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Problem F. Nim without Zero Alice: "Hi, Bob! Let's play Nim!" Bob: "Are you serious? I don't want to play it. I know how to win the game." Alice: "Right, there is an algorithm to calculate the optimal move using XOR. How about changing the rule so that a player loses a game if he or she makes the XOR to $0$?" Bob: "It sounds much better now, but I suspect you know the surefire way to win." Alice: "Do you wanna test me?" This game is defined as follows. The game starts with $N$ heaps where the $i$-th of them consists of $a_i$ stones. A player takes any positive number of stones from any single one of the heaps in one move. Alice moves first. The two players alternately move. If the XOR sum, $a_1$ XOR $a_2$ XOR $...$ XOR $a_N$, of the numbers of remaining stones of these heaps becomes $0$ as a result of a player's move, the player loses. Your task is to find which player will win if they do the best move. Input The input consists of a single test case in the format below. $N$ $a_1$ $\vdots$ $a_N$ The first line contains an integer $N$ which is the number of the heaps ($1 \leq N \leq 10^5$). Each of the following $N$ lines gives the number of stones in each heap ($1 \leq a_i \leq 10^9$). Output Output the winner, Alice or Bob, when they do the best move. Examples Sample Input 1 2 1 1 Output for Sample Input 1 Alice Sample Input 2 5 1 2 3 4 5 Output for Sample Input 2 Bob Sample Input 3 10 1 2 3 4 5 6 7 8 9 10 Output for Sample Input 3 Alice In the first example, the XOR sum is 0 in the initial state, but the game is going because nobody moves yet. First Alice takes a stone and the XOR sum becomes 1, then Bob takes the last stone and the XOR sum becomes 0. Therefore, Alice will win, and Bob will lose. | 37,645 |
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Map: Search For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that each key in $M$ must be unique . insert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$. If there is an element with $key$, replace the corresponding value with $x$. get($key$): Print the value with the specified $key$. Input The input is given in the following format. $q$ $query_1$ $query_2$ : $query_q$ Each query $query_i$ is given by 0 $key$ $x$ or 1 $key$ where the first digits 0 , 1 and 2 represent insert and get operations respectively. Output For each get operation, print an integer in a line. Constraints $1 \leq q \leq 200,000$ $1 \leq x \leq 1,000,000,000$ $1 \leq $ length of $key$ $ \leq 20$ $key$ consits of lower-case letter For a get operation, the element with the specified key exists in $M$. Sample Input 1 7 0 blue 4 0 red 1 0 white 5 1 red 1 blue 0 black 8 1 black Sample Output 1 1 4 8 | 37,647 |
Score : 100 points Problem Statement There are N stones, numbered 1, 2, \ldots, N . For each i ( 1 \leq i \leq N ), the height of Stone i is h_i . There is a frog who is initially on Stone 1 . He will repeat the following action some number of times to reach Stone N : If the frog is currently on Stone i , jump to one of the following: Stone i + 1, i + 2, \ldots, i + K . Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on. Find the minimum possible total cost incurred before the frog reaches Stone N . Constraints All values in input are integers. 2 \leq N \leq 10^5 1 \leq K \leq 100 1 \leq h_i \leq 10^4 Input Input is given from Standard Input in the following format: N K h_1 h_2 \ldots h_N Output Print the minimum possible total cost incurred. Sample Input 1 5 3 10 30 40 50 20 Sample Output 1 30 If we follow the path 1 â 2 â 5 , the total cost incurred would be |10 - 30| + |30 - 20| = 30 . Sample Input 2 3 1 10 20 10 Sample Output 2 20 If we follow the path 1 â 2 â 3 , the total cost incurred would be |10 - 20| + |20 - 10| = 20 . Sample Input 3 2 100 10 10 Sample Output 3 0 If we follow the path 1 â 2 , the total cost incurred would be |10 - 10| = 0 . Sample Input 4 10 4 40 10 20 70 80 10 20 70 80 60 Sample Output 4 40 If we follow the path 1 â 4 â 8 â 10 , the total cost incurred would be |40 - 70| + |70 - 70| + |70 - 60| = 40 . | 37,648 |
Score : 1600 points Problem Statement 2^N players competed in a tournament. Each player has a unique ID number from 1 through 2^N . When two players play a match, the player with the smaller ID always wins. This tournament was a little special, in which losers are not eliminated to fully rank all the players. We will call such a tournament that involves 2^n players a full tournament of level n . In a full tournament of level n , the players are ranked as follows: In a full tournament of level 0 , the only player is ranked first. In a full tournament of level n\ (1 \leq n) , initially all 2^n players are lined up in a row. Then: First, starting from the two leftmost players, the players are successively divided into 2^{n-1} pairs of two players. Each of the pairs plays a match. The winner enters the "Won" group, and the loser enters the "Lost" group. The players in the "Won" group are lined up in a row, maintaining the relative order in the previous row. Then, a full tournament of level n-1 is held to fully rank these players. The players in the "Lost" group are also ranked in the same manner, then the rank of each of these players increases by 2^{n-1} . For example, the figure below shows how a full tournament of level 3 progresses when eight players are lined up in the order 3,4,8,6,2,1,7,5 . The list of the players sorted by the final ranking will be 1,3,5,6,2,4,7,8 . Takahashi has a sheet of paper with the list of the players sorted by the final ranking in the tournament, but some of it blurred and became unreadable. You are given the information on the sheet as a sequence A of length N . When A_i is 1 or greater, it means that the i -th ranked player had the ID A_i . If A_i is 0 , it means that the ID of the i -th ranked player is lost. Determine whether there exists a valid order in the first phase of the tournament which is consistent with the sheet. If it exists, provide one such order. Constraints 1 \leq N \leq 18 0 \leq A_i \leq 2^N No integer, except 0 , occurs more than once in A_i . Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_{2^N} Output If there exists a valid order in the first phase of the tournament, print YES first, then in the subsequent line, print the IDs of the players sorted by the final ranking, with spaces in between. If there is no such order, print NO instead. Sample Input 1 3 0 3 0 6 0 0 0 8 Sample Output 1 YES 3 4 8 6 2 1 7 5 This is the same order as the one in the statement. Sample Input 2 1 2 1 Sample Output 2 NO | 37,649 |
Score : 300 points Problem Statement There are N boxes arranged in a row. Initially, the i -th box from the left contains a_i candies. Snuke can perform the following operation any number of times: Choose a box containing at least one candy, and eat one of the candies in the chosen box. His objective is as follows: Any two neighboring boxes contain at most x candies in total. Find the minimum number of operations required to achieve the objective. Constraints 2 †N †10^5 0 †a_i †10^9 0 †x †10^9 Input The input is given from Standard Input in the following format: N x a_1 a_2 ... a_N Output Print the minimum number of operations required to achieve the objective. Sample Input 1 3 3 2 2 2 Sample Output 1 1 Eat one candy in the second box. Then, the number of candies in each box becomes (2, 1, 2) . Sample Input 2 6 1 1 6 1 2 0 4 Sample Output 2 11 For example, eat six candies in the second box, two in the fourth box, and three in the sixth box. Then, the number of candies in each box becomes (1, 0, 1, 0, 0, 1) . Sample Input 3 5 9 3 1 4 1 5 Sample Output 3 0 The objective is already achieved without performing operations. Sample Input 4 2 0 5 5 Sample Output 4 10 All the candies need to be eaten. | 37,650 |
Score : 600 points Problem Statement We have a sequence of k numbers: d_0,d_1,...,d_{k - 1} . Process the following q queries in order: The i -th query contains three integers n_i , x_i , and m_i . Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray} Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i) . Here (y~\textrm{mod}~z) denotes the remainder of y divided by z , for two integers y and z~(z > 0) . Constraints All values in input are integers. 1 \leq k, q \leq 5000 0 \leq d_i \leq 10^9 2 \leq n_i \leq 10^9 0 \leq x_i \leq 10^9 2 \leq m_i \leq 10^9 Input Input is given from Standard Input in the following format: k q d_0 d_1 ... d_{k - 1} n_1 x_1 m_1 n_2 x_2 m_2 : n_q x_q m_q Output Print q lines. The i -th line should contain the response to the i -th query. Sample Input 1 3 1 3 1 4 5 3 2 Sample Output 1 1 For the first query, the sequence { a_j } will be 3,6,7,11,14 . (a_0~\textrm{mod}~2) > (a_1~\textrm{mod}~2) (a_1~\textrm{mod}~2) < (a_2~\textrm{mod}~2) (a_2~\textrm{mod}~2) = (a_3~\textrm{mod}~2) (a_3~\textrm{mod}~2) > (a_4~\textrm{mod}~2) Thus, the response to this query should be 1 . Sample Input 2 7 3 27 18 28 18 28 46 1000000000 1000000000 1 7 1000000000 2 10 1000000000 3 12 Sample Output 2 224489796 214285714 559523809 | 37,651 |
Knapsack Problem with Limitations You have N items that you want to put them into a knapsack. Item i has value v i , weight w i and limitation m i . You want to find a subset of items to put such that: The total value of the items is as large as possible. The items have combined weight at most W , that is capacity of the knapsack. You can select at most m i items for i th item. Find the maximum total value of items in the knapsack. Input N W v 1 w 1 m 1 v 2 w 2 m 2 : v N w N m N The first line consists of the integers N and W . In the following N lines, the value, weight and limitation of the i -th item are given. Output Print the maximum total values of the items in a line. Constraints 1 †N †100 1 †v i †1,000 1 †w i †1,000 1 †m i †10,000 1 †W †10,000 Sample Input 1 4 8 4 3 2 2 1 1 1 2 4 3 2 2 Sample Output 1 12 Sample Input 2 2 100 1 1 100 2 1 50 Sample Output 2 150 | 37,652 |
Score : 1900 points Problem Statement Snuke has a grid with H rows and W columns. The square at the i -th row and j -th column contains a character S_{i,j} . He can perform the following two kinds of operation on the grid: Row-reverse: Reverse the order of the squares in a selected row. Column-reverse: Reverse the order of the squares in a selected column. For example, reversing the 2 -nd row followed by reversing the 4 -th column will result as follows: By performing these operations any number of times in any order, how many placements of characters on the grid can be obtained? Constraints 1âŠH,WâŠ200 S_{i,j} is a lowercase English letter ( a - z ). Input The input is given from Standard Input in the following format: H W S_{1,1} S_{1,2} ... S_{1,W} S_{2,1} S_{2,2} ... S_{2,W} : S_{H,1} S_{H,2} ... S_{H,W} Output Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7) . Sample Input 1 2 2 cf cf Sample Output 1 6 The following 6 placements of characters can be obtained: Sample Input 2 1 12 codefestival Sample Output 2 2 | 37,653 |
Score : 800 points Problem Statement Given is a string S consisting of 0 and 1 . Find the number of strings, modulo 998244353 , that can result from applying the following operation on S between 0 and K times (inclusive): Choose a pair of integers i, j (1\leq i < j\leq |S|) such that the i -th and j -th characters of S are 0 and 1 , respectively. Remove the j -th character from S and insert it to the immediate left of the i -th character. Constraints 1 \leq |S| \leq 300 0 \leq K \leq 10^9 S consists of 0 and 1 . Input Input is given from Standard Input in the following format: S K Output Find the number of strings, modulo 998244353 , that can result from applying the operation on S between 0 and K times (inclusive). Sample Input 1 0101 1 Sample Output 1 4 Four strings, 0101 , 0110 , 1001 , and 1010 , can result. Sample Input 2 01100110 2 Sample Output 2 14 Sample Input 3 1101010010101101110111100011011111011000111101110101010010101010101 20 Sample Output 3 113434815 | 37,654 |
Problem D: Indian Puzzle In the Indian Puzzle, one is intended to fill out blanks with numbers and operators in a n by n grid in order to make equalities in the grid true (See Figure 1). Figure 1 A blank cell should be filled out with a number (from 0 to 9 inclusive) or an operator ( + , - , à , ÷ , = ), and black cells split equalities. Initially, some cells are already filled with numbers or operators. The objective of this puzzle is to fill out all the blank cells with numbers (from 0 to 9 inclusive) and operators ( + , - , à , ÷ ) in a given list. All the numbers and operators in the list must be used to fill out the blank cells. A equality is organized by more than 2 consecutive left-to-right or top-to-bottom white cells. You can assume that a equality contains exactly one cell with ' = ' which connects two expressions. The expressions conform to the order of operations and semantics of conventional four arithmetic operations. First, do all multiplication and division, starting from the left (top). Then, do all addition and subtraction, starting from the left (top). In addition, this puzzle has the following rules: Division by zero and division leaving a remainder, are not allowed. Leading zeros are not allowed. Unary operators like 3Ã-8=-24 are not allowed. In a formal description, the equality must conform the syntax in the following BNF: <Eq> ::= <Ex> = <Ex> <Ex> ::= <N0> | <Ex> <Op> <N0> <N0> ::= <N> | 0 <N> ::= <D> | <N> <D> | <N> 0 <Op> ::= + | - | à | ÷ <D> ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Of course, puzzle creators must make solvable puzzle. Your task is to write a program which verifies whether given puzzle is solvable or not. Input Input consists of several datasets. Each dataset consists of: H W H à W characters n n characters The integers H and W are the numbers of rows and columns of the grid, respectively. H à W characters denote the grid which contains ' . ' representing a blank cell, ' # ' representing a black cell, numbers (from 0 to 9 inclusive), operators(' + ',' - ', ' * ', ' / ', ' = ')( à is represented by ' * ' and ÷ is represented by ' / '). The integer n is the number of characters in the list. The last line of a dataset contains n characters indicating numbers and operators for the blank cells. The end of input is indicated by a line containing two zeros separated by a space. Output For each dataset, print " Yes " if the given puzzle is solvable, " No " if not. Constraints Judge data includes at most 100 data sets. H , W †10 n †10 Sample Input 5 5 4=..2 +#=#+ .-2=. =#*#= .-.=3 6 7 3 1 4 / 8 1 6 8..3=2 2 2 + 0 0 Output for the Sample Input Yes No | 37,655 |
Doubly Linked List Your task is to implement a double linked list. Write a program which performs the following operations: insert x: insert an element with key x into the front of the list. delete x: delete the first element which has the key of x from the list. If there is not such element, you need not do anything. deleteFirst: delete the first element from the list. deleteLast: delete the last element from the list. Input The input is given in the following format: n command 1 command 2 ... command n In the first line, the number of operations n is given. In the following n lines, the above mentioned operations are given in the following format: insert x delete x deleteFirst deleteLast Output Print all the element (key) in the list after the given operations. Two consequtive keys should be separated by a single space. Constraints The number of operations †2,000,000 The number of delete operations †20 0 †value of a key †10 9 The number of elements in the list does not exceed 10 6 For a delete, deleteFirst or deleteLast operation, there is at least one element in the list. Sample Input 1 7 insert 5 insert 2 insert 3 insert 1 delete 3 insert 6 delete 5 Sample Output 1 6 1 2 Sample Input 2 9 insert 5 insert 2 insert 3 insert 1 delete 3 insert 6 delete 5 deleteFirst deleteLast Sample Output 2 1 | 37,656 |
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¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã 1 †N †150 0 †X i1 , Y i1 , X i2 , Y i2 †200 (1 †i †N ) X i1 = X i2 ãŸã㯠Y i1 = Y i2 (1 †i †N ) èšç®ã®éäžãšçµæã«çŸããæ°ã¯ç¬Šå·ä»ã32ãããæŽæ°ã«åãŸã Output åã±ãŒã¹ã®èšç®çµæãäžè¡ã«åºåããã Sample Input 1 4 1 1 1 5 3 3 5 3 4 2 4 4 7 1 7 5 Sample Output 1 2 Sample Input 2 23 1 1 3 1 3 1 3 3 3 3 1 3 1 3 1 5 1 5 3 5 5 2 7 2 7 2 7 4 7 4 5 4 5 4 5 6 5 6 7 6 11 4 13 4 13 0 15 0 15 0 15 4 18 2 18 2 21 5 23 5 21 5 21 7 21 7 23 7 23 7 23 9 23 9 21 9 24 0 26 0 24 0 24 4 24 4 26 4 26 0 26 4 Sample Output 2 -328 Hint 1ã€ã®ã°ãªããã2床以äžå¡ãã€ã¶ãããšããã '1'ãªã©ã1ã€ã®ç·åã§è¡šãããšãå¯èœã§ãã2ã€ä»¥äžã®ç·åã§è¡šãå Žåããã Sample Input 1ã®æ°åŒã Sample Input 2ã®æ°åŒã"-7"ã®éšåã®ããã«ãããæåãèŠãæå°ã®é·æ¹åœ¢ã®å
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Score : 200 points Problem Statement Takahashi is competing in a sumo tournament. The tournament lasts for 15 days, during which he performs in one match per day. If he wins 8 or more matches, he can also participate in the next tournament. The matches for the first k days have finished. You are given the results of Takahashi's matches as a string S consisting of o and x . If the i -th character in S is o , it means that Takahashi won the match on the i -th day; if that character is x , it means that Takahashi lost the match on the i -th day. Print YES if there is a possibility that Takahashi can participate in the next tournament, and print NO if there is no such possibility. Constraints 1 \leq k \leq 15 S is a string of length k consisting of o and x . Input Input is given from Standard Input in the following format: S Output Print YES if there is a possibility that Takahashi can participate in the next tournament, and print NO otherwise. Sample Input 1 oxoxoxoxoxoxox Sample Output 1 YES Takahashi has 7 wins and 7 losses before the last match. If he wins that match, he will have 8 wins. Sample Input 2 xxxxxxxx Sample Output 2 NO | 37,659 |
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¥åã®ïŒè¡ç®ã«ã¯ãæŽæ° N ïŒ3 †N †100,000ïŒãæžãããŠãããããã¯ãã¹ãŽãã¯ã®ãã¹æ°ãããããããã¹ã«ã¯1 çªãã N çªãŸã§ã®çªå·ããµãããŠãããã¹ã¿ãŒãã®ãã¹ã1 çªã§ãããããã¹ã¿ãŒãã«è¿ãé ã«2 çªã3 çªãâŠâŠã N - 1 çªãšç¶ãããŽãŒã«ã®ãã¹ã N çªã§ããã i çªã®ãã¹ã§ãµã€ã³ããæ¯ã£ãŠj ã®ç®ãåºããã i + j çªã®ãã¹ãžãšç§»åããããã ããããã i + j ã N ãè¶
ããŠããããäœã£ãæ°ã ãæ»ã£ããã¯ããããŽãŒã«ãããšã¿ãªãããã ç¶ã N è¡ã«ã¯ãæŽæ° p i ïŒ-100,000 †p i †100,000ïŒãæžãããŠããã1 ïŒ i è¡ç®ã«æžãããæŽæ° p i ã¯ãi çªã®ãã¹ã«æžãããŠããæ瀺ãããããã p i > 0 ãªãã°ã p i ãã¹é²ããã p i < 0 ãªãã°ã- p i ãã¹æ»ããã§ããã p i = 0 ãªãã°ãã®ãã¹ã«ã¯äœã®å¹æããªãã p 1 ãš p N ã¯å¿
ã0 ã§ããããã¹ã®å¹æã§ãã¹ã¿ãŒãããåããŽãŒã«ããåŸã«ç§»åãããšæ瀺ãããããšã¯ãªãã ãªããäžããããã¹ãŽãã¯ã¯ããŽãŒã«ããããšãå¯èœã§ãããšä»®å®ããŠããã Output ãŽãŒã«ãããŸã§ã«ãµã€ã³ããæ¯ãåæ°ã®æå°å€ãåºåããã Sample Input 1 11 0 0 -2 0 -4 1 -1 2 0 0 0 Sample Output 1 3 Sample Input 2 12 0 0 7 0 2 0 0 3 -6 -2 1 0 Sample Output 2 1 Sample Input 3 8 0 4 -1 1 -2 -2 0 0 Sample Output 3 2 | 37,660 |
Score : 200 points Problem Statement The postal code in Atcoder Kingdom is A+B+1 characters long, its (A+1) -th character is a hyphen - , and the other characters are digits from 0 through 9 . You are given a string S . Determine whether it follows the postal code format in Atcoder Kingdom. Constraints 1â€A,Bâ€5 |S|=A+B+1 S consists of - and digits from 0 through 9 . Input Input is given from Standard Input in the following format: A B S Output Print Yes if S follows the postal code format in AtCoder Kingdom; print No otherwise. Sample Input 1 3 4 269-6650 Sample Output 1 Yes The (A+1) -th character of S is - , and the other characters are digits from 0 through 9 , so it follows the format. Sample Input 2 1 1 --- Sample Output 2 No S contains unnecessary - s other than the (A+1) -th character, so it does not follow the format. Sample Input 3 1 2 7444 Sample Output 3 No | 37,661 |
Problem I: Operator The customer telephone support center of the computer sales company called JAG is now in- credibly confused. There are too many customers who request the support, and they call the support center all the time. So, the company wants to figure out how many operators needed to handle this situation. For simplicity, let us focus on the following simple simulation. Let N be a number of customers. The i -th customer has id i , and is described by three numbers, M i , L i and K i . M i is the time required for phone support, L i is the maximum stand by time until an operator answers the call, and K i is the interval time from hanging up to calling back. Let us put these in other words: It takes M i unit times for an operator to support i -th customer. If the i -th customer is not answered by operators for L i unit times, he hangs up the call. K i unit times after hanging up, he calls back. One operator can support only one customer simultaneously. When an operator finish a call, he can immediately answer another call. If there are more than one customer waiting, an operator will choose the customer with the smallest id. At the beginning of the simulation, all customers call the support center at the same time. The simulation succeeds if operators can finish answering all customers within T unit times. Your mission is to calculate the minimum number of operators needed to end this simulation successfully. Input The input contains multiple datasets. Each dataset has the following format: N T M 1 L 1 K 1 . . . M N L N K N The first line of a dataset contains two positive integers, N and T (1 †N †1000, 1 †T †1000). N indicates the number of customers in the dataset, and T indicates the time limit of the simulation. The following N lines describe the information of customers. The i -th line contains three integers, M i , L i and K i (1 †M i †T , 1 †L i †1000, 1 †K i †1000), describing i -th customer's information. M i indicates the time required for phone support, Li indicates the maximum stand by time until an operator answers the call, and Ki indicates the is the interval time from hanging up to calling back. The end of input is indicated by a line containing two zeros. This line is not part of any dataset and hence should not be processed. Output For each dataset, print the minimum number of operators needed to end the simulation successfully in a line. Sample Input 3 300 100 50 150 100 50 150 100 50 150 3 300 100 50 150 100 50 150 200 50 150 9 18 3 1 1 3 1 1 3 1 1 4 100 1 5 100 1 5 100 1 10 5 3 10 5 3 1 7 1000 10 18 1 2 3 2 3 4 3 4 5 4 5 6 5 6 7 6 7 8 7 8 9 8 9 10 9 10 11 10 11 12 0 0 Output for the Sample Input 2 3 3 4 | 37,662 |
Ciel, an idol whose appearance and behavior are similar to a fox, is participating in a rehearsal for the live concert which takes place in a few days. To become a top idol, a large amount of effort is required! The live stage can be expressed as a two-dimensional surface. The live stage has N spotlights to illuminate the stage. The i -th spotlight casts a light in the range of a circle with radius r_{i} . The center of the light cast by the i -th spotlight moves along an orbital path R_{i} . R_{i} is described as a closed polygon, though R_{i} might contain self-intersections. The spotlight begins to move from the first vertex of R_{i} . All of the orbital period of each spotlight are the same. Each spotlight moves at a constant speed, and all of them return to the starting point at the same time. In the rehearsal, Ciel has to move from the starting point to the ending point indicated on the live stage. To achieve her goal, it is not allowed to fall out from the area illuminated with the spotlight. But, she doesn't have to be illuminated with the spotlight as long as she is standing on the starting point. You may assume that she can move fast enough. Answer if it is possible for her to move to the ending point. Input Each input dataset is given in the following format: N sx sy ex ey r_{1} K_{1} x_{11} y_{11} x_{12} y_{12} ... x_{1K_{1}} y_{1K_{1}} r_{2} K_{2} x_{21} y_{21} x_{22} y_{22} ... x_{2K_{2}} y_{2K_{2}} : : r_{N} K_{N} x_{N1} y_{N1} x_{N2} y_{N2} ... x_{NK_{N}} y_{NK_{N}} All inputs are integer. All coordinate information satisfies -10,000 \leq x , y \leq 10,000 . N ( 1 \leq N \leq 100 ) indicates the number of spotlights. (sx, sy) and (ex, ey) indicate the starting point and the ending point of Ciel's path, respectively. The following N lines denote the information of each spotlight. r_{i} ( 1 \leq r_{i} \leq 100 ) indicates the radius of the spotlight. K_{i} ( 2 \leq K_{i} \leq 10 ) indicates the number of vertices in the orbital path. Then, K_{i} vertices are given. Two consecutive vertices on the same orbital path are located at different places. The spotlight moves from the first point (x_{i1}, y_{i1}) to the second point (x_{i2}, y_{i2}) , then moves to the third point (x_{i3}, y_{i3}) , and so on. After moving to the K_{i} -th point (x_{iK_{i}}, y_{iK_{i}}) , the spotlight returns to the first point (x_{i1}, y_{i1}) and repeats again its movement. Let d_{ij} be the closest distance between two central points of spotlight i and spotlight j . d_{ij} satisfies either of the following: d_{ij} > r_{i} + r_{j} + 0.000001 d_{ij} < r_{i} + r_{j} - 0.000001 Furthermore, let d_{i} be the closest distance between a central point of spotlight i and either the starting point or the ending point. d_{i} satisfies either of the following: d_{i} > r_{i} + 0.000001 d_{i} < r_{i} - 0.000001 Output If it is possible for Ciel to move the ending point without falling out from the illuminated area, output Yes in one line. Otherwise, output No . Sample Input 1 2 1 1 9 -1 2 2 1 1 -9 1 1 2 -1 -1 9 -1 Output for the Sample Input 1 Yes Sample Input 2 2 1 1 9 -1 2 2 1 1 -9 1 1 2 9 -1 -1 -1 Output for the Sample Input 2 No Sample Input 3 2 11 6 -9 1 6 4 10 5 10 0 5 0 5 5 5 4 -10 0 -10 5 -5 5 -5 0 Output for the Sample Input 3 Yes Sample Input 4 1 1 9999 -1 0 100 2 0 0 0 10000 Output for the Sample Input 4 Yes | 37,663 |
Problem G: Concert Hall Scheduling You are appointed director of a famous concert hall, to save it from bankruptcy. The hall is very popular, and receives many requests to use its two fine rooms, but unfortunately the previous director was not very efficient, and it has been losing money for many years. The two rooms are of the same size and arrangement. Therefore, each applicant wishing to hold a concert asks for a room without specifying which. Each room can be used for only one concert per day. In order to make more money, you have decided to abandon the previous fixed price policy, and rather let applicants specify the price they are ready to pay. Each application shall specify a period [ i , j ] and an asking price w , where i and j are respectively the first and last days of the period (1 †i †j †365), and w is a positive integer in yen, indicating the amount the applicant is willing to pay to use a room for the whole period. You have received applications for the next year, and you should now choose the applications you will accept. Each application should be either accepted for its whole period or completely rejected. Each concert should use the same room during the whole applied period. Considering the dire economic situation of the concert hall, artistic quality is to be ignored, and you should just try to maximize the total income for the whole year by accepting the most profitable applications. Input The input has multiple data sets, each starting with a line consisting of a single integer n, the number of applications in the data set. Then, it is followed by n lines, each of which represents one application with a period [ i , j ] and an asking price w yen in the following format. i j w A line containing a single zero indicates the end of the input. The maximum number of applications in a data set is one thousand, and the maximum asking price is one million yen. Output For each data set, print a single line containing an integer, the maximum total income in yen for the data set. Sample Input 4 1 2 10 2 3 10 3 3 10 1 3 10 6 1 20 1000 3 25 10000 5 15 5000 22 300 5500 10 295 9000 7 7 6000 8 32 251 2261 123 281 1339 211 235 5641 162 217 7273 22 139 7851 194 198 9190 119 274 878 122 173 8640 0 Output for the Sample Input 30 25500 38595 | 37,664 |
Score : 200 points Problem Statement Takahashi has A cookies, and Aoki has B cookies. Takahashi will do the following action K times: If Takahashi has one or more cookies, eat one of his cookies. Otherwise, if Aoki has one or more cookies, eat one of Aoki's cookies. If they both have no cookies, do nothing. In the end, how many cookies will Takahashi and Aoki have, respectively? Constraints 0 \leq A \leq 10^{12} 0 \leq B \leq 10^{12} 0 \leq K \leq 10^{12} All values in input are integers. Input Input is given from Standard Input in the following format: A B K Output Print the numbers of Takahashi's and Aoki's cookies after K actions. Sample Input 1 2 3 3 Sample Output 1 0 2 Takahashi will do the following: He has two cookies, so he eats one of them. Now he has one cookie left, and he eats it. Now he has no cookies left, but Aoki has three, so Takahashi eats one of them. Thus, in the end, Takahashi will have 0 cookies, and Aoki will have 2 . Sample Input 2 500000000000 500000000000 1000000000000 Sample Output 2 0 0 Watch out for overflows. | 37,665 |
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Problem E: Combinatorial Topology It was long believed that a 2-dimensional place can not be filled with a finite set of polygons in aperiodic way. British mathematician, Sir Roger Penrose, developed an aperiodic tiling over the years and established a theory of what is known today as quasicrystals. The classic Penrose tiles consist of two rhombi with angles 36 and 72 degrees, see Figure 1. The edges of the rhombi are all of equal unit length, 1. These can fill the entire place without holes and overlaps (see Figure 2). Example: the bold line boundary in Figure 1 is filled with 20 thin tiles and 20 thick tiles. Given a boundary (set of adjacent vertices counter-clock-wise oriented), how many thin tiles (36 degrees) and how many thick tiles (72 degrees) do you need to fill it (without any holes and intersections)? Input Each data set is defined as follows: Line 1 : Number of vertices N ( N < 100). N lines : x and y coordinates of each vertex per line separated by blanks (| x | < 100, | y | < 100). All floats in the input have 6 digits after the decimal point. The required precision is 4 digits. Input file includes several data sets. The number of data sets is less than 20. Output Each line contains the solution for one set. First, there is the number of thin tiles, then the number of thick tiles, separated by a space. If the boundary is illegal for the above problem, the output should be "-1 -1". Sample Input 4 -5.000000 0.000000 5.000000 0.000000 9.635255 14.265848 -0.364745 14.265848 3 -1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 Output for the Sample Input 0 150 -1 -1 | 37,670 |
Problem G: Walk under a Scorching Sun Edward R. Nelson is visiting a strange town for some task today. This city is built on a two-dimensional flat ground with several vertical buildings each of which forms a convex polygon when seen from above on it (that is to say, the buidlings are convex polygon columns). Edward needs to move from the point S to the point T by walking along the roads on the ground. Since today the sun is scorching and it is very hot, he wants to walk in the sunshine as less as possible. Your task is to write program that outputs the route whose length in the sunshine is the shortest, given the information of buildings, roads and the direction of the sun. Input The input consists of multiple data sets. Each data set is given in the following format: N M NV 1 H 1 X 1,1 Y 1,1 X 1,2 Y 1,2 . . . X 1, NV 1 Y 1, NV 1 ... NV N H N X N ,1 Y N ,1 X N ,2 Y N ,2 . . . X N , NV N Y N , NV N RX 1,1 RY 1,1 RX 1,2 RY 1,2 ... RX M ,1 RY M ,1 RX M ,2 RY M ,2 Ξ Ï SX SY TX TY All numbers are integers. N is the number of the buildings (1 †N †15). M is the number of the roads (1 †M †15). NV i is the number of the vertices of the base of the i -th building (3 †NV i †10). H i is the height of the i -th building. X i , j and Y i , j are the ( x , y )-coordinates of the j -th vertex of the base of the i -th building. RX k ,. and RY k ,. are the coordinates of the endpoints of the k-th roads. Ξ is the direction of the sun, which is given by a counterclockwise degree which starts in the positive direction of x (0 †Ξ < 360). Ï is the elevation angle of the sun (0 < Ï < 90). ( SX , SY ) and ( TX , TY ) are the coordinates of the points S and T , respectively. All coordinates range from 0 to 1000. The end of the input is represented by a line with N = M = 0. This line should not be processed. It is guaranteed that both the points S and T are on the roads. No pair of an edge of a shade and a road is parallel. You should assume that the sun is located infinitely far away and that it doesnât move while Edward is walking. Output For each data set, output in one line the length for which he has to walk in the sunshine at least. Your program may output an arbitrary number of digits after the decimal point. However, the error should be 0.001 or less. Sample Input 1 1 4 10 0 0 10 0 10 10 0 10 -5 -20 30 15 135 45 0 -15 15 0 0 0 Output for the Sample Input 11.213 | 37,671 |
Score : 400 points Problem Statement Snuke has a large collection of cards. Each card has an integer between 1 and N , inclusive, written on it. He has A_i cards with an integer i . Two cards can form a pair if the absolute value of the difference of the integers written on them is at most 1 . Snuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create. Constraints 1 ⊠N ⊠10^5 0 ⊠A_i ⊠10^9 (1 ⊠i ⊠N) All input values are integers. Input The input is given from Standard Input in the following format: N A_1 : A_N Output Print the maximum number of pairs that Snuke can create. Sample Input 1 4 4 0 3 2 Sample Output 1 4 For example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4) . Sample Input 2 8 2 0 1 6 0 8 2 1 Sample Output 2 9 | 37,672 |
F - Point Distance Problem Statement You work for invention center as a part time programmer. This center researches movement of protein molecules. It needs how molecules make clusters, so it will calculate distance of all pair molecules and will make a histogram. Moleculesâ positions are given by a N x N grid map. Value C_{xy} of cell (x, y) in a grid map means that C_{xy} molecules are in the position (x, y) . You are given a grid map, please calculate histogram of all pair molecules. Input Input is formatted as follows. N C_{11} C_{12} ... C_{1N} C_{21} C_{22} ... C_{2N} ... C_{N1} C_{N2} ... C_{NN} First line contains the grid map size N ( 1 \leq N \leq 1024 ). Each next N line contains N numbers. Each numbers C_{xy} ( 0 \leq C_{xy} \leq 9 ) means the number of molecule in position (x,y). There are at least 2 molecules. Output Output is formatted as follows. D_{ave} d_{1} c_{1} d_{2} c_{2} ... d_{m} c_{m} Print D_{ave} which an average distance of all pair molecules on first line. Next, print histogram of all pair distance. Each line contains a distance d_i and the number of pair molecules c_i(0 \lt c_i) . The distance d_i should be calculated by squared Euclidean distance and sorted as increasing order. If the number of different distance is more than 10,000, please show the first 10,000 lines. The answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10^{-8} . Sample Input 1 2 1 0 0 1 Output for the Sample Input 1 1.4142135624 2 1 Sample Input 2 3 1 1 1 1 1 1 1 1 1 Output for the Sample Input 2 1.6349751825 1 12 2 8 4 6 5 8 8 2 Sample Input 3 5 0 1 2 3 4 5 6 7 8 9 1 2 3 2 1 0 0 0 0 0 0 0 0 0 1 Output for the Sample Input 3 1.8589994382 0 125 1 379 2 232 4 186 5 200 8 27 9 111 10 98 13 21 16 50 17 37 18 6 20 7 25 6 | 37,673 |
Problem D Making Perimeter of the Convex Hull Shortest The convex hull of a set of three or more planar points is, when not all of them are on one line, the convex polygon with the smallest area that has all the points of the set on its boundary or in its inside. Your task is, given positions of the points of a set, to find how much shorter the perimeter of the convex hull can be made by excluding two points from the set. The figures below correspond to the three cases given as Sample Input 1 to 3. Encircled points are excluded to make the shortest convex hull depicted as thick dashed lines. Sample Input 1 Sample Input 2 Sample Input 3 Input The input consists of a single test case in the following format. $n$ $x_1$ $y_1$ ... $x_n$ $y_n$ Here, $n$ is the number of points in the set satisfying $5 \leq n \leq 10^5$. For each $i$, ($x_i, y_i$) gives the coordinates of the position of the $i$-th point in the set. $x_i$ and $y_i$ are integers between $-10^6$ and $10^6$, inclusive. All the points in the set are distinct, that is, $x_j \ne x_k$ or $y_j \ne y_k$ holds when $j \ne k$. It is guaranteed that no single line goes through $n - 2$ or more points in the set. Output Output the difference of the perimeter of the convex hull of the original set and the shortest of the perimeters of the convex hulls of the subsets with two points excluded from the original set. The output should not have an error greater than $10^{-4}$. Sample Input 1 10 -53 62 -19 58 -11 11 -9 -22 45 -7 37 -39 47 -58 -2 41 -37 10 13 42 Sample Output 1 72.96316928 Sample Input 2 10 -53 62 -19 58 -11 11 -9 -22 45 -7 43 -47 47 -58 -2 41 -37 10 13 42 Sample Output 2 62.62947992 Sample Input 3 10 -53 62 -35 47 -11 11 -9 -22 45 -7 43 -47 47 -58 -2 41 -37 10 13 42 Sample Output 3 61.58166534 | 37,674 |
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Minimum Cost Flow Find the minimum cost to send a certain amount of flow through a flow network. The flow network is a directed graph where each edge $e$ has capacity $c(e)$ and cost $d(e)$. Each edge $e$ can send an amount of flow $f(e)$ where $f(e) \leq c(e)$. Find the minimum value of $\sum_{e} (f(e) \times d(e))$ to send an amount of flow $F$ from source $s$ to sink $t$. Input A flow network $G(V,E)$ is given in the following format. $|V|\;|E|\;F$ $u_0\;v_0\;c_0\;d_0$ $u_1\;v_1\;c_1\;d_1$ : $u_{|E|1}\;v_{|E|-1}\;c_{|E|-1}\;d_{|E|-1}$ $|V|$, $|E|$, $F$ are the number of vertices, the number of edges, and the amount of flow of the flow network respectively. The vertices in $G$ are named with the numbers $0, 1,..., |V|â1$. The source is $0$ and the sink is $|V|â1$. $u_i$, $v_i$, $c_i$, $d_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$, and $c_i$ and $d_i$ are the capacity and the cost of $i$-th edge respectively. Output Print the minimum value in a line. If it is impossible to send the flow from the source $s$ to the sink $t$, print -1 . Constraints 2 †$|V|$ †100 1 †$|E|$ †1000 0 †$F$ †1000 0 †$c_i$, $d_i$ †1000 $u_i$ $\ne$ $v_i$ If there is an edge from vertex $x$ to vertex $y$, there is no edge from vertex $y$ to vertex $x$. Sample Input 4 5 2 0 1 2 1 0 2 1 2 1 2 1 1 1 3 1 3 2 3 2 1 Sample Output 6 | 37,676 |
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ã§ãªããŠã¯ãªããªãïŒ å°éã§ããªãå Žåã¯ïŒ-1 ã1è¡ã«åºåããïŒ Sample Input 3 1 4 -5 5 5 -5 10 1 10 -10 5 5 -10 5 3 5 -20 0 20 0 8 1 9 -14 58 6 24 2 2 8 -57 -113 42 -31 4 1 4 -4 -5 4 5 0 Output for Sample Input 17.5032106371 41.3850388846 -1 102.0656847372 178.1399151364 19.5548716821 | 37,677 |
Score : 200 points Problem Statement You are given two integers K and S . Three variable X, Y and Z takes integer values satisfying 0â€X,Y,Zâ€K . How many different assignments of values to X, Y and Z are there such that X + Y + Z = S ? Constraints 2â€Kâ€2500 0â€Sâ€3K K and S are integers. Input The input is given from Standard Input in the following format: K S Output Print the number of the triples of X, Y and Z that satisfy the condition. Sample Input 1 2 2 Sample Output 1 6 There are six triples of X, Y and Z that satisfy the condition: X = 0, Y = 0, Z = 2 X = 0, Y = 2, Z = 0 X = 2, Y = 0, Z = 0 X = 0, Y = 1, Z = 1 X = 1, Y = 0, Z = 1 X = 1, Y = 1, Z = 0 Sample Input 2 5 15 Sample Output 2 1 The maximum value of X + Y + Z is 15 , achieved by one triple of X, Y and Z . | 37,678 |
Score : 500 points Problem Statement You are going to eat X red apples and Y green apples. You have A red apples of deliciousness p_1,p_2, \dots, p_A , B green apples of deliciousness q_1,q_2, \dots, q_B , and C colorless apples of deliciousness r_1,r_2, \dots, r_C . Before eating a colorless apple, you can paint it red or green, and it will count as a red or green apple, respectively. From the apples above, you will choose the apples to eat while making the sum of the deliciousness of the eaten apples as large as possible. Find the maximum possible sum of the deliciousness of the eaten apples that can be achieved when optimally coloring zero or more colorless apples. Constraints 1 \leq X \leq A \leq 10^5 1 \leq Y \leq B \leq 10^5 1 \leq C \leq 10^5 1 \leq p_i \leq 10^9 1 \leq q_i \leq 10^9 1 \leq r_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: X Y A B C p_1 p_2 ... p_A q_1 q_2 ... q_B r_1 r_2 ... r_C Output Print the maximum possible sum of the deliciousness of the eaten apples. Sample Input 1 1 2 2 2 1 2 4 5 1 3 Sample Output 1 12 The maximum possible sum of the deliciousness of the eaten apples can be achieved as follows: Eat the 2 -nd red apple. Eat the 1 -st green apple. Paint the 1 -st colorless apple green and eat it. Sample Input 2 2 2 2 2 2 8 6 9 1 2 1 Sample Output 2 25 Sample Input 3 2 2 4 4 4 11 12 13 14 21 22 23 24 1 2 3 4 Sample Output 3 74 | 37,679 |
Score : 400 points Problem Statement In the year 2168, AtCoder Inc., which is much larger than now, is starting a limited express train service called AtCoder Express . In the plan developed by the president Takahashi, the trains will run as follows: A train will run for (t_1 + t_2 + t_3 + ... + t_N) seconds. In the first t_1 seconds, a train must run at a speed of at most v_1 m/s (meters per second). Similarly, in the subsequent t_2 seconds, a train must run at a speed of at most v_2 m/s, and so on. According to the specifications of the trains, the acceleration of a train must be always within ±1m/s^2 . Additionally, a train must stop at the beginning and the end of the run. Find the maximum possible distance that a train can cover in the run. Constraints 1 \leq N \leq 100 1 \leq t_i \leq 200 1 \leq v_i \leq 100 All input values are integers. Input Input is given from Standard Input in the following format: N t_1 t_2 t_3 ⊠t_N v_1 v_2 v_3 ⊠v_N Output Print the maximum possible that a train can cover in the run. Output is considered correct if its absolute difference from the judge's output is at most 10^{-3} . Sample Input 1 1 100 30 Sample Output 1 2100.000000000000000 The maximum distance is achieved when a train runs as follows: In the first 30 seconds, it accelerates at a rate of 1m/s^2 , covering 450 meters. In the subsequent 40 seconds, it maintains the velocity of 30m/s , covering 1200 meters. In the last 30 seconds, it decelerates at the acceleration of -1m/s^2 , covering 450 meters. The total distance covered is 450 + 1200 + 450 = 2100 meters. Sample Input 2 2 60 50 34 38 Sample Output 2 2632.000000000000000 The maximum distance is achieved when a train runs as follows: In the first 34 seconds, it accelerates at a rate of 1m/s^2 , covering 578 meters. In the subsequent 26 seconds, it maintains the velocity of 34m/s , covering 884 meters. In the subsequent 4 seconds, it accelerates at a rate of 1m/s^2 , covering 144 meters. In the subsequent 8 seconds, it maintains the velocity of 38m/s , covering 304 meters. In the last 38 seconds, it decelerates at the acceleration of -1m/s^2 , covering 722 meters. The total distance covered is 578 + 884 + 144 + 304 + 722 = 2632 meters. Sample Input 3 3 12 14 2 6 2 7 Sample Output 3 76.000000000000000 The maximum distance is achieved when a train runs as follows: In the first 6 seconds, it accelerates at a rate of 1m/s^2 , covering 18 meters. In the subsequent 2 seconds, it maintains the velocity of 6m/s , covering 12 meters. In the subsequent 4 seconds, it decelerates at the acceleration of -1m/s^2 , covering 16 meters. In the subsequent 14 seconds, it maintains the velocity of 2m/s , covering 28 meters. In the last 2 seconds, it decelerates at the acceleration of -1m/s^2 , covering 2 meters. The total distance covered is 18 + 12 + 16 + 28 + 2 = 76 meters. Sample Input 4 1 9 10 Sample Output 4 20.250000000000000000 The maximum distance is achieved when a train runs as follows: In the first 4.5 seconds, it accelerates at a rate of 1m/s^2 , covering 10.125 meters. In the last 4.5 seconds, it decelerates at the acceleration of -1m/s^2 , covering 10.125 meters. The total distance covered is 10.125 + 10.125 = 20.25 meters. Sample Input 5 10 64 55 27 35 76 119 7 18 49 100 29 19 31 39 27 48 41 87 55 70 Sample Output 5 20291.000000000000 | 37,680 |
Score : 200 points Problem Statement Determine if an N -sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane. You can use the following theorem: Theorem : an N -sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides. Constraints All values in input are integers. 3 \leq N \leq 10 1 \leq L_i \leq 100 Input Input is given from Standard Input in the following format: N L_1 L_2 ... L_N Output If an N -sided polygon satisfying the condition can be drawn, print Yes ; otherwise, print No . Sample Input 1 4 3 8 5 1 Sample Output 1 Yes Since 8 < 9 = 3 + 5 + 1 , it follows from the theorem that such a polygon can be drawn on a plane. Sample Input 2 4 3 8 4 1 Sample Output 2 No Since 8 \geq 8 = 3 + 4 + 1 , it follows from the theorem that such a polygon cannot be drawn on a plane. Sample Input 3 10 1 8 10 5 8 12 34 100 11 3 Sample Output 3 No | 37,681 |
Score : 100 points Problem Statement There are N students in a school. We will divide these students into some groups, and in each group they will discuss some themes. You think that groups consisting of two or less students cannot have an effective discussion, so you want to have as many groups consisting of three or more students as possible. Divide the students so that the number of groups consisting of three or more students is maximized. Constraints 1 \leq N \leq 1000 All input values are integers. Input Input is given from Standard Input in the following format: N Output If you can form at most x groups consisting of three or more students, print x . Sample Input 1 8 Sample Output 1 2 For example, you can form a group of three students and another of five students. Sample Input 2 2 Sample Output 2 0 Sometimes you cannot form any group consisting of three or more students, regardless of how you divide the students. Sample Input 3 9 Sample Output 3 3 | 37,682 |
Score : 300 points Problem Statement You are given an integer N . Find a triple of positive integers h , n and w such that 4/N = 1/h + 1/n + 1/w . If there are multiple solutions, any of them will be accepted. Constraints It is guaranteed that, for the given integer N , there exists a solution such that h,n,w \leq 3500 . Inputs Input is given from Standard Input in the following format: N Outputs Print a triple of positive integers h , n and w that satisfies the condition, in the following format: h n w Sample Input 1 2 Sample Output 1 1 2 2 4/2 = 1/1 + 1/2 + 1/2 . Sample Input 2 3485 Sample Output 2 872 1012974 1539173474040 It is allowed to use an integer exceeding 3500 in a solution. Sample Input 3 4664 Sample Output 3 3498 3498 3498 | 37,683 |
Score : 300 points Problem Statement N tiles are arranged in a row from left to right. The initial color of each tile is represented by a string S of length N . The i -th tile from the left is painted black if the i -th character of S is 0 , and painted white if that character is 1 . You want to repaint some of the tiles black or white, so that any two adjacent tiles have different colors. At least how many tiles need to be repainted to satisfy the condition? Constraints 1 \leq |S| \leq 10^5 S_i is 0 or 1 . Input Input is given from Standard Input in the following format: S Output Print the minimum number of tiles that need to be repainted to satisfy the condition. Sample Input 1 000 Sample Output 1 1 The condition can be satisfied by repainting the middle tile white. Sample Input 2 10010010 Sample Output 2 3 Sample Input 3 0 Sample Output 3 0 | 37,684 |
Problem is available from here. | 37,685 |
How Many Divisors? Write a program which reads three integers a , b and c , and prints the number of divisors of c between a and b . Input Three integers a , b and c are given in a line separated by a single space. Output Print the number of divisors in a line. Constraints 1 †a , b , c †10000 a †b Sample Input 1 5 14 80 Sample Output 1 3 | 37,686 |
Score : 100 points Problem Statement CODE FESTIVAL 2016 is going to be held. For the occasion, Mr. Takahashi decided to make a signboard. He intended to write CODEFESTIVAL2016 on it, but he mistakenly wrote a different string S . Fortunately, the string he wrote was the correct length. So Mr. Takahashi decided to perform an operation that replaces a certain character with another in the minimum number of iterations, changing the string to CODEFESTIVAL2016 . Find the minimum number of iterations for the rewrite operation. Constraints S is 16 characters long. S consists of uppercase and lowercase alphabet letters and numerals. Input Inputs are provided from Standard Input in the following form. S Output Output an integer representing the minimum number of iterations needed for the rewrite operation. Sample Input 1 C0DEFESTIVAL2O16 Sample Output 1 2 The second character 0 must be changed to O and the 14 th character O changed to 0 . Sample Input 2 FESTIVAL2016CODE Sample Output 2 16 | 37,687 |
Score : 600 points Problem Statement Given are a sequence of N positive integers A_1 , A_2 , \ldots , A_N and another positive integer S . For a non-empty subset T of the set \{1, 2, \ldots , N \} , let us define f(T) as follows: f(T) is the number of different non-empty subsets \{x_1, x_2, \ldots , x_k \} of T such that A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S . Find the sum of f(T) over all 2^N-1 subsets T of \{1, 2, \ldots , N \} . Since the sum can be enormous, print it modulo 998244353 . Constraints All values in input are integers. 1 \leq N \leq 3000 1 \leq S \leq 3000 1 \leq A_i \leq 3000 Input Input is given from Standard Input in the following format: N S A_1 A_2 ... A_N Output Print the sum of f(T) modulo 998244353 . Sample Input 1 3 4 2 2 4 Sample Output 1 6 For each T , the value of f(T) is shown below. The sum of these values is 6 . f(\{1\}) = 0 f(\{2\}) = 0 f(\{3\}) = 1 (One subset \{3\} satisfies the condition.) f(\{1, 2\}) = 1 ( \{1, 2\} ) f(\{2, 3\}) = 1 ( \{3\} ) f(\{1, 3\}) = 1 ( \{3\} ) f(\{1, 2, 3\}) = 2 ( \{1, 2\}, \{3\} ) Sample Input 2 5 8 9 9 9 9 9 Sample Output 2 0 Sample Input 3 10 10 3 1 4 1 5 9 2 6 5 3 Sample Output 3 3296 | 37,688 |
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é è»äž¡ããã®åè»ã®ç·šæãçŸãæååã i è¡ç®ã«åºåããŠãã ããã Sample Input 4 a->e->c->b->d b<-c<-a<-d<-e b->a->c<-a->c->d<-c<-a<-b->a->c->d->e<-d a->e<-a<-d->a->e<-a<-d<-c->d->a<-d<-c<-b->c->d<-c Output for the Sample Input aecbd edacb bacde bcdae | 37,689 |
Semiexpress The JOI Railways is the only railway company in the Kingdom of JOI. There are $N$ stations numbered from $1$ to $N$ along a railway. Currently, two kinds of trains are operated; one is express and the other one is local. A local train stops at every station. For each $i$ ($1 \leq i < N$), by a local train, it takes $A$ minutes from the station $i$ to the station ($i + 1$). An express train stops only at the stations $S_1, S_2, ..., S_M$ ($1 = S_1 < S_2 < ... < S_M = N$). For each $i$ ($1 \leq i < N$), by an express train, it takes $B$ minutes from the station $i$ to the station ($i + 1$). The JOI Railways plans to operate another kind of trains called "semiexpress." For each $i$ ($1 \leq i < N$), by a semiexpress train, it takes $C$ minutes from the station $i$ to the station ($i + 1$). The stops of semiexpress trains are not yet determined. But they must satisfy the following conditions: Semiexpress trains must stop at every station where express trains stop. Semiexpress trains must stop at $K$ stations exactly. The JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes. The JOI Railways plans to determine the stops of semiexpress trains so that this number is maximized. We do not count the standing time of trains. When we travel from the station 1 to another station, we can take trains only to the direction where the numbers of stations increase. If several kinds of trains stop at the station $i$ ($2 \leq i \leq N - 1$), you can transfer between any trains which stop at that station. When the stops of semiexpress trains are determined appropriately, what is the maximum number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes? Task Given the number of stations of the JOI Railways, the stops of express trains, the speeds of the trains, and maximum travel time, write a program which calculates the maximum number of stations which satisfy the condition on the travel time. Input Read the following data from the standard input. The first line of input contains three space separated integers $N$, $M$, $K$. This means there are $N$ stations of the JOI Railways, an express train stops at $M$ stations, and a semiexpress train stops at $K$ stations, The second line of input contains three space separated integers $A$, $B$, $C$. This means it takes $A$, $B$, $C$ minutes by a local, express, semiexpress train to travel from a station to the next station, respectively. >li> The third line of input contains an integer $T$. This means the JOI Railways wants to maximize the number of stations (except for the station 1) to which we can travel from the station 1 within $T$ minutes. The $i$-th line ($1 \leq i \leq M$) of the following $M$ lines contains an integer $S_i$. This means an express train stops at the station $S_i$. Output Write one line to the standard output. The output contains the maximum number of stations satisfying the condition on the travel time. Constraints All input data satisfy the following conditions. $2 \leq N \leq 1 000 000 000ïŒ$ $2 \leq M \leq K \leq 3 000ïŒ$ $K \leq NïŒ$ $1 \leq B < C < A \leq 1 000 000 000ïŒ$ $1 \leq T \leq 10^{18}$ $1 = S_1 < S_2 < ... < S_M = N$ Sample Input and Output Sample Input 1 10 3 5 10 3 5 30 1 6 10 Sample Output 1 8 In this sample input, there are 10 stations of the JOI Railways. An express train stops at three stations 1, 6, 10. Assume that the stops of an semiexpress train are 1, 5, 6, 8, 10. Then, among the stations 2, 3, ...10, we can travel from the station 1 to every station except for the station 9 within 30 minutes. For some $i$, the travel time and the route from the station 1 to the station $i$ are as follows: From the station 1 to the station 3, we can travel using a local train only. The travel time is 20 minutes. From the station 1 to the station 7, we travel from the station 1 to the station 6 by an express train, and transfer to a local train. The travel time is 25 minutes. From the station 1 to the station 8, we travel from the station 1 to the station 6 by an express train, and transfer to a semiexpress train. The travel time is 25 minutes. From the station 1 to the station 9, we travel from the station 1 to the station 6 by an express train, from the station 6 to the station 8 by a semiexpress train, and from the station 8 to the station 9 by a local train. In total, the travel time is 35 minutes. Sample Input 2 10 3 5 10 3 5 25 1 6 10 Sample Output 2 7 Sample Input 3 90 10 12 100000 1000 10000 10000 1 10 20 30 40 50 60 70 80 90 Sample Output 2 2 Sample Input 4 12 3 4 10 1 2 30 1 11 12 Sample Output 4 8 Sample Input 5 300 8 16 345678901 123456789 234567890 12345678901 1 10 77 82 137 210 297 300 Sample Output 5 72 Sample Input 6 1000000000 2 3000 1000000000 1 2 1000000000 1 1000000000 Sample Output 6 3000 The 16th Japanese Olympiad in Informatics (JOI 2016/2017) Final Round | 37,690 |
Problem G: Color the Map You were lucky enough to get a map just before entering the legendary magical mystery world. The map shows the whole area of your planned exploration, including several countries with complicated borders. The map is clearly drawn, but in sepia ink only; it is hard to recognize at a glance which region belongs to which country, and this might bring you into severe danger. You have decided to color the map before entering the area. âA good deal depends on preparation,â you talked to yourself. Each country has one or more territories, each of which has a polygonal shape. Territories belonging to one country may or may not âtouchâ each other, i.e. there may be disconnected territories. All the territories belonging to the same country must be assigned the same color. You can assign the same color to more than one country, but, to avoid confusion, two countries âadjacentâ to each other should be assigned different colors. Two countries are considered to be âadjacentâ if any of their territories share a border of non-zero length. Write a program that finds the least number of colors required to color the map. Input The input consists of multiple map data. Each map data starts with a line containing the total number of territories n , followed by the data for those territories. n is a positive integer not more than 100. The data for a territory with m vertices has the following format: String x 1 y 1 x 2 y 2 ... x m y m -1 â String â (a sequence of alphanumerical characters) gives the name of the country it belongs to. A country name has at least one character and never has more than twenty. When a country has multiple territories, its name appears in each of them. Remaining lines represent the vertices of the territory. A vertex data line has a pair of nonneg- ative integers which represent the x - and y -coordinates of a vertex. x - and y -coordinates are separated by a single space, and y-coordinate is immediately followed by a newline. Edges of the territory are obtained by connecting vertices given in two adjacent vertex data lines, and byconnecting vertices given in the last and the first vertex data lines. None of x - and y -coordinates exceeds 1000. Finally, -1 in a line marks the end of vertex data lines. The number of vertices m does not exceed 100. You may assume that the contours of polygons are simple, i.e. they do not cross nor touch themselves. No two polygons share a region of non-zero area. The number of countries in a map does not exceed 10. The last map data is followed by a line containing only a zero, marking the end of the input data. Output For each map data, output one line containing the least possible number of colors required to color the map satisfying the specified conditions. Sample Input 6 Blizid 0 0 60 0 60 60 0 60 0 50 50 50 50 10 0 10 -1 Blizid 0 10 10 10 10 50 0 50 -1 Windom 10 10 50 10 40 20 20 20 20 40 10 50 -1 Accent 50 10 50 50 35 50 35 25 -1 Pilot 35 25 35 50 10 50 -1 Blizid 20 20 40 20 20 40 -1 4 A1234567890123456789 0 0 0 100 100 100 100 0 -1 B1234567890123456789 100 100 100 200 200 200 200 100 -1 C1234567890123456789 0 100 100 100 100 200 0 200 -1 D123456789012345678 100 0 100 100 200 100 200 0 -1 0 Output for the Sample Input 4 2 | 37,691 |
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¥åã«å«ãŸããå€ã¯ãã¹ãŠæŽæ° 0 < a < b < e < c †1000 0 < d †100000 0 †na , nb , nc †100000 0 < na + nb + nc ããŒã¿ã»ããã®æ°ã¯100åä»¥äž Output åããŒã¿ã»ããã«ã€ããã»ããã¬ã³ã¿ã«ãæé©ã«é©çšããæã®æéã1è¡ã«åºåããã Sample Input 70 100 340 4 200 1 1 4 70 100 340 4 200 0 1 3 70 100 340 4 200 1 1 2 0 0 0 0 0 Sample Output 970 800 800 | 37,694 |
Ranks A finite field F 2 consists of two elements: 0 and 1. Addition and multiplication on F 2 are those on integers modulo two, as defined below. + 0 1 0 0 1 1 1 0 $\times$ 0 1 0 0 0 1 0 1 A set of vectors $v_1, ... , v_k$ over F 2 with the same dimension is said to be linearly independent when, for $c_1, ... , c_k \in $ F 2 , $c_1v_1 + ... + c_kv_k = 0$ is equivalent to $c_1 = ... = c_k = 0$, where $0$ is the zero vector, the vector with all its elements being zero. The rank of a matrix is the maximum cardinality of its linearly independent sets of column vectors. For example, the rank of the matrix $ \left[ \begin{array}{rrr} 0 & 0 & 1 \\ 1 & 0 & 1 \end{array} \right] $ is two; the column vectors $ \left[ \begin{array}{rrr} 0 \\ 1 \end{array} \right] $ and $ \left[ \begin{array}{rrr} 1 \\ 1 \end{array} \right] $ (the first and the third columns) are linearly independent while the set of all three column vectors is not linearly independent. Note that the rank is zero for the zero matrix. Given the above definition of the rank of matrices, the following may be an intriguing question. How does a modification of an entry in a matrix change the rank of the matrix? To investigate this question, let us suppose that we are given a matrix $A$ over F 2 . For any indices $i$ and $j$, let $A^{(ij)}$ be a matrix equivalent to $A$ except that the $(i, j)$ entry is flipped. \begin{equation*} A^{(ij)}_{kl}= \left \{ \begin{array}{ll} A_{kl} + 1 & (k = i \; {\rm and} \; l = j) \\ A_{kl} & ({\rm otherwise}) \\ \end{array} \right. \end{equation*} In this problem, we are interested in the rank of the matrix $A^{(ij)}$. Let us denote the rank of $A$ by $r$, and that of $A^{(ij)}$ by $r^{(ij)}$. Your task is to determine, for all $(i, j)$ entries, the relation of ranks before and after flipping the entry out of the following possibilities: $(i) r^{(ij)} < r, (ii) r^{(ij)} = r$, or $(iii) r^{(ij)} > r$. Input The input consists of a single test case of the following format. $n$ $m$ $A_{11}$ ... $A_{1m}$ . . . $A_{n1}$ ... $A_{nm}$ $n$ and $m$ are the numbers of rows and columns in the matrix $A$, respectively ($1 \leq n \leq 1000, 1 \leq m \leq 1000$). In the next $n$ lines, the entries of $A$ are listed without spaces in between. $A_{ij}$ is the entry in the $i$-th row and $j$-th column, which is either 0 or 1. Output Output $n$ lines, each consisting of $m$ characters. The character in the $i$-th line at the $j$-th position must be either - (minus), 0 (zero), or + (plus). They correspond to the possibilities (i), (ii), and (iii) in the problem statement respectively. Sample Input 1 2 3 001 101 Sample Output 1 -0- -00 Sample Input 2 5 4 1111 1000 1000 1000 1000 Sample Output 2 0000 0+++ 0+++ 0+++ 0+++ Sample Input 3 10 10 1000001001 0000010100 0000100010 0001000001 0010000010 0100000100 1000001000 0000010000 0000100000 0001000001 Sample Output 3 000-00000- 0-00000-00 00-00000-0 +00000+000 00-0000000 0-00000000 000-00000- 0-000-0-00 00-0-000-0 +00000+000 Sample Input 4 1 1 0 Sample Output 4 + | 37,695 |
I - Ï å€§ãã N ã®é åãšã¯ïŒæ°å (1, 2, 3, âŠ, N) ã®åèŠçŽ ã䞊ã¹æ¿ãããã®ã§ããïŒ äŸãã° (5, 2, 1, 4, 3) ã¯å€§ãã 5 ã®é åã ãïŒäžæ¹ã§ (1, 5, 1, 2, 3) ã¯ããã§ã¯ãªãïŒ ãã®åé¡ã¯ãªã¢ã¯ãã£ãæ¹åŒã®ã¿ã¹ã¯ã§ããïŒããªãã¯å¿çããã°ã©ã ãšãé ååœãŠã²ãŒã ããè¡ãïŒ ãŸãæåã«ïŒå¿çããã°ã©ã ã¯é å Ï ã1ã€å
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Problem Statement We have an undirected graph with N vertices and M edges. The vertices are numbered 1 through N , and the edges are numbered 1 through M . Edge i connects vertices a_i and b_i . The graph is connected. On this graph, Q pairs of brothers are participating in an activity called Stamp Rally . The Stamp Rally for the i -th pair will be as follows: One brother starts from vertex x_i , and the other starts from vertex y_i . The two explore the graph along the edges to visit z_i vertices in total, including the starting vertices. Here, a vertex is counted only once, even if it is visited multiple times, or visited by both brothers. The score is defined as the largest index of the edges traversed by either of them. Their objective is to minimize this value. Find the minimum possible score for each pair. Constraints 3â€Nâ€10^5 Nâ1â€Mâ€10^5 1â€a_i<b_iâ€N The given graph is connected. 1â€Qâ€10^5 1â€x_j<y_jâ€N 3â€z_jâ€N Input The input is given from Standard Input in the following format: N M a_1 b_1 a_2 b_2 : a_M b_M Q x_1 y_1 z_1 x_2 y_2 z_2 : x_Q y_Q z_Q Output Print Q lines. The i -th line should contain the minimum possible score for the i -th pair of brothers. Sample Input 1 5 6 2 3 4 5 1 2 1 3 1 4 1 5 6 2 4 3 2 4 4 2 4 5 1 3 3 1 3 4 1 3 5 Sample Output 1 1 2 3 1 5 5 | 37,698 |
Problem A: Defend the Nation Two nations Drone and Moonlamb have been engaged in a war. You have been called up for service as a talented programmer in Drone. Recently, the army of Moonlamb has set up a new cannon on the field. The army of Drone knows exactly where it has been placed, but not how it can be destroyed; direct attacks would not be successful because the army of Moonlamb has also set up a special barrier around the cannon. Fortunately, it seems that no projectiles have reached the troops yet. Nevertheless, the army of Drone immediately requires an effective means to intercept pro- jectiles fired from the cannon. Otherwise they would definitely take severe damage once the army of Moonlamb started attacks with the cannon. The generals of Drone have decided to build a new interception system that consists of a radar system, a control program, and an auto-operated cannon. As neither of the cannons of Moonlamb and Drone can change the firing directions except the elevation angles, the auto-operated cannon will be placed so the two barrels face each other. This way the army of Drone will have a better possibility of successful interception. The figure below depicts this situation. The interception system works as follows. When the radar system detects projectiles fired from the barriered cannon, it immediately sends their initial velocities and elevation angles to the control program. Then the control program determines the elevation angles at which the interceptors should be fired in order to destroy the targeted projectiles on the fly, and sends firing commands to the auto-operated cannon. Finally, the auto-operated cannon fires interceptors according to the received commands. For the maximum safety of the auto-operated cannon and other installations behind, the army of Drone wants to destroy the projectiles at the earliest possible time. On the other hand, the interceptors can be fired only with their fixed initial velocities. The control program thus can only control the elevation angles and the firing times. In addition, the interceptors cannot be fired in less than γ seconds from when the targeted projectiles are fired, because of delay in detecting those projectiles. The trajectories of the projectiles and the interceptors shape parabolas, both affected only by the gravity with the acceleration of 9.8 [m/s 2 ]. The sizes of the projectiles, the interceptors, and the cannons are all negligible. Your task is to write the control program and defend the nation Drone! Input The first line of the input contains a single integer that indicates the number of test cases. Each test case consists of a line with five integers d , γ, v 1 , Ξ 1 , and v 2 , in this order. d denotes the distance between the two cannons in meters (1 †d †1000); γ denotes the minimum time needed in seconds between the projectile and the interceptor (0 †γ †100); v 1 denotes the initial velocity of the projectile in meters per second (1 †v 1 †1000); Ξ 1 denotes the elevation angle of the targeted projectile in degrees (1 †Ξ 1 †89); and v 2 denotes the initial velocity of the interceptor in meters per second (1 †v 2 †1000). Output For each test case, your program should print the elevation angle of the interceptor, and the time elapsing between the projectile being fired from Moonlamb and it being destroyed. The angle and the time should be given in degrees and seconds respectively, and both should be printed with exactly six fractional digits. In case of multiple angles giving the same minimum elapsing time, your program may print any of them. If it is impossible to destroy the projectile before reaching the land, your program should report as such. The output should be formatted as shown in the sample below. Print an empty line between test cases. Sample Input 2 150 1 50 30 50 100 1 20 30 40 Output for the Sample Input Case 1: Fire at 37.995392 degree(s). Projectile destroyed in 2.290123 second(s). Case 2: Projectile reaches the land. | 37,699 |
Score : 400 points Problem Statement In some other world, today is Christmas. Mr. Takaha decides to make a multi-dimensional burger in his party. A level- L burger ( L is an integer greater than or equal to 0 ) is the following thing: A level- 0 burger is a patty. A level- L burger (L \geq 1) is a bun, a level- (L-1) burger, a patty, another level- (L-1) burger and another bun, stacked vertically in this order from the bottom. For example, a level- 1 burger and a level- 2 burger look like BPPPB and BBPPPBPBPPPBB (rotated 90 degrees), where B and P stands for a bun and a patty. The burger Mr. Takaha will make is a level- N burger. Lunlun the Dachshund will eat X layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat? Constraints 1 \leq N \leq 50 1 \leq X \leq ( the total number of layers in a level- N burger ) N and X are integers. Input Input is given from Standard Input in the following format: N X Output Print the number of patties in the bottom-most X layers from the bottom of a level- N burger. Sample Input 1 2 7 Sample Output 1 4 There are 4 patties in the bottom-most 7 layers of a level- 2 burger ( BBPPPBPBPPPBB ). Sample Input 2 1 1 Sample Output 2 0 The bottom-most layer of a level- 1 burger is a bun. Sample Input 3 50 4321098765432109 Sample Output 3 2160549382716056 A level- 50 burger is rather thick, to the extent that the number of its layers does not fit into a 32 -bit integer. | 37,700 |
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Ring Write a program which finds a pattern $p$ in a ring shaped text $s$. Input In the first line, the text $s$ is given. In the second line, the pattern $p$ is given. Output If $p$ is in $s$, print Yes in a line, otherwise No . Constraints $1 \leq $ length of $p \leq $ length of $s \leq 100$ $s$ and $p$ consists of lower-case letters Sample Input 1 vanceknowledgetoad advance Sample Output 1 Yes Sample Input 2 vanceknowledgetoad advanced Sample Output 2 No | 37,703 |
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Score : 700 points Problem Statement We have a string s consisting of lowercase English letters. Snuke is partitioning s into some number of non-empty substrings. Let the subtrings obtained be s_1 , s_2 , ... , s_N from left to right. (Here, s = s_1 + s_2 + ... + s_N holds.) Snuke wants to satisfy the following condition: For each i ( 1 \leq i \leq N ), it is possible to permute the characters in s_i and obtain a palindrome. Find the minimum possible value of N when the partition satisfies the condition. Constraints 1 \leq |s| \leq 2 \times 10^5 s consists of lowercase English letters. Input Input is given from Standard Input in the following format: s Output Print the minimum possible value of N when the partition satisfies the condition. Sample Input 1 aabxyyzz Sample Output 1 2 The solution is to partition s as aabxyyzz = aab + xyyzz . Here, aab can be permuted to form a palindrome aba , and xyyzz can be permuted to form a palindrome zyxyz . Sample Input 2 byebye Sample Output 2 1 byebye can be permuted to form a palindrome byeeyb . Sample Input 3 abcdefghijklmnopqrstuvwxyz Sample Output 3 26 Sample Input 4 abcabcxabcx Sample Output 4 3 The solution is to partition s as abcabcxabcx = a + b + cabcxabcx . | 37,706 |
Score : 300 points Problem Statement Given is a positive integer L . Find the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L . Constraints 1 †L †1000 L is an integer. Input Input is given from Standard Input in the following format: L Output Print the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L . Your output is considered correct if its absolute or relative error from our answer is at most 10^{-6} . Sample Input 1 3 Sample Output 1 1.000000000000 For example, a rectangular cuboid whose dimensions are 0.8 , 1 , and 1.2 has a volume of 0.96 . On the other hand, if the dimensions are 1 , 1 , and 1 , the volume of the rectangular cuboid is 1 , which is greater. Sample Input 2 999 Sample Output 2 36926037.000000000000 | 37,707 |
Score : 1100 points Problem Statement There is a set consisting of N distinct integers. The i -th smallest element in this set is S_i . We want to divide this set into two sets, X and Y , such that: The absolute difference of any two distinct elements in X is A or greater. The absolute difference of any two distinct elements in Y is B or greater. How many ways are there to perform such division, modulo 10^9 + 7 ? Note that one of X and Y may be empty. Constraints All input values are integers. 1 ⊠N ⊠10^5 1 ⊠A , B ⊠10^{18} 0 ⊠S_i ⊠10^{18}(1 ⊠i ⊠N) S_i < S_{i+1}(1 ⊠i ⊠N - 1) Input The input is given from Standard Input in the following format: N A B S_1 : S_N Output Print the number of the different divisions under the conditions, modulo 10^9 + 7 . Sample Input 1 5 3 7 1 3 6 9 12 Sample Output 1 5 There are five ways to perform division: X= { 1,6,9,12 }, Y= { 3 } X= { 1,6,9 }, Y= { 3,12 } X= { 3,6,9,12 }, Y= { 1 } X= { 3,6,9 }, Y= { 1,12 } X= { 3,6,12 }, Y= { 1,9 } Sample Input 2 7 5 3 0 2 4 7 8 11 15 Sample Output 2 4 Sample Input 3 8 2 9 3 4 5 13 15 22 26 32 Sample Output 3 13 Sample Input 4 3 3 4 5 6 7 Sample Output 4 0 | 37,708 |
Score : 900 points Problem Statement Snuke loves permutations. He is making a permutation of length N . Since he hates the integer K , his permutation will satisfy the following: Let the permutation be a_1, a_2, ..., a_N . For each i = 1,2,...,N , |a_i - i| \neq K . Among the N! permutations of length N , how many satisfies this condition? Since the answer may be extremely large, find the answer modulo 924844033 (prime). Constraints 2 ⊠N ⊠2000 1 ⊠K ⊠N-1 Input The input is given from Standard Input in the following format: N K Output Print the answer modulo 924844033 . Sample Input 1 3 1 Sample Output 1 2 2 permutations (1, 2, 3) , (3, 2, 1) satisfy the condition. Sample Input 2 4 1 Sample Output 2 5 5 permutations (1, 2, 3, 4) , (1, 4, 3, 2) , (3, 2, 1, 4) , (3, 4, 1, 2) , (4, 2, 3, 1) satisfy the condition. Sample Input 3 4 2 Sample Output 3 9 Sample Input 4 4 3 Sample Output 4 14 Sample Input 5 425 48 Sample Output 5 756765083 | 37,709 |
Single Source Shortest Path For a given weighted graph G(V, E) and a source r , find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path). Input An edge-weighted graph G ( V , E ) and the source r . | V | | E | r s 0 t 0 d 0 s 1 t 1 d 1 : s |E|-1 t |E|-1 d |E|-1 |V| is the number of vertices and |E| is the number of edges in G . The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph. s i and t i represent source and target vertices of i -th edge (directed) and d i represents the cost of the i -th edge. Output Print the costs of SSSP in the following format. c 0 c 1 : c |V|-1 The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF . Constraints 1 †|V| †100000 0 †d i †10000 0 †|E| †500000 There are no parallel edges There are no self-loops Sample Input 1 4 5 0 0 1 1 0 2 4 1 2 2 2 3 1 1 3 5 Sample Output 1 0 1 3 4 Sample Input 2 4 6 1 0 1 1 0 2 4 2 0 1 1 2 2 3 1 1 3 2 5 Sample Output 2 3 0 2 INF | 37,710 |
Problem C: Yanagi's Comic Yanagi is a high school student, and she is called "Hime" by her boyfriend who is a ninja fanboy. She likes picture books very much, so she often writes picture books by herself. She always asks you to make her picture book as an assistant. Today, you got asked to help her with making a comic. She sometimes reads her picture books for children in kindergartens. Since Yanagi wants to let the children read, she wants to insert numbers to frames in order. Of course, such a task should be done by the assistant, you. You want to do the task easily and fast, so you decide to write a program to output the order of reading frames based on the positions of the frames. Write a program to print the number of order for each frame. The comics in this problem satisfy the following rules. The each comic is drawn on a sheet of rectangle paper. You can assume that the top side of the paper is on the x-axis. And you can assume that the right-hand side of the paper is on the y-axis. The positive direction of the x-axis is leftward. The positive direction of the y-axis is down direction. The paper is large enough to include all frames of the comic. In other words, no area in a frame is out of the paper. The area of each frame is at least one. All sides of each frame are parallel to the x-axis or the y-axis. The frames can't overlap one another. However the frames may share the line of side. You must decide the order to read K , where K is a set of frames, with the following steps. Step 1 :You must choose an unread frame at the right-most position in K . If you find such frames multiple, you must choose the frame at the top position among them. If you can't find any unread frames, you stop reading K . The frame you chose is "Starting Frame". In step 1, you assume that the position of a frame is the top-right point of the frame. Step 2 :You should draw a line from the right-bottom point of "Starting Frame" to leftward horizontally. If the line touch the right-hand side of other frame, you should stop drawing. If the line is on the side of other frame, you should not stop drawing. If the line touch the edge of paper, you should stop drawing. Step 3 :The set of the unread frames which are above the line ( they may be the bottom-side on the line ) drawn at Step 2 is L . And you should read L . Step 4 : Go back to Step 1. Input The input consists of multiple datasets. The last dataset is followed by a line containing one zero. You don't have to process this data. Each datasets is in the following format. n x 01 y 01 x 11 y 11 x 02 y 02 x 12 y 12 .... x 0n y 0n x 1n y 1n All numbers of the datasets are integer. They are separated by a space. The first line of a dataset contains one integer. n is the number of frames of the comic. x 0i , y 0i , x 1i , y 1i are two non-neighboring points of i th frame in the line. Constraints 0 < n < 10 ( x 0i != x 1i ) and ( y 0i != y 1i ) 0 †x 0i , y 0i , x 1i , y 1i †500 Output Print n lines for each dataset. Print the number of order for i th frame in the i th line. And you should print blank line between the datasets. Output format: num 1 num 2 ... num i ... num n Sample input 4 0 0 100 60 0 60 50 90 50 60 100 90 0 90 100 120 6 0 0 100 40 0 40 50 70 50 40 100 60 50 60 100 80 0 70 50 120 50 80 100 120 0 Sample output 1 2 3 4 1 2 4 5 3 6 These pictures are related to first sample and second sample. Gray frames have been read already. A red line denotes the line drawn at Step 2. Numbers in the figures denote the order of frames given by input. This is related to the first sample. These are related to the second sample. | 37,711 |
Score : 2400 points Problem Statement There are N people (with different names) and K clubs. For each club you know the list of members (so you have K unordered lists). Each person can be a member of many clubs (and also 0 clubs) and two different clubs might have exactly the same members. The value of the number K is the minimum possible such that the following property can be true for at least one configuration of clubs. If every person changes her name (maintaining the property that all names are different) and you know the new K lists of members of the clubs (but you don't know which list corresponds to which club), you are sure that you would be able to match the old names with the new ones. Count the number of such configurations of clubs (or say that there are more than 1000 ). Two configurations of clubs that can be obtained one from the other if the N people change their names are considered equal. Formal statement : A club is a (possibly empty) subset of \{1,\dots, N\} (the subset identifies the members, assuming that the people are indexed by the numbers 1, 2,\dots, N ). A configuration of clubs is an unordered collection of K clubs (not necessarily distinct). Given a permutation \sigma(1), \dots, \sigma(N) of \{1,\dots, N\} and a configuration of clubs L=\{C_1, C_2, \dots, C_K\} , we denote with \sigma(L) the configuration of clubs \{\sigma(C_1), \sigma(C_2), \dots, \sigma(C_K)\} (if C is a club, \sigma(C)=\{\sigma(x):\, x\in C\} ). A configuration of clubs L is name-preserving if for any pair of distinct permutations \sigma\not=\tau , it holds \sigma(L)\not=\tau(L) . You have to count the number of name-preserving configurations of clubs with the minimum possible number of clubs (so K is minimum). Two configurations L_1, L_2 such that L_2=\sigma(L_1) (for some permutation \sigma ) are considered equal. If there are more than 1000 such configurations, print -1 . Constraints 2 \le N \le 2\cdot10^{18} Input The input is given from Standard Input in the format N Output If ans is the number of configurations with the properties described in the statement, you should print on Standard Output ans If there are more than 1000 such configurations, print -1 . Sample Input 1 2 Sample Output 1 1 The value of K is 1 and the unique name-preserving configuration of clubs is \{\{1\}\} (the configuration \{\{2\}\} is considered the same). Sample Input 2 3 Sample Output 2 1 The value of K is 2 and the unique (up to permutation) name-preserving configuration of clubs is \{\{1\}, \{1, 2\}\} . Sample Input 3 4 Sample Output 3 7 The value of K is 3 and the name-preserving configurations of clubs with 3 clubs are: \{\{1\}, \{2\}, \{1, 3\}\} \{\{1\}, \{1, 2\}, \{2, 3\}\} \{\{1, 2\}, \{1, 2\}, \{1, 3\}\} \{\{1\}, \{1, 2\}, \{1, 2, 3\}\} \{\{1\}, \{2, 3\}, \{1, 2, 4\}\} \{\{1, 2\}, \{1, 3\}, \{1, 2, 4\} \{\{1, 2\}, \{1, 2, 3\}, \{2, 3, 4\}\} Sample Input 4 13 Sample Output 4 6 Sample Input 5 26 Sample Output 5 -1 Sample Input 6 123456789123456789 Sample Output 6 -1 | 37,712 |
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¥åãšããã¢ã€ã¹ã¯ãªãŒã ã®çš®é¡ããšã«è²©å£²ããæ°ã ã * (åè§ã¢ã¹ã¿ãªã¹ã¯) ãåºåããããã°ã©ã ãäœæããŠãã ããããã ããã¢ã€ã¹ã¯ãªãŒã ã®çš®é¡ã 0 ãã 9 ãŸã§ã®æŽæ°ã§è¡šãããŸãããŸãã販売åæ°ããŒãã®ã¢ã€ã¹ã¯ãªãŒã ã¯ã- (åè§ãã€ãã³) ãã²ãšã€åºåããŸãã Input è€æ°ã®ããŒã¿ã»ããã®äžŠã³ãå
¥åãšããŠäžããããŸããå
¥åã®çµããã¯ãŒãã²ãšã€ã®è¡ã§ç€ºãããŸãã åããŒã¿ã»ããã¯ä»¥äžã®åœ¢åŒã§äžããããŸãã n c 1 c 2 : c n 1 è¡ç®ã«äžæ¥ã«è²©å£²ãããã¢ã€ã¹ã¯ãªãŒã ã®ç·æ° n (1 †n †10000) ãäžããããŸããç¶ã n è¡ã«ç¬¬ i ã®ã¢ã€ã¹ã¯ãªãŒã ã®çš®é¡ c i (0 †c i †9) ãäžããããŸãã ããŒã¿ã»ããã®æ°ã¯ 20 ãè¶
ããŸããã Output å
¥åããŒã¿ã»ããããšã«ãåã¢ã€ã¹ã¯ãªãŒã ã®çš®é¡ã®çªå·é ã«è²©å£²æ°ãåºåããŸãã Sample Input 15 2 6 7 0 1 9 8 7 3 8 9 4 8 2 2 3 9 1 5 0 Output for the Sample Input * * *** * * - * ** *** ** - * - - - * - - - * | 37,714 |
N: 3人ååã²ãŒã ãªã¢ã¯ãã£ãåé¡ã§ãã åé¡æ $1000$ ãããã®éè² æŽæ°ã $200$ åããã$a_1, \ldots, a_{100}, b_1, \ldots, b_{100}$ ãšããŸãã ã¢ãªã¹ã¯ $a_1, \ldots, a_{100}$ ã確èªãã$3000$ ãããã®ã¡ã¢ $X$ ããã£ãŒãªãŒã®ããã«æ®ããŸãã ãã㯠$b_1, \ldots, b_{100}$ ã確èªãã$3000$ ãããã®ã¡ã¢ $Y$ ããã£ãŒãªãŒã®ããã«æ®ããŸãã ãã£ãŒãªãŒã¯ã¡ã¢ $X, Y$ ã®æ
å ±ãããšã«ã$100$ åã®è³ªåã«çããŸãã $i$ çªç®ã®è³ªå㯠$1000$ ãããã®éè² æŽæ° $c_i$ ã§è¡šããããã£ãŒãªãŒã¯ $a_{x_i}$ ãš $b_{y_i}$ ã®ãããããšã®æä»çè«çåã $c_i$ ã«çãããªããã㪠$x_i, y_i$ ãçããŸãã $100$ åã®è³ªåã®ãã¡ã$95$ å以äžã®è³ªåã«æ£çã§ããæŠç¥ãèããŠãã ããã å¶çŽ $a_1, \ldots, a_{100}, b_1, \ldots, b_{100}, c_1, \ldots, c_{100}$ 㯠$2$ é²æ°è¡šèšã§äžãããã 0 ïŒ 1 ãããªãé·ã $1000$ ã®æååã§ããã $a_1, \ldots, a_{100}$ ã¯äºãã«ç°ãªãã $b_1, \ldots, b_{100}$ ã¯äºãã«ç°ãªãã $c_1, \ldots, c_{100}$ ã¯äºãã«ç°ãªãã $i = 1, 2, \ldots, 100$ ã«ã€ããŠã$a_j$ ãš $b_k$ ã®ãããããšã®æä»çè«çåã $c_i$ ã«ãªããã㪠$j, k$ ãååšããã å
¥åºåãšãžã£ããž ããªãã®ããã°ã©ã 㯠$1$ ã€ã®ãã¹ãã±ãŒã¹ã«å¯Ÿã㊠$3$ åå®è¡ãããã $1$ åç®ã®å®è¡ã§ã¯æ¬¡ã®å
¥å圢åŒã§ã¢ãªã¹ãžã®æ
å ±ãäžããããã Alice $a_1$ $a_2$ $\vdots$ $a_{100}$ $1$ è¡ç®ã«å¿
ã Alice ã®æååãäžããããã ãã®å Žåãå
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šãŠåãåã£ãåŸ 0 ïŒ 1 ãããªãé·ã $3000$ ã®æåå $X$ ãåºåããããã°ã©ã ãå³åº§ã«çµäºãããªããã°ãªããªãã $2$ åç®ã®å®è¡ã§ã¯æ¬¡ã®å
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å ±ãäžããããã Bob $b_1$ $b_2$ $\vdots$ $b_{100}$ $1$ è¡ç®ã«å¿
ã Bob ã®æååãäžããããã ãã®å Žåãå
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šãŠåãåã£ãåŸ 0 ïŒ 1 ãããªãé·ã $3000$ ã®æåå $Y$ ãåºåããããã°ã©ã ãå³åº§ã«çµäºãããªããã°ãªããªãã $3$ åç®ã®å®è¡ã§ã¯æ¬¡ã®å
¥å圢åŒã§ãã£ãŒãªãŒãžã®è³ªåããã³ã¡ã¢ã®æ
å ±ãäžããããã Charlie $X$ $Y$ $c_1$ $c_2$ $\vdots$ $c_{100}$ $1$ è¡ç®ã«å¿
ã Charlie ã®æååãäžããããã å
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šãŠåãåã£ãåŸ $1$ ä»¥äž $100$ 以äžã®æŽæ° $x_1, x_2, \ldots, x_{100}$ ãš $1$ ä»¥äž $100$ 以äžã®æŽæ° $y_1, y_2, \ldots, y_{100}$ ã以äžã®åœ¢åŒã§åºåããããã°ã©ã ãå³åº§ã«çµäºãããªããã°ãªããªãã $x_1$ $y_1$ $x_2$ $y_2$ $\vdots$ $x_{100}$ $y_{100}$ ãžã£ããžã¯ã$i = 1, 2, \ldots, 100$ ã«ã€ã㊠$a_{x_i}$ ãš $b_{y_i}$ ã®ãããããšã®æä»çè«çåã $c_i$ ã«äžèŽããã調ã¹ãäžèŽæ°ã $95$ å以äžã§ããã°æ£çãããã§ãªããã°èª€çãšå€å®ããã äžæ£ãªå€ãäžæ£ãªåœ¢åŒã§ã®åºåããã£ãå Žåã«ã誀çãšããã 泚æ åºåã®åºŠã«æšæºåºåã flush ãããããããªãå ŽåãTLE ãšãªãå¯èœæ§ãããã ã©ã®çš®é¡ã®å
¥åã®æ«å°Ÿã«ã EOF ãäžããããã ããã»ã¹ã¯ãäžèšã«ãã£ãŠèŠå®ããã以å€ã®ãããªãéä¿¡ãè¡ã£ãŠã¯ãªããªãã å
¥åºåäŸ1 以äžã¯ãããæ°ãéè² æŽæ°ã®æ°ã質åã®æ°ãç°ãªããã$a = (000, 011), b = (110, 111), c = (101, 100)$ ãšãããšãã®å¯Ÿè©±äŸã§ããã 解çããã°ã©ã ã®åºå 解çããã°ã©ã ãžã®å
¥å 説æ 解çããã°ã©ã ïŒã¢ãªã¹ïŒãå®è¡ããã Alice $000$ $011$ ã¢ãªã¹ã¯ $a = (000, 011)$ ã®æ
å ±ãåŸã $0000110\ldots 0$ ã¢ãªã¹ã¯ã¡ã¢ $X = 0000110\ldots 0$ ãæ®ã 解çããã°ã©ã ïŒã¢ãªã¹ïŒã®å®è¡ãçµäºããæ°ããªè§£çããã°ã©ã ïŒããïŒãå®è¡ããã Bob $110$ $111$ ãã㯠$b = (110, 111)$ ã®æ
å ±ãåŸã $1101110\ldots 0$ ããã¯ã¡ã¢ $Y = 1101110\ldots 0$ ãæ®ã 解çããã°ã©ã ïŒããïŒã®å®è¡ãçµäºããæ°ããªè§£çããã°ã©ã ïŒãã£ãŒãªãŒïŒãå®è¡ããã Charlie $0000110\ldots 0$ $1101110\ldots 0$ $101$ $100$ ãã£ãŒãªãŒã¯ $X, Y$ ã®æ
å ±ãåŸãããšã質åã®æ
å ± $c = (101, 100)$ ãåŸã $2$ $1$ $2$ $2$ ãã£ãŒãªãŒã¯ $1$ ã€ç®ã®è³ªåã«å¯Ÿã㊠$(x_1, y_1) = (2, 1)$ã$2$ ã€ç®ã®è³ªåã«å¯Ÿã㊠$(x_2, y_2) = (2, 2)$ ãšåçãã | 37,715 |
Score : 800 points Problem Statement You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0 . Find all prime numbers p that divide f(x) for every integer x . Constraints 0 \leq N \leq 10^4 |a_i| \leq 10^9(0\leq i\leq N) a_N \neq 0 All values in input are integers. Input Input is given from Standard Input in the following format: N a_N : a_0 Output Print all prime numbers p that divide f(x) for every integer x , in ascending order. Sample Input 1 2 7 -7 14 Sample Output 1 2 7 2 and 7 divide, for example, f(1)=14 and f(2)=28 . Sample Input 2 3 1 4 1 5 Sample Output 2 There may be no integers that satisfy the condition. Sample Input 3 0 998244353 Sample Output 3 998244353 | 37,716 |
Point in The Triangle Problem ç¹(0,0),( n -1,0),(0, m -1),( n -1, m -1)ã«å²ãŸããé·æ¹åœ¢ã®éåºéå
ããæ Œåç¹ã3ç¹éžã³ãäžè§åœ¢ãäœãã ãã®ãšããç¹( x 1 , y 1 )ãå«ããç¹( x 2 , y 2 )ãå«ãŸãªãäžè§åœ¢ã®æ°ãšç¹( x 2 , y 2 )ãå«ããç¹( x 1 , y 1 )ãå«ãŸãªãäžè§åœ¢ã®æ°ã®å·®ã®çµ¶å¯Ÿå€ãæ±ããã ç¹ãå¢çç·äžã«ãããã®ã¯äžè§åœ¢ã«å«ãŸããŠãããšã¿ãªãã ãã ãã3ç¹ãäžçŽç·äžã«äžŠãã§ãããã®ã¯äžè§åœ¢ãšã¯ã¿ãªããªãã Input n m x 1 y 1 x 2 y 2 å
¥åã¯å
šãŠæŽæ°ã§äžããããã 1è¡ã« n , m , x 1 , y 1 , x 2 , y 2 ã空çœåºåãã§äžããããã Constraints 2 †n , m †500 0 †x 1 , x 2 †n -1 0 †y 1 , y 2 †m -1 ( x 1 , y 1 ) â ( x 2 , y 2 ) Output å·®ã®çµ¶å¯Ÿå€ã1è¡ã«åºåããã Sample Input 1 2 2 0 0 0 1 Sample Output 1 0 Sample Input 2 3 2 1 0 0 0 Sample Output 2 3 | 37,717 |
Score: 300 points Problem Statement We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j) , where (i, j) denotes the square at the i -th row from the top and the j -th column from the left. According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j . Determine if he is correct. Constraints c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive). Input Input is given from Standard Input in the following format: c_{1,1} c_{1,2} c_{1,3} c_{2,1} c_{2,2} c_{2,3} c_{3,1} c_{3,2} c_{3,3} Output If Takahashi's statement is correct, print Yes ; otherwise, print No . Sample Input 1 1 0 1 2 1 2 1 0 1 Sample Output 1 Yes Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1 . Sample Input 2 2 2 2 2 1 2 2 2 2 Sample Output 2 No Takahashi is incorrect in this case. Sample Input 3 0 8 8 0 8 8 0 8 8 Sample Output 3 Yes Sample Input 4 1 8 6 2 9 7 0 7 7 Sample Output 4 No | 37,718 |
B: Brilliant Stars ICPC ã§è¯ãæ瞟ãåããã«ã¯ä¿®è¡ãæ¬ ãããªãïŒããã㯠ICPC ã§åã¡ããã®ã§ïŒä»æ¥ãä¿®è¡ãããããšã«ããïŒ ä»æ¥ã®ä¿®è¡ã¯ïŒå€ç©ºã«èŒãããããã®æãã¡ã芳枬ããŠïŒèŠåãšéäžåãéããããšãããã®ã§ããïŒãããã¯ç¬èªã®ã»ã³ã¹ã§æã®ç¹åŸŽãèšé²ããŠããããšãã§ããïŒ ãããã¯ãæã®èŠ³æž¬æ¥èšããšããŠèšé²ããæã®ç¹åŸŽãããŒãã«ã€ããŠããããšã«ããïŒããã§ïŒã䌌ãŠããã 2 ã€ã®æããšãã«èšé²ããããšã¯é¿ãããïŒ2 ã€ã®æãã䌌ãŠããããã©ããã¯ïŒãã¹ãŠãããã®å€æã§æ±ºãŸã£ãŠããïŒã䌌ãŠããããã©ããã®é¢ä¿ã¯ããŸãè€éã§ã¯ãªãïŒä»¥äžã®æ¡ä»¶ãæºããïŒ æ¡ä»¶ïŒ ç°ãªã 4 ã€ã®æ A, B, C, D ãããïŒA ãš BïŒB ãš CïŒC ãš D ãããããã䌌ãŠããããšããïŒãã®ãšãïŒA ãš C ãã䌌ãŠããããïŒB ãš D ãã䌌ãŠããããïŒãããã¯ãã®äž¡æ¹ãæãç«ã€ïŒ ãããã¯ã䌌ãŠããã 2 ã€ã®æãèšé²ããªãããã«ãªãã¹ãããããã®æãèšé²ãããïŒãŸãïŒãã®ããã«ããæ¹æ³ãäœéãããããç¥ãããïŒ Input N M X 1 Y 1 ... X M Y M N ã¯æã®åæ°ïŒ M ã¯ã䌌ãŠããã 2 ã€ã®æã®çµã®åæ°ã§ããïŒæ㯠1 ä»¥äž N 以äžã®æŽæ°ã®çªå·ã«ããè¡šããïŒ X i , Y i (1 †i †M ) ã¯æ X i ãšæ Y i ãã䌌ãŠãããããšãè¡šãïŒ 1 †N †100,000ïŒ0 †M †200,000ïŒ1 †X i < Y i †N ãæºããïŒ( X i , Y i ) ãšããŠåäžã®çµã¯è€æ°åçŸããªãïŒã䌌ãŠããããã©ããã®é¢ä¿ã¯ïŒåé¡æã§æå®ãããæ¡ä»¶ãæºããïŒ Output 1 è¡ç®ã«ïŒã䌌ãŠããã 2 ã€ã®æãèšé²ããªãããã«èšé²ã§ããæã®åæ°ã®æ倧å€ãïŒ2 è¡ç®ã«ïŒãã®æ倧å€ãå®çŸã§ããæã®çµã¿åããã®åæ° (èšé²ããé çªã®ã¿ãå€ãããã®ã¯åããšèãã) ã 1,000,000,009 ã§å²ã£ãäœããåºåããïŒ Sample Input 1 4 3 1 2 1 3 1 4 Sample Output 1 3 1 Sample Input 2 11 5 1 2 3 4 5 6 7 8 9 10 Sample Output 2 6 32 Sample Input 3 9 14 1 2 1 3 2 3 3 4 3 5 3 6 3 7 3 8 3 9 4 5 4 6 5 6 7 8 8 9 Sample Output 3 4 6 | 37,719 |
Problem F: UTF-8 UTF-8ã¯ãã«ããã€ãæåã笊å·åããææ³ã®äžã€ã§ããã æåã¯èšç®æ©äžã§ã¯ãã€ãåãšããŠæ±ããããè±èªã ãã§ããã°ã©ãã³ã¢ã«ãã¡ãããããã³æ°åãèšå·ãåãããŠã 1byteã§è¡šçŸã§ããããæ®å¿µãªããäžçäžã§å©çšãããŠããæåã1byteã§è¡šçŸããããšã¯ã§ããªããããè€æ°ã®ãã€ããçšããŠæåãè¡šãå¿
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Score : 100 points Problem Statement Given is an integer r . How many times is the area of a circle of radius r larger than the area of a circle of radius 1 ? It can be proved that the answer is always an integer under the constraints given. Constraints 1 \leq r \leq 100 All values in input are integers. Input Input is given from Standard Input in the following format: r Output Print the area of a circle of radius r , divided by the area of a circle of radius 1 , as an integer. Sample Input 1 2 Sample Output 1 4 The area of a circle of radius 2 is 4 times larger than the area of a circle of radius 1 . Note that output must be an integer - for example, 4.0 will not be accepted. Sample Input 2 100 Sample Output 2 10000 | 37,721 |
Problem A: Grey Area Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the world everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is a simple self-made histogram generator. Figure 1 is an example of histogram automatically produced by his histogram. A histogram is a visual display of frequencies of value occurrences as bars. In this example, values in the interval 0-9 occur five times, those in the interval 10-19 occur three times, and 20-29 and 30-39 once each. Dr. Greyâs histogram generator is a simple tool. First, the height of the histogram is fixed, that is, the height of the highest bar is always the same and those of the others are automatically adjusted proportionately. Second, the widths of bars are also fixed. It can only produce a histogram of uniform intervals, that is, each interval of a histogram should have the same width (10 in the above example). Finally, the bar for each interval is painted in a grey color, where the colors of the leftmost and the rightmost intervals are black and white, respectively, and the darkness of bars monotonically decreases at the same rate from left to right. For instance, in Figure 1, the darkness levels of the four bars are 1, 2/3, 1/3, and 0, respectively. In this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness. Input The input consists of multiple datasets, each of which contains integers and specifies a value table and intervals for the histogram generator, in the following format. n w v 1 v 2 . . v n n is the total number of value occurrences for the histogram, and each of the n lines following the first line contains a single value. Note that the same value may possibly occur multiple times. w is the interval width. A value v is in the first (i.e. leftmost) interval if 0 †v < w , the second one if w †v < 2 w , and so on. Note that the interval from 0 (inclusive) to w (exclusive) should be regarded as the leftmost even if no values occur in this interval. The last (i.e. rightmost) interval is the one that includes the largest value in the dataset. You may assume the following. 1 †n †100 10 †w †50 0 †v i †100 for 1 †i †n You can also assume that the maximum value is no less than w . This means that the histogram has more than one interval. The end of the input is indicated by a line containing two zeros. Output For each dataset, output a line containing the amount of ink consumed in printing the histogram. One unit of ink is necessary to paint one highest bar black. Assume that 0.01 units of ink per histogram is consumed for various purposes except for painting bars such as drawing lines and characters (see Figure 1). For instance, the amount of ink consumed in printing the histogram in Figure 1 is: Each output value should be in a decimal fraction and may have an error less than 10 -5 . Sample Input 3 50 100 0 100 3 50 100 100 50 10 10 1 2 3 4 5 16 17 18 29 30 0 0 Output for the Sample Input 0.51 0.26 1.4766666666666667 | 37,722 |
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Maximum Sum Sequence Given a sequence of numbers a 1 , a 2 , a 3 , ..., a n , find the maximum sum of a contiguous subsequence of those numbers. Note that, a subsequence of one element is also a contiquous subsequence. Input The input consists of multiple datasets. Each data set consists of: n a 1 a 2 . . a n You can assume that 1 †n †5000 and -100000 †a i †100000. The input end with a line consisting of a single 0. Output For each dataset, print the maximum sum in a line. Sample Input 7 -5 -1 6 4 9 -6 -7 13 1 2 3 2 -2 -1 1 2 3 2 1 -2 1 3 1000 -200 201 0 Output for the Sample Input 19 14 1001 | 37,728 |
Problem D: Reaction You are a hero of a role playing game, asked by the king to defeat monsters threating peopleâs life. You have been making a long journey with your colleagues, and you are now in the town closest to the final dungeon where the head of monsters dwells. You have heard from people that the head monster hits with his strong arms, casts powerful spells, and has many special abilities, and your party would be easily killed off without powerful equipments due to severe damages. Thus you need to prepare the equipments. On the other hand, you have a number of magical spheres collected during the journey. Those spheres are not useful themselves, but they can be turned into special items by a spell of reaction. You can obtain some amount of money by selling those special items to shops in the town, then buy the equipments by that money. The spell of reaction works as follows. Each sphere has a color, and either positive attribute or negative attribute. You choose one sphere with positive attribute and another with negative attribute, and you cast the spell to the two spheres. Then the spheres will make reaction to have a set of special items produced. Those spheres will disappear after the reaction. The set of items you will obtain solely depends on the colors of the two spheres. You can cast the spell as many as you want, but of course you cannot cast the spell to spheres that have disappeared. Also, not all pairs of colors of spheres make reaction. It is natural that you want to obtain money as much as possible. So you should choose carefully the pairs of spheres before casting the spell. On the other hand, you should be an excellent programmer, so it should be an easy task to write a program that finds the best way using your computer. Your task is now clear - write a program and get ready for the battle with the head monster! Input The input is a sequence of datasets. Each dataset is formatted as follows: N - N + Number of available spheres Definition of items Definition of reactions The first line contains two integers N - and N + , which are the numbers of different colors of spheres with negative and positive attributes, respectively. The rest of the dataset is divided into three parts. The first part describes the number of available spheres. This part has the following format: K 1 - K 2 - ... K N - - K 1 + K 2 + ... K N + + K i - is the number of spheres of the i -th color with negative attribute, and K i + is the number of spheres of the i -th color with positive attribute. The second part contains the definition of items. This part is formatted as follows: M A 1 P 1 ... A M P M Here, M is the number of items that can be produced. Each of the following M lines contains a string A i and an integer P i , which are the name and the selling price of the i -th item respectively. The last part gives the details of reactions. This part has the following format: L I 1 - I 1 + NJ 1 J 1,1 ... J 1, NJ 1 ... I L - I L + NJ L J L ,1 ... J L , NJ L The first line contains an integer L , which is the number of pairs of colors of spheres that can make reaction. Each of the next L lines starts with two integers I i - and I i + , which denote the colors of negative and positive spheres respectively. The next integer NJ i is the number of items produced by reaction between spheres I i - and I i + . The line is then followed by NJ i strings, each of which is an item name. You may assume all the following: 1 †N - , N + †100; 1 †K i - , K i + †100; 1 †M †100; 1 †P i †100; 1 †L †100; 1 †NJ i †10. You may also assume that an item name consists only of alphanumeric characters and the length of the name does not exceed ten. The end of input is represented by a line with two zeros. This line is not part of any dataset. Output For each dataset, print a line that contains the maximum possible total selling price. Sample Input 2 2 1 1 1 1 4 A 10 B 20 C 30 D 40 4 1 1 3 A A A 1 2 2 B C 2 1 1 D 2 2 3 A A B 2 2 1 2 2 1 3 Scroll 50 Bastard 100 Heal100 10 3 1 1 1 Scroll 2 1 1 Bastard 2 2 1 Heal100 0 0 Output for the Sample Input 90 200 | 37,729 |
Problem J New Game AI Aoba is a beginner programmer who works for a game company. She was appointed to develop a battle strategy for the enemy AI (Artificial Intelligence) in a new game. In this game, each character has two parameters, hit point ($hp$) and defence point ($dp$). No two characters have the same $hp$ and $dp$ at the same time. The player forms a party by selecting one or more characters to battle with the enemy. Aoba decided to develop a strategy in which the AI attacks the weakest character in the party: that is, the AI attacks the character with the minimum hit point in the party (or, if there are several such characters, the character with the minimum defense point among them). She wrote a function selectTarget ($v$) that takes an array of characters representing a party and returns a character that her AI will attack. However, the project manager Ms. Yagami was not satisfied with the behavior of her AI. Ms. Yagami said this AI was not interesting. Aoba struggled a lot, and eventually she found that it is interesting if she substitutes one of the constant zeros in her program with a constant $C$. The rewritten program is as follows. Note that Character is a type representing a character and has fields $hp$ and $dp$ which represent the hit point and the defense point of the character respectively. int C = <constant integer>; Character selectTarget(Character v[]) { int n = length(v); int r = 0; for (int i = 1; i < n; i++) { if (abs(v[r].hp - v[i].hp) > C) { if (v[r].hp > v[i].hp) r = i; } else { if (v[r].dp > v[i].dp) r = i; } } return v[r]; } By the way, this function may return different characters according to the order of the characters in $v$, even if $v$ contains the same set of characters. Ms. Yagami wants to know how many characters in a party may become the target of the new AI. Aoba's next task is to write a program that takes a given party $v$ and a constant $C$, and then counts the number of characters that may become the return value of selectTarget ($v$) if $v$ is re-ordered. Input The input consists of a single test case. The first line contains two integers $N$ $(1 \leq N \leq 50,000)$ and $C$ $(0 \leq C \leq 10^9)$. The first integer $N$ represents the size of $v$. The second integer $C$ represents the constant $C$ in Aoba's program. The i -th line of the following $N$ lines contains two integers $hp_i$ and $dp_i$ $(0 \leq hp_i, dp_i \leq 10^9)$. $hp_i$ represents the hit point of the $i$-th character in $v$, and $dp_i$ represents the defense point of the $i$-th character in $v$. You can assume that $hp_i \ne hp_j$ or $dpi \ne dp_j$ if $i \ne j$ for any $1 \leq i, j \leq N$. Output Display the number of characters that may become the return value of selectTarget ($v$), if $v$ is shuffled in an arbitrary order. Sample Input 1 5 3 1 5 3 4 5 3 7 2 9 1 Output for the Sample Input 1 5 Sample Input 2 3 2 1 2 3 1 5 1 Output for the Sample Input 2 2 Sample Input 3 4 1 2 0 0 4 1 1 5 9 Output for the Sample Input 3 3 Sample Input 4 5 9 4 10 12 4 2 14 9 19 7 15 Output for the Sample Input 4 3 | 37,730 |
Problem H: Don't Burst the Balloon An open-top box having a square bottom is placed on the floor. You see a number of needles vertically planted on its bottom. You want to place a largest possible spheric balloon touching the box bottom, interfering with none of the side walls nor the needles. Java Specific: Submitted Java programs may not use "java.awt.geom.Area". You may use it for your debugging purposes. Figure H.1 shows an example of a box with needles and the corresponding largest spheric balloon. It corresponds to the first dataset of the sample input below. Figure H.1. The upper shows an example layout and the lower shows the largest spheric balloon that can be placed. Input The input is a sequence of datasets. Each dataset is formatted as follows. n w x 1 y 1 h 1 : x n y n h n The first line of a dataset contains two positive integers, n and w , separated by a space. n represents the number of needles, and w represents the height of the side walls. The bottom of the box is a 100 à 100 square. The corners of the bottom face are placed at positions (0, 0, 0), (0, 100, 0), (100, 100, 0), and (100, 0, 0). Each of the n lines following the first line contains three integers, x i , y i , and h i . ( x i , y i , 0) and h i represent the base position and the height of the i -th needle. No two needles stand at the same position. You can assume that 1 †n †10, 10 †w †200, 0 < x i < 100, 0 < y i < 100 and 1 †h i †200. You can ignore the thicknesses of the needles and the walls. The end of the input is indicated by a line of two zeros. The number of datasets does not exceed 1000. Output For each dataset, output a single line containing the maximum radius of a balloon that can touch the bottom of the box without interfering with the side walls or the needles. The output should not contain an error greater than 0.0001. Sample Input 5 16 70 66 40 38 52 20 40 35 10 70 30 10 20 60 10 1 100 54 75 200 1 10 90 10 1 1 11 54 75 200 3 10 53 60 1 61 38 1 45 48 1 4 10 20 20 10 20 80 10 80 20 10 80 80 10 0 0 Output for the Sample Input 26.00000 39.00000 130.00000 49.49777 85.00000 95.00000 | 37,731 |
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å ±ãäžããããã1ã€ã®ç·åã¯ãç·åã®ç«¯ç¹(xai, yai)ãš(xbi, ybi)ã«ãã£ãŠè¡šããããã Constraints 1 <= N <= 50 -1000 <= åº§æš <= 1000 (xai, yai)ãš(xbi, ybi)ã®äœçœ®ã¯ç°ãªã 2ã€ã®ç·åã亀差ããŠãããšãã2ã€ã®ç·åã®ç«¯ç¹4ã€ãäžçŽç·äžã«äžŠã¶ããšã¯ãªã Output ç©Žã®åæ°ã1è¡ã§åºåããã Sample Input 1 8 5 0 5 10 5 10 0 5 0 5 5 0 10 0 10 10 10 10 5 5 5 5 10 0 10 2 15 5 15 5 10 8 Output for the Sample Input 1 2 Sample Input 2 11 0 0 10 0 10 0 10 10 10 10 0 10 0 10 0 0 1 2 9 2 8 1 8 9 9 8 1 8 2 9 2 1 8 11 11 8 8 11 14 10 11 8 10 14 Output for the Sample Input 2 1 | 37,732 |
Balls and Boxes 6 Balls Boxes Any way At most one ball At least one ball Distinguishable Distinguishable 1 2 3 Indistinguishable Distinguishable 4 5 6 Distinguishable Indistinguishable 7 8 9 Indistinguishable Indistinguishable 10 11 12 Problem You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions: Each ball is not distinguished from the other. Each box is distinguished from the other. Each ball can go into only one box and no one remains outside of the boxes. Each box must contain at least one ball. Note that you must print this count modulo $10^9+7$. Input $n$ $k$ The first line will contain two integers $n$ and $k$. Output Print the number of ways modulo $10^9+7$ in a line. Constraints $1 \le n \le 1000$ $1 \le k \le 1000$ Sample Input 1 5 3 Sample Output 1 6 Sample Input 2 10 5 Sample Output 2 126 Sample Input 3 100 30 Sample Output 3 253579538 | 37,733 |
Score : 200 points Problem Statement Given is an integer N . Find the number of digits that N has in base K . Notes For information on base- K representation, see Positional notation - Wikipedia . Constraints All values in input are integers. 1 \leq N \leq 10^9 2 \leq K \leq 10 Input Input is given from Standard Input in the following format: N K Output Print the number of digits that N has in base K . Sample Input 1 11 2 Sample Output 1 4 In binary, 11 is represented as 1011 . Sample Input 2 1010101 10 Sample Output 2 7 Sample Input 3 314159265 3 Sample Output 3 18 | 37,734 |
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¥åã®çµãã㯠N = M = 0 ã®ããŒã¿ã»ããã§è¡šãããïŒ ãã®ããŒã¿ã»ããã«ã€ããŠåºåãè¡ã£ãŠã¯ãªããªãïŒ Output åããŒã¿ã»ããã«ã€ããŠïŒ M æ¥éã®äžå¿«åºŠã®åã®æå°å€ã 1 è¡ã«åºåããïŒ Sample Input 1 1 5 6 1 1 5 2 1 1 20 5 4 1 2 4 5 9 8 4 3 3 5 2 1 10 4 7 5 5 2 2 2 2 2 1 3 5 7 9 2 5 2 5 2 5 2 5 2 0 0 Output for Sample Input 1 2 5 1 1 5 4 5 ã€ç®ã®ã±ãŒã¹ã«ã€ããŠã¯ïŒäžãã 5, 2, 3, 1 ãšæŒå
¥ãã«çœ®ãïŒ1 æ¥ç®ã¯ 3 æåãåºã |10 - (5 + 2 + 3)| = 0ïŒ2 æ¥ç®ã¯ 2 æããŸã |4 - 5| = 1ïŒ3 æ¥ç®ã¯ 1 æåãåºã |7 - (5+2)| = 0 ã§ïŒåèš 0 + 1 + 0 = 1 ãšãªãïŒ | 37,736 |
Score : 1000 points Problem Statement Ringo has a string S . He can perform the following N kinds of operations any number of times in any order. Operation i : For each of the characters from the L_i -th through the R_i -th characters in S , replace it with its succeeding letter in the English alphabet. (That is, replace a with b , replace b with c and so on.) For z , we assume that its succeeding letter is a . Ringo loves palindromes and wants to turn S into a palindrome. Determine whether this is possible. Constraints 1 \leq |S| \leq 10^5 S consists of lowercase English letters. 1 \leq N \leq 10^5 1 \leq L_i \leq R_i \leq |S| Input Input is given from Standard Input in the following format: S N L_1 R_1 L_2 R_2 : L_N R_N Output Print YES if it is possible to turn S into a palindrome; print NO if it is impossible. Sample Input 1 bixzja 2 2 3 3 6 Sample Output 1 YES For example, if we perform Operation 1 , 2 and 1 in this order, S changes as bixzja â bjyzja â bjzakb â bkaakb and becomes a palindrome. Sample Input 2 abc 1 2 2 Sample Output 2 NO Sample Input 3 cassert 4 1 2 3 4 1 1 2 2 Sample Output 3 YES | 37,737 |
Score : 100 points Problem Statement There is a simple directed graph G with N vertices, numbered 1, 2, \ldots, N . For each i and j ( 1 \leq i, j \leq N ), you are given an integer a_{i, j} that represents whether there is a directed edge from Vertex i to j . If a_{i, j} = 1 , there is a directed edge from Vertex i to j ; if a_{i, j} = 0 , there is not. Find the number of different directed paths of length K in G , modulo 10^9 + 7 . We will also count a path that traverses the same edge multiple times. Constraints All values in input are integers. 1 \leq N \leq 50 1 \leq K \leq 10^{18} a_{i, j} is 0 or 1 . a_{i, i} = 0 Input Input is given from Standard Input in the following format: N K a_{1, 1} \ldots a_{1, N} : a_{N, 1} \ldots a_{N, N} Output Print the number of different directed paths of length K in G , modulo 10^9 + 7 . Sample Input 1 4 2 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 Sample Output 1 6 G is drawn in the figure below: There are six directed paths of length 2 : 1 â 2 â 3 1 â 2 â 4 2 â 3 â 4 2 â 4 â 1 3 â 4 â 1 4 â 1 â 2 Sample Input 2 3 3 0 1 0 1 0 1 0 0 0 Sample Output 2 3 G is drawn in the figure below: There are three directed paths of length 3 : 1 â 2 â 1 â 2 2 â 1 â 2 â 1 2 â 1 â 2 â 3 Sample Input 3 6 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 Sample Output 3 1 G is drawn in the figure below: There is one directed path of length 2 : 4 â 5 â 6 Sample Input 4 1 1 0 Sample Output 4 0 Sample Input 5 10 1000000000000000000 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 Sample Output 5 957538352 Be sure to print the count modulo 10^9 + 7 . | 37,738 |
Score : 800 points Problem Statement There are N positive integers A_1, A_2, ..., A_N . Takahashi can perform the following operation on these integers any number of times: Choose 1 \leq i \leq N and multiply the value of A_i by -2 . Notice that he multiplies it by minus two. He would like to make A_1 \leq A_2 \leq ... \leq A_N holds. Find the minimum number of operations required. If it is impossible, print -1 . Constraints 1 \leq N \leq 200000 1 \leq A_i \leq 10^9 Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the answer. Sample Input 1 4 3 1 4 1 Sample Output 1 3 One possible solution is: Choose i=4 and multiply the value of A_4 by -2 . A_1, A_2, A_3, A_4 are now 3, 1, 4, -2 . Choose i=1 and multiply the value of A_1 by -2 . A_1, A_2, A_3, A_4 are now -6, 1, 4, -2 . Choose i=4 and multiply the value of A_4 by -2 . A_1, A_2, A_3, A_4 are now -6, 1, 4, 4 . Sample Input 2 5 1 2 3 4 5 Sample Output 2 0 A_1 \leq A_2 \leq ... \leq A_N holds before any operation is performed. Sample Input 3 8 657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097 Sample Output 3 7 | 37,739 |
Score : 1100 points Problem Statement There are N white balls arranged in a row, numbered 1,2,..,N from left to right. AtCoDeer the deer is thinking of painting some of these balls red and blue, while leaving some of them white. You are given a string s of length K . AtCoDeer performs the following operation for each i from 1 through K in order: The i -th operation: Choose a contiguous segment of balls ( possibly empty ), and paint these balls red if the i -th character in s is r ; paint them blue if the character is b . Here, if a ball which is already painted is again painted, the color of the ball will be overwritten. However, due to the properties of dyes, it is not possible to paint a white, unpainted ball directly in blue. That is, when the i -th character in s is b , the chosen segment must not contain a white ball. After all the operations, how many different sequences of colors of the balls are possible? Since the count can be large, find it modulo 10^9+7 . Constraints 1 †N †70 1 †K †70 |s| = K s consists of r and b . N and K are integers. Input Input is given from Standard Input in the following format: N K s Output Print the number of the different possible sequences of colors of the balls after all the operations, modulo 10^9+7 . Sample Input 1 2 2 rb Sample Output 1 9 There are nine possible sequences of colors of the balls, as follows: ww , wr , rw , rr , wb , bw , bb , rb , br . Here, r represents red, b represents blue and w represents white. Sample Input 2 5 2 br Sample Output 2 16 Since we cannot directly paint white balls in blue, we can only choose an empty segment in the first operation. Sample Input 3 7 4 rbrb Sample Output 3 1569 Sample Input 4 70 70 bbrbrrbbrrbbbbrbbrbrrbbrrbbrbrrbrbrbbbbrbbrbrrbbrrbbbbrbbrbrrbbrrbbbbr Sample Output 4 841634130 | 37,740 |
Score : 400 points Problem Statement Your friend gave you a dequeue D as a birthday present. D is a horizontal cylinder that contains a row of N jewels. The values of the jewels are V_1, V_2, ..., V_N from left to right. There may be jewels with negative values. In the beginning, you have no jewel in your hands. You can perform at most K operations on D , chosen from the following, at most K times (possibly zero): Operation A: Take out the leftmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty. Operation B: Take out the rightmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty. Operation C: Choose a jewel in your hands and insert it to the left end of D . You cannot do this operation when you have no jewel in your hand. Operation D: Choose a jewel in your hands and insert it to the right end of D . You cannot do this operation when you have no jewel in your hand. Find the maximum possible sum of the values of jewels in your hands after the operations. Constraints All values in input are integers. 1 \leq N \leq 50 1 \leq K \leq 100 -10^7 \leq V_i \leq 10^7 Input Input is given from Standard Input in the following format: N K V_1 V_2 ... V_N Output Print the maximum possible sum of the values of jewels in your hands after the operations. Sample Input 1 6 4 -10 8 2 1 2 6 Sample Output 1 14 After the following sequence of operations, you have two jewels of values 8 and 6 in your hands for a total of 14 , which is the maximum result. Do operation A. You take out the jewel of value -10 from the left end of D . Do operation B. You take out the jewel of value 6 from the right end of D . Do operation A. You take out the jewel of value 8 from the left end of D . Do operation D. You insert the jewel of value -10 to the right end of D . Sample Input 2 6 4 -6 -100 50 -2 -5 -3 Sample Output 2 44 Sample Input 3 6 3 -6 -100 50 -2 -5 -3 Sample Output 3 0 It is optimal to do no operation. | 37,741 |
Score : 100 points Problem Statement Takahashi is participating in a programming contest, AXC001. He has just submitted his code to Problem A. The problem has N test cases, all of which must be passed to get an AC verdict. Takahashi's submission has passed M cases out of the N test cases. Determine whether Takahashi's submission gets an AC. Constraints 1 \leq N \leq 100 0 \leq M \leq N All values in input are integers. Input Input is given from Standard Input in the following format: N M Output If Takahashi's submission gets an AC, print Yes ; otherwise, print No . Sample Input 1 3 3 Sample Output 1 Yes All three test cases have been passed, so his submission gets an AC. Sample Input 2 3 2 Sample Output 2 No Only two out of the three test cases have been passed, so his submission does not get an AC. Sample Input 3 1 1 Sample Output 3 Yes | 37,742 |
Koch Curve Write a program which reads an integer n and draws a Koch curve based on recursive calles of depth n . The Koch curve is well known as a kind of fractals . You can draw a Koch curve in the following algorithm: Divide a given segment (p1, p2) into three equal segments. Replace the middle segment by the two sides of an equilateral triangle (s, u, t) of the same length as the segment. Repeat this procedure recursively for new segments (p1, s), (s, u), (u, t), (t, p2). You should start (0, 0), (100, 0) as the first segment. Input An integer n is given. Output Print each point (x, y) of the Koch curve. Print a point in a line. You should start the point(0, 0), which is the endpoint of the first segment and end with the point (100, 0), the other endpoint so that you can draw the Koch curve as an unbroken line. Each solution should be given as a decimal with an arbitrary number of fractional digits, and with an absolute error of at most 10-4. Constraints 0 †n †6 Sample Input 1 1 Sample Output 1 0.00000000 0.00000000 33.33333333 0.00000000 50.00000000 28.86751346 66.66666667 0.00000000 100.00000000 0.00000000 Sample Input 2 2 Sample Output 2 0.00000000 0.00000000 11.11111111 0.00000000 16.66666667 9.62250449 22.22222222 0.00000000 33.33333333 0.00000000 38.88888889 9.62250449 33.33333333 19.24500897 44.44444444 19.24500897 50.00000000 28.86751346 55.55555556 19.24500897 66.66666667 19.24500897 61.11111111 9.62250449 66.66666667 0.00000000 77.77777778 0.00000000 83.33333333 9.62250449 88.88888889 0.00000000 100.00000000 0.00000000 Notes | 37,743 |
Score : 300 points Problem Statement We have two desks: A and B. Desk A has a vertical stack of N books on it, and Desk B similarly has M books on it. It takes us A_i minutes to read the i -th book from the top on Desk A (1 \leq i \leq N) , and B_i minutes to read the i -th book from the top on Desk B (1 \leq i \leq M) . Consider the following action: Choose a desk with a book remaining, read the topmost book on that desk, and remove it from the desk. How many books can we read at most by repeating this action so that it takes us at most K minutes in total? We ignore the time it takes to do anything other than reading. Constraints 1 \leq N, M \leq 200000 1 \leq K \leq 10^9 1 \leq A_i, B_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N M K A_1 A_2 \ldots A_N B_1 B_2 \ldots B_M Output Print an integer representing the maximum number of books that can be read. Sample Input 1 3 4 240 60 90 120 80 150 80 150 Sample Output 1 3 In this case, it takes us 60 , 90 , 120 minutes to read the 1 -st, 2 -nd, 3 -rd books from the top on Desk A, and 80 , 150 , 80 , 150 minutes to read the 1 -st, 2 -nd, 3 -rd, 4 -th books from the top on Desk B, respectively. We can read three books in 230 minutes, as shown below, and this is the maximum number of books we can read within 240 minutes. Read the topmost book on Desk A in 60 minutes, and remove that book from the desk. Read the topmost book on Desk B in 80 minutes, and remove that book from the desk. Read the topmost book on Desk A in 90 minutes, and remove that book from the desk. Sample Input 2 3 4 730 60 90 120 80 150 80 150 Sample Output 2 7 Sample Input 3 5 4 1 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 Sample Output 3 0 Watch out for integer overflows. | 37,744 |
Max Score: $400$ Points Problem Statement Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01) Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct. He made a sequence $b$, but actually, he is not remembered it. However, he is remembered a few things about sequence $b$. All elements in $b$ are distinct. All elements in $b$ is in $a$. $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR] For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$. He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him. Since the answer can be large, print the answer modulo $1,000,000,007$. Input The input is given from Standard Input in the following format: $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$ Output Print the number of ways to make sequence $b$. Print the answer modulo $1,000,000,007$. Constraints $1 \le n \le 100$ $1 \le a_i, k \le 255$ $i \neq j \Rightarrow a_i \neq a_j$ Subtasks Subtask 1 [ $50$ points ] $1 \le n \le 4$ Subtask 2 [ $170$ points ] $1 \le n \le 20$ Subtask 3 [ $180$ points ] There are no additional constraints. Sample Input 1 3 1 1 2 3 Sample Output 1 3 You can make 3 patterns: $b = \{ 1 \}, \{ 2, 3 \}, \{ 3, 2 \}$ Sample Input 2 3 10 8 7 5 Sample Output 2 6 You can make 6 patterns: $b = \{ 5, 7, 8 \}, \{ 5, 8, 7 \}, \{ 7, 5, 8 \}, \{ 7, 8, 5 \}, \{ 8, 5, 7 \}, \{ 8, 7, 5 \}$. Sample Input 4 25 127 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 Sample Output 4 235924722 Please output answer mod $1,000,000,007$. writer: E869120 | 37,745 |
Balls and Boxes 7 Balls Boxes Any way At most one ball At least one ball Distinguishable Distinguishable 1 2 3 Indistinguishable Distinguishable 4 5 6 Distinguishable Indistinguishable 7 8 9 Indistinguishable Indistinguishable 10 11 12 Problem You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions: Each ball is distinguished from the other. Each box is not distinguished from the other. Each ball can go into only one box and no one remains outside of the boxes. Each box can contain an arbitrary number of balls (including zero). Note that you must print this count modulo $10^9+7$. Input $n$ $k$ The first line will contain two integers $n$ and $k$. Output Print the number of ways modulo $10^9+7$ in a line. Constraints $1 \le n \le 1000$ $1 \le k \le 1000$ Sample Input 1 3 5 Sample Output 1 5 Sample Input 2 5 3 Sample Output 2 41 Sample Input 3 100 100 Sample Output 3 193120002 | 37,746 |
Score : 300 points Problem Statement There are N people living on a number line. The i -th person lives at coordinate X_i . You are going to hold a meeting that all N people have to attend. The meeting can be held at any integer coordinate . If you choose to hold the meeting at coordinate P , the i -th person will spend (X_i - P)^2 points of stamina to attend the meeting. Find the minimum total points of stamina the N people have to spend. Constraints All values in input are integers. 1 \leq N \leq 100 1 \leq X_i \leq 100 Input Input is given from Standard Input in the following format: N X_1 X_2 ... X_N Output Print the minimum total stamina the N people have to spend. Sample Input 1 2 1 4 Sample Output 1 5 Assume the meeting is held at coordinate 2 . In this case, the first person will spend (1 - 2)^2 points of stamina, and the second person will spend (4 - 2)^2 = 4 points of stamina, for a total of 5 points of stamina. This is the minimum total stamina that the 2 people have to spend. Note that you can hold the meeting only at an integer coordinate. Sample Input 2 7 14 14 2 13 56 2 37 Sample Output 2 2354 | 37,747 |
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ã® 0 ä»¥äž 1 以äžã®å®æ°ã§ããïŒ m i 㯠i çªç®ã®åå è
ãç¥ã£ãŠããé£çµ¡å
ã®æ°ã§ããïŒ0 ä»¥äž N 以äžã®æŽæ°ã§ããïŒ a (i, j) 㯠i çªç®ã®åå è
ãç¥ã£ãŠãã j çªç®ã®é£çµ¡å
ã a (i, j) çªç®ã®åå è
ã®ãã®ã§ããããšãè¡šãïŒ a (i, j) 㯠N ãè¶ããªãæ£ã®æŽæ°ã§ããïŒ å
¥åã®çµããã¯ïŒ1 ã€ã®ãŒããããªãè¡ã§ç€ºãïŒ Output åããŒã¿ã»ããã«ã€ããŠïŒå
šå¡ãèµ·åºã§ãã確çã 1 è¡ã«åºåããïŒåºåã«ã¯ 0.00001 以äžã®èª€å·®ãå«ãã§ã¯ãªããªãïŒ Sample Input 2 0.60 1 2 0.60 0 2 0.60 1 2 0.60 1 1 5 0.10 1 2 0.20 1 3 0.30 1 4 0.40 1 5 0.50 1 1 5 0.10 0 0.20 1 1 0.30 1 1 0.40 1 1 0.50 1 1 5 0.10 4 2 3 4 5 0.20 0 0.30 0 0.40 0 0.50 0 4 0.10 1 2 0.20 0 0.30 1 4 0.40 1 3 5 0.10 0 0.20 0 0.30 0 0.40 0 0.50 0 0 Output for Sample Input 0.400000000 0.640000000 0.998800000 0.168000000 0.900000000 0.792000000 0.151200000 | 37,748 |
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