a/b ⌋ = a mod b. Here, ⌊ a/b ⌋ is the result of the integer division between a and b, while a mod b is its remainder.
You are given two integers x and y. Find the number of special pairs (a,b) such that 1≤ a ≤ x and 1 ≤ b ≤ y... | Step 1: The problem requires finding special pairs of integers (a,b) such that 1≤ a ≤ x and 1 ≤ b ≤ y and ⌊ a/b ⌋ = a mod b.
Step 2: The given code uses a loop to iterate through the values of i, x, and y to calculate the number of special pairs.
Step 3: We need to understand the logic of the code and ensure that it... | 51a03ec43647a972efd00374eeac70c87eb323dda7805b23f8ecb0ff1aa8ba82_1_1 | 37d2f13059f6fdeadda96fd7495ef800421d966705ee7827b48f348785f83d97 |
Coding | codecontest | Write Python code to solve the task.
You can't possibly imagine how cold our friends are this winter in Nvodsk! Two of them play the following game to warm up: initially a piece of paper has an integer q. During a move a player should write any integer number that is a non-trivial divisor of the last written number. Th... | Step 1: The problem requires us to determine which player wins a game based on the rules described. The key aspect to consider is finding non-trivial divisors of a given number and using the divisors to determine the winning or losing player.
Step 2: The main function needs to read the input number q, find the diviso... | 8382d98efe02f565e54d8479ea77bf92efc4888ae63273c74a0f1c4fa956e434_1_1 | ce286254ce09c5ac2aa6d6429486041dfd79a8c52a575ae79595aa3eeee19809 |
Coding | codecontest | Write Python code to solve the task.
You can't possibly imagine how cold our friends are this winter in Nvodsk! Two of them play the following game to warm up: initially a piece of paper has an integer q. During a move a player should write any integer number that is a non-trivial divisor of the last written number. Th... | Step 1: The problem requires us to create a function to determine which player wins the game by considering that both players play optimally.
Step 2: We need to find the non-trivial divisors of the given number.
Step 3: Then we need to determine which player will win the game based on the non-trivial divisors.
Step ... | fd2eda79de9b0bf28e5a00340993652b6f78d81a5d85ff9da3f8252a3629f084_1_1 | ce286254ce09c5ac2aa6d6429486041dfd79a8c52a575ae79595aa3eeee19809 |
Coding | codecontest | Write Python code to solve the task.
Limak is a little polar bear. He likes nice strings — strings of length n, consisting of lowercase English letters only.
The distance between two letters is defined as the difference between their positions in the alphabet. For example, <image>, and <image>.
Also, the distance bet... | Step 1: To solve this problem, we need to understand the constraints and how the distance between letters in the alphabet affects the nice string.
Step 2: We can calculate the distance between each letter of the input string and determine if it is possible to transform the string into a nice string that satisfies the... | 23997a4ee491c87e562b61f438ec6c395792541fc4875043f1351799ffa3dbdf_1_1 | bd0fb2926f9c34937e4ae1ab94a11568aa0d8be51e2b16ba1f2d6e16950a4f9a |
Coding | codecontest | Write Python code to solve the task.
Limak is a little polar bear. He likes nice strings — strings of length n, consisting of lowercase English letters only.
The distance between two letters is defined as the difference between their positions in the alphabet. For example, <image>, and <image>.
Also, the distance bet... | Step 1: To solve this problem, we need to understand the requirements for a nice string s' that satisfies the given conditions.
Step 2: We need to calculate the distance between Limak's given string s and the desired nice string s' to check if it is possible to form such a string.
Step 3: If the distance between the... | f14259ff2e57d23ece8645984e0f97718999386cf1886a7e2e00cf528de1649d_1_1 | bd0fb2926f9c34937e4ae1ab94a11568aa0d8be51e2b16ba1f2d6e16950a4f9a |
Coding | codecontest | Write Python code to solve the task.
You're given a tree with n vertices.
Your task is to determine the maximum possible number of edges that can be removed in such a way that all the remaining connected components will have even size.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) denoting the size of th... | Step 1:
The problem seems to be asking for a way to remove the maximum number of edges from a tree such that all the remaining connected components have an even number of vertices. We need to think about the approach to solving this problem.
We could start by creating a graph data structure to represent the tree, and... | ac5c4219be74851e0352ec626fa9dd44a7a7f6d60faab359343d0c5ed6aabab9_1_1 | 0bf2ea8473de1a4b45b6253391d007321dc3057418f47342b34eddf33b1c19a9 |
Coding | codecontest | Write Python code to solve the task.
You're given a tree with n vertices.
Your task is to determine the maximum possible number of edges that can be removed in such a way that all the remaining connected components will have even size.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) denoting the size of th... | Step 1: To solve this problem, An even-sized connected component of a tree is obtained when every node in that component has an even number of children. This means that the problem is equivalent to finding the number of edges whose removal would create connected components with even cardinality.
Step 2: For a tree to... | 7336d442fbdd223175d9c723bb4f9fbf0e3bbe798a39ba16a5a8f712c3da916f_1_1 | 0bf2ea8473de1a4b45b6253391d007321dc3057418f47342b34eddf33b1c19a9 |
Coding | codecontest | Write Python code to solve the task.
You are given sequences A and B consisting of non-negative integers. The lengths of both A and B are N, and the sums of the elements in A and B are equal. The i-th element in A is A_i, and the i-th element in B is B_i.
Tozan and Gezan repeats the following sequence of operations:
... | Step 1: The problem requires finding the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.
Step 2: To solve the problem, we can use recursion to explore all possible operations for Tozan and Gezan and find the optimal number of candies given to Takahashi.
Step 3: We can... | d7731ff6c71c18b86b849470da63a6729816dbe90de6cbf8f6386f5da6a3bdfb_1_1 | 1e22e644b697eec326bbfb7b41caf9e175cf6e13414e6ab0381feb232b2614be |
Coding | codecontest | Write Python code to solve the task.
You are given sequences A and B consisting of non-negative integers. The lengths of both A and B are N, and the sums of the elements in A and B are equal. The i-th element in A is A_i, and the i-th element in B is B_i.
Tozan and Gezan repeats the following sequence of operations:
... | Step 1: The problem requires finding the optimal number of candies given to Takahashi during a sequence of operations between Tozan and Gezan.
Step 2: To model the optimal sequence of operations, we need to iterate through each positive element in A and B to find the maximum and minimum number of candies given to Tak... | eea04bbcfcfc739a1f2d8665426fdc60e24ff31eb4b279138ee3974f89becde8_1_1 | 1e22e644b697eec326bbfb7b41caf9e175cf6e13414e6ab0381feb232b2614be |
Coding | codecontest | Write Python code to solve the task.
Nantendo Co., Ltd. has released a game software called Packet Monster. This game was intended to catch, raise, and fight monsters, and was a very popular game all over the world.
This game had features not found in traditional games. There are two versions of this game, Red and Gre... | Step 1: To solve this problem, we need to create a program that simulates the movement of the packages on the conveyor belt and records the packages that arrive at the far right.
Step 2: The program should take the input strings for the Red, Green, and bottom packages. Then, according to the rules given, simulate the... | f515ddd5c0226f29b60736ebe7f02083ba3a47db0ad07e55ed035c6dfdb67c6c_1_1 | 9e2f69cb39fc0901595e07aaa5408a1b92ed89c859e8ab3930fa14c6e4c875e9 |
Coding | codecontest | Write Python code to solve the task.
Nantendo Co., Ltd. has released a game software called Packet Monster. This game was intended to catch, raise, and fight monsters, and was a very popular game all over the world.
This game had features not found in traditional games. There are two versions of this game, Red and Gre... | Step 1: The program needs to read multiple datasets and process each dataset separately.
Step 2: It takes inputs for the Red package, Green package, and the package that reaches the bottom from each dataset.
Step 3: By following the given rules of agitation, the program determines the packages that arrive at the far... | 9c43e0fbb1e5f9c293c401102c1236c9b260eda708148a134ae9f75f3bc85dfd_1_1 | 9e2f69cb39fc0901595e07aaa5408a1b92ed89c859e8ab3930fa14c6e4c875e9 |
Coding | codecontest | Write Python code to solve the task.
As a German University in Cairo (GUC) student and a basketball player, Herr Wafa was delighted once he heard the news. GUC is finally participating in the Annual Basketball Competition (ABC).
A team is to be formed of n players, all of which are GUC students. However, the team mig... | Step 1:
This problem involves calculating the probability of having at least one teammate belonging to a specific department when forming a team from multiple departments. The probability is dependent on the number of players in each department and the number of players to be chosen for the team.
To solve this proble... | 20a0090fe28097401d2000c35c86e1e869f26c1f9aea2eb1598d3f034e5b2ee1_1_1 | aaeb1aac2e56e3a9acb62fba3af5ae77c4f3b94ead09cfd7d1d88a5c812863f6 |
Coding | codecontest | Write Python code to solve the task.
As a German University in Cairo (GUC) student and a basketball player, Herr Wafa was delighted once he heard the news. GUC is finally participating in the Annual Basketball Competition (ABC).
A team is to be formed of n players, all of which are GUC students. However, the team mig... | Step 1: To solve this problem, we need to calculate the probability that Herr Wafa will have at least one teammate from his department.
Step 2: We can start by calculating the total number of possible teams that can be formed. This will involve calculating the binomial coefficients (n choose k) for the available play... | d11edd300c7b012c0e9fee0e4f16490bcb56070a466c0b859221a3103a8e684d_1_1 | aaeb1aac2e56e3a9acb62fba3af5ae77c4f3b94ead09cfd7d1d88a5c812863f6 |
Coding | codecontest | Write Python code to solve the task.
Little Petya loves training spiders. Petya has a board n × m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idl... | Step 1:
The problem asks for the maximum possible number of spider-free cells after one second based on the command Petya gives to each spider. We can calculate this by evaluating the result of commands given for spiders on the board.
It seems there are probabilities or math logic involved in calculating the maximum ... | 0b0198969b218e0a557f178af3807b3bfecb7fcf4a8bb3a688b0a4ca9c0a9b7c_1_1 | e3362141442c04f2752e6e8012847e8328059cc2f66b4bca470179bde7368d8f |
Coding | codecontest | Write Python code to solve the task.
Little Petya loves training spiders. Petya has a board n × m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idl... | Step 1: The problem requires finding the maximum possible number of spider-free cells after one second.
Step 2: To solve the problem, we can either traverse and iterate through all possible combinations of spider movements or come up with a mathematical model to calculate the maximum number of cells without spiders b... | 4c47cbea41f8e4e2fb625087d981c0dd047d932a0272f784be0c087b9b4a6587_1_1 | e3362141442c04f2752e6e8012847e8328059cc2f66b4bca470179bde7368d8f |
Coding | codecontest | Write Python code to solve the task.
Treeland consists of n cities and n-1 roads. Each road is bidirectional and connects two distinct cities. From any city you can get to any other city by roads. Yes, you are right — the country's topology is an undirected tree.
There are some private road companies in Treeland. The ... | Step 1: This problem involves assigning roads to companies to minimize the number of cities with multiple roads of one company and minimize the number of companies needed.
Step 2: We need to keep track of the roads and cities to determine the number of companies required and how to assign the roads to minimize the nu... | 470457c34e496f271a91eca68c28714edf40126b0f5a095b17fbaf78ed543aab_1_1 | d97f34add34a5075f50f7744d69b9fbf9d7448dd74b04103c9f993b770c9c1b3 |
Coding | codecontest | Write Python code to solve the task.
Treeland consists of n cities and n-1 roads. Each road is bidirectional and connects two distinct cities. From any city you can get to any other city by roads. Yes, you are right — the country's topology is an undirected tree.
There are some private road companies in Treeland. The ... | Step 1: To solve this problem, we need to find the minimum number of companies required such that each city has at most k roads owned by the same company.
Step 2: The primary idea is to assign companies to roads in such a way that the number of cities with more than k roads of the same company is minimized.
Step 3: ... | 859004606726c479f2a6cbc3c2b849a9dc59edbce3c7b1421d677db55e0334cb_1_1 | d97f34add34a5075f50f7744d69b9fbf9d7448dd74b04103c9f993b770c9c1b3 |
Coding | codecontest | Write Python code to solve the task.
The territory of Berland is represented by a rectangular field n × m in size. The king of Berland lives in the capital, located on the upper left square (1, 1). The lower right square has coordinates (n, m). One day the king decided to travel through the whole country and return bac... | Step 1: To solve this problem, we need to find the minimum number of teleporters required to fulfill the king's travel requirements.
Step 2: We also need to calculate the journey path route for the king.
Step 3: We can first check the corner cases and then consider the general case for the field size n x m.
Step 4: ... | bccba18814b72972fd662314f0fe0070ae5c23226846eabad6dff20e9b609301_1_1 | 73671a975fb6b1bc335b1ad67b2462ade542529002695409c30b2aa0fc509720 |
Coding | codecontest | Write Python code to solve the task.
The territory of Berland is represented by a rectangular field n × m in size. The king of Berland lives in the capital, located on the upper left square (1, 1). The lower right square has coordinates (n, m). One day the king decided to travel through the whole country and return bac... | Step 1:
The problem involves calculating the minimum number of teleporters needed for the king to travel through all squares of the country and return to the capital, having visited every square exactly once. The king can only move to side-neighboring squares and to the squares where a teleporter leads.
One way to a... | d0fce0d1f5d8e819faedb44e51a19b43366075a757880d112e89b68f79507b62_1_1 | 73671a975fb6b1bc335b1ad67b2462ade542529002695409c30b2aa0fc509720 |
Coding | codecontest | Write Python code to solve the task.
An exam for n students will take place in a long and narrow room, so the students will sit in a line in some order. The teacher suspects that students with adjacent numbers (i and i + 1) always studied side by side and became friends and if they take an exam sitting next to each oth... | Step 1: To solve this problem, we need to find a way to maximize the number of students that can be seated in a line without any adjacent students sitting next to each other.
Step 2: At most 2 consecutive students can sit next to each other. We need to consider and handle these cases as well.
Step 3: We need to co... | dff59685f012d7d8fe6035142f1dfc550eacecebe5e850eb4a21dff70b194926_1_1 | de94facd59e70a385f7eb0280ce7fcf86f9f317f93467f451ae2dfd2c0e652c1 |
Coding | codecontest | Write Python code to solve the task.
An exam for n students will take place in a long and narrow room, so the students will sit in a line in some order. The teacher suspects that students with adjacent numbers (i and i + 1) always studied side by side and became friends and if they take an exam sitting next to each oth... | Step 1: To solve this problem, we need to find a way to arrange the students such that no two students with adjacent numbers sit side by side.
Step 2: We can start by considering the different cases for the number of students and determining the maximum number of students that can be seated with the given conditions.... | c536f2203382bca210abc9fb4f8e31e70c5d6080339fdbffc2cc72a8301c15d1_1_1 | de94facd59e70a385f7eb0280ce7fcf86f9f317f93467f451ae2dfd2c0e652c1 |
Coding | codecontest | Write Python code to solve the task.
You and your friends live in n houses. Each house is located on a 2D plane, in a point with integer coordinates. There might be different houses located in the same point. The mayor of the city is asking you for places for the building of the Eastern exhibition. You have to find the... | Step 1: The main problem is to determine the number of possible locations for the exhibition such that the summary distance from all the houses is minimal.
Step 2: We need to find a way to calculate the number of possible locations based on the positions of the houses and then output the results.
Step 3: The soluti... | 314e4de25b0d5fec9ac838fc25362c58a78190864293f0fedb9ec886b24ad5c6_1_1 | e429db2d0e0e00810b5d25915c2fc7ffe2aebeb27efefc2535c04de79f23558e |
Coding | codecontest | Write Python code to solve the task.
You and your friends live in n houses. Each house is located on a 2D plane, in a point with integer coordinates. There might be different houses located in the same point. The mayor of the city is asking you for places for the building of the Eastern exhibition. You have to find the... | Step 1: To solve this problem, we need to find the position with the minimum total distance from all the houses to the exhibition.
Step 2: We can calculate the Manhattan distance for each possible position.
Step 3: For each test case, we will need to find the minimum distance for x-coordinates and y-coordinates sepa... | d24110bdd59338b6067609aa70c8485ae66308c66174bb63af1cbcb020fcea91_1_1 | e429db2d0e0e00810b5d25915c2fc7ffe2aebeb27efefc2535c04de79f23558e |
Coding | codecontest | Write Python code to solve the task.
A very brave explorer Petya once decided to explore Paris catacombs. Since Petya is not really experienced, his exploration is just walking through the catacombs.
Catacombs consist of several rooms and bidirectional passages between some pairs of them. Some passages can connect a r... | Step 1: The goal is to determine the minimum possible number of rooms in the Paris catacombs based on an explorer's logbook.
Step 2: The logbook contains notes of the rooms the explorer visited, with certain rules for recording the notes.
Step 3: To solve this problem, we need to consider the relationship between th... | d3a80201b3d58e89ac2fb2a04a473e2aa18bdcc8948428fab19c76eeeefe7551_1_1 | 1c4ad8ef251652e6ab993db46422134cb026e89f1f8b52b5c1934b43e807b0b0 |
Coding | codecontest | Write Python code to solve the task.
A very brave explorer Petya once decided to explore Paris catacombs. Since Petya is not really experienced, his exploration is just walking through the catacombs.
Catacombs consist of several rooms and bidirectional passages between some pairs of them. Some passages can connect a r... | Step 1: This problem involves finding the minimum possible number of rooms in Paris catacombs according to Petya's logbook.
Step 2: The logbook contains notes indicating the room Petya visited at each minute and the minute he was in each room.
Step 3: The minimum number of rooms depends on the unique rooms Petya vis... | 5b3fcaf8a8b99b18e7a064acab59d12f22c694694813093257be85c9ba454ceb_1_1 | 1c4ad8ef251652e6ab993db46422134cb026e89f1f8b52b5c1934b43e807b0b0 |
Coding | codecontest | Write Python code to solve the task.
Problem H: Squid Multiplication
Squid Eiko loves mathematics. Especially she loves to think about integer. One day, Eiko found a math problem from a website.
"A sequence b ={ai + aj | i < j } is generated from a sequence a ={a0 , ... , an | ai is even if i is 0, otherwise ai is od... | Step 1: The problem requires us to find the sequence a, given the sequence b, such that b = {ai * aj | i < j}.
Step 2: We can start by parsing the input to extract the sequence b and the number of odd integers in the sequence a (n).
Step 3: We then need to find the sequence a such that b = {ai * aj | i < j}.
Step 4:... | 3315615a5342dee409ae5615a66c03c5e15795a7aa70e749dc182318e23b10cf_1_1 | 903b0217eaf8635e37bfb79ad1a47e7357809cbfbb54ecfe0cbf05647772428e |
Coding | codecontest | Write Python code to solve the task.
Problem H: Squid Multiplication
Squid Eiko loves mathematics. Especially she loves to think about integer. One day, Eiko found a math problem from a website.
"A sequence b ={ai + aj | i < j } is generated from a sequence a ={a0 , ... , an | ai is even if i is 0, otherwise ai is od... | Step 1: The given problem involves generating a sequence b from a sequence a by multiplying a pair of elements i and j from sequence a where i < j.
Step 2: The input consists of multiple datasets, so we need to process each dataset separately.
Step 3: We can start by reading the input dataset and then calculating th... | 17cfc2ea80bd0be6db53ae291a0007c4d221de580f841b7fa7e73e2134d42e2d_1_1 | 903b0217eaf8635e37bfb79ad1a47e7357809cbfbb54ecfe0cbf05647772428e |
Coding | codecontest | Write Python code to solve the task.
Petya has a rectangular Board of size n × m. Initially, k chips are placed on the board, i-th chip is located in the cell at the intersection of sx_i-th row and sy_i-th column.
In one action, Petya can move all the chips to the left, right, down or up by 1 cell.
If the chip was in... | Step 1: The problem requires a solution to determine the sequence of operations to move chips on a rectangular board so that each chip visits the position selected for it at least once.
Step 2: To solve this problem, we need to understand the layout of the board, the positions of the chips, and the positions each chi... | 6f75931b18fb8d1ed4503d60250dd27653c097dd9d12f566f233e6e1aabb703b_1_1 | b8cc81873bee3540ff55e7c0e5cac4d8f9713086360af342be31bce0e6dbc84e |
Coding | codecontest | Write Python code to solve the task.
Petya has a rectangular Board of size n × m. Initially, k chips are placed on the board, i-th chip is located in the cell at the intersection of sx_i-th row and sy_i-th column.
In one action, Petya can move all the chips to the left, right, down or up by 1 cell.
If the chip was in... | Step 1: The problem requires finding the necessary actions to move the chips on the board so that each chip visits the destination position specified by Petya.
Step 2: We need to consider the possible ways to move a chip on the board and the resulting sequence of actions required to accomplish this for each chip. The... | 12b2f97c5d61199e7e6787c8a08c7538cd4dd231f65525e6b87440bb06ede513_1_1 | b8cc81873bee3540ff55e7c0e5cac4d8f9713086360af342be31bce0e6dbc84e |
Coding | codecontest | Write Python code to solve the task.
Berland year consists of m months with d days each. Months are numbered from 1 to m. Berland week consists of w days. The first day of the year is also the first day of the week. Note that the last week of the year might be shorter than w days.
A pair (x, y) such that x < y is ambi... | Step 1: The problem requires us to compute the number of ambiguous date pairs given the number of months in a year, the number of days in a month, and the number of days in a week.
Step 2: To solve this problem, we need to come up with an algorithm to identify and count the ambiguous date pairs for each given input.
... | ed80bc005d0e564b82c35cceb0adf335240cc3543c18f294b5764995f1631575_1_1 | 171a84ded98ba452214acfd4be68205db81fa374f00aca1a85e61eebe7cc025a |
Coding | codecontest | Write Python code to solve the task.
Berland year consists of m months with d days each. Months are numbered from 1 to m. Berland week consists of w days. The first day of the year is also the first day of the week. Note that the last week of the year might be shorter than w days.
A pair (x, y) such that x < y is ambi... | Step 1: The problem asks us to count the number of ambiguous pairs, i.e., pairs (x, y) where x < y and day x of month y is the same day of the week as day y of month x.
Step 2: To solve the problem, we need to create a function to calculate the number of ambiguous pairs given the number of months in a year, the numbe... | 68b985b2b12a6776f37ff5c46d7b2842ba4c6f7792ccba7f86711b762862f143_1_1 | 171a84ded98ba452214acfd4be68205db81fa374f00aca1a85e61eebe7cc025a |
Coding | codecontest | Write Python code to solve the task.
On February, 30th n students came in the Center for Training Olympiad Programmers (CTOP) of the Berland State University. They came one by one, one after another. Each of them went in, and before sitting down at his desk, greeted with those who were present in the room by shaking ha... | Step 1: The problem is asking us to determine the possible order in which students entered the Center for Training Olympiad Programmers (CTOP).
Step 2: We will need to read the input, organize the students' handshakes, and come up with a possible order for the students' entrance.
Step 3: We may need to use iteration... | b9269d8b7279e9247b5beab6ca30d54afbeb212dd461809dfa04ea630d23c78b_1_1 | 6625d3e7a5c4ea1e6c278ba0a3521b5f78d9be82595fed2d7723c6d50690cece |
Coding | codecontest | Write Python code to solve the task.
On February, 30th n students came in the Center for Training Olympiad Programmers (CTOP) of the Berland State University. They came one by one, one after another. Each of them went in, and before sitting down at his desk, greeted with those who were present in the room by shaking ha... | Step 1: The problem is asking to find the possible order in which the students could have come to the Center for Training Olympiad Programmers (CTOP) based on the number of hands they shook with each student.
Step 2: We could start by understanding the relationship between the number of handshakes and the order of th... | f9c29b27cddf9b9115900699ab48b7910b748d0994f676cd315087c6a1aedc59_1_1 | 6625d3e7a5c4ea1e6c278ba0a3521b5f78d9be82595fed2d7723c6d50690cece |
Coding | codecontest | Write Python code to solve the task.
Anchored Balloon
A balloon placed on the ground is connected to one or more anchors on the ground with ropes. Each rope is long enough to connect the balloon and the anchor. No two ropes cross each other. Figure E-1 shows such a situation.
<image>
Figure E-1: A balloon and ropes o... | Step 1: To solve this problem, we need to find the maximum height that the balloon can go up while keeping the rope connections.
Step 2: We need to work with the positions of the anchors and the lengths of the ropes to figure out the maximum height.
Step 3: We will use a binary search algorithm to find this maximum ... | a6b9c06146f2c8f0834a45b49b8ac10d12dfbcb3116d96bcfcdb42bc31b21d0c_1_1 | 791cdf8e368e452e442c157c84116c23a7c4d465909e27e1375954d2a7eb07cf |
Coding | codecontest | Write Python code to solve the task.
Anchored Balloon
A balloon placed on the ground is connected to one or more anchors on the ground with ropes. Each rope is long enough to connect the balloon and the anchor. No two ropes cross each other. Figure E-1 shows such a situation.
<image>
Figure E-1: A balloon and ropes o... | Step 1: To solve this problem, we need to find the maximum height that a balloon can reach while respecting the rope connections. This problem involves calculating the distances between different anchor positions and computing the maximum extension of the ropes. We then need to find the highest point where the balloon... | fc6886bc0372b8f71f9effdce7b7b217a475e7073ccc9dbe04c37f0d79c9b804_1_1 | 791cdf8e368e452e442c157c84116c23a7c4d465909e27e1375954d2a7eb07cf |
Coding | codecontest | Write Python code to solve the task.
Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:
* the Euclidean distance between A and B is one unit and neither A nor B i... | Step 1: To solve this problem, we need to calculate the minimum number of points that need to be picked in order to prevent any special point from being 4-connected to some non-special point.
Step 2: Each special point with a Euclidean distance from the origin no more than n can be 4-connected to at most 4 other poin... | a7af5028e19f6a183d3e821d19b3faa136a83be3533bc4afe5f1efd4ad8cbf6d_1_1 | a6b84a31074ce7ee7584c61fb1d5e6d9392e60314e743172c6f3d02d73eb48d4 |
Coding | codecontest | Write Python code to solve the task.
Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:
* the Euclidean distance between A and B is one unit and neither A nor B i... | Step 1: We need to find the minimum number of points that should be blocked to satisfy the given property.
Step 2: We can calculate the number of blocked points based on the given Euclidean distance from the origin.
Step 3: We can consider the points on a circle with radius n as special points and check the adjacen... | f35e6b3c819d25ec67e5c845987b7e8f800d8334dbe793ed3b8b15513eafffb8_1_1 | a6b84a31074ce7ee7584c61fb1d5e6d9392e60314e743172c6f3d02d73eb48d4 |
Coding | codecontest | Write Python code to solve the task.
Santa Claus has received letters from n different kids throughout this year. Of course, each kid wants to get some presents from Santa: in particular, the i-th kid asked Santa to give them one of k_i different items as a present. Some items could have been asked by multiple kids.
S... | Step 1: The problem requires us to calculate the probability that a decision generated according to the bot's algorithm is valid.
Step 2: To solve this, we need to understand the algorithm and the calculations involved to determine the probability.
Step 3: We also need to use appropriate mathematical functions, such... | 9f525efce0aa10ea953341a69f13f92a201534c3a83c1df305a98a195bea0216_1_1 | a4fd6c05bde07282e3231f7c62c55bf13e98f9c2fe831f1a6f1e85ee1779dcf2 |
Coding | codecontest | Write Python code to solve the task.
Santa Claus has received letters from n different kids throughout this year. Of course, each kid wants to get some presents from Santa: in particular, the i-th kid asked Santa to give them one of k_i different items as a present. Some items could have been asked by multiple kids.
S... | Step 1: The goal of this problem is to calculate the probability that the Bot produces a valid decision according to the algorithm.
Step 2: We can start by analyzing the algorithm and how it affects the probability of producing a valid decision.
Step 3: The algorithm involves choosing a kid, an item, and a recipient... | 90816b7fc65de320438ebd21afb91cb328ac0debe47cb45e588b2fd157150acb_1_1 | a4fd6c05bde07282e3231f7c62c55bf13e98f9c2fe831f1a6f1e85ee1779dcf2 |
Coding | codecontest | Write Python code to solve the task.
Vasya plays The Elder Trolls IV: Oblivon. Oh, those creators of computer games! What they do not come up with! Absolutely unique monsters have been added to the The Elder Trolls IV: Oblivon. One of these monsters is Unkillable Slug. Why it is "Unkillable"? Firstly, because it can be... | Step 1: The problem involves finding the maximum number of pieces Vasya can cut the Unkillable Slug into with at most k strokes.
Step 2: We need to determine how to cut the parallelepiped with the given dimensions to achieve the maximum number of pieces.
Step 3: We'll need to consider the minimum number of dimension... | f3d49a443be2b3606a95236786602003473c82c90728b8669535d3928dc390b7_1_1 | 96cdbf9e8f1ea7e743e0a7f1819addb3b730364b1e98f91bd9b5a8efae89f647 |
Coding | codecontest | Write Python code to solve the task.
Vasya plays The Elder Trolls IV: Oblivon. Oh, those creators of computer games! What they do not come up with! Absolutely unique monsters have been added to the The Elder Trolls IV: Oblivon. One of these monsters is Unkillable Slug. Why it is "Unkillable"? Firstly, because it can be... | Step 1: The problem requires us to find the maximum number of pieces Vasya can cut the Unkillable Slug into after making at most k cuts.
Step 2: To solve this problem, we need to consider the dimensions of the rectangular parallelepiped and the number of cuts Vasya can make.
Step 3: We also need to find the maximum ... | 16c4c657127332e866b5e290774017653836fc3150e0a11d7b6a69a1d814ac28_1_1 | 96cdbf9e8f1ea7e743e0a7f1819addb3b730364b1e98f91bd9b5a8efae89f647 |
Coding | codecontest | Write Python code to solve the task.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence o... | Step 1:
The problem can be solved using a stack to keep track of the current state of the multiset. We can use recursion and backtracking to determine the minimum number of operations required to delete all elements from the multiset.
We need to carefully handle the two types of operations that can be applied to the m... | d0bcc48aed04491a554040b660ebd03b21d3ffbeb3818e4231e9908e8a4e1128_1_1 | d928ebcfaa7fa6f3b28421b71b0a83d4fa0603bff990695a8b019f379f118266 |
Coding | codecontest | Write Python code to solve the task.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence o... | Step 1: The problem requires finding the minimum number of operations required to delete all elements from the multiset.
Step 2: We can solve this problem using recursion, where we progressively remove occurrences of the elements.
Step 3: To solve the problem, we should use iteration instead as it is easier to keep ... | 8a90cb88dbc1b3a3eabf2283b25aadc06a51d8a9546ce4abca419ef8f0a91323_1_1 | d928ebcfaa7fa6f3b28421b71b0a83d4fa0603bff990695a8b019f379f118266 |
Coding | codecontest | Write Python code to solve the task.
There are n animals in the queue to Dr. Dolittle. When an animal comes into the office, the doctor examines him, gives prescriptions, appoints tests and may appoint extra examination. Doc knows all the forest animals perfectly well and therefore knows exactly that the animal number ... | Step 1: This problem poses a queueing problem where each element in the queue has a specific number of visits required.
Step 2: We need to iterate through the queue while keeping track of the number of visits and the remaining visits for each element.
Step 3: The iterations will continue until the total number of vi... | c4962ca251ce46b099df9941b6342930c064738a105f5993c480595597706f39_1_1 | 3c81804c9738f2d2929319526665e4fc664ac8dd969e5b287e0531f1accd551d |
Coding | codecontest | Write Python code to solve the task.
There are n animals in the queue to Dr. Dolittle. When an animal comes into the office, the doctor examines him, gives prescriptions, appoints tests and may appoint extra examination. Doc knows all the forest animals perfectly well and therefore knows exactly that the animal number ... | Step 1:
The given problem involves processing a queue of animals based on the number of times each animal needs to undergo a certain number of examinations. The doctor plans to examine k animals, and the doctor needs to determine the sequence of the animals in the queue at that moment.
- Calculate the total number of... | 0134411cefd4a4b8684ccd1ec9239684a08150c5e4dce26840ae39c2ce65952d_1_1 | 3c81804c9738f2d2929319526665e4fc664ac8dd969e5b287e0531f1accd551d |
Coding | codecontest | Write Python code to solve the task.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multi... | Step 1: The problem asks to determine if it is possible to make all integers in the sequence equal to a given value k by applying a specific operation multiple times.
Step 2: We need to iterate through the queries and check if it is possible to turn all elements of the sequence into the given value k.
Step 3: We can... | c47ddaef5a71513b59857c35cb12b5fd7e9779c5fce77133d543e14ae8046905_1_1 | 503776594325253a1130c706e75d94bde890d62ec2ee6d30add901e653ff6b19 |
Coding | codecontest | Write Python code to solve the task.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multi... | Step 1: The problem requires determining if it is possible to make all integers in the array equal to k by performing a specific operation.
Step 2: We need to understand the conditions under which this objective can be achieved and implement the logic to answer the queries.
Step 3: To solve the problem, we should i... | 0d3ff3fcc7e05f0b728f4b2d6ace312965b1123cebacf5df36edf708ee034278_1_1 | 503776594325253a1130c706e75d94bde890d62ec2ee6d30add901e653ff6b19 |
Coding | codecontest | Write Python code to solve the task.
You are given a table consisting of n rows and m columns. Each cell of the table contains a number, 0 or 1. In one move we can choose some row of the table and cyclically shift its values either one cell to the left, or one cell to the right.
To cyclically shift a table row one cel... | Step 1: The problem asks to determine the minimum number of moves needed to make some table column consist only of numbers 1.
Step 2: We can think about calculating the minimum number of moves required for each row to make that row entirely 1s. Next, we need to consider the minimum number of moves required for a spec... | 02ef2a912c121028e28b2c09cab3921b507a1b45500945c64b2a4e7cd7727fcc_1_1 | f50015f0cab2035078b27123887e0a1c9e142b8a1ffe717dfc8e929634acc56b |
Coding | codecontest | Write Python code to solve the task.
You are given a table consisting of n rows and m columns. Each cell of the table contains a number, 0 or 1. In one move we can choose some row of the table and cyclically shift its values either one cell to the left, or one cell to the right.
To cyclically shift a table row one cel... | Step 1: The problem requires finding the minimum number of moves to make some table column consist only of numbers 1.
Step 2: We need to take each row and cyclically shift its values either one cell to the left or one cell to the right to achieve the goal.
Step 3: To solve this problem, we can iterate through each ... | 8880ef1bb56cc508e456925bdc8939160be2a7534e1076464cdf7e584a499ffd_1_1 | f50015f0cab2035078b27123887e0a1c9e142b8a1ffe717dfc8e929634acc56b |
Coding | codecontest | Write Python code to solve the task.
Anya and Kirill are doing a physics laboratory work. In one of the tasks they have to measure some value n times, and then compute the average value to lower the error.
Kirill has already made his measurements, and has got the following integer values: x1, x2, ..., xn. It is import... | Step 1: The solution seems to solve this problem by checking the difference between the minimum and maximum value of measurements from Kirill. If the difference is at most 1, Anya will just copy Kirill's measurements. If the difference is more than 1, the solution will manipulate the measurements such that the average... | af5349e570605caf2ec49b8460363ba06cbef9ef1335609b14deb46ec08ffb7f_1_1 | 449da8010734c3cf5a99701ad186627a8221a58aaa6167ce92a78826b5be7621 |
Coding | codecontest | Write Python code to solve the task.
Anya and Kirill are doing a physics laboratory work. In one of the tasks they have to measure some value n times, and then compute the average value to lower the error.
Kirill has already made his measurements, and has got the following integer values: x1, x2, ..., xn. It is import... | Step 1: The problem is about finding a set of integers for Anya's measurements that satisfy certain conditions based on Kirill's measurements.
Step 2: We need to find a configuration of integers that meet the conditions, minimize the number of equal measurements in Anya's work, and have the average value equal to tha... | cac5dd61dbbace4d3ea5fefba54701f637594dba4db96e7bda93fa47d863797c_1_1 | 449da8010734c3cf5a99701ad186627a8221a58aaa6167ce92a78826b5be7621 |
Coding | codecontest | Write Python code to solve the task.
Vasiliy is fond of solving different tasks. Today he found one he wasn't able to solve himself, so he asks you to help.
Vasiliy is given n strings consisting of lowercase English letters. He wants them to be sorted in lexicographical order (as in the dictionary), but he is not allo... | Step 1: The problem requires us to find the minimum total energy that Vasiliy needs to spend to reverse the given strings so that they are located in lexicographical order.
Step 2: We will use dynamic programming to solve this problem.
Step 3: We will maintain a 2D array to store the minimum amount of energy require... | 3b7c082043a024c934052de2d4bfea417a1e606a27e7add6384f1a4f3e5277e6_1_1 | eb104d5458fe8e5b7f8f6e55146d5e5041663a09a7ef325a9d6a4ed9cb0675a7 |
Coding | codecontest | Write Python code to solve the task.
Vasiliy is fond of solving different tasks. Today he found one he wasn't able to solve himself, so he asks you to help.
Vasiliy is given n strings consisting of lowercase English letters. He wants them to be sorted in lexicographical order (as in the dictionary), but he is not allo... | Step 1: The problem requires us to sort the given strings in lexicographical order using the minimum amount of energy possible.
Step 2: We can calculate the total cost of reordering the strings by reversing the strings and determine the minimum cost required for the strings to be sorted lexicographically.
Step 3: To... | 6169986addfe8e972b5ec535c634b9a3934a27ec94eba086de00d80ed26c2bf2_1_1 | eb104d5458fe8e5b7f8f6e55146d5e5041663a09a7ef325a9d6a4ed9cb0675a7 |
Coding | codecontest | Write Python code to solve the task.
Rahul is a young chap who loves strings but simply hates mathematics. While his friend Ramesh is in love with mathematics but hates strings. So their teacher decided to take a test which combined both these topics so that neither of them gets a better hand over the other.
Their tea... | Step 1: The problem seems to involve division of a string into K parts such that each part does not exceed a maximum value Z.
Step 2: We need to find the maximum sum of K parts. In other words, we're trying to maximize the sum of subparts while adhering to the given constraints.
Step 3: We can start by creating a s... | 7ab73fb24b60296567f84121be8df371d8715d1fdad12b2e9b925685882fef1e_1_1 | 33c3e934e9400d8644f560eaf1ab5bf1b7f791dd53e3072098ca160402a5e31d |
Coding | codecontest | Write Python code to solve the task.
Rahul is a young chap who loves strings but simply hates mathematics. While his friend Ramesh is in love with mathematics but hates strings. So their teacher decided to take a test which combined both these topics so that neither of them gets a better hand over the other.
Their tea... | Step 1: To solve this problem, we need to find the maximum sum possible when dividing the string into K parts, each part of which should not exceed the specified value Z.
Step 2: We can use dynamic programming to keep track of the maximum sum for different parts of the string. We can use subproblems to build up the s... | 62334d7b86aa9e85a396e11b7c039abd295389cc03ff14c7af48748f57888d1e_1_1 | 33c3e934e9400d8644f560eaf1ab5bf1b7f791dd53e3072098ca160402a5e31d |
Coding | codecontest | Write Python code to solve the task.
Bob is about to take a hot bath.
There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusi... | Step 1: To solve this problem, we need to find the amount of hot and cold water that should be mixed to achieve the desired temperature of the bath as close as possible to t0. We also need to consider the flow rate of the taps and determine the optimal configuration of the taps to fill the bath in the quickest way.
St... | 51f3914edd6a85f0ddb87b4853c1ed9876833bb5ce5c62d9ad8654be0ebe3e10_1_1 | 204cf9abfa7f60a104e1c3c0558532472a140941dda03102d02e94709056b9d8 |
Coding | codecontest | Write Python code to solve the task.
Bob is about to take a hot bath.
There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusi... | Step 1: To solve this problem, we need to determine the flow rates of hot and cold water taps that will result in a bath water temperature as close as possible to t0.
Step 2: We can start by considering all possible combinations of flow rates of hot and cold water taps from 0 to their max flow rates.
Step 3: We wil... | 8f60a0142edcd3c30e0f67e6aa803331f97d036a013212048c9ae3aabab79cb7_1_1 | 204cf9abfa7f60a104e1c3c0558532472a140941dda03102d02e94709056b9d8 |
Coding | codecontest | Write Python code to solve the task.
You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner:
* If gcd(a_i, a_{i+1}, a_{i+2}, ..., a_{j})... | Step 1: To solve this problem, we need to extract the numbers of vertices, the parameter p, and the array values of a, and then calculate the graph with the minimum spanning tree.
Step 2: From the given problem, input contains a series of integers to represent the number of test cases, vertices, and their values. It ... | d4830b6c78e2d80297c1c3366943409c799059e385163f0c96dedd46b713dcc9_1_1 | 844908bd2564318de9907aa9a7a68785d64cbe19a8fff0399e1c739457e9e3ba |
Coding | codecontest | Write Python code to solve the task.
You are given an array a of n (n ≥ 2) positive integers and an integer p. Consider an undirected weighted graph of n vertices numbered from 1 to n for which the edges between the vertices i and j (i<j) are added in the following manner:
* If gcd(a_i, a_{i+1}, a_{i+2}, ..., a_{j})... | Step 1: The problem is asking us to find the weight of the minimum spanning tree of an undirected weighted graph created based on the given conditions.
Step 2: The graph is created by following the conditions for adding edges between vertices based on the GCD and given parameter p.
Step 3: To solve this problem, we'... | 1040d6925f8e86342003373ad3b314d1077fd6cb533ed1f5efc09179d5adef7c_1_1 | 844908bd2564318de9907aa9a7a68785d64cbe19a8fff0399e1c739457e9e3ba |
Coding | codecontest | Write Python code to solve the task.
Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry.
He bought n pieces of jewelry. The i-th piece has price equal to i + 1, that is, the prices of the jewelry are 2, 3, 4, ... n + 1.
Watson gave Sherlock a challenge to c... | Step 1: To solve this problem, we need a method to generate prime numbers.
Step 2: We will use the sieve of Eratosthenes to efficiently generate prime numbers up to n+1.
Step 3: Then, we will color each piece of jewelry such that no two pieces with a prime divisor of the other piece's price have the same color.
Step... | 04df43411b60137378e1d3da3b70b374fd341de5c025cab67f62ea25e747e199_1_1 | 7dffa1dfa3e74a8a72dc37f0f5697171efa05d35235d887f6c011e245b023ca3 |
Coding | codecontest | Write Python code to solve the task.
Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry.
He bought n pieces of jewelry. The i-th piece has price equal to i + 1, that is, the prices of the jewelry are 2, 3, 4, ... n + 1.
Watson gave Sherlock a challenge to c... | Step 1: The problem description suggests primality and coloring the pieces of jewelry based on certain constraints.
Step 2: To solve this problem, we should start by employing the Sieve of Eratosthenes algorithm to determine prime numbers that are less than or equal to n.
Step 3: Once we have determined the prime n... | 1862b5a692b3550e6805ddacd46dda964b982760d5c82b0ad1bbad9b0d605045_1_1 | 7dffa1dfa3e74a8a72dc37f0f5697171efa05d35235d887f6c011e245b023ca3 |
Coding | codecontest | Write Python code to solve the task.
A line on the plane is described by an equation Ax + By + C = 0. You are to find any point on this line, whose coordinates are integer numbers from - 5·1018 to 5·1018 inclusive, or to find out that such points do not exist.
Input
The first line contains three integers A, B and C ... | Step 1: The problem requires finding a point on a line described by the equation Ax + By + C = 0, where the coordinates of the point are integer numbers within a specific range.
Step 2: We can approach the problem by first determining whether such a point exists, and if it does, finding the coordinates of the point.
... | 5e11ce20e0e40942a432b55372b5e3227a64d241914f4c6cea7e954ea5cbade2_1_1 | 2dae4f518176ecb88e3e8f8aa480f60d24d1601fcd374c879fe05d35be1305a2 |
Coding | codecontest | Write Python code to solve the task.
A line on the plane is described by an equation Ax + By + C = 0. You are to find any point on this line, whose coordinates are integer numbers from - 5·1018 to 5·1018 inclusive, or to find out that such points do not exist.
Input
The first line contains three integers A, B and C ... | Step 1: To solve this problem, we need to find a point on a given line that satisfies the equation Ax + By + C = 0, where A, B, and C are the coefficients of the line equation.
Step 2: We can use the extended Euclidean algorithm to find the Bezout coefficients of A and B, which will help us find the integer coordinat... | eecff22478fb7044e4fe07aa2ed9e2f3f8e83c1b2e271c6cff53d41120766db9_1_1 | 2dae4f518176ecb88e3e8f8aa480f60d24d1601fcd374c879fe05d35be1305a2 |
Coding | codecontest | Write Python code to solve the task.
There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find ... | Step 1: The problem requires finding the minimum number of segments needed to form a polyline that passes through the given three points.
Step 2: We can start by parsing the input and storing the coordinates of the points.
Step 3: Then, we can determine the number of segments by analyzing the coordinates of the poin... | 5c8c911841444fad5e3cc6fa4b8776c460d0d28cde0c0996b4d3792f5e62f141_1_1 | 6b7786f796b0c521876e11c9038fcc354059002510fa7a30bad03415a44c1e06 |
Coding | codecontest | Write Python code to solve the task.
There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find ... | Step 1: The problem requires finding the minimum number of segments a polyline may consist of to pass through three distinct points.
Step 2: We need to determine the possible variants of the polyline and calculate the minimum number of segments for each variant.
Step 3: The polyline must consist of only segments par... | 11acb459a4f8ed5bc2a79d2eceea8cc74dceb45d24f999ba0f99d6537d739048_1_1 | 6b7786f796b0c521876e11c9038fcc354059002510fa7a30bad03415a44c1e06 |
Coding | codecontest | Write Python code to solve the task.
This is an interactive problem. Refer to the Interaction section below for better understanding.
Ithea and Chtholly want to play a game in order to determine who can use the kitchen tonight.
<image>
Initially, Ithea puts n clear sheets of paper in a line. They are numbered from 1... | Step 1:
The problem requires processing input in each round, making decisions based on Chtholly's goal of filling all sheets with numbers in non-decreasing order, and providing an output. Implement a solution to record the process of filling in numbers and making decisions based on the interaction and the state of fil... | 1aeb279ca5e58fd70ee4a3e7a0102cb46b422eda07a2b7748778f24ee855c261_1_1 | 904b69e1f821e90ace80a8671ac107d89ceea4de18d7aa18793582a0edc871a3 |
Coding | codecontest | Write Python code to solve the task.
This is an interactive problem. Refer to the Interaction section below for better understanding.
Ithea and Chtholly want to play a game in order to determine who can use the kitchen tonight.
<image>
Initially, Ithea puts n clear sheets of paper in a line. They are numbered from 1... | Step 1: To solve this problem, we need to write a program that takes the input values and interacts with the user based on the input and output requirements mentioned.
Step 2: We need to read the initial parameters from the input and use them to determine the location of numbers that Chtholly will write on the sheets... | f09f9eaea438e79bdd79cf17d63fd5f6a768a2700108cb65efec8cfdcd91a0e0_1_1 | 904b69e1f821e90ace80a8671ac107d89ceea4de18d7aa18793582a0edc871a3 |
Coding | codecontest | Write Python code to solve the task.
There are N dishes, numbered 1, 2, \ldots, N. Initially, for each i (1 \leq i \leq N), Dish i has a_i (1 \leq a_i \leq 3) pieces of sushi on it.
Taro will perform the following operation repeatedly until all the pieces of sushi are eaten:
* Roll a die that shows the numbers 1, 2, ... | Step 1: The problem involves finding the expected number of times an operation is performed. We need to understand the constraints and the input format.
Step 2: We also need to determine the logic for calculating the expected number of times the operation is performed with various sushi counts on dishes.
Step 3: For... | a995a692985456cf18f5ec517fbe1da78f5633ddc9b347c8d1a14dddc180ba45_1_1 | 35257bd2d08de06ca3faf1136d3a1586683d5b7a352c890205ec74e0665ba644 |
Coding | codecontest | Write Python code to solve the task.
There are N dishes, numbered 1, 2, \ldots, N. Initially, for each i (1 \leq i \leq N), Dish i has a_i (1 \leq a_i \leq 3) pieces of sushi on it.
Taro will perform the following operation repeatedly until all the pieces of sushi are eaten:
* Roll a die that shows the numbers 1, 2, ... | Step 1:
The problem requires finding the expected number of times the operation is performed before all the pieces of sushi are eaten.
We can use dynamic programming to solve this problem. By keeping track of the number of pieces of each type of sushi left on each dish and the expected number of times the operation is... | cbba83abaa6afa7290ba92b239784a9b226785536ec10c346d22bfdb474ed7e7_1_1 | 35257bd2d08de06ca3faf1136d3a1586683d5b7a352c890205ec74e0665ba644 |
Coding | codecontest | Write Python code to solve the task.
You are given a tree, which consists of n vertices. Recall that a tree is a connected undirected graph without cycles.
<image> Example of a tree.
Vertices are numbered from 1 to n. All vertices have weights, the weight of the vertex v is a_v.
Recall that the distance between two... | Step 1: This problem involves finding the subset of vertices with the maximum total weight, such that there is no pair of vertices with a distance k or less between them.
Step 2: Our approach will likely involve traversing the tree and considering the weight of each vertex.
Step 3: We will also need to keep track of... | b176e3da306422dfc3fa27aaa7f4a9e2fd0733dedf03aa99cbe238cac0928937_1_1 | 7b0172a862fdebbc91fe523e3f34d617e93548ed8de0a32172d1265e7b797276 |
Coding | codecontest | Write Python code to solve the task.
You are given a tree, which consists of n vertices. Recall that a tree is a connected undirected graph without cycles.
<image> Example of a tree.
Vertices are numbered from 1 to n. All vertices have weights, the weight of the vertex v is a_v.
Recall that the distance between two... | Step 1: The approach for this problem involves the use of dynamic programming and a recursive function to traverse the tree.
Step 2: We need to find the subset of vertices with the maximum weight, such that no pair of vertices within the subset has a distance k or less between them.
Step 3: To achieve this, we can c... | d4756ee8b6cc3eee7c5125a2d9474ab02b1a855b500d247621f049cee7f714c9_1_1 | 7b0172a862fdebbc91fe523e3f34d617e93548ed8de0a32172d1265e7b797276 |
Coding | codecontest | Write Python code to solve the task.
Arkadiy has lots square photos with size a × a. He wants to put some of them on a rectangular wall with size h × w.
The photos which Arkadiy will put on the wall must form a rectangular grid and the distances between neighboring vertically and horizontally photos and also the dist... | Step 1: The problem seems to involve the arrangement of square photos on a rectangular wall while satisfying certain constraints.
Step 2: We need to determine the minimum value of x, which represents the distance between neighboring photos and the outer rows/columns of photos to the nearest bound of the wall.
Step 3:... | 936ce50135e3ba0d10aa5df70d04a770bdc09d569940be3cfc0c7c1cfdd64439_1_1 | 56a3c2cdd058197888c3cf1ac0169158cc158fafcbff855be14096d325c8a290 |
Coding | codecontest | Write Python code to solve the task.
Arkadiy has lots square photos with size a × a. He wants to put some of them on a rectangular wall with size h × w.
The photos which Arkadiy will put on the wall must form a rectangular grid and the distances between neighboring vertically and horizontally photos and also the dist... | Step 1: To solve this problem, we need to consider the constraints for placing photos on the wall, specifically the requirement that the photo grid should form a rectangular grid with equal distances between neighboring photos and the outside rows and columns of photos to the nearest bound of the wall.
Step 2: We can... | d604c7881ecb7eb865ecae5738ea7a07ec83642b25471812da4e887627a89381_1_1 | 56a3c2cdd058197888c3cf1ac0169158cc158fafcbff855be14096d325c8a290 |
Coding | codecontest | Write Python code to solve the task.
Problem description
Chef Juno's girlfriend, May, is a programmer and a mathematician, and she loves solving problems. Everyday Chef Juno comes up with new problems for her to solve, otherwise she gets bored and depressed. He doesn't want her to feel so, but he has run out of all pro... | Step 1: The problem is about finding the number of ways to open restaurants in each cell of an N-dimensional hyperrectangle such that the sum of the restaurants in every sub-block is divisible by V.
Step 2: The input includes the number of test cases, V, N, P[], Q[], A0, B0, C0, M0, A1, B1, C1, M1, and constraints.
S... | e7d9565e3f62f07fb58ec26b42eb296c01da5156f57355cdfc713039704e109b_1_1 | e2e485ef70b74e179baad8f108f114fe5356fa3c87f6041320118c250103259d |
Coding | codecontest | Write Python code to solve the task.
Problem description
Chef Juno's girlfriend, May, is a programmer and a mathematician, and she loves solving problems. Everyday Chef Juno comes up with new problems for her to solve, otherwise she gets bored and depressed. He doesn't want her to feel so, but he has run out of all pro... | Step 1: The given problem requires us to calculate the number of ways to open restaurants in each cell of a city such that the sum of the number of restaurants in every sub-block is divisible by V.
Step 2: We can solve this by generating the dimensions of the city using the specified input scheme and then calculating... | 6b2aca72996db687f63382b3b4689773cb81a269447b0b2d7c6ca7296b211d74_1_1 | e2e485ef70b74e179baad8f108f114fe5356fa3c87f6041320118c250103259d |
Coding | codecontest | Write Python code to solve the task.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one... | Step 1: To solve this problem, we need to split the given number n into three positive integers a, b, and c such that none of them is a multiple of 3 and they sum up to n.
Step 2: We can start by checking the remainder of n when divided by 3 to determine the initial values for a, b, and c.
Step 3: Then we will print... | 9691f5a2d5fd08fba6502a38591e645bec1bec9f3c4559be12f0dfcf2bfa5f75_1_1 | dd57b69172b36d529c309f51a539213334e537dede9342379046bf929fc8ccc4 |
Coding | codecontest | Write Python code to solve the task.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one... | Step 1: To solve this problem, we need to find a way to split a positive integer n into three positive integers a, b, and c such that none of the integers is a multiple of 3 and the sum of a, b, and c is equal to n.
Step 2: We'll first determine if n is a multiple of 3 or not. If n = 3k (where k is an integer), then ... | 1edb450fa072814d464f732da38268d172aaa6e017a2d1da7454d0bcc05601f2_1_1 | dd57b69172b36d529c309f51a539213334e537dede9342379046bf929fc8ccc4 |
Coding | codecontest | Write Python code to solve the task.
Berhattan is the capital of Berland. There are n streets running parallel in the east-west direction (horizontally), and there are m avenues running parallel in the south-north direction (vertically). Each street intersects with each avenue, forming a crossroad. So in total there ar... | Step 1: The problem requires us to minimize the number of inconvenient crossroads in Berhattan after the naming process. To do this, the first step is to parse the input and extract the necessary information such as the number of streets, the number of avenues, the number of names in the committee's list, and the firs... | 04998592d297111cd6689c31f78a2b62641aa0cbd7b842fa76950d834ffc1008_1_1 | be0de4e41e2ba73904688fc67014391922171133c94a43b8a10ab38f523e1190 |
Coding | codecontest | Write Python code to solve the task.
Berhattan is the capital of Berland. There are n streets running parallel in the east-west direction (horizontally), and there are m avenues running parallel in the south-north direction (vertically). Each street intersects with each avenue, forming a crossroad. So in total there ar... | Step 1: The problem requires finding the minimal number of inconvenient crossroads in Berhattan after naming streets and avenues based on first letters of committee members' names.
Step 2: We need to devise a strategy to minimize the inconvenience for the residents.
Step 3: The given solution iterates through test c... | 73c67f2f43671278a7c97418b6063dbd196221076c8edd62a5741140f45dbfb0_1_1 | be0de4e41e2ba73904688fc67014391922171133c94a43b8a10ab38f523e1190 |
Coding | codecontest | Write Python code to solve the task.
Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task.
Recently, out of blue Ca... | Step 1: To solve this problem, we need to find a way to represent a given integer as the sum of 4 different positive integers, at least 3 of which should be nearly prime.
Step 2: We need to determine if the given integer can be represented as the sum of 4 different positive integers, where at least 3 of them are near... | 7f92e1d085c725e1881336795e146f9b499ef072f32086f72713ebe2bd97967b_1_1 | 2ab8ca303653b87d3dc1d755d6afde80b4d38b49508176f1fc220827c5f7ec0d |
Coding | codecontest | Write Python code to solve the task.
Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task.
Recently, out of blue Ca... | Step 1: The problem requires us to determine if a given positive integer can be represented as the sum of 4 different positive integers where at least 3 of them are nearly prime.
Step 2: To solve this, we need to identify if the given number can be expressed as the sum of 4 different positive integers and if at leas... | 5699fdea6b0f69851cba8d96f5184d356bdd1a1b3bfbd812e6377dd86ad0d4e4_1_1 | 2ab8ca303653b87d3dc1d755d6afde80b4d38b49508176f1fc220827c5f7ec0d |
Coding | codecontest | Write Python code to solve the task.
You are given a multiset of powers of two. More precisely, for each i from 0 to n exclusive you have cnt_i elements equal to 2^i.
In one operation, you can choose any one element 2^l > 1 and divide it into two elements 2^{l - 1}.
You should perform q queries. Each query has one of... | Step 1: To solve this problem, we need to parse the input to extract the values of n, q, and the array cnt.
Step 2: We also need to handle the two types of queries: assignment and calculation of minimum operations.
Step 3: For each query, we need to check the type and perform the appropriate actions.
Step 4: We'll... | b161158cecec052c413cb4c72c51579ebc56652d97ba8039b7c69771f43cc861_1_1 | 63ac4683d0f9206c517daf70ed5e2721cd38321887742e9c24181e6769969463 |
Coding | codecontest | Write Python code to solve the task.
You are given a multiset of powers of two. More precisely, for each i from 0 to n exclusive you have cnt_i elements equal to 2^i.
In one operation, you can choose any one element 2^l > 1 and divide it into two elements 2^{l - 1}.
You should perform q queries. Each query has one of... | Step 1: The goal of this problem is to process a series of queries and perform operations based on the type of query.
Step 2: To solve this, we need to implement logic to handle both types of queries and perform the required operations (assigning values or calculating the minimum number of operations).
Step 3: We sh... | 1937e8ad4a1faa40e16ddd4c0ad7ddd222d01144808ed9b4c3f7b876c270aa04_1_1 | 63ac4683d0f9206c517daf70ed5e2721cd38321887742e9c24181e6769969463 |
Coding | codecontest | Write Python code to solve the task.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bride... | Step 1: The problem presents a scenario where bridegrooms need to choose brides in a circular layout such that the maximum distance traveled by a bride is minimized.
Step 2: We can solve this problem by iterating through the distances of the bridegrooms and the brides in a dynamic way to find the optimum solution fo... | 09f5253f7b11c3aaf3915d7b64609296f6388e75e5e3fb513f1b8e02bc5df210_1_1 | 2808808707e7a682bee0e219afc520d9e75a96c96a436b5d77155c3c551c07d8 |
Coding | codecontest | Write Python code to solve the task.
It's marriage season in Ringland!
Ringland has a form of a circle's boundary of length L. There are n bridegrooms and n brides, and bridegrooms decided to marry brides.
Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bride... | Step 1: The given problem of finding the smallest possible inconvenience of a marriage involves computing the maximum distance that some bride should walk along the circle from her palace to her bridegroom's castle.
Step 2: We are given the distances of bridegrooms' castles and brides' palaces from the capital in clo... | 57ee4dcb3cdcc01823a67cdfb726456f079fc0d032c029565c23e4766cba5ff4_1_1 | 2808808707e7a682bee0e219afc520d9e75a96c96a436b5d77155c3c551c07d8 |
Coding | codecontest | Write Python code to solve the task.
Alice decides to challenge Bob to a problem. She gives him a number.
Bob can rearrange the digits of this number by applying pair-wise swaps between any 2 digits in the number as many times as he wants. Now Alice asks him to write down all the distinct numbers that he can form and... | Step 1: To solve this problem, we need to iterate through the input numbers and perform arrangements by applying pair-wise swaps between any 2 digits in the number. Then, we need to sort and print the 3rd smallest and 3rd largest number from the distinct numbers formed.
Step 2: The main challenge in solving this pro... | 6393306889a46aadd0a1e92e40924541520e55f3ac7eb6d40f33cbe792f873fa_1_1 | 4816def971c3e4809fd8d5ea7f542debac472d47573668f0a337205e747176c5 |
Coding | codecontest | Write Python code to solve the task.
Alice decides to challenge Bob to a problem. She gives him a number.
Bob can rearrange the digits of this number by applying pair-wise swaps between any 2 digits in the number as many times as he wants. Now Alice asks him to write down all the distinct numbers that he can form and... | Step 1: To solve this problem, we need to understand how to generate all distinct numbers by rearranging the digits of a given number.
Step 2: We need to consider how to use these rearranged numbers to find the 3rd smallest and the 3rd largest number.
Step 3: We can start by writing the logic for generating all poss... | 47439da93afc342fe1b4ea906ac94f1c26e47056fbfe36a9618252b6002457d6_1_1 | 4816def971c3e4809fd8d5ea7f542debac472d47573668f0a337205e747176c5 |
Coding | codecontest | Write Python code to solve the task.
Reading books is one of Sasha's passions. Once while he was reading one book, he became acquainted with an unusual character. The character told about himself like that: "Many are my names in many countries. Mithrandir among the Elves, Tharkûn to the Dwarves, Olórin I was in my yout... | Step 1: To solve this problem, we need to find the minimum number of cuts needed to transform the given palindrome string into a new palindrome string.
Step 2: We can start by checking whether the length of the string is even or odd, and then implement different logic for each case.
Step 3: For an even length palind... | f954d25f7827d7eafc90b0ee3c79a2d9ae7af980fe4f654ee784357c83e34bcb_1_1 | c24bd9062d3ca8bda56ee7cffa6dda4e406207f02cedc50804de0aab694900b9 |
Coding | codecontest | Write Python code to solve the task.
Reading books is one of Sasha's passions. Once while he was reading one book, he became acquainted with an unusual character. The character told about himself like that: "Many are my names in many countries. Mithrandir among the Elves, Tharkûn to the Dwarves, Olórin I was in my yout... | Step 1: To solve this problem, we need to find the minimum number of cuts needed to transform the input palindrome string into a new string that is also a palindrome but different from the input string.
Step 2: First, we should check if the input string is an even-length palindrome or an odd-length palindrome.
Step 3... | efbeed79385f2281a472eb35a55275435d934722b54801037737b3ad87c91314_1_1 | c24bd9062d3ca8bda56ee7cffa6dda4e406207f02cedc50804de0aab694900b9 |
Coding | codecontest | Write Python code to solve the task.
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm × h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.
In order not to... | Step 1: The problem describes Leonid's process of making vertical and horizontal cuts through a sheet of glass, resulting in smaller rectangular fragments of glass. After each cut, we need to determine the area of the largest currently available glass fragment.
Step 2: The strategy is to keep track of the cuts made, ... | c822c817585437ff567ce81bb0dbccfc4439a5a7c039af495d9e276414abe386_1_1 | 4b574bb1d917786eb72430254f5d4b53aa0f74ab93b28a64e2d07de8eedebc27 |
Coding | codecontest | Write Python code to solve the task.
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm × h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.
In order not to... | Step 1:
The problem requires us to calculate the area of the largest available glass fragment after each vertical or horizontal cut is made to a rectangular sheet of glass of dimensions w * h mm.
To solve the problem, we can implement a function to calculate the area of the maximum available glass fragment after each... | 2d698466896d12d5898bb4848417ecd512ed46b9d5458c43c93f18abdf96f15d_1_1 | 4b574bb1d917786eb72430254f5d4b53aa0f74ab93b28a64e2d07de8eedebc27 |
Coding | codecontest | Write Python code to solve the task.
Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc.
We'll say that string s can be obtained from string t, if we can remove some characters from string t and... | Step 1: The task requires finding the largest integer p such that concatenating 'q' p times can be obtained from string 'w'.
Step 2: We need to compare the string characters of 'w' and 'q' to see if 'q' can be obtained from 'w'.
Step 3: If 'q' is found as a substring of 'w', we need to compute how many times it can ... | fe69f93dd2207ea1fa97f356d8a2bfdad7b7711f6448beeadf0944df1c017e5b_1_1 | 7d94531d45900772ac392069237de8638079809254ab08411baef53090299240 |
Coding | codecontest | Write Python code to solve the task.
Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc.
We'll say that string s can be obtained from string t, if we can remove some characters from string t and... | Step 1: The problem wants to find the largest integer p such that the string q repeated p times (i.e., [q, p]) can be obtained from the string w.
Step 2: To solve the problem, we need to compare the characters of s and t to check if the characters of s can be formed by the characters of t.
Step 3: We also need to fi... | 7e6b81b795a7cd5a7332c5ffb705e54c636143b9056e5770b54c1dba673fc03a_1_1 | 7d94531d45900772ac392069237de8638079809254ab08411baef53090299240 |
Coding | codecontest | Write Python code to solve the task.
Hermione is very good in Magic but she is not good enough in Mathematics. She got stuck in a problem of mathematics in which she has to find out whether a combination M objects out of N is even or odd.
Harry is quite good in mathematics so Hermione goes to get the help from Harry.
... | Step 1: This problem involves calculating combinations and determining whether the result is even or odd.
Step 2: We need to understand the properties of combinations and how to determine the parity (even or odd) of a specific combination.
Step 3: Given the input values of N and M, we need to calculate the combinati... | a0ec9900bd246d9cfa27858c83aa0743a94d8e56e1ef83c1f402e722a28e358a_1_1 | dabcdb13498c0e38a675fffab5155dcb3a061b18960da8d639317cce27b76aa9 |
Coding | codecontest | Write Python code to solve the task.
Hermione is very good in Magic but she is not good enough in Mathematics. She got stuck in a problem of mathematics in which she has to find out whether a combination M objects out of N is even or odd.
Harry is quite good in mathematics so Hermione goes to get the help from Harry.
... | Step 1: The given problem requires us to determine whether the combination of M objects out of N is even or odd.
Step 2: We can use the concept of combinations from mathematics to solve this problem.
Step 3: To implement this, we need to consider the rules for combinations and check if certain conditions are met to ... | 6ab79bcd74a59d23fc62de2721b49885cf66e11a81a485f1ae9548143bd8f6de_1_1 | dabcdb13498c0e38a675fffab5155dcb3a061b18960da8d639317cce27b76aa9 |
Coding | codecontest | Write Python code to solve the task.
You have a bag of size n. Also you have m boxes. The size of i-th box is a_i, where each a_i is an integer non-negative power of two.
You can divide boxes into two parts of equal size. Your goal is to fill the bag completely.
For example, if n = 10 and a = [1, 1, 32] then you have... | Step 1: The goal is to find the minimum number of divisions required to fill the bag of size n with the given boxes.
Step 2: We need to consider the sizes of the boxes and the binary representations of the bag size and box sizes to determine the minimum divisions required.
Step 3: We also need to handle cases where ... | ee459286c85e1e0db3e42ff8418fa4162edf7a1726ae6f4e2764ce2363ca58f6_1_1 | 252df7530c2acecc6b92bdd5c3abedb36d7cae97c23b88744dd38534557a2b1b |
Coding | codecontest | Write Python code to solve the task.
You have a bag of size n. Also you have m boxes. The size of i-th box is a_i, where each a_i is an integer non-negative power of two.
You can divide boxes into two parts of equal size. Your goal is to fill the bag completely.
For example, if n = 10 and a = [1, 1, 32] then you have... | Step 1: The problem requires calculating the minimum number of divisions required to fill the bag of size n with boxes of various sizes.
Step 2: Initially, I need to iterate through each test case and calculate the minimum divisions required.
Step 3: I would create a list to count the boxes of each power of two si... | 87624493bf074c6fa379a664437a8fd3821070f159587b442114e4626cfabc0e_1_1 | 252df7530c2acecc6b92bdd5c3abedb36d7cae97c23b88744dd38534557a2b1b |
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: We need to calculate the expected number of times "ab" will occur across all valid sequences in the resulting sequence.
Step 2: To do this, we should consider the probability of adding 'a' and 'b' to the sequence at each second.
Step 3: We can use dynamic programming to calculate the expected number of times... | 6d793328c28f21624032b907b24e6ab155e3db2be72b536b5540f833295222d7_1_1 | 786ea014d2739fb5b4d5c30b9c520598d3b3528fe2bcfb3d68603456355ac5a8 |
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