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Problem B: Book Replacement The deadline of Prof. Hachiojiâs assignment is tomorrow. To complete the task, students have to copy pages of many reference books in the library. All the reference books are in a storeroom and only the librarian is allowed to enter it. To obtain a copy of a reference bookâs page, a student should ask the librarian to make it. The librarian brings books out of the storeroom and makes page copies according to the requests. The overall situation is shown in Figure 1. Students queue up in front of the counter. Only a single book can be requested at a time. If a student has more requests, the student goes to the end of the queue after the request has been served. In the storeroom, there are m desks D 1 , ... , D m , and a shelf. They are placed in a line in this order, from the door to the back of the room. Up to c books can be put on each of the desks. If a student requests a book, the librarian enters the storeroom and looks for it on D 1 , ... , D m in this order, and then on the shelf. After finding the book, the librarian takes it and gives a copy of a page to the student. Then the librarian returns to the storeroom with the requested book, to put it on D 1 according to the following procedure. If D 1 is not full (in other words, the number of books on D 1 < c ), the librarian puts the requested book there. If D 1 is full, the librarian temporarily puts the requested book on the non-full desk closest to the entrance or, in case all the desks are full, on the shelf, finds the book on D 1 that has not been requested for the longest time (i.e. the least recently used book) and takes it, puts it on the non-full desk (except D 1 ) closest to the entrance or, in case all the desks except D 1 are full, on the shelf, takes the requested book from the temporary place, and finally puts it on D 1 . Your task is to write a program which simulates the behaviors of the students and the librarian, and evaluates the total cost of the overall process. Costs are associated with accessing a desk or the shelf, that is, putting/taking a book on/from it in the description above. The cost of an access is i for desk D i and m + 1 for the shelf. That is, an access to D 1 , ... , D m , and the shelf costs 1, ... , m , and m + 1, respectively. Costs of other actions are ignored. Initially, no books are put on desks. No new students appear after opening the library. Input The input consists of multiple datasets. The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset. The format of each dataset is as follows. m c n k 1 b 11 . . . b 1 k 1 . . . k n b n 1 . . . b nk n Here, all data items are positive integers. m is the number of desks not exceeding 10. c is the number of books allowed to put on a desk, which does not exceed 30. n is the number of students not exceeding 100. k i is the number of books requested by the i -th student, which does not exceed 50. b ij is the ID number of the book requested by the i -th student on the j -th turn. No two books have the same ID number. Note that a student may request the same book more than once. b ij is less than 100. Here we show you an example of cost calculation for the following dataset. 3 1 2 3 60 61 62 2 70 60 In this dataset, there are 3 desks ( D 1 , D 2 , D 3 ). At most 1 book can be put on each desk. The number of students is 2. The first student requests 3 books of which IDs are 60, 61, and 62, respectively, and the second student 2 books of which IDs are 70 and 60, respectively. The calculation of the cost for this dataset is done as follows. First, for the first request of the first student, the librarian takes the book 60 from the shelf and puts it on D 1 and the first student goes to the end of the queue, costing 5. Next, for the first request of the second student, the librarian takes the book 70 from the shelf, puts it on D 2 , moves the book 60 from D 1 to D 3 , and finally moves the book 70 from D 2 to D 1 , costing 13. Similarly, the cost for the books 61, 60, and 62, are calculated as 14, 12, 14, respectively. Therefore, the total cost is 58. Output For each dataset, output the total cost of processing all the requests, in a separate line. Sample Input 2 1 1 1 50 2 1 2 1 50 1 60 2 1 2 2 60 61 1 70 4 2 3 3 60 61 62 1 70 2 80 81 3 1 2 3 60 61 62 2 70 60 1 2 5 2 87 95 3 96 71 35 2 68 2 3 3 18 93 2 57 2 2 2 1 5 1 2 1 3 1 0 0 0 Output for the Sample Input 4 16 28 68 58 98 23 | 35,300 |
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ãã誀差ããã£ãŠã¯ãªããªãïŒ Sample Input 4 5 5 1 0 0 10 0 10 10 0 10 8 5 5 1 0 0 9 0 9 1 10 1 10 9 9 9 9 10 0 10 12 25 5 1 0 0 10 0 10 4 20 4 20 0 40 0 40 10 20 10 20 5 10 5 10 10 0 10 0 0 0 0 Output for the Sample Input 99.1415926535897 96.7123889804 199.2321787 | 35,301 |
Score : 1100 points Problem Statement Coloring of the vertices of a tree G is called a good coloring when, for every pair of two vertices u and v painted in the same color, picking u as the root and picking v as the root would result in isomorphic rooted trees. Also, the colorfulness of G is defined as the minimum possible number of different colors used in a good coloring of G . You are given a tree with N vertices. The vertices are numbered 1 through N , and the i -th edge connects Vertex a_i and Vertex b_i . We will construct a new tree T by repeating the following operation on this tree some number of times: Add a new vertex to the tree by connecting it to one of the vertices in the current tree with an edge. Find the minimum possible colorfulness of T . Additionally, print the minimum number of leaves (vertices with degree 1 ) in a tree T that achieves the minimum colorfulness. Notes The phrase "picking u as the root and picking v as the root would result in isomorphic rooted trees" for a tree G means that there exists a bijective function f_{uv} from the vertex set of G to itself such that both of the following conditions are met: f_{uv}(u)=v For every pair of two vertices (a,b) , edge (a,b) exists if and only if edge (f_{uv}(a),f_{uv}(b)) exists. Constraints 2 \leq N \leq 100 1 \leq a_i,b_i \leq N(1\leq i\leq N-1) The given graph is a tree. Input Input is given from Standard Input in the following format: N a_1 b_1 : a_{N-1} b_{N-1} Output Print two integers with a space in between. First, print the minimum possible colorfulness of a tree T that can be constructed. Second, print the minimum number of leaves in a tree that achieves it. It can be shown that, under the constraints of this problem, the values that should be printed fit into 64 -bit signed integers. Sample Input 1 5 1 2 2 3 3 4 3 5 Sample Output 1 2 4 If we connect a new vertex 6 to vertex 2 , painting the vertices (1,4,5,6) red and painting the vertices (2,3) blue is a good coloring. Since painting all the vertices in a single color is not a good coloring, we can see that the colorfulness of this tree is 2 . This is actually the optimal solution. There are four leaves, so we should print 2 and 4 . Sample Input 2 8 1 2 2 3 4 3 5 4 6 7 6 8 3 6 Sample Output 2 3 4 Sample Input 3 10 1 2 2 3 3 4 4 5 5 6 6 7 3 8 5 9 3 10 Sample Output 3 4 6 Sample Input 4 13 5 6 6 4 2 8 4 7 8 9 3 2 10 4 11 10 2 4 13 10 1 8 12 1 Sample Output 4 4 12 | 35,302 |
Score : 300 points Problem Statement Find the maximum possible sum of the digits (in base 10 ) of a positive integer not greater than N . Constraints 1\leq N \leq 10^{16} N is an integer. Input Input is given from Standard Input in the following format: N Output Print the maximum possible sum of the digits (in base 10 ) of a positive integer not greater than N . Sample Input 1 100 Sample Output 1 18 For example, the sum of the digits in 99 is 18 , which turns out to be the maximum value. Sample Input 2 9995 Sample Output 2 35 For example, the sum of the digits in 9989 is 35 , which turns out to be the maximum value. Sample Input 3 3141592653589793 Sample Output 3 137 | 35,303 |
Score: 300 points Problem Statement In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6 )! There are five means of transport in this empire: Train: travels from City 1 to 2 in one minute. A train can occupy at most A people. Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people. Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people. Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people. Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people. For each of them, one vehicle leaves the city at each integer time (time 0 , 1 , 2 , ... ). There is a group of N people at City 1 , and they all want to go to City 6 . At least how long does it take for all of them to reach there? You can ignore the time needed to transfer. Constraints 1 \leq N, A, B, C, D, E \leq 10^{15} All values in input are integers. Input Input is given from Standard Input in the following format: N A B C D E Output Print the minimum time required for all of the people to reach City 6 , in minutes. Sample Input 1 5 3 2 4 3 5 Sample Output 1 7 One possible way to travel is as follows. First, there are N = 5 people at City 1 , as shown in the following image: In the first minute, three people travels from City 1 to City 2 by train. Note that a train can only occupy at most three people. In the second minute, the remaining two people travels from City 1 to City 2 by train, and two of the three people who were already at City 2 travels to City 3 by bus. Note that a bus can only occupy at most two people. In the third minute, two people travels from City 2 to City 3 by train, and another two people travels from City 3 to City 4 by taxi. From then on, if they continue traveling without stopping until they reach City 6 , all of them can reach there in seven minutes. There is no way for them to reach City 6 in 6 minutes or less. Sample Input 2 10 123 123 123 123 123 Sample Output 2 5 All kinds of vehicles can occupy N = 10 people at a time. Thus, if they continue traveling without stopping until they reach City 6 , all of them can reach there in five minutes. Sample Input 3 10000000007 2 3 5 7 11 Sample Output 3 5000000008 Note that the input or output may not fit into a 32 -bit integer type. | 35,304 |
Optimal Binary Search Tree Optimal Binary Search Tree is a binary search tree constructed from $n$ keys and $n+1$ dummy keys so as to minimize the expected value of cost for a search operation. We are given a sequence $K = {k_1, k_2, ..., k_n}$ of $n$ distinct keys in sorted order $(k_1 < k_2 < ... < k_n)$, and we wish to construct a binary search tree. For each key $k_i$, we have a probability $p_i$ that a search will be for $k_i$. Some searches may be for values not in $K$, and so we also have $n+1$ dummy keys $d_0, d_1, d_2, ..., d_n$ representing values not in $K$. The dummy keys $d_i (0 \le i \le n)$ are defined as follows: if $i=0$, then $d_i$ represents all values less than $k_1$ if $i=n$, then $d_i$ represents all values greater than $k_n$ if $1 \le i \le n-1$, then $d_i$ represents all values between $k_i$ and $k_{i+1}$ For each dummy key $d_i$, we have a probability $q_i$ that a search will correspond to $d_i$. For $p_i (1 \le i \le n)$ and $q_i (0 \le i \le n)$, we have \[ \sum_{i=1}^n p_i + \sum_{i=0}^n q_i = 1 \] Then the expected cost of a search in a binary search tree $T$ is \[ E_T = \sum_{i=1}^n (depth_T(k_i) + 1) \cdot p_i + \sum_{i=0}^n (depth_T(d_i) + 1) \cdot q_i \] where $depth_T(v)$ is the depth of node $v$ in $T$. For a given set of probabilities, our goal is to construct a binary search tree whose expected search cost is smallest. We call such a tree an optimal binary search tree . Each key $k_i$ is an internal node and each dummy key $d_i$ is a leaf. For example, the following figure shows the optimal binary search tree obtained from Sample Input 1. Task Write a program which calculates the expected value of a search operation on the optimal binary search tree obtained by given $p_i$ that a search will be for $k_i$ and $q_i$ that a search will correspond to $d_i$. Input $n$ $p_1$ $p_2$ ... $p_n$ $q_0$ $q_1$ $q_2$ ... $q_n$ In the first line, an integer $n$ which represents the number of keys is given. In the second line, $p_i (1 \le i \le n)$ are given in real numbers with four decimal places. In the third line, $q_i (0 \le i \le n)$ are given in real numbers with four decimal places. Output Print the expected value for a search operation on the optimal binary search tree in a line. The output must not contain an error greater than $10^{â4}$. Constraints $1 \le n \le 500$ $0 \lt p_i, q_i \lt 1$ $\displaystyle \sum_{i=1}^n p_i + \sum_{i=0}^n q_i = 1$ Sample Input 1 5 0.1500 0.1000 0.0500 0.1000 0.2000 0.0500 0.1000 0.0500 0.0500 0.0500 0.1000 Sample Output 1 2.75000000 Sample Input 2 7 0.0400 0.0600 0.0800 0.0200 0.1000 0.1200 0.1400 0.0600 0.0600 0.0600 0.0600 0.0500 0.0500 0.0500 0.0500 Sample Output 2 3.12000000 | 35,305 |
Score : 700 points Problem Statement There are N towns numbered 1, 2, \cdots, N . Some roads are planned to be built so that each of them connects two distinct towns bidirectionally. Currently, there are no roads connecting towns. In the planning of construction, each town chooses one town different from itself and requests the following: roads are built so that the chosen town is reachable from itself using one or more roads. These requests from the towns are represented by an array P_1, P_2, \cdots, P_N . If P_i = -1 , it means that Town i has not chosen the request; if 1 \leq P_i \leq N , it means that Town i has chosen Town P_i . Let K be the number of towns i such that P_i = -1 . There are (N-1)^K ways in which the towns can make the requests. For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo ( 10^9+7 ). Constraints 2 \leq N \leq 5000 P_i = -1 or 1 \leq P_i \leq N . P_i \neq i All values in input are integers. Input Input is given from Standard Input in the following format: N P_1 P_2 \cdots P_N Output For each way to make requests, find the minimum number of roads needed to meet all the requests, and print the sum of those (N-1)^K numbers, modulo ( 10^9+7 ). Sample Input 1 4 2 1 -1 3 Sample Output 1 8 There are three ways to make requests, as follows: Choose P_1 = 2, P_2 = 1, P_3 = 1, P_4 = 3 . In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests. Choose P_1 = 2, P_2 = 1, P_3 = 2, P_4 = 3 . In this case, at least three roads - for example, (1,2),(1,3),(3,4) - are needed to meet the requests. Choose P_1 = 2, P_2 = 1, P_3 = 4, P_4 = 3 . In this case, at least two roads - for example, (1,2),(3,4) - are needed to meet the requests. Note that it is not mandatory to connect Town i and Town P_i directly. The sum of the above numbers is 8 . Sample Input 2 2 2 1 Sample Output 2 1 There may be just one fixed way to make requests. Sample Input 3 10 2 6 9 -1 6 9 -1 -1 -1 -1 Sample Output 3 527841 | 35,306 |
Route Calculator You have a grid with $H$ rows and $W$ columns. $H + W$ is even. We denote the cell at the $i$-th row from the top and the $j$-th column from the left by ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either ' + ' or ' * ' is written if $i+j$ is odd. You can get a mathematical expression by moving right or down $H + W - 2$ times from ($1, 1$) to ($H, W$) and concatenating all the characters written in the cells you passed in order. Your task is to maximize the calculated value of the resulting mathematical expression by choosing an arbitrary path from ($1, 1$) to ($H, W$). If the maximum value is $10^{15}$ or less, print the value. Otherwise, print $-1$. Input The input consists of a single test case in the format below. $H$ $W$ $a_{1,1}$ ... $a_{1,W}$ ... $a_{H,1}$ ... $a_{H,W}$ The first line consists of two $H$ integers and $W$ ($1 \leq H, W \leq 50$). It is guaranteed that $H + W$ is even. The following $H$ lines represent the characters on the grid. $a_{i,j}$ represents the character written in the cell ($i, j$). In any cell ($i, j$), an integer between $1$ and $9$ is written if $i+j$ is even, and either ' + ' or ' * ' is written if $i+1$ is odd. Output Print the answer in one line. Sample Input 1 3 3 1+2 +9* 1*5 Output for Sample Input 1 46 The maximum value is obtained by passing through the following cells: $(1,1), (2,1), (2,2), (2,3), (3,3)$. Sample Input 2 1 31 9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9 Output for Sample Input 2 -1 You can obtain $9^{16}$, but it's too large. Sample Input 3 5 5 2+2+1 +1+1+ 1+2+2 +1+1+ 1+1+2 Output for Sample Input 3 10 Sample Input 4 9 7 8+9*4*8 *5*2+3+ 1*3*2*2 *5*1+9+ 1+2*2*2 *3*6*2* 7*7+6*5 *5+7*2+ 3+3*6+8 Output for Sample Input 4 86408 | 35,307 |
Score : 1100 points Problem Statement There are N strings of lowercase alphabet only. The i -th string is S_i . Every string is unique. Provide answers for the Q queries below. The i -th query has the following format: Query: An integer k_i and a string p_{i,1}p_{i,2}...p_{i,26} that results from permuting { a , b ,..., z } are given. Output the sequence of the string S_{k_i} among the N strings in lexicographical order when the literal sequence is p_{i,1}<p_{i,2}<...<p_{i,26} . Constraints 1 ⊠N,Q ⊠100000 1 ⊠|S_i| (1 ⊠i ⊠N) S_i (1 ⊠i ⊠N) is a string of lowercase alphabet. The sum of |S_i| is no more than 400000 . Every S_i is unique. 1 ⊠k_i ⊠N (1 ⊠i ⊠Q) For all 1 ⊠i ⊠Q , p_{i,1}p_{i,2}...p_{i,26} is a permutation of abcd...z . Input Inputs are provided from standard inputs in the following form. N S_1 : S_N Q k_1 p_{1,1}p_{1,2}...p_{1,26} : k_Q p_{Q,1}p_{Q,2}...p_{Q,26} Output Output Q lines. On line i , for the i -th query, output an integer indicating the sequence of the string S_{k_i} among the N strings in lexicographical order. Sample Input 1 5 aa abbaa abbba aaab aaaaaba 5 1 abcdefghijklmnopqrstuvwxyz 2 bacdefghijklmnopqrstuvwxyz 3 abcdefghijklmnopqrstuvwxyz 4 bacdefghijklmnopqrstuvwxyz 5 abcdefghijklmnopqrstuvwxyz Sample Output 1 1 2 5 4 2 When the literal sequence is a < b , sorting the input strings in lexicographical order yields aa , aaaaaba , aaab , abbaa , abbba . The answers to queries 1 , 3 , and 5 are thus 1 , 5 , and 2 , respectively. When the literal sequence is b < a , sorting the input strings in lexicographical order yields abbba , abbaa , aa , aaab , aaaaaba . The answers to queries 2 and 4 are thus 2 and 4 , respectively. Sample Input 2 8 abrakatabra abadaba abracadabra atcoder grand contest ababa a 6 3 abcdefghijklmnopqrstuvwxyz 6 qwertyuiopasdfghjklzxcvbnm 8 poiuytrewqlkjhgfdsamnbvcxz 2 qazwsxedcrfvtgbyhnujmikolp 1 plokmijnuhbygvtfcrdxeszwaq 4 mnbvcxzasdfghjklpoiuytrewq Sample Output 2 4 8 2 3 4 7 | 35,308 |
Score : 300 points Problem Statement There are N observatories in AtCoder Hill, called Obs. 1 , Obs. 2 , ... , Obs. N . The elevation of Obs. i is H_i . There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j . Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints 2 \leq N \leq 10^5 1 \leq M \leq 10^5 1 \leq H_i \leq 10^9 1 \leq A_i,B_i \leq N A_i \neq B_i Multiple roads may connect the same pair of observatories. All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Sample Input 1 4 3 1 2 3 4 1 3 2 3 2 4 Sample Output 1 2 From Obs. 1 , you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3 , so Obs. 1 is not good. From Obs. 2 , you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3 , so Obs. 2 is not good. From Obs. 3 , you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2 , so Obs. 3 is good. From Obs. 4 , you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2 , so Obs. 4 is good. Thus, the good observatories are Obs. 3 and 4 , so there are two good observatories. Sample Input 2 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Sample Output 2 3 | 35,309 |
LCA: Lowest Common Ancestor For a rooted tree, find the lowest common ancestor of two nodes u and v . The given tree consists of n nodes and every node has a unique ID from 0 to n -1 where 0 is the root. Input n k 0 c 1 c 2 ... c k 0 k 1 c 1 c 2 ... c k 1 : k n-1 c 1 c 2 ... c k n-1 q u 1 v 1 u 2 v 2 : u q v q The first line of the input includes an integer n , the number of nodes of the tree. In the next n lines, the information of node i is given. k i is the number of children of node i , and c 1 , ... c k i are node IDs of 1st, ... k th child of node i . In the next line, the number of queryies q is given. In the next q lines, pairs of u and v are given as the queries. Output For each query, print the LCA of u and v in a line. Constraints 1 †n †100000 1 †q †100000 Sample Input 1 8 3 1 2 3 2 4 5 0 0 0 2 6 7 0 0 4 4 6 4 7 4 3 5 2 Sample Output 1 1 1 0 0 | 35,310 |
Score : 100 points Problem Statement A string of length 6 consisting of lowercase English letters is said to be coffee-like if and only if its 3 -rd and 4 -th characters are equal and its 5 -th and 6 -th characters are also equal. Given a string S , determine whether it is coffee-like. Constraints S is a string of length 6 consisting of lowercase English letters. Input Input is given from Standard Input in the following format: S Output If S is coffee-like, print Yes ; otherwise, print No . Sample Input 1 sippuu Sample Output 1 Yes In sippuu , the 3 -rd and 4 -th characters are equal, and the 5 -th and 6 -th characters are also equal. Sample Input 2 iphone Sample Output 2 No Sample Input 3 coffee Sample Output 3 Yes | 35,311 |
Score : 500 points Problem Statement There are N towns on a line running east-west. The towns are numbered 1 through N , in order from west to east. Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value. The coordinate of town i is X_i . You are now at town 1 , and you want to visit all the other towns. You have two ways to travel: Walk on the line. Your fatigue level increases by A each time you travel a distance of 1 , regardless of direction. Teleport to any location of your choice. Your fatigue level increases by B , regardless of the distance covered. Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways. Constraints All input values are integers. 2â€Nâ€10^5 1â€X_iâ€10^9 For all i(1â€iâ€N-1) , X_i<X_{i+1} . 1â€Aâ€10^9 1â€Bâ€10^9 Input The input is given from Standard Input in the following format: N A B X_1 X_2 ... X_N Output Print the minimum possible total increase of your fatigue level when you visit all the towns. Sample Input 1 4 2 5 1 2 5 7 Sample Output 1 11 From town 1 , walk a distance of 1 to town 2 , then teleport to town 3 , then walk a distance of 2 to town 4 . The total increase of your fatigue level in this case is 2Ã1+5+2Ã2=11 , which is the minimum possible value. Sample Input 2 7 1 100 40 43 45 105 108 115 124 Sample Output 2 84 From town 1 , walk all the way to town 7 . The total increase of your fatigue level in this case is 84 , which is the minimum possible value. Sample Input 3 7 1 2 24 35 40 68 72 99 103 Sample Output 3 12 Visit all the towns in any order by teleporting six times. The total increase of your fatigue level in this case is 12 , which is the minimum possible value. | 35,312 |
Score : 1000 points Problem Statement For two permutations p and q of the integers from 1 through N , let f(p,q) be the permutation that satisfies the following: The p_i -th element ( 1 \leq i \leq N ) in f(p,q) is q_i . Here, p_i and q_i respectively denote the i -th element in p and q . You are given two permutations p and q of the integers from 1 through N . We will now define a sequence { a_n } of permutations of the integers from 1 through N , as follows: a_1=p , a_2=q a_{n+2}=f(a_n,a_{n+1}) ( n \geq 1 ) Given a positive integer K , find a_K . Constraints 1 \leq N \leq 10^5 1 \leq K \leq 10^9 p and q are permutations of the integers from 1 through N . Input Input is given from Standard Input in the following format: N K p_1 ... p_N q_1 ... q_N Output Print N integers, with spaces in between. The i -th integer ( 1 \leq i \leq N ) should be the i -th element in a_K . Sample Input 1 3 3 1 2 3 3 2 1 Sample Output 1 3 2 1 Since a_3=f(p,q) , we just need to find f(p,q) . We have p_i=i here, so f(p,q)=q . Sample Input 2 5 5 4 5 1 2 3 3 2 1 5 4 Sample Output 2 4 3 2 1 5 Sample Input 3 10 1000000000 7 10 6 5 4 2 9 1 3 8 4 1 9 2 3 7 8 10 6 5 Sample Output 3 7 9 4 8 2 5 1 6 10 3 | 35,313 |
Score : 1000 points Problem Statement There are N non-negative integers written on a blackboard. The i -th integer is A_i . Takahashi can perform the following two kinds of operations any number of times in any order: Select one integer written on the board (let this integer be X ). Write 2X on the board, without erasing the selected integer. Select two integers, possibly the same, written on the board (let these integers be X and Y ). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers. How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353 . Constraints 1 \leq N \leq 6 1 \leq X < 2^{4000} 1 \leq A_i < 2^{4000}(1\leq i\leq N) All input values are integers. X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1 . Input Input is given from Standard Input in the following format: N X A_1 : A_N Output Print the number of different integers not exceeding X that can be written on the blackboard. Sample Input 1 3 111 1111 10111 10010 Sample Output 1 4 Initially, 15 , 23 and 18 are written on the blackboard. Among the integers not exceeding 7 , four integers, 0 , 3 , 5 and 6 , can be written. For example, 6 can be written as follows: Double 15 to write 30 . Take XOR of 30 and 18 to write 12 . Double 12 to write 24 . Take XOR of 30 and 24 to write 6 . Sample Input 2 4 100100 1011 1110 110101 1010110 Sample Output 2 37 Sample Input 3 4 111001100101001 10111110 1001000110 100000101 11110000011 Sample Output 3 1843 Sample Input 4 1 111111111111111111111111111111111111111111111111111111111111111 1 Sample Output 4 466025955 Be sure to find the count modulo 998244353 . | 35,314 |
Score : 600 points Problem Statement Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions: He never visits a point with coordinate less than 0 , or a point with coordinate greater than L . He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate. He only changes direction at a point with integer coordinate. Each time when Snuke passes a point with coordinate i-0.5 , where i is an integer, he put a stone in his i -th ear. After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i , Snuke's i -th ear contains A_i stones: Put a stone in one of Snuke's ears. Remove a stone from one of Snuke's ears. Find the minimum number of operations required when Ringo can freely decide how Snuke walks. Constraints 1 \leq L \leq 2\times 10^5 0 \leq A_i \leq 10^9(1\leq i\leq L) All values in input are integers. Input Input is given from Standard Input in the following format: L A_1 : A_L Output Print the minimum number of operations required when Ringo can freely decide how Snuke walks. Sample Input 1 4 1 0 2 3 Sample Output 1 1 Assume that Snuke walks as follows: He starts walking at coordinate 3 and finishes walking at coordinate 4 , visiting coordinates 3,4,3,2,3,4 in this order. Then, Snuke's four ears will contain 0,0,2,3 stones, respectively. Ringo can satisfy the requirement by putting one stone in the first ear. Sample Input 2 8 2 0 0 2 1 3 4 1 Sample Output 2 3 Sample Input 3 7 314159265 358979323 846264338 327950288 419716939 937510582 0 Sample Output 3 1 | 35,315 |
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ããŸããã Output ããŒã¿ã»ããããšã«ã島ã®æ°ãïŒè¡ã«åºåããŸãã Sample Input 111100001111 111000001111 110000001111 100000001111 000100010000 000000111000 000001111100 100011111110 110001111100 111000111000 111100010000 000000000000 010001111100 110010000010 010010000001 010000000001 010000000110 010000111000 010000000100 010000000010 010000000001 010010000001 010010000010 111001111100 000000000000 111111111111 100010100001 100010100001 100010100001 100010100001 100100100101 101000011101 100000000001 100000000001 111111111111 100000000001 Output for the Sample Input 5 13 4 Hint 以äžã¯ãµã³ãã«ã€ã³ããããâ ãšâ¡ã§è¡šãããã®ã§ãã â â â â â¡â¡â¡â¡â â â â â¡â â¡â¡â¡â â â â â â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡ â â â â¡â¡â¡â¡â¡â â â â â â â¡â¡â â¡â¡â¡â¡â¡â â¡ â â â â â â â â â â â â â â â¡â¡â¡â¡â¡â¡â â â â â¡â â¡â¡â â¡â¡â¡â¡â¡â¡â â â¡â¡â¡â â¡â â¡â¡â¡â¡â â â¡â¡â¡â¡â¡â¡â¡â â â â â¡â â¡â¡â¡â¡â¡â¡â¡â¡â¡â â â¡â¡â¡â â¡â â¡â¡â¡â¡â â¡â¡â¡â â¡â¡â¡â â¡â¡â¡â¡ â¡â â¡â¡â¡â¡â¡â¡â¡â â â¡ â â¡â¡â¡â â¡â â¡â¡â¡â¡â â¡â¡â¡â¡â¡â¡â â â â¡â¡â¡ â¡â â¡â¡â¡â¡â â â â¡â¡â¡ â â¡â¡â¡â â¡â â¡â¡â¡â¡â â¡â¡â¡â¡â¡â â â â â â¡â¡ â¡â â¡â¡â¡â¡â¡â¡â¡â â¡â¡ â â¡â¡â â¡â¡â â¡â¡â â¡â â â¡â¡â¡â â â â â â â â¡ â¡â â¡â¡â¡â¡â¡â¡â¡â¡â â¡ â â¡â â¡â¡â¡â¡â â â â¡â â â â¡â¡â¡â â â â â â¡â¡ â¡â â¡â¡â¡â¡â¡â¡â¡â¡â¡â â â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â â â â â¡â¡â¡â â â â¡â¡â¡ â¡â â¡â¡â â¡â¡â¡â¡â¡â¡â â â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â â â â â â¡â¡â¡â â¡â¡â¡â¡ â¡â â¡â¡â â¡â¡â¡â¡â¡â â¡ â â â â â â â â â â â â â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡ â â â â¡â¡â â â â â â¡â¡ â â¡â¡â¡â¡â¡â¡â¡â¡â¡â¡â | 35,317 |
Score : 1700 points Problem Statement Snuke got a grid from his mother, as a birthday present. The grid has H rows and W columns. Each cell is painted black or white. All black cells are 4-connected , that is, it is possible to traverse from any black cell to any other black cell by just visiting black cells, where it is only allowed to move horizontally or vertically. The color of the cell at the i -th row and j -th column (1 ⊠i ⊠H, 1 ⊠j ⊠W) is represented by a character s_{ij} . If s_{ij} is # , the cell is painted black. If s_{ij} is . , the cell is painted white. At least one cell is painted black. We will define fractals as follows. The fractal of level 0 is a 1 à 1 grid with a black cell. The fractal of level k+1 is obtained by arranging smaller grids in H rows and W columns, following the pattern of the Snuke's grid. At a position that corresponds to a black cell in the Snuke's grid, a copy of the fractal of level k is placed. At a position that corresponds to a white cell in the Snuke's grid, a grid whose cells are all white, with the same dimensions as the fractal of level k , is placed. You are given the description of the Snuke's grid, and an integer K . Find the number of connected components of black cells in the fractal of level K , modulo 10^9+7 . Constraints 1 ⊠H,W ⊠1000 0 ⊠K ⊠10^{18} Each s_{ij} is either # or . . All black cells in the given grid are 4-connected. There is at least one black cell in the given grid. Input The input is given from Standard Input in the following format: H W K s_{11} .. s_{1W} : s_{H1} .. s_{HW} Output Print the number of connected components of black cells in the fractal of level K , modulo 10^9+7 . Sample Input 1 3 3 3 .#. ### #.# Sample Output 1 20 The fractal of level K=3 in this case is shown below. There are 20 connected components of black cells. .............#............. ............###............ ............#.#............ ..........#..#..#.......... .........#########......... .........#.##.##.#......... ..........#.....#.......... .........###...###......... .........#.#...#.#......... ....#........#........#.... ...###......###......###... ...#.#......#.#......#.#... .#..#..#..#..#..#..#..#..#. ########################### #.##.##.##.##.##.##.##.##.# .#.....#..#.....#..#.....#. ###...######...######...### #.#...#.##.#...#.##.#...#.# ....#.................#.... ...###...............###... ...#.#...............#.#... .#..#..#...........#..#..#. #########.........######### #.##.##.#.........#.##.##.# .#.....#...........#.....#. ###...###.........###...### #.#...#.#.........#.#...#.# Sample Input 2 3 3 3 ### #.# ### Sample Output 2 1 Sample Input 3 11 15 1000000000000000000 .....#......... ....###........ ....####....... ...######...... ...#######..... ..##.###.##.... ..##########... .###.....####.. .####...######. ############### #.##..##..##..# Sample Output 3 301811921 | 35,318 |
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¥åããããšåã圢åŒã§åºåããïŒ ããŒã¿ã»ããã®éã«ã¯1è¡ã®ç©ºè¡ãåºåããïŒ æåŸã®ããŒã¿ã»ããã®åŸã«äœèšãªç©ºè¡ãåºåããªããã泚æããããšïŒ Sample Input 4 4 6 *.*..* *..... ..-... ^.*#.. 10 SRSSRRUSSR 2 2 <. .. 12 DDSRRSUUSLLS 3 5 >-#** .-*#* .-**# 15 SSSDRSSSDRSSSUU 5 5 v**** ***** ***** ***** ***** 44 SSSSDDRSDRSRDSULUURSSSSRRRRDSSSSDDLSDLSDLSSD Output for the Sample Input *....* ...... ..-... ..>#.. <. .. ^-#** .-.#* .-..# ..... .***. ..*.. ..*.. ....v | 35,319 |
Problem H Homework Taro is a student of Ibaraki College of Prominent Computing. In this semester, he takes two courses, mathematics and informatics. After each class, the teacher may assign homework. Taro may be given multiple assignments in a single class, and each assignment may have a different deadline. Each assignment has a unique ID number. Everyday after school, Taro completes at most one assignment as follows. First, he decides which course's homework to do at random by ipping a coin. Let $S$ be the set of all the unfinished assignments of the chosen course whose deadline has not yet passed. If $S$ is empty, he plays a video game without doing any homework on that day even if there are unfinished assignments of the other course. Otherwise, with $T \subseteq S$ being the set of assignments with the nearest deadline among $S$, he completes the one with the smallest assignment ID among $T$. The number of assignments Taro will complete until the end of the semester depends on the result of coin ips. Given the schedule of homework assignments, your task is to compute the maximum and the minimum numbers of assignments Taro will complete. Input The input consists of a single test case in the following format. $n$ $m$ $s_1$ $t_1$ ... $s_n$ $t_n$ The first line contains two integers $n$ and $m$ satisfying $1 \leq m < n \leq 400$. $n$ denotes the total number of assignments in this semester, and $m$ denotes the number of assignments of the mathematics course (so the number of assignments of the informatics course is $n - m$). Each assignment has a unique ID from $1$ to $n$; assignments with IDs $1$ through $m$ are those of the mathematics course, and the rest are of the informatics course. The next $n$ lines show the schedule of assignments. The $i$-th line of them contains two integers $s_i$ and $t_i$ satisfying $1 \leq s_i \leq t_i \leq 400$, which means that the assignment of ID $i$ is given to Taro on the $s_i$-th day of the semester, and its deadline is the end of the $t_i$-th day. Output In the first line, print the maximum number of assignments Taro will complete. In the second line, print the minimum number of assignments Taro will complete. Sample Input 1 6 3 1 2 1 5 2 3 2 6 4 5 4 6 Sample Output 1 6 2 Sample Input 2 6 3 1 1 2 3 4 4 1 1 2 4 3 3 Sample Output 2 4 3 | 35,320 |
Score : 300 points Problem Statement There are N+1 towns. The i -th town is being attacked by A_i monsters. We have N heroes. The i -th hero can defeat monsters attacking the i -th or (i+1) -th town, for a total of at most B_i monsters. What is the maximum total number of monsters the heroes can cooperate to defeat? Constraints All values in input are integers. 1 \leq N \leq 10^5 1 \leq A_i \leq 10^9 1 \leq B_i \leq 10^9 Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_{N+1} B_1 B_2 ... B_N Output Print the maximum total number of monsters the heroes can defeat. Sample Input 1 2 3 5 2 4 5 Sample Output 1 9 If the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result. The first hero defeats two monsters attacking the first town and two monsters attacking the second town. The second hero defeats three monsters attacking the second town and two monsters attacking the third town. Sample Input 2 3 5 6 3 8 5 100 8 Sample Output 2 22 Sample Input 3 2 100 1 1 1 100 Sample Output 3 3 | 35,321 |
J - Tree Reconstruction Problem Statement You have a directed graph. Some non-negative value is assigned on each edge of the graph. You know that the value of the graph satisfies the flow conservation law That is, for every node v , the sum of values on edges incoming to v equals to the sum of values of edges outgoing from v . For example, the following directed graph satisfies the flow conservation law. Suppose that you choose a subset of edges in the graph, denoted by E' , and then you erase all the values on edges other than E' . Now you want to recover the erased values by seeing only remaining information. Due to the flow conservation law, it may be possible to recover all the erased values. Your task is to calculate the smallest possible size for such E' . For example, the smallest subset E' for the above graph will be green edges in the following figure. By the flow conservation law, we can recover values on gray edges. Input The input consists of multiple test cases. The format of each test case is as follows. N M s_1 t_1 ... s_M t_M The first line contains two integers N ( 1 \leq N \leq 500 ) and M ( 0 \leq M \leq 3,000 ) that indicate the number of nodes and edges, respectively. Each of the following M lines consists of two integers s_i and t_i ( 1 \leq s_i, t_i \leq N ). This means that there is an edge from s_i to t_i in the graph. You may assume that the given graph is simple: There are no self-loops: s_i \neq t_i . There are no multi-edges: for all i < j , \{s_i, t_i\} \neq \{s_j, t_j\} . Also, it is guaranteed that each component of the given graph is strongly connected. That is, for every pair of nodes v and u , if there exist a path from v to u , then there exists a path from u to v . Note that you are NOT given information of values on edges because it does not effect the answer. Output For each test case, print an answer in one line. Sample Input 1 9 13 1 2 1 3 2 9 3 4 3 5 3 6 4 9 5 7 6 7 6 8 7 9 8 9 9 1 Output for the Sample Input 1 5 Sample Input 2 7 9 1 2 1 3 2 4 3 4 4 5 4 6 5 7 6 7 7 1 Output for the Sample Input 2 3 Sample Input 3 4 4 1 2 2 1 3 4 4 3 Output for the Sample Input 3 2 | 35,322 |
Problem E: Alice and Bomb Alice and Bob were in love with each other, but they hate each other now. One day, Alice found a bag. It looks like a bag that Bob had used when they go on a date. Suddenly Alice heard tick-tack sound. Alice intuitively thought that Bob is to kill her with a bomb. Fortunately, the bomb has not exploded yet, and there may be a little time remained to hide behind the buildings. The appearance of the ACM city can be viewed as an infinite plane and each building forms a polygon. Alice is considered as a point and the bomb blast may reach Alice if the line segment which connects Alice and the bomb does not intersect an interior position of any building. Assume that the speed of bomb blast is infinite; when the bomb explodes, its blast wave will reach anywhere immediately, unless the bomb blast is interrupted by some buildings. The figure below shows the example of the bomb explosion. Left figure shows the bomb and the buildings(the polygons filled with black). Right figure shows the area(colored with gray) which is under the effect of blast wave after the bomb explosion. Figure 6: The example of the bomb explosion Note that even if the line segment connecting Alice and the bomb touches a border of a building, bomb blast still can blow off Alice. Since Alice wants to escape early, she wants to minimize the length she runs in order to make herself hidden by the building. Your task is to write a program which reads the positions of Alice, the bomb and the buildings and calculate the minimum distance required for Alice to run and hide behind the building. Input The input contains multiple test cases. Each test case has the following format: N bx by m 1 x 1,1 y 1,1 ... x 1, m 1 y 1, m 1 . . . m N x N ,1 y N ,1 ... x N , m N y N , m N The first line of each test case contains an integer N (1 †N †100), which denotes the number of buildings. In the second line, there are two integers bx and by (-10000 †bx , by †10000), which means the location of the bomb. Then, N lines follows, indicating the information of the buildings. The information of building is given as a polygon which consists of points. For each line, it has an integer m i (3 †m i †100, â N i =1 m i †500) meaning the number of points the polygon has, and then m i pairs of integers x i,j , y i,j follow providing the x and y coordinate of the point. You can assume that the polygon does not have self-intersections. any two polygons do not have a common point. the set of points is given in the counter-clockwise order. the initial positions of Alice and bomb will not by located inside the polygon. there are no bomb on the any extended lines of the given polygonâs segment. Alice is initially located at (0, 0). It is possible that Alice is located at the boundary of a polygon. N = 0 denotes the end of the input. You may not process this as a test case. Output For each test case, output one line which consists of the minimum distance required for Alice to run and hide behind the building. An absolute error or relative error in your answer must be less than 10 -6 . Sample Input 1 1 1 4 -1 0 -2 -1 -1 -2 0 -1 1 0 3 4 1 1 1 2 -1 2 -1 1 1 -6 -6 6 1 -2 2 -2 2 3 -2 3 -2 1 1 1 1 -10 0 4 0 -5 1 -5 1 5 0 5 1 10 1 4 5 1 6 2 5 3 4 2 2 -47 -37 4 14 3 20 13 9 12 15 9 4 -38 -3 -34 -19 -34 -14 -24 -10 0 Output for the Sample Input 1.00000000 0.00000000 3.23606798 5.00000000 1.00000000 11.78517297 | 35,323 |
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Problem C: Area of Polygons Yokoâs math homework today was to calculate areas of polygons in the xy -plane. Vertices are all aligned to grid points (i.e. they have integer coordinates). Your job is to help Yoko, not good either at math or at computer programming, get her home- work done. A polygon is given by listing the coordinates of its vertices. Your program should approximate its area by counting the number of unit squares (whose vertices are also grid points) intersecting the polygon. Precisely, a unit square âintersects the polygonâ if and only if the in- tersection of the two has non-zero area. In the figure below, dashed horizontal and vertical lines are grid lines, and solid lines are edges of the polygon. Shaded unit squares are considered inter- secting the polygon. Your program should output 55 for this polygon (as you see, the number of shaded unit squares is 55). Figure 1: A polygon and unit squares intersecting it Input The input file describes polygons one after another, followed by a terminating line that only contains a single zero. A description of a polygon begins with a line containing a single integer, m (⥠3), that gives the number of its vertices. It is followed by m lines, each containing two integers x and y , the coordinates of a vertex. The x and y are separated by a single space. The i -th of these m lines gives the coordinates of the i -th vertex ( i = 1, ... , m ). For each i = 1, ... , m - 1, the i -th vertex and the ( i + 1)-th vertex are connected by an edge. The m -th vertex and the first vertex are also connected by an edge (i.e., the curve is closed). Edges intersect only at vertices. No three edges share a single vertex (i.e., the curve is simple). The number of polygons is no more than 100. For each polygon, the number of vertices ( m ) is no more than 100. All coordinates x and y satisfy -2000 †x †2000 and -2000 †y †2000. Output The output should consist of as many lines as the number of polygons. The k -th output line should print an integer which is the area of the k -th polygon, approximated in the way described above. No other characters, including whitespaces, should be printed. Sample Input 4 5 -3 1 0 1 7 -7 -1 3 5 5 18 5 5 10 3 -5 -5 -5 -10 -18 -10 5 0 0 20 2 11 1 21 2 2 0 0 Output for the Sample Input 55 41 41 23 | 35,325 |
Ievan Ritola is a researcher of behavioral ecology. Her group visited a forest to analyze an ecological system of some kinds of foxes. The forest can be expressed as a two-dimensional plane. With her previous research, foxes in the forest are known to live at lattice points. Here, lattice points are the points whose x and y coordinates are both integers. Two or more foxes might live at the same point. To observe the biology of these foxes, they decided to put a pair of sensors in the forest. The sensors can be put at lattice points. Then, they will be able to observe all foxes inside the bounding rectangle (including the boundary) where the sensors are catty-corner to each other. The sensors cannot be placed at the points that have the same x or y coordinate; in other words the rectangle must have non-zero area. The more foxes can be observed, the more data can be collected; on the other hand, monitoring a large area consumes a large amount of energy. So they want to maximize the value given by N' / (|x_1 â x_2| à |y_1 â y_2|) , where N' is the number of foxes observed and (x_1, y_1) and (x_2, y_2) are the positions of the two sensors. Let's help her observe cute foxes! Input The input is formatted as follows. N x_1 y_1 w_1 x_2 y_2 w_2 : : x_N y_N w_N The first line contains a single integer N ( 1 †N †10^5 ) indicating the number of the fox lairs in the forest. Each of the next N lines contains three integers x_i , y_i ( |x_i|,\, |y_i| †10^9 ) and w_i ( 1 †w_i †10^4 ), which represent there are w_i foxes at the point (x_i, y_i) . It is guaranteed that all points are mutually different. Output Output the maximized value as a fraction: a / b where a and b are integers representing the numerator and the denominato respectively. There should be exactly one space before and after the slash. The fraction should be written in the simplest form, that is, a and b must not have a common integer divisor greater than one. If the value becomes an integer, print a fraction with the denominator of one (e.g. 5 / 1 to represent 5). This implies zero should be printed as 0 / 1 (without quotes). Sample Input 1 2 1 1 2 2 2 3 Output for the Sample Input 1 5 / 1 | 35,326 |
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šéšã€ãªããŠãïŒæåããšã«åºåã£ãŠã¿ãªããã ããŒã¿ãŒ : ã¯ãã¯ããã€ãªããŠåºåããšã 11111 00011 11101 00010 11110 01010 01110 01111 10100 0 ãããªæãã«ãªããŸããããã©ãæåŸã®ã0ãã ãã®ãã€ã¯ã©ãããŸãã? å士 : ïŒãä»ãå ããŠïŒæåã«ããŠãããŠããã ããŒã¿ãŒ : ããŒãšæåŸãïŒã1åã ãã ããïŒãããšïŒã€å ããŠããã°ãããã§ãããã§ããŸããã 11111 00011 11101 00010 11110 01010 01110 01111 10100 00000 å士 : 次ã¯ãã®è¡šã䜿ãã®ã ã ç¬Šå· æå 00000 A 00001 B 00010 C 00011 D 00100 E 00101 F 00110 G 00111 H ç¬Šå· æå 01000 I 01001 J 01010 K 01011 L 01100 M 01101 N 01110 O 01111 P ç¬Šå· æå 10000 Q 10001 R 10010 S 10011 T 10100 U 10101 V 10110 W 10111 X ç¬Šå· æå 11000 Y 11001 Z 11010 ïŒç©ºçœïŒ 11011 . 11100 , 11101 - 11110 ' 11111 ? ããŒã¿ãŒ : ãããã©ã䜿ããã§ããâŠããã!ä»åºŠã¯ç¬Šå·ããæåã«çœ®ãæããã®ã! å士 : ãããããã11111ãã ã£ããã?ãã«ãã00011ãã ã£ãããDãã«ãšãã£ãŠããã°ãããã ãã ããŒã¿ãŒ : ããã¯åçŽã§ããâŠâŠããŒãšã?D-C'KOPUAãã«ãªããŸãããã§ãæå³äžæã§ããã å士 : æåæ°ãæ°ããŠãããã ããŒã¿ãŒ : ïŒïŒæåã§ããããã£ããPETER POTTERãã¯ïŒïŒæåã ã£ãã®ã«ïŒæåæžã£ãŠããŸãã å士 : ããããã®è¡šã䜿ãã°æåãæžããããšãã§ããã®ã ãããããä»åºŠã¯ãã®æç« ã§åãããšãã㣠ãŠãããã PETER PIPER PICKED A PECK OF PICKLED PEPPERS. A PECK OF PICKLED PEPPERS PETER PIPER PICKED. IF PETER PIPER PICKED A PECK OF PICKLED PEPPERS, WHERE'S THE PECK OF PICKLED PEPPERS PETER PIPER PICKED? ããŒã¿ãŒ : ãããããè¡ãåãããŠããŸãããã©ããããã§ãã? å士 : çŽã®éœåã§ïŒè¡ã«ãªã£ãŠããŸã£ãããæ¹è¡æåã®ãããã«ç©ºçœãããé·ãïŒè¡ã ãšæã£ãŠãããã ããŒã¿ãŒ : ã¯ãã¯ããè¡ãšè¡ã®éã«ããã®ã¯ç©ºçœã ãšããããé¢åã ãªâŠâŠã å士 : ã ã£ããããã°ã©ã ã«ããããã°ããã§ã¯ãªããã ãšããããšã§ãããŒã¿ãŒã®ä»£ããã«ãèªã¿èŸŒãã æååã笊å·ã«å€æãåºåããããã°ã©ã ãäœæããŠãã ããã å
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ããŸããã Output åããŒã¿ã»ããã«ã€ããŠãçåã®å Žå㯠OKãããã§ãªãå Žå㯠NA ãïŒè¡ã«åºåããŠãã ããã Sample Input 6 1 10 6 4 3 3 1 2 0 5 4 6 1 8 5 9 7 7 8 6 8 3 6 1 10 6 4 3 3 1 2 0 5 4 6 1 8 5 9 7 7 8 6 9 0 0 0 Output for the Sample Input OK NA | 35,329 |
Score : 500 points Problem Statement There are N Snuke Cats numbered 1, 2, \ldots, N , where N is even . Each Snuke Cat wears a red scarf, on which his favorite non-negative integer is written. Recently, they learned the operation called xor (exclusive OR). What is xor? For n non-negative integers x_1, x_2, \ldots, x_n , their xor, x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~x_n is defined as follows: When x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~x_n is written in base two, the digit in the 2^k 's place ( k \geq 0 ) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k 's place is odd, and 0 if that count is even. For example, 3~\textrm{xor}~5 = 6 . They wanted to use this operation quickly, so each of them calculated the xor of the integers written on their scarfs except his scarf. We know that the xor calculated by Snuke Cat i , that is, the xor of the integers written on the scarfs except the scarf of Snuke Cat i is a_i . Using this information, restore the integer written on the scarf of each Snuke Cat. Constraints All values in input are integers. 2 \leq N \leq 200000 N is even . 0 \leq a_i \leq 10^9 There exists a combination of integers on the scarfs that is consistent with the given information. Input Input is given from Standard Input in the following format: N a_1 a_2 \ldots a_N Output Print a line containing N integers separated with space. The i -th of the integers from the left should represent the integer written on the scarf of Snuke Cat i . If there are multiple possible solutions, you may print any of them. Sample Input 1 4 20 11 9 24 Sample Output 1 26 5 7 22 5~\textrm{xor}~7~\textrm{xor}~22 = 20 26~\textrm{xor}~7~\textrm{xor}~22 = 11 26~\textrm{xor}~5~\textrm{xor}~22 = 9 26~\textrm{xor}~5~\textrm{xor}~7 = 24 Thus, this output is consistent with the given information. | 35,330 |
Score : 1000 points Problem Statement Rng is baking cookies. Initially, he can bake one cookie per second. He can also eat the cookies baked by himself. When there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x . Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1 . When he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them. It takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked. He wants to give N cookies to Grandma. Find the shortest time needed to produce at least N cookies not yet eaten. Constraints 1âŠNâŠ10^{12} 0âŠAâŠ10^{12} A is an integer. Partial Score 500 points will be awarded for passing the test set satisfying NâŠ10^6 and AâŠ10^6 . Additional 500 points will be awarded for passing the test set without additional constraints. Input The input is given from Standard Input in the following format: N A Output Print the shortest time needed to produce at least N cookies not yet eaten. Sample Input 1 8 1 Sample Output 1 7 It is possible to produce 8 cookies in 7 seconds, as follows: After 1 second: 1 cookie is done. After 2 seconds: 1 more cookie is done, totaling 2 . Now, Rng starts eating those 2 cookies. After 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second. After 4 seconds: 2 cookies are done. After 5 seconds: 2 more cookies are done, totaling 4 . After 6 seconds: 2 more cookies are done, totaling 6 . After 7 seconds: 2 more cookies are done, totaling 8 . Sample Input 2 1000000000000 1000000000000 Sample Output 2 1000000000000 | 35,331 |
Score : 100 points Problem Statement You are given a string S consisting of letters b , d , p and q . Determine whether S is a mirror string . Here, a mirror string is a string S such that the following sequence of operations on S results in the same string S : Reverse the order of the characters in S . Replace each occurrence of b by d , d by b , p by q , and q by p , simultaneously. Constraints 1 \leq |S| \leq 10^5 S consists of letters b , d , p , and q . Input The input is given from Standard Input in the following format: S Output If S is a mirror string, print Yes . Otherwise, print No . Sample Input 1 pdbq Sample Output 1 Yes Sample Input 2 ppqb Sample Output 2 No | 35,332 |
Stable Sort Let's arrange a deck of cards. There are totally 36 cards of 4 suits(S, H, C, D) and 9 values (1, 2, ... 9). For example, 'eight of heart' is represented by H8 and 'one of diamonds' is represented by D1 . Your task is to write a program which sorts a given set of cards in ascending order by their values using the Bubble Sort algorithms and the Selection Sort algorithm respectively. These algorithms should be based on the following pseudocode: BubbleSort(C) 1 for i = 0 to C.length-1 2 for j = C.length-1 downto i+1 3 if C[j].value < C[j-1].value 4 swap C[j] and C[j-1] SelectionSort(C) 1 for i = 0 to C.length-1 2 mini = i 3 for j = i to C.length-1 4 if C[j].value < C[mini].value 5 mini = j 6 swap C[i] and C[mini] Note that, indices for array elements are based on 0-origin. For each algorithm, report the stability of the output for the given input (instance). Here, 'stability of the output' means that: cards with the same value appear in the output in the same order as they do in the input (instance). Input The first line contains an integer N , the number of cards. N cards are given in the following line. Each card is represented by two characters. Two consecutive cards are separated by a space character. Output In the first line, print the arranged cards provided by the Bubble Sort algorithm. Two consecutive cards should be separated by a space character. In the second line, print the stability (" Stable " or " Not stable ") of this output. In the third line, print the arranged cards provided by the Selection Sort algorithm. Two consecutive cards should be separated by a space character. In the fourth line, print the stability (" Stable " or " Not stable ") of this output. Constraints 1 †N †36 Sample Input 1 5 H4 C9 S4 D2 C3 Sample Output 1 D2 C3 H4 S4 C9 Stable D2 C3 S4 H4 C9 Not stable Sample Input 2 2 S1 H1 Sample Output 2 S1 H1 Stable S1 H1 Stable | 35,333 |
Score : 1200 points Problem Statement Snuke is playing with red and blue balls, placing them on a two-dimensional plane. First, he performed N operations to place red balls. In the i -th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i) . Then, he performed another N operations to place blue balls. In the i -th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i) . The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i . Let this value be S . Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by| . Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs. Constraints 1 \leq N \leq 1000 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9 1 \leq RC_i,BC_i \leq 10 \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i All values in input are integers. Input Input is given from Standard Input in the following format: N RX_1 RY_1 RC_1 RX_2 RY_2 RC_2 \vdots RX_N RY_N RC_N BX_1 BY_1 BC_1 BX_2 BY_2 BC_2 \vdots BX_N BY_N BC_N Output Print the maximum possible sum of the scores of the pairs. Sample Input 1 2 0 0 1 3 2 1 2 2 1 5 0 1 Sample Output 1 8 If we pair the red ball at coordinates (0,0) and the blue ball at coordinates (2,2) , the score of this pair is |0-2| + |0-2|=4 . Then, if we pair the red ball at coordinates (3,2) and the blue ball at coordinates (5,0) , the score of this pair is |3-5| + |2-0|=4 . Making these two pairs results in the total score of 8 , which is the maximum result. Sample Input 2 3 0 0 1 2 2 1 0 0 2 1 1 1 1 1 1 3 3 2 Sample Output 2 16 Snuke may have performed multiple operations at the same coordinates. Sample Input 3 10 582463373 690528069 8 621230322 318051944 4 356524296 974059503 6 372751381 111542460 9 392867214 581476334 6 606955458 513028121 5 882201596 791660614 9 250465517 91918758 3 618624774 406956634 6 426294747 736401096 5 974896051 888765942 5 726682138 336960821 3 715144179 82444709 6 599055841 501257806 6 390484433 962747856 4 912334580 219343832 8 570458984 648862300 6 638017635 572157978 10 435958984 585073520 7 445612658 234265014 6 Sample Output 3 45152033546 | 35,334 |
Score : 200 points Problem Statement An X -layered kagami mochi (X ⥠1) is a pile of X round mochi (rice cake) stacked vertically where each mochi (except the bottom one) has a smaller diameter than that of the mochi directly below it. For example, if you stack three mochi with diameters of 10 , 8 and 6 centimeters from bottom to top in this order, you have a 3 -layered kagami mochi; if you put just one mochi, you have a 1 -layered kagami mochi. Lunlun the dachshund has N round mochi, and the diameter of the i -th mochi is d_i centimeters. When we make a kagami mochi using some or all of them, at most how many layers can our kagami mochi have? Constraints 1 †N †100 1 †d_i †100 All input values are integers. Input Input is given from Standard Input in the following format: N d_1 : d_N Output Print the maximum number of layers in a kagami mochi that can be made. Sample Input 1 4 10 8 8 6 Sample Output 1 3 If we stack the mochi with diameters of 10 , 8 and 6 centimeters from bottom to top in this order, we have a 3 -layered kagami mochi, which is the maximum number of layers. Sample Input 2 3 15 15 15 Sample Output 2 1 When all the mochi have the same diameter, we can only have a 1 -layered kagami mochi. Sample Input 3 7 50 30 50 100 50 80 30 Sample Output 3 4 | 35,335 |
Problem D: Rock Man You were the master craftsman in the stone age, and you devoted your life to carving many varieties of tools out of natural stones. Your works have ever been displayed respectfully in many museums, even in 2006 A.D. However, most people visiting the museums do not spend so much time to look at your works. Seeing the situation from the Heaven, you brought back memories of those days you had frantically lived. One day in your busiest days, you got a number of orders for making tools. Each order requested one tool which was different from the other orders. It often took some days to fill one order without special tools. But you could use tools which you had already made completely, in order to carve new tools more quickly. For each tool in the list of the orders, there was exactly one tool which could support carving it. In those days, your schedule to fill the orders was not so efficient. You are now thinking of making the most efficient schedule, i.e. the schedule for all orders being filled in the shortest days, using the program you are going to write. Input The input consists of a series of test cases. Each case begins with a line containing a single integer N which represents the number of ordered tools. Then N lines follow, each specifying an order by four elements separated by one or more space: name , day 1 , sup and day 2 . name is the name of the tool in the corresponding order. day 1 is the number of required days to make the tool without any support tool. sup is the name of the tool that can support carving the target tool. day 2 is the number of required days make the tool with the corresponding support tool. The input terminates with the case where N = 0. You should not process this case. You can assume that the input follows the constraints below: N †1000; name consists of no longer than 32 non-space characters, and is unique in each case; sup is one of all names given in the same case; and 0 < day 2 < day 1 < 20000. Output For each test case, output a single line containing an integer which represents the minimum number of days required to fill all N orders. Sample Input 3 gu 20 pa 10 ci 20 gu 10 pa 20 ci 10 2 tool 20 tool 10 product 1000 tool 10 8 fishhook 21 disk 3 mill 14 axe 7 boomerang 56 sundial 28 flint 35 fishhook 5 axe 35 flint 14 disk 42 disk 2 sundial 14 disk 7 hammer 28 mill 7 0 Output for the Sample Input 40 30 113 | 35,336 |
Score : 100 points Problem Statement You are given strings s and t . Find one longest string that is a subsequence of both s and t . Notes A subsequence of a string x is the string obtained by removing zero or more characters from x and concatenating the remaining characters without changing the order. Constraints s and t are strings consisting of lowercase English letters. 1 \leq |s|, |t| \leq 3000 Input Input is given from Standard Input in the following format: s t Output Print one longest string that is a subsequence of both s and t . If there are multiple such strings, any of them will be accepted. Sample Input 1 axyb abyxb Sample Output 1 axb The answer is axb or ayb ; either will be accepted. Sample Input 2 aa xayaz Sample Output 2 aa Sample Input 3 a z Sample Output 3 The answer is (an empty string). Sample Input 4 abracadabra avadakedavra Sample Output 4 aaadara | 35,337 |
Longest Lane Mr. KM, the mayor of KM city, decided to build a new elementary school. The site for the school has an awkward polygonal shape, which caused several problems. The most serious problem was that there was not enough space for a short distance racetrack. Your task is to help Mr. KM to calculate the maximum possible length for the racetrack that can be built in the site. The track can be considered as a straight line segment whose width can be ignored. The boundary of the site has a simple polygonal shape without self-intersection, and the track can touch the boundary. Note that the boundary might not be convex. Input The input consists of multiple test cases, followed by a line containing "0". Each test case has the following format. The first line contains an integer N ( 3 \leq N \leq 100 ). Each of the following N lines contains two integers x_i and y_i ( -1,000 \leq x_i, y_i \leq 1,000 ), which describe the coordinates of a vertex of the polygonal border of the site, in counterclockwise order. Output For each test case, print its case number and the maximum possible length of the track in a line. The answer should be given as a floating point number with an absolute error of at most 10^{-6} . Sample Input 4 0 0 10 0 10 10 0 10 3 0 0 1 0 0 1 0 Output for the Sample Input Case 1: 14.142135624 Case 2: 1.41421356 | 35,338 |
Score : 500 points Problem Statement In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi. Takahashi checked and found that the time gap (defined below) between the local times in his city and the i -th person's city was D_i hours. The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours. Here, we are using 24 -hour notation. That is, the local time in the i -th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example. Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours. Find the maximum possible value of s . Constraints 1 \leq N \leq 50 0 \leq D_i \leq 12 All input values are integers. Input Input is given from Standard Input in the following format: N D_1 D_2 ... D_N Output Print the maximum possible value of s . Sample Input 1 3 7 12 8 Sample Output 1 4 For example, consider the situation where it is 7 , 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours. Sample Input 2 2 11 11 Sample Output 2 2 Sample Input 3 1 0 Sample Output 3 0 Note that Takahashi himself is also a participant. | 35,339 |
Score: 400 points Problem Statement We have N integers A_1, A_2, ..., A_N . There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K -th number in that list? Constraints All values in input are integers. 2 \leq N \leq 2 \times 10^5 1 \leq K \leq \frac{N(N-1)}{2} -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N) Input Input is given from Standard Input in the following format: N K A_1 A_2 \dots A_N Output Print the answer. Sample Input 1 4 3 3 3 -4 -2 Sample Output 1 -6 There are six ways to form a pair. The products of those pairs are 9 , -12 , -6 , -12 , -6 , 8 . Sorting those numbers in ascending order, we have -12 , -12 , -6 , -6 , 8 , 9 . The third number in this list is -6 . Sample Input 2 10 40 5 4 3 2 -1 0 0 0 0 0 Sample Output 2 6 Sample Input 3 30 413 -170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0 Sample Output 3 448283280358331064 | 35,340 |
Problem D: Off Balance You are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building. Submitted designs will look like a screenshot of a well known game as shown below. This is because the center specifies that the building should be constructed by stacking regular units called pieces , each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions. All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position. All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse. The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces. The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below. It will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows. Assume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy -coordinates of its left-bottom corner. The unit length is the edge length of a block. Among the blocks of the piece that touch another piece or the ground on their bottom faces, let x L be the leftmost x -coordinate of the leftmost block, and let x R be the rightmost x -coordinate of the rightmost block. Let the x -coordinate of its accumulated center of mass of the piece be M , where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P , in addition to P itself. Then the piece is stable, if and only if x L < M < x R . Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable. Note that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable. Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable. Write a program that judges stability of each design based on the above quick check rules. Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset, which represents a front view of a building, is formatted as follows. w h p 0( h -1) p 1( h -1) ... p ( w -1)( h -1) ... p 01 p 11 ... p ( w -1)1 p 00 p 10 ... p ( w -1)0 The integers w and h separated by a space are the numbers of columns and rows of the layout, respectively. You may assume 1 †w †10 and 1 †h †60. The next h lines specify the placement of the pieces. The character p xy indicates the status of a block at ( x , y ), either ` . ', meaning empty, or one digit character between ` 1 ' and ` 9 ', inclusive, meaning a block of a piece. (As mentioned earlier, we denote a location of a block by xy -coordinates of its left-bottom corner.) When two blocks with the same number touch each other by any of their top, bottom, left or right face, those blocks are of the same piece. (Note that there might be two different pieces that are denoted by the same number.) The bottom of a block at ( x ,0) touches the ground. You may assume that the pieces in each dataset are stacked in a tree-like form. Output For each dataset, output a line containing a word STABLE when the design is stable with respect to the above quick check rules. Otherwise, output UNSTABLE . The output should be written with uppercase letters, and should not contain any other extra characters. Sample Input 4 5 ..33 ..33 2222 ..1. .111 5 7 ....1 .1..1 .1..1 11..1 .2222 ..111 ...1. 3 6 .3. 233 23. 22. .11 .11 4 3 2222 ..11 ..11 4 5 .3.. 33.. 322. 2211 .11. 3 3 222 2.1 111 3 4 11. 11. .2. 222 3 4 .11 .11 .2. 222 2 7 11 .1 21 22 23 .3 33 2 3 1. 11 .1 0 0 Output for the Sample Input STABLE STABLE STABLE UNSTABLE STABLE STABLE UNSTABLE UNSTABLE UNSTABLE UNSTABLE | 35,341 |
Score : 600 points Problem Statement On the x y -plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t) . He can move in arbitrary directions with speed 1 . Here, we will consider him as a point without size. There are N circular barriers deployed on the plane. The center and the radius of the i -th barrier are (x_i, y_i) and r_i , respectively. The barriers may overlap or contain each other. A point on the plane is exposed to cosmic rays if the point is not within any of the barriers. Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel. Constraints All input values are integers. -10^9 †x_s, y_s, x_t, y_t †10^9 (x_s, y_s) â (x_t, y_t) 1â€Nâ€1,000 -10^9 †x_i, y_i †10^9 1 †r_i †10^9 Input The input is given from Standard Input in the following format: x_s y_s x_t y_t N x_1 y_1 r_1 x_2 y_2 r_2 : x_N y_N r_N Output Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9} . Sample Input 1 -2 -2 2 2 1 0 0 1 Sample Output 1 3.6568542495 An optimal route is as follows: Sample Input 2 -2 0 2 0 2 -1 0 2 1 0 2 Sample Output 2 0.0000000000 An optimal route is as follows: Sample Input 3 4 -2 -2 4 3 0 0 2 4 0 1 0 4 1 Sample Output 3 4.0000000000 An optimal route is as follows: | 35,342 |
Chinese Postman Problem For a given weighted undirected graph G(V, E) , find the distance of the shortest route that meets the following criteria: It is a closed cycle where it ends at the same point it starts. The route must go through every edge at least once. Input |V| |E| s 0 t 0 d 0 s 1 t 1 d 1 : s |E|-1 t |E|-1 d |E|-1 , where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V| -1 respectively. s i and t i represent source and target verticess of i -th edge (undirected) and d i represents the distance between s i and t i (the i -th edge). Note that there can be multiple edges between a pair of vertices. Output Print the shortest distance in a line. Constraints 2 †|V| †15 0 †|E| †1,000 0 †d i †1,000 s i â t i The graph is connected Sample Input 1 4 4 0 1 1 0 2 2 1 3 3 2 3 4 Sample Output 1 10 Sample Input 2 4 5 0 1 1 0 2 2 1 3 3 2 3 4 1 2 5 Sample Output 2 18 Sample Input 3 2 3 0 1 1 0 1 2 0 1 3 Sample Output 3 7 | 35,343 |
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Problem J: Exhibition The city government is planning an exhibition and collecting industrial products. There are $n$ candidates of industrial products for the exhibition, and the city government decided to choose $k$ of them. They want to minimize the total price of the $k$ products. However, other criteria such as their sizes and weights should be also taken into account. To address this issue, the city government decided to use the following strategy: The $i$-th product has three parameters, price, size, and weight, denoted by $x_i$, $y_i$, and $z_i$, respectively. Then, the city government chooses $k$ items $i_1, . . . , i_k$ ($1 \leq i_j \leq n$) that minimizes the evaluation measure \[ e = (\sum^k_{j=1}x_{ij}) (\sum^k_{j=1}y_{ij}) (\sum^k_{j=1}z_{ij}), \] which incorporates the prices, the sizes, and the weights of products. If there are two or more choices that minimize $e$, the government chooses one of them uniformly at random. You are working for the company that makes the product 1. The company has decided to cut the price, reduce the size, and/or reduce the weight of the product so that the city government may choose the product of your company, that is, to make the probability of choosing the product positive. We have three parameters $A$, $B$, and $C$. If we want to reduce the price, size, and weight to $(1 â \alpha)x_1$, $(1 â \beta)y_1$, and $(1 â \gamma)z_1$ ($0 \leq \alpha, \beta, \gamma \leq 1$), respectively, then we have to invest $\alpha A + \beta B + \gamma C$ million yen. We note that the resulting price, size, and weight do not have to be integers. Your task is to compute the minimum investment required to make the city government possibly choose the product of your company. You may assume that employees of all the other companies are too lazy to make such an effort. Input The input consists of a single test case with the following format. $n$ $k$ $A$ $B$ $C$ $x_1$ $y_1$ $z_1$ $x_2$ $y_2$ $z_2$ . . . $x_n$ $y_n$ $z_n$ The first line contains five integers. The integer $n$ ($1 \leq n \leq 50$) is the number of industrial products, and the integer $k$ ($1 \leq k \leq n$) is the number of products that will be chosen by the city government. The integers $A$, $B$, $C$ ($1 \leq A, B, C \leq 100$) are the parameters that determine the cost of changing the price, the size, and the weight, respectively, of the product 1. Each of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ ($1 \leq x_i, y_i, z_i \leq 100$), which are the price, the size, and the weight, respectively, of the $i$-th product. Output Output the minimum cost (in million yen) in order to make the city government possibly choose the product of your company. The output should not contain an absolute error greater than $10^{â4}$. Sample Input 1 6 5 1 2 3 5 5 5 1 5 5 2 5 4 3 5 3 4 5 2 5 5 1 Sample Output 1 0.631579 Sample Input 2 6 1 1 2 3 10 20 30 1 2 3 2 4 6 3 6 9 4 8 12 5 10 15 Sample Output 2 0.999000 | 35,345 |
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šãŠã®ææ¥ãæå³ãã time â {All, Day, Night} All 㯠[0:00~24:00), Day 㯠[6:00~18:00), Night 㯠[18:00~6:00) ã®æé垯ãæå³ããã 1 <= p <= 99999 1 <= m <= 100 å
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Problem F: City Merger Recent improvements in information and communication technology have made it possible to provide municipal service to a wider area more quickly and with less costs. Stimulated by this, and probably for saving their not sufficient funds, mayors of many cities started to discuss on mergers of their cities. There are, of course, many obstacles to actually put the planned mergers in practice. Each city has its own culture of which citizens are proud. One of the largest sources of friction is with the name of the new city. All citizens would insist that the name of the new city should have the original name of their own city at least as a part of it. Simply concatenating all the original names would, however, make the name too long for everyday use. You are asked by a group of mayors to write a program that finds the shortest possible name for the new city that includes all the original names of the merged cities. If two or more cities have common parts, they can be overlapped. For example, if "FUKUOKA", "OKAYAMA", and "YAMAGUCHI" cities are to be merged, "FUKUOKAYAMAGUCHI" is such a name that include all three of the original city names. Although this includes all the characters of the city name "FUKUYAMA" in this order, it does not appear as a consecutive substring, and thus "FUKUYAMA" is not considered to be included in the name. Input The input is a sequence of datasets. Each dataset begins with a line containing a positive integer n ( n †14), which denotes the number of cities to be merged. The following n lines contain the names of the cities in uppercase alphabetical letters, one in each line. You may assume that none of the original city names has more than 20 characters. Of course, no two cities have the same name. The end of the input is indicated by a line consisting of a zero. Output For each dataset, output the length of the shortest possible name of the new city in one line. The output should not contain any other characters. Sample Input 3 FUKUOKA OKAYAMA YAMAGUCHI 3 FUKUOKA FUKUYAMA OKAYAMA 2 ABCDE EDCBA 4 GA DEFG CDDE ABCD 2 ABCDE C 14 AAAAA BBBBB CCCCC DDDDD EEEEE FFFFF GGGGG HHHHH IIIII JJJJJ KKKKK LLLLL MMMMM NNNNN 0 Output for the Sample Input 16 19 9 9 5 70 | 35,348 |
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Problem C: Swimming Jam Despite urging requests of the townspeople, the municipal office cannot afford to improve many of the apparently deficient city amenities under this recession. The city swimming pool is one of the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under this circumstances, settled usage rules so that the limited facilities can be utilized fully. Two lanes are to be used for one-way swimming of different directions. Swimmers are requested to start swimming in one of the lanes, from its one end to the other, and then change the lane to swim his/her way back. When he or she reaches the original starting end, he/she should return to his/her initial lane and starts swimming again. Each swimmer has his/her own natural constant pace. Swimmers, however, are not permitted to pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that might cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the slower swimmer at the slower pace until the end of the lane is reached. Note that the blocking swimmerâs natural pace may be faster than the blocked swimmer; the blocking swimmer might also be blocked by another swimmer ahead, whose natural pace is slower than the blocked swimmer. Blocking would have taken place whether or not a faster swimmer was between them. Swimmers can change their order if they reach the end of the lane simultaneously. They change their order so that ones with faster natural pace swim in front. When a group of two or more swimmers formed by a congestion reaches the end of the lane, they are considered to reach there simultaneously, and thus change their order there. The number of swimmers, their natural paces in times to swim from one end to the other, and the numbers of laps they plan to swim are given. Note that here one "lap" means swimming from one end to the other and then swimming back to the original end. Your task is to calculate the time required for all the swimmers to finish their plans. All the swimmers start from the same end of the pool at the same time, the faster swimmers in front. In solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time required to change the lanes and the order in a group of swimmers at an end of the lanes. Input The input is a sequence of datasets. Each dataset is formatted as follows. n t 1 c 1 ... t n c n n is an integer (1 †n †50) that represents the number of swimmers. t i and c i are integers (1 †t i †300, 1 †c i †250) that represent the natural pace in times to swim from one end to the other and the number of planned laps for the i -th swimmer, respectively. ti and ci are separated by a space. The end of the input is indicated by a line containing one zero. Output For each dataset, output the time required for all the swimmers to finish their plans in a line. No extra characters should occur in the output. Sample Input 2 10 30 15 20 2 10 240 15 160 3 2 6 7 2 8 2 4 2 4 7 2 8 2 18 1 0 Output for the Sample Input 600 4800 36 40 | 35,354 |
Score : 100 points Problem Statement Three poles stand evenly spaced along a line. Their heights are a , b and c meters, from left to right. We will call the arrangement of the poles beautiful if the tops of the poles lie on the same line, that is, b-a = c-b . Determine whether the arrangement of the poles is beautiful. Constraints 1 \leq a,b,c \leq 100 a , b and c are integers. Input Input is given from Standard Input in the following format: a b c Output Print YES if the arrangement of the poles is beautiful; print NO otherwise. Sample Input 1 2 4 6 Sample Output 1 YES Since 4-2 = 6-4 , this arrangement of poles is beautiful. Sample Input 2 2 5 6 Sample Output 2 NO Since 5-2 \neq 6-5 , this arrangement of poles is not beautiful. Sample Input 3 3 2 1 Sample Output 3 YES Since 1-2 = 2-3 , this arrangement of poles is beautiful. | 35,355 |
E : Sigma / Σ Problem å°åŠçã®ã¥ããåã¯åã足ãç®ã«ãåŸæäžåŸæãããã 0 以äžã®æŽæ° X , Y ã«å¯ŸããŠã X + Y ãèšç®ããã®ã«ãããæé(ç§)ã次ã®ããã«æ±ºãŸãã 1 ã®äœããé çªã«èšç®ããŠããã 10 é²æ°è¡šèšã§ 10 i äœã®èšç®ã«ã¯ x i à y i + c i ç§ãããã x i 㯠X ã®10é²æ°è¡šèšã§ 10 i ã®äœã®æ°ã§ããã y i 㯠Y ã®10é²æ°è¡šèšã§ 10 i ã®äœã®æ°ã§ããã ãã ã i ã X ã®æ¡æ°ãã倧ãããªãæ㯠x i = 0 ãšããã Y ã«ã€ããŠãåæ§ã§ããã c i ã¯ã i = 0 ãŸã㯠x i-1 + y i-1 + c i-1 < 10 ãªãã° 0ã ããã§ãªããã° 1 ã§ããã 0 以äžã®æŽæ° i ã«ã€ããŠã® x i à y i + c i ã®ç·åã X + Y ã®èšç®ã«ãããæéã§ããã ããæ¥ãã¥ããåã®å
çã¯é·ã N ã®æŽæ°å a 0 , ... , a N-1 ã®åãèšç®ãã宿é¡ãåºãããã¥ããåã¯æ°åã®é çªã䞊ã³æ¿ããããšã¯ã§ããªããã足ãç®ã®åŒã«æ¬åŒ§ãä»ããããšã«ããã足ãç®ã®é çªãèªç±ã«å€ããããšãã§ãããäŸãã° N = 4 ã®å Žåãé çªã¯æ¬¡ã® 5 éãããã (( a 0 + a 1 ) + a 2 ) + a 3 ( a 0 + a 1 ) + ( a 2 + a 3 ) ( a 0 + ( a 1 + a 2 )) + a 3 a 0 + (( a 1 + a 2 ) + a 3 ) a 0 + ( a 1 + ( a 2 + a 3 )) ããããã®æ¬åŒ§ ( x + y ) ã®äžã§äžã§èª¬æããæéãããããšãããšãç·åãæ±ããã®ã«ãããæéã¯æå°ã§äœç§ã«ãªãã ãããã Input å
¥åã¯æ¬¡ã®ãããªåœ¢åŒã§äžããããã N a 0 a 1 ... a N-1 Constraints å
¥åã¯ãã¹ãŠæŽæ°ã§ããã 2 ⊠N ⊠300 0 ⊠a i ⊠1,000,000 Output çãã®ç§æ°ã1è¡ã§åºåããã Samples Sample Input 1 3 1 2 3 Sample Output 1 11 次ã®ããã«èšç®ãããšæãéãã 2 + 3 = 5 ( 2 à 3 = 6 ç§ããã) 1 + 5 = 6 ( 1 à 5 = 5 ç§ããã) | 35,356 |
Score : 300 points Problem Statement Snuke has an integer sequence A of length N . He will freely choose an integer b . Here, he will get sad if A_i and b+i are far from each other. More specifically, the sadness of Snuke is calculated as follows: abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N)) Here, abs(x) is a function that returns the absolute value of x . Find the minimum possible sadness of Snuke. Constraints 1 \leq N \leq 2 \times 10^5 1 \leq A_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible sadness of Snuke. Sample Input 1 5 2 2 3 5 5 Sample Output 1 2 If we choose b=0 , the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2 . Any choice of b does not make the sadness of Snuke less than 2 , so the answer is 2 . Sample Input 2 9 1 2 3 4 5 6 7 8 9 Sample Output 2 0 Sample Input 3 6 6 5 4 3 2 1 Sample Output 3 18 Sample Input 4 7 1 1 1 1 2 3 4 Sample Output 4 6 | 35,357 |
Problem B: Let's JUMPSTYLE Description èžãã®å¥œããªFã¯ïŒãšãããã³ã¹ããŒã«ã§JUMPSTYLEãšåŒã°ããããŒãã³ã¢ãªèžãã®ç·Žç¿ãããããšã«ããïŒ ããã¢ã¯NÃNã®æ Œåç¶ã«ã¿ã€ã«ãæ·ãè©°ããããŠããïŒ èžãã®ç·Žç¿ããµããŒãããããïŒåã¿ã€ã«ã«ã¯æ¬¡ã®ã¹ãããã«é£ã³ç§»ãã¹ãã¿ã€ã«ã®åº§æšãæžãããŠããïŒFã¯æ¥ã
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ã®x座æšããã³y座æšãè¡šãïŒåº§æšã¯0-originã§ããïŒãã¹ãŠã®åº§æšã®å€ã¯0以äžNæªæºã®æŽæ°ã§ããïŒ å
¥åã¯0ã®ã¿ããæãè¡ã§çµããïŒ Output åãã¹ãã±ãŒã¹ã«å¯ŸãïŒç°ãªãã«ãŒãã®åæ°ã1è¡ã§åºåããïŒ Sample Input 1 0 0 2 1 1 0 1 1 0 0 0 2 1 1 0 1 1 1 1 0 3 0 1 2 2 2 1 0 2 1 2 2 1 0 0 0 1 1 1 4 3 2 2 0 3 2 2 1 1 1 0 3 1 1 3 1 0 3 2 3 3 0 2 3 1 1 1 1 3 2 1 3 0 Output for Sample Input 1 2 1 2 3 | 35,358 |
Let's Move Tiles! You have a framed square board forming a grid of square cells. Each of the cells is either empty or with a square tile fitting in the cell engraved with a Roman character. You can tilt the board to one of four directions, away from you, toward you, to the left, or to the right, making all the tiles slide up, down, left, or right, respectively, until they are squeezed to an edge frame of the board. The figure below shows an example of how the positions of the tiles change by tilting the board toward you. Let the characters U , D , L , and R represent the operations of tilting the board away from you, toward you, to the left, and to the right, respectively. Further, let strings consisting of these characters represent the sequences of corresponding operations. For example, the string DRU means a sequence of tilting toward you first, then to the right, and, finally, away from you. This will move tiles down first, then to the right, and finally, up. To deal with very long operational sequences, we introduce a notation for repeated sequences. For a non-empty sequence seq , the notation ( seq ) k means that the sequence seq is repeated k times. Here, k is an integer. For example, (LR)3 means the same operational sequence as LRLRLR . This notation for repetition can be nested. For example, ((URD)3L)2R means URDURDURDLURDURDURDLR . Your task is to write a program that, given an initial positions of tiles on the board and an operational sequence, computes the tile positions after the given operations are finished. Input The input consists of at most 100 datasets, each in the following format. n s 11 ... s 1 n ... s n 1 ... s nn seq In the first line, n is the number of cells in one row (and also in one column) of the board (2 †n †50). The following n lines contain the initial states of the board cells. s ij is a character indicating the initial state of the cell in the i -th row from the top and in the j -th column from the left (both starting with one). It is either â . â (a period), meaning the cell is empty, or an uppercase letter â A â-â Z â, meaning a tile engraved with that character is there. seq is a string that represents an operational sequence. The length of seq is between 1 and 1000, inclusive. It is guaranteed that seq denotes an operational sequence as described above. The numbers in seq denoting repetitions are between 2 and 10 18 , inclusive, and are without leading zeros. Furthermore, the length of the operational sequence after unrolling all the nested repetitions is guaranteed to be at most 10 18 . The end of the input is indicated by a line containing a zero. Output For each dataset, output the states of the board cells, after performing the given operational sequence starting from the given initial states. The output should be formatted in n lines, in the same format as the initial board cell states are given in the input. Sample Input 4 ..E. .AD. B... ..C. D 4 ..E. .AD. B... ..C. DR 3 ... .A. BC. ((URD)3L)2R 5 ...P. PPPPP PPP.. PPPPP ..P.. LRLR(LR)12RLLR 20 .................... .................... .III..CC..PPP...CC.. ..I..C..C.P..P.C..C. ..I..C....P..P.C.... ..I..C....PPP..C.... ..I..C....P....C.... ..I..C..C.P....C..C. .III..CC..P.....CC.. .................... ..XX...XX...X...XX.. .X..X.X..X..X..X..X. ....X.X..X..X..X..X. ...X..X..X..X..X..X. ...X..X..X..X...XXX. ..X...X..X..X.....X. ..X...X..X..X.....X. .XXXX..XX...X...XX.. .................... .................... ((LDRU)1000(DLUR)2000(RULD)3000(URDL)4000)123456789012 6 ...NE. MFJ..G ...E.. .FBN.K ....MN RA.I.. ((((((((((((((((((((((((URD)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L)2L 0 Output for the Sample Input .... ..E. ..D. BAC. .... ...E ...D .BAC ... ..C .AB ....P PPPPP ..PPP PPPPP ....P .................... .................... .................... .................... .................... XXXX................ PXXXX............... CXXXX............... XXXXX............... XXPCXX.............. CCXXCX.............. CXXXXX.............. CXXXXX.............. CPCIXXX............. CXPPCXX............. PCXXXIC............. CPPCCXI............. CXCIPXXX............ XCPCICIXX........... PIPPICIXII.......... ...... ...... N..... JNG... RMMKFE BEAIFN | 35,359 |
Problem C: Complex Integer Solutions Let f ( x ) = a 0 + a 1 x + a 2 x 2 + ... + a d x d be the function where each a i (0 †i †d ) is a constant integer (and a d is non-zero) and x is a variable. Your task is to write a program that finds all complex integer solutions of the equation f ( x ) = 0 for a given f ( x ). Here, by complex integers, we mean complex numbers whose real and imaginary parts are both integers. Input The input consists of two lines. The first line of the input contains d , the degree of f ( x ). The second line contains ( d + 1) integers a 0 , ... , a d , the coeffcients of the equation. You may assume all the following: 1 †d †10, | a i | †10 6 and a d â 0. Output There should be two lines in the output. In the first line, print the number m of complex integer solutions. In the second line, print m solutions separated by space. Each solution should be counted and printed exactly once even if it is a multiple root. The solutions should be printed in ascending order of their real parts then their imaginary parts, and in the following fashion: 0 , -2 , i , -3i , 2+i , and 3-4i . Sample Input 1 4 -2 0 0 0 2 Output for the Sample Input 1 4 -1 -i i 1 Sample Input 2 8 0 0 25 15 17 -10 1 -1 1 Output for the Sample Input 2 5 -1-2i -1+2i 0 2-i 2+i | 35,360 |
Deadlock Detection In concurrent processing environments, a deadlock is an undesirable situation where two or more threads are mutually waiting for others to finish using some resources and cannot proceed further. Your task is to detect whether there is any possibility of deadlocks when multiple threads try to execute a given instruction sequence concurrently. The instruction sequence consists of characters ' u ' or digits from ' 0 ' to ' 9 ', and each of them represents one instruction. 10 threads are trying to execute the same single instruction sequence. Each thread starts its execution from the beginning of the sequence and continues in the given order, until all the instructions are executed. There are 10 shared resources called locks from L 0 to L 9 . A digit k is the instruction for acquiring the lock L k . After one of the threads acquires a lock L k , it is kept by the thread until it is released by the instruction ' u '. While a lock is kept, none of the threads, including one already acquired it, cannot newly acquire the same lock L k . Precisely speaking, the following steps are repeated until all threads finish. One thread that has not finished yet is chosen arbitrarily. The chosen thread tries to execute the next instruction that is not executed yet. If the next instruction is a digit k and the lock L k is not kept by any thread, the thread executes the instruction k and acquires L k . If the next instruction is a digit k and the lock L k is already kept by some thread, the instruction k is not executed. If the next instruction is ' u ', the instruction is executed and all the locks currently kept by the thread are released. After executing several steps, sometimes, it falls into the situation that the next instructions of all unfinished threads are for acquiring already kept locks. Once such a situation happens, no instruction will ever be executed no matter which thread is chosen. This situation is called a deadlock . There are instruction sequences for which threads can never reach a deadlock regardless of the execution order. Such instruction sequences are called safe . Otherwise, in other words, if there exists one or more execution orders that lead to a deadlock, the execution sequence is called unsafe . Your task is to write a program that tells whether the given instruction sequence is safe or unsafe. Input The input consists of at most 50 datasets, each in the following format. n s n is the length of the instruction sequence and s is a string representing the sequence. n is a positive integer not exceeding 10,000. Each character of s is either a digit (' 0 ' to ' 9 ') or ' u ', and s always ends with ' u '. The end of the input is indicated by a line with a zero. Output For each dataset, if the given instruction sequence is safe, then print "SAFE" in a line. If it is unsafe, then print "UNSAFE" in a line. Sample Input 11 01u12u0123u 6 01u10u 8 201u210u 9 01u12u20u 3 77u 12 9u8u845u954u 0 Output for the Sample Input SAFE UNSAFE SAFE UNSAFE UNSAFE UNSAFE The second input " 01u10u " may possibly cause a deadlock. After one thread has executed the initial four instructions " 01u1 ", the thread keeps only one lock L 1 . If another thread executes the first instruction ' 0 ' at this time, this thread acquires L 0 . Then, the first thread tries to acquire L 0 , already kept by the second thread, while the second thread tries to acquire L 1 , kept by the first thread; This leads to a deadlock. â â Figure 1: Why the Sample Input 2 " 01u10u " is unsafe. Contrarily, the third input " 201u210u " is safe. If one thread had executed up to " 201u21 " and another to " 20 ", then one may think it would lead to a deadlock, but this can never happen because no two threads can simultaneously keep L 2 . | 35,361 |
Problem E: Twirl Around Let's think about a bar rotating clockwise as if it were a twirling baton moving on a planar surface surrounded by a polygonal wall (see Figure 1). Figure 1. A bar rotating in a polygon Initially, an end of the bar (called "end A") is at (0,0), and the other end (called "end B") is at (0, L ) where L is the length of the bar. Initially, the bar is touching the wall only at the end A. The bar turns fixing a touching point as the center. The center changes as a new point touches the wall. Your task is to calculate the coordinates of the end A when the bar has fully turned by the given count R . Figure 2. Examples of turning bars In Figure 2, some examples are shown. In cases (D) and (E), the bar is stuck prematurely (cannot rotate clockwise anymore with any point touching the wall as the center) before R rotations. In such cases, you should answer the coordinates of the end A in that (stuck) position. You can assume the following: When the bar's length L changes by ε (|ε| < 0.00001), the final ( x , y ) coordinates will not change more than 0.0005. Input The input consists of multiple datasets. The number of datasets is no more than 100. The end of the input is represented by "0 0 0". The format of each dataset is as follows: L R N X 1 Y 1 X 2 Y 2 ... X N Y N L is the length of the bar. The bar rotates 2Ïà R radians (if it is not stuck prematurely). N is the number of vertices which make the polygon. The vertices of the polygon are arranged in a counter-clockwise order. You may assume that the polygon is simple , that is, its border never crosses or touches itself. N , X i and Y i are integer numbers; R and L are decimal fractions. Ranges of those values are as follows: 1.0 †L †500.0, 1.0 †R †10.0, 3 †N †100, -1000 †X i †1000, -1000 †Y i †1000, X 1 †-1, Y 1 = 0, X 2 ⥠1, Y 2 = 0. Output For each dataset, print one line containing x- and y- coordinates of the final position of the end A, separated by a space. The value may contain an error less than or equal to 0.001. You may print any number of digits after the decimal point. Sample Input 4.0 2.0 8 -1 0 5 0 5 -2 7 -2 7 0 18 0 18 6 -1 6 4.0 2.0 4 -1 0 10 0 10 12 -1 12 4.0 1.0 7 -1 0 2 0 -1 -3 -1 -8 6 -8 6 6 -1 6 4.0 2.0 6 -1 0 10 0 10 3 7 3 7 5 -1 5 5.0 2.0 6 -1 0 2 0 2 -4 6 -4 6 6 -1 6 6.0 1.0 8 -1 0 8 0 7 2 9 2 8 4 11 4 11 12 -1 12 0 0 0 Output for the Sample Input 16.0 0.0 9.999999999999998 7.4641016151377535 0.585786437626906 -5.414213562373095 8.0 0.0 6.0 0.0 9.52786404500042 4.0 Note that the above sample input corresponds to the cases in Figure 2. For convenience, in Figure 3, we will show an animation and corresponding photographic playback for the case (C). Figure 3. Animation and photographic playback for case (C) | 35,362 |
Problem B: Vector Field In 20015, JAG (Jagan Acceleration Group) has succeeded in inventing a new accelerator named Force Point for an experiment of proton collision on the two-dimensional $xy$-plane. If a proton touches a Force Point, it is accelerated to twice its speed and its movement direction is veered. A proton may be veered by a Force Field in four ways: the positive or negative directions parallel to the $x$- or the $y$-axis. The direction in which a proton veers is determined by the type of the Force Point. A Force Point can accelerate a proton only once because the Force Point disappears immediately after the acceleration. Generating many Force Points on the two-dimensional plane, which is called a 2D Force Point Field, allows us to accelerate a proton up to a target speed by sequentially accelerating the proton with the Force Points in the 2D Force Point Filed. The Force Point generation method is still under experiment and JAG has the following technical limitations: JAG cannot generate a Force Point with a specified position and a type. JAG cannot generate a Force Point after putting a proton into a 2D Force Point Field. JAG cannot move Force Points. JAG cannot change a protons direction except by the effect of Force Points. JAG can use only one proton for a 2D Force Point Field. JAG can put a proton moving in any direction with its speed 1 at any position in a 2D Force Point Field. In order to achieve the maximum speed of a proton, the engineers at JAG have to choose the optimal initial position and the optimal initial direction of the proton so that the proton is accelerated by as many Force Points as possible, after carefully observing the generated 2D Force Point Field. By observing a generated 2D Force Point Field, the number of the generated Force Points is known to be $n$. The position ($x_i$, $y_i$) and the direction veering type $d_i$ of the $i$-th point are also known. Your task is to write a program to calculate the maximum speed of a proton by acceleration on a given 2D Force Point Field when JAG puts a proton optimally. Input The input consists of a single test case which describes a 2D Force Point Field in the following format. $n$ $x_1$ $y_1$ $d_1$ ... $x_n$ $y_n$ $d_n$ The first line contains one integer $n$ ($1 \leq n \leq 3,000$) which is the number of the Force Points on the 2D Force Point Field. Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($|x_i|$, $|y_i| \leq 10^9$) and one character $d_i$ ($d_i$ is one of '>', 'v', '<' or '^'). $x_i$ and $y_i$ represent a coordinate of the $i$-th Force Point, and $d_i$ is the direction veering type of the $i$-th force point. A force point with a type '>' changes protons direction to the positive direction of the $x$-axis, 'v' represents the positive direction of the $y$-axis, '<' represents the negative direction of the $x$-axis, and '^' represents the negative direction of the $y$-axis. You can assume that any two Force Points are not generated on the same coordinates. Output Display a line containing the integer $log_2 v_{max}$, where $v_{max}$ is the protons possible fastest speed. Sample Input 9 0 0 v 1 0 > 2 0 < 0 1 > 1 1 v 2 1 v 0 2 ^ 1 2 ^ 2 2 < Output for the Sample Input 9 The input looks like the following diagram. All the Force Points will disappear if you put a proton at (1, 1). v>< >vv ^^< Sample Input 9 0 0 ^ 1 0 ^ 2 0 ^ 0 1 < 1 1 ^ 2 1 > 0 2 v 1 2 v 2 2 v Output for the Sample Input 2 | 35,363 |
Charging System for Network There is a network consisting of N machines (sequentially numbered from 0 to N -1) interconnected through N -1 bidirectional communication cables. Any two machines can perform bidirectional communication through one or more cables. From time to time, machines in the network are renewed. When a new machine is introduced, the cables directly connected to it are also replaced with thicker ones to cope with the increased volume of communication traffic. The communication fee arising from communication traffic between any two machines is calculated by summing the charges assigned to all the cables routing via the two. A unique charging scheme is employed in this system: if the size of a cable is a multiple of K , then the cable is not charged (free of charge). Other cables are charged according to their sizes. Based on the given information on the network topology and Q instructions, write a program to execute each instruction. Increase the sizes of all cables directly connected to the machine x by d . Report the communication charge between the machines s and t . Input The input is given in the following format. N K a_1 b_1 c_1 a_2 b_2 c_2 : a_{Nâ1} b_{Nâ1} c_{Nâ1} Q query_1 query_2 : query_Q The first line provides the number of machines N (2 †N †10 5 ) and the cable size K (1 †K †10 5 ) (the reference value for determining free of charge cables). Each of subsequent N -1 lines provides the i -th cable information that directly connects two machines a_i and b_i (0 †a_i < b_i †N -1), followed by the cableâs initial size c_i (1 †c_i †10 5 ). For any pair of machines, the number of cables directly connecting them is either one or zero. The next line following them provides the number of instructions Q (1 †Q †10 5 ). Each of the Q lines following it provides the i -th instruction query_i , which is either one of the following two: add x d or send s t The instruction add x d increase the size of all cables directly connected to machine x (0 †x †N -1) by d (1 †d †10 5 ). The instruction send s t reports the charge imposed to the communication between the two machines s (0 †s †N -1) and t (0 †t †N -1), where s â t . At least one send instruction is included in the input information. Output For each send command, output the communication charge between s and t . Sample Input 1 6 3 0 1 1 0 2 1 0 3 1 2 4 1 2 5 1 3 send 1 4 add 2 2 send 1 4 Sample Output 1 3 1 | 35,364 |
Missing Numbers Toshizo is the manager of a convenience store chain in Hakodate. Every day, each of the stores in his chain sends him a table of the products that they have sold. Toshizo's job is to compile these figures and calculate how much the stores have sold in total. The type of a table that is sent to Toshizo by the stores looks like this (all numbers represent units of products sold): Store1 Store2 Store3 Totals Product A -5 40 70 | 105 Product B 20 50 80 | 150 Product C 30 60 90 | 180 ----------------------------------------------------------- Store's total sales 45 150 240 435 By looking at the table, Toshizo can tell at a glance which goods are selling well or selling badly, and which stores are paying well and which stores are too empty. Sometimes, customers will bring products back, so numbers in a table can be negative as well as positive. Toshizo reports these figures to his boss in Tokyo, and together they sometimes decide to close stores that are not doing well and sometimes decide to open new stores in places that they think will be profitable. So, the total number of stores managed by Toshizo is not fixed. Also, they often decide to discontinue selling some products that are not popular, as well as deciding to stock new items that are likely to be popular. So, the number of products that Toshizo has to monitor is also not fixed. One New Year, it is very cold in Hakodate. A water pipe bursts in Toshizo's office and floods his desk. When Toshizo comes to work, he finds that the latest sales table is not legible. He can make out some of the figures, but not all of them. He wants to call his boss in Tokyo to tell him that the figures will be late, but he knows that his boss will expect him to reconstruct the table if at all possible. Waiting until the next day won't help, because it is the New Year, and his shops will be on holiday. So, Toshizo decides either to work out the values for himself, or to be sure that there really is no unique solution. Only then can he call his boss and tell him what has happened. But Toshizo also wants to be sure that a problem like this never happens again. So he decides to write a computer program that all the managers in his company can use if some of the data goes missing from their sales tables. For instance, if they have a table like: Store 1 Store 2 Store 3 Totals Product A ? ? 70 | 105 Product B ? 50 ? | 150 Product C 30 60 90 | 180 -------------------------------------------------------- Store's total sales 45 150 240 435 then Toshizo's program will be able to tell them the correct figures to replace the question marks. In some cases, however, even his program will not be able to replace all the question marks, in general. For instance, if a table like: Store 1 Store 2 Totals Product A ? ? | 40 Product B ? ? | 40 --------------------------------------------- Store's total sales 40 40 80 is given, there are infinitely many possible solutions. In this sort of case, his program will just say "NO". Toshizo's program works for any data where the totals row and column are still intact. Can you reproduce Toshizo's program? Input The input consists of multiple data sets, each in the following format: p s row 1 row 2 ... row p totals The first line consists of two integers p and s , representing the numbers of products and stores, respectively. The former is less than 100 and the latter is less than 10. They are separated by a blank character. Each of the subsequent lines represents a row of the table and consists of s +1 elements, each of which is either an integer or a question mark. The i -th line (1 <= i <= p ) corresponds to the i -th product and the last line the totals row. The first s elements in a line represent the sales of each store and the last one the total sales of the product. Numbers or question marks in a line are separated by a blank character. There are no missing numbers in the totals column or row. There is at least one question mark in each data set. The known numbers in the table except the totals row and column is between -1,000 and 1,000, inclusive. However, unknown numbers, represented by question marks, may not be in this range. The total sales number of each product is between -10,000 and 10,000, inclusive. The total sales number of each store is between -100,000 and 100,000, inclusive. There is a blank line between each data set in the input, and the input is terminated by a line consisting of a zero. Output When there is a unique solution, your program should print the missing numbers in the occurrence order in the input data set. Otherwise, your program should print just "NO". The answers of consecutive data sets should be separated by an empty line. Each non-empty output line contains only a single number or "NO". Sample Input 3 3 ? ? 70 105 ? 50 ? 150 30 60 90 180 45 150 240 435 2 2 ? ? 40 ? ? 40 40 40 80 2 3 ? 30 40 90 50 60 70 180 70 90 110 270 0 Output for the Sample Input -5 40 20 80 NO 20 | 35,365 |
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Farm Village There is a village along a road. This village has $N$ houses numbered $1$ to $N$ in order along the road. Each house has a field that can make up to two units of the crop and needs just one unit of the crop. The total cost to distribute one unit of the crop to each house is the summation of carrying costs and growing costs. The carrying cost: The cost to carry one unit of the crop between the $i$-th house and the ($i+1$)-th house is $d_i$. It takes the same cost in either direction to carry. The growing cost: The cost to grow one unit of the crop in the $i$-th house's field is $g_i$. Your task is to calculate the minimum total cost to supply one unit of the crop to each house. Input The input consists of a single test case formatted as follows. $N$ $d_1$ ... $d_{N-1}$ $g_1$ ... $g_{N}$ The first line consists of an integer $N$ ($2 \leq 200,000$), which is the number of the houses. The second line consists of $N-1$ integers separated by spaces. The $i$-th integer $d_i$ ($1 \leq d_i \leq 10^9$, $1 \leq i \leq N-1$)represents the carrying cost between the $i$-th and the ($i+1$)-th houses. The third line consists of $N$ integers separated by spaces. The $i$-th integer $g_i$ ($1 \leq g_i \leq 10^9$, $1 \leq i \leq N$) represents the growing cost of the $i$-th house's field. Output Print the minimum cost to supply one unit of the crop to each house. Sample Input 1 2 3 1 5 Output for Sample Input 1 5 Sample Input 2 3 100 100 1 2 3 Output for Sample Input 2 6 Sample Input 3 4 1 2 3 1 1 100 100 Output for Sample Input 3 12 | 35,367 |
Score : 200 points Problem Statement There are K pieces of cakes. Mr. Takahashi would like to eat one cake per day, taking K days to eat them all. There are T types of cake, and the number of the cakes of type i ( 1 †i †T ) is a_i . Eating the same type of cake two days in a row would be no fun, so Mr. Takahashi would like to decide the order for eating cakes that minimizes the number of days on which he has to eat the same type of cake as the day before. Compute the minimum number of days on which the same type of cake as the previous day will be eaten. Constraints 1 †K †10000 1 †T †100 1 †a_i †100 a_1 + a_2 + ... + a_T = K Input The input is given from Standard Input in the following format: K T a_1 a_2 ... a_T Output Print the minimum number of days on which the same type of cake as the previous day will be eaten. Sample Input 1 7 3 3 2 2 Sample Output 1 0 For example, if Mr. Takahashi eats cakes in the order of 2, 1, 2, 3, 1, 3, 1 , he can avoid eating the same type of cake as the previous day. Sample Input 2 6 3 1 4 1 Sample Output 2 1 There are 6 cakes. For example, if Mr. Takahashi eats cakes in the order of 2, 3, 2, 2, 1, 2 , he has to eat the same type of cake (i.e., type 2 ) as the previous day only on the fourth day. Since this is the minimum number, the answer is 1 . Sample Input 3 100 1 100 Sample Output 3 99 Since Mr. Takahashi has only one type of cake, he has no choice but to eat the same type of cake as the previous day from the second day and after. | 35,368 |
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Problem J: Matrix Problem é·ã$H$ã®æ°å$A$ãšé·ã$W$ã®æ°å$B$ãäžããããã $H$è¡$W$åãããªãè¡å$C$ã以äžã®ããã«å®çŸ©ããã $ C_{i,j} = A_i \times B_j (1 \leq i \leq H, 1 \leq j \leq W) $ 以äžã®åçš®é¡ã®ã¯ãšãªãåèš$Q$ååŠçããã ã¯ãšãª1 $1$ $a$ $b$ $v$ $ A_i ( a \leq i \leq b) $ã«$v$ãå ãã ã¯ãšãª2 $2$ $c$ $d$ $v$ $ B_j ( c \leq j \leq d) $ã«$v$ãå ãã ã¯ãšãª3 $3$ $a$ $b$ $c$ $d$ $ C_{i,j} ( a \leq i \leq b, c \leq j \leq d) $ã®æå°å€ãšãã®åæ°ãåºåãã ã¯ãšãª4 $4$ $a$ $b$ $c$ $d$ $ C_{i,j} ( a \leq i \leq b, c \leq j \leq d) $ã®æ倧å€ãšãã®åæ°ãåºåãã 詳ããã¯ãµã³ãã«å
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¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã $H$ $W$ $Q$ $A_1$ $A_2$ ... $A_H$ $B_1$ $B_2$ ... $B_W$ $query_1$ $query_2$ ... $query_Q$ åã¯ãšãªã¯ä»¥äžã®åçš®é¡ã®ããããã®åœ¢åŒã§äžããããã $1$ $a$ $b$ $v$ $2$ $c$ $d$ $v$ $3$ $a$ $b$ $c$ $d$ $4$ $a$ $b$ $c$ $d$ å
¥åã¯ãã¹ãŠæŽæ°ã§äžããããã 1è¡ç®ã«$H$, $W$, $Q$ã空çœåºåãã§äžããããã 2è¡ç®ã«æ°å$A$ã®èŠçŽ $A_i$($1 \leq i \leq H$)ã空çœåºåãã§äžããããã 3è¡ç®ã«æ°å$B$ã®èŠçŽ $B_j$($1 \leq j \leq W$)ã空çœåºåãã§äžããããã 4è¡ç®ä»¥éã®$Q$è¡ã«ã¯ãšãªãæ¹è¡åºåãã§äžããããã åã¯ãšãªå
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¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã $1 \leq H, W, Q\leq 10^5 $ $-1000 \leq A_i \leq 1000 $ $-1000 \leq B_j \leq 1000 $ åã¯ãšãªã«ã€ããŠãå
¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã $1 \leq a \leq b \leq H$ $1 \leq c \leq d \leq W$ $-1000 \leq v \leq 1000$ Output åã¯ãšãª3åã³ã¯ãšãª4ã«ã€ããŠãå€ãšåæ°ã空çœåºåãã§äžè¡ã«åºåããã Sample Input 1 4 4 7 1 2 3 4 1 2 3 4 3 2 3 2 3 4 2 3 2 3 3 1 1 1 1 4 1 1 1 1 1 1 1 1 3 1 4 1 2 4 2 3 2 4 Sample Output 1 4 1 9 1 1 1 1 1 2 2 12 1 ã¯ãšãª1, 2ã§æå®ãããŠããç¯å²ã¯ä»¥äžã®ç»åã®ç·è²ã«å¡ãããé åã§ããã ã¯ãšãª3, 4ã§æå®ãããŠããç¯å²ã¯ä»¥äžã®ç»åã®æ©è²ã«å¡ãããé åã§ããã ã¯ãšãª5ã«ãã£ãŠ$A_1$ã«1ãå ããããã ã¯ãšãª6ã§æå®ãããŠããç¯å²ã¯ä»¥äžã®ç»åã®æ°Žè²ã«å¡ãããé åã§ããã ã¯ãšãª7ã§æå®ãããŠããç¯å²ã¯ä»¥äžã®ç»åã®çŽ«è²ã«å¡ãããé åã§ããã Sample Input 2 4 4 6 1 1 1 1 1 1 1 1 3 1 4 1 4 4 1 4 1 4 1 2 3 1 2 2 3 1 3 1 4 1 4 4 1 4 1 4 Sample Output 2 1 16 1 16 1 4 4 4 åæç¶æ
ã®$C$ã¯ä»¥äžã®ããã«ãªãã ã¯ãšãª3, 4以åŸã®$C$ã¯ä»¥äžã®ããã«ãªãã Sample Input 3 4 4 7 0 1 0 1 1 0 1 0 3 2 4 1 3 4 1 4 1 4 1 1 4 -1 3 1 3 1 3 1 3 3 2 2 3 3 -2 3 2 4 2 4 Sample Output 3 0 5 1 4 -1 4 -1 1 Sample Input 4 36 4 20 -523 -460 -536 -885 652 782 513 -558 -521 -808 124 -708 -943 52 -856 -755 -958 913 380 -767 373 -731 -492 213 538 392 -39 509 -840 135 78 -285 -241 522 -572 -915 -691 -16 812 -385 4 7 17 4 4 3 24 33 1 1 4 3 35 2 4 3 28 32 4 4 2 3 3 438 3 7 15 1 1 4 2 17 4 4 3 24 28 2 4 4 15 16 4 4 4 18 29 1 1 3 24 27 2 4 2 2 3 -828 3 18 23 3 3 1 27 31 -701 2 2 3 298 1 21 32 237 2 3 3 -71 1 14 29 772 4 13 19 3 3 3 19 34 1 2 Sample Output 4 368830 1 -371758 1 741356 1 -195965 1 -354483 1 368830 1 -207130 1 329560 1 580440 1 -207130 1 -323674 1 1093565 1 -1068977 1 | 35,372 |
Problem B: GPA JANKEN Problem GPAãšã¯ãGalaxy Point of Aizuãã®ç¥ã§ã0ãã4ãŸã§ã®å®æ°å€ãåãã GPAãããããã¯äºäººã§è¡ãã²ãŒã ã§ãããåã
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ãšãªããåãå Žåã¯åŒãåããšãªãã N 人ã®GPAã®ããŒã¿ãäžããããã®ã§ãç·åœããæŠãããæã®ããããã®åã¡ç¹ãåºåããã ãã ããåã¡ç¹ã¯åã¡ã®æ3ãåŒãåãã®æ1ãè² ãã®æ0ãšããã ç·åœããæŠãšã¯ãã¹ãŠã®åå è
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¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã N a 1 a 2 ... a N äžè¡ç®ã«GPAããããããããäººæ° N ãäžããããã ç¶ã N è¡ã« i çªç®ã®äººã®GPAã®ããŒã¿ a i ãäžè¡ã«äžããããã Constraints å
¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã 2 †N †10 5 N ã¯æŽæ° 0.000 †a i †4.000 ( 1 †i †N ) a i ã¯å®æ° ( 1 †i †N ) åGPAã¯å°æ°ç¹ä»¥äž3æ¡ãŸã§äžãããã Output i è¡ç®ã« i çªç®ã®äººã®åã¡ç¹ãäžè¡ã«åºåããã ( 1 †i †N ) Sample Input 1 3 1.000 3.000 3.000 Sample Output 1 0 4 4 Sample Input 2 3 1.000 2.000 3.000 Sample Output 2 0 3 6 | 35,373 |
Score : 100 points Problem Statement You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1} . Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)} , defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353 . Constraints 1 \leq N, M \leq 524288 0 \leq a_i, b_i < 998244353 All values in Input are integer. Input Input is given from Standard Input in the following format: N M a_0 a_1 ... a_{N-1} b_0 b_1 ... b_{M-1} Output Print the answer in the following format: c_0 c_1 ... c_{(N - 1) + (M - 1)} Sample Input 1 4 5 1 2 3 4 5 6 7 8 9 Sample Output 1 5 16 34 60 70 70 59 36 Sample Input 2 1 1 10000000 10000000 Sample Output 2 871938225 | 35,374 |
Score : 200 points Problem Statement Given are strings s and t of length N each, both consisting of lowercase English letters. Let us form a new string by alternating the characters of S and the characters of T , as follows: the first character of S , the first character of T , the second character of S , the second character of T , ... , the N -th character of S , the N -th character of T . Print this new string. Constraints 1 \leq N \leq 100 |S| = |T| = N S and T are strings consisting of lowercase English letters. Input Input is given from Standard Input in the following format: N S T Output Print the string formed. Sample Input 1 2 ip cc Sample Output 1 icpc Sample Input 2 8 hmhmnknk uuuuuuuu Sample Output 2 humuhumunukunuku Sample Input 3 5 aaaaa aaaaa Sample Output 3 aaaaaaaaaa | 35,375 |
Score : 400 points Problem Statement There is a directed graph with N vertices and M edges. The i -th edge (1â€iâ€M) points from vertex a_i to vertex b_i , and has a weight c_i . We will play the following single-player game using this graph and a piece. Initially, the piece is placed at vertex 1 , and the score of the player is set to 0 . The player can move the piece as follows: When the piece is placed at vertex a_i , move the piece along the i -th edge to vertex b_i . After this move, the score of the player is increased by c_i . The player can end the game only when the piece is placed at vertex N . The given graph guarantees that it is possible to traverse from vertex 1 to vertex N . When the player acts optimally to maximize the score at the end of the game, what will the score be? If it is possible to increase the score indefinitely, print inf . Constraints 2â€Nâ€1000 1â€Mâ€min(N(N-1),2000) 1â€a_i,b_iâ€N (1â€iâ€M) a_iâ b_i (1â€iâ€M) a_iâ a_j or b_iâ b_j (1â€i<jâ€M) -10^9â€c_iâ€10^9 (1â€iâ€M) c_i is an integer. In the given graph, there exists a path from vertex 1 to vertex N . Input Input is given from Standard Input in the following format: N M a_1 b_1 c_1 a_2 b_2 c_2 : a_M b_M c_M Output Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf . Sample Input 1 3 3 1 2 4 2 3 3 1 3 5 Sample Output 1 7 There are two ways to move the piece to vertex N=3 : vertex 1 â vertex 2 â vertex 3 : score 4+3=7 vertex 1 â vertex 3 : score 5 Thus, the maximum possible score at the end of the game is 7 . Sample Input 2 2 2 1 2 1 2 1 1 Sample Output 2 inf It is possible to increase the score indefinitely by alternating between vertex 1 and 2 . Sample Input 3 6 5 1 2 -1000000000 2 3 -1000000000 3 4 -1000000000 4 5 -1000000000 5 6 -1000000000 Sample Output 3 -5000000000 | 35,376 |
Score : 700 points Problem Statement There are N cats. We number them from 1 through N . Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me." Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats. Constraints 2 †N †10^5 1 †a_i †N-1 Input Input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise. Sample Input 1 3 1 2 2 Sample Output 1 Yes For example, if cat 1 , 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats. Sample Input 2 3 1 1 2 Sample Output 2 No From the remark of cat 1 , we can see that cat 2 and 3 wear hats of the same color. Also, from the remark of cat 2 , we can see that cat 1 and 3 wear hats of the same color. Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3 . Sample Input 3 5 4 3 4 3 4 Sample Output 3 No Sample Input 4 3 2 2 2 Sample Output 4 Yes Sample Input 5 4 2 2 2 2 Sample Output 5 Yes Sample Input 6 5 3 3 3 3 3 Sample Output 6 No | 35,377 |
Score : 500 points Problem Statement "Teishi-zushi", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter. Nakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i -th sushi is placed, is x_i meters. Also, the i -th sushi has a nutritive value of v_i kilocalories. Nakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter. Whenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. Constraints 1 †N †10^5 2 †C †10^{14} 1 †x_1 < x_2 < ... < x_N < C 1 †v_i †10^9 All values in input are integers. Subscores 300 points will be awarded for passing the test set satisfying N †100 . Input Input is given from Standard Input in the following format: N C x_1 v_1 x_2 v_2 : x_N v_N Output If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c . Sample Input 1 3 20 2 80 9 120 16 1 Sample Output 1 191 There are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value. Sample Input 2 3 20 2 80 9 1 16 120 Sample Output 2 192 The second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value. Sample Input 3 1 100000000000000 50000000000000 1 Sample Output 3 0 Even though the only sushi is so far that it does not fit into a 32 -bit integer, its nutritive value is low, thus he should immediately leave without doing anything. Sample Input 4 15 10000000000 400000000 1000000000 800000000 1000000000 1900000000 1000000000 2400000000 1000000000 2900000000 1000000000 3300000000 1000000000 3700000000 1000000000 3800000000 1000000000 4000000000 1000000000 4100000000 1000000000 5200000000 1000000000 6600000000 1000000000 8000000000 1000000000 9300000000 1000000000 9700000000 1000000000 Sample Output 4 6500000000 All these sample inputs above are included in the test set for the partial score. | 35,378 |
Problem C Distribution Center The factory of the Impractically Complicated Products Corporation has many manufacturing lines and the same number of corresponding storage rooms. The same number of conveyor lanes are laid out in parallel to transfer goods from manufacturing lines directly to the corresponding storage rooms. Now, they plan to install a number of robot arms here and there between pairs of adjacent conveyor lanes so that goods in one of the lanes can be picked up and released down on the other, and also in the opposite way. This should allow mixing up goods from different manufacturing lines to the storage rooms. Depending on the positions of robot arms, the goods from each of the manufacturing lines can only be delivered to some of the storage rooms. Your task is to find the number of manufacturing lines from which goods can be transferred to each of the storage rooms, given the number of conveyor lanes and positions of robot arms. Input The input consists of a single test case, formatted as follows. $n$ $m$ $x_1$ $y_1$ ... $x_m$ $y_m$ An integer $n$ ($2 \leq n \leq 200000$) in the first line is the number of conveyor lanes. The lanes are numbered from 1 to $n$, and two lanes with their numbers differing with 1 are adjacent. All of them start from the position $x = 0$ and end at $x = 100000$. The other integer $m$ ($1 \leq m < 100000$) is the number of robot arms. The following $m$ lines indicate the positions of the robot arms by two integers $x_i$ ($0 < x_i < 100000$) and $y_i$ ($1 \leq y_i < n$). Here, $x_i$ is the x -coordinate of the $i$-th robot arm, which can pick goods on either the lane $y_i$ or the lane $y_i + 1$ at position $x = x_i$, and then release them on the other at the same x -coordinate. You can assume that positions of no two robot arms have the same $x$-coordinate, that is, $x_i \ne x_j$ for any $i \ne j$. Figure C.1. Illustration of Sample Input 1 Output Output $n$ integers separated by a space in one line. The $i$-th integer is the number of the manufacturing lines from which the storage room connected to the conveyor lane $i$ can accept goods. Sample Input 1 4 3 1000 1 2000 2 3000 3 Sample Output 1 2 3 4 4 Sample Input 2 4 3 1 1 3 2 2 3 Sample Output 2 2 4 4 2 | 35,379 |
Score : 300 points Problem Statement Snuke has N hats. The i -th hat has an integer a_i written on it. There are N camels standing in a circle. Snuke will put one of his hats on each of these camels. If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes ; otherwise, print No . The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself. What is XOR? The bitwise XOR x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows: - When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k 's place ( k \geq 0 ) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k 's place is odd, and 0 if that count is even. For example, 3 \oplus 5 = 6 . Constraints All values in input are integers. 3 \leq N \leq 10^{5} 0 \leq a_i \leq 10^{9} Input Input is given from Standard Input in the following format: N a_1 a_2 \ldots a_{N} Output Print the answer. Sample Input 1 3 1 2 3 Sample Output 1 Yes If we put the hats with 1 , 2 , and 3 in this order, clockwise, the condition will be satisfied for every camel, so the answer is Yes . Sample Input 2 4 1 2 4 8 Sample Output 2 No There is no such way to distribute the hats; the answer is No . | 35,380 |
Score : 1000 points Problem Statement There are N balls in a row. Initially, the i -th ball from the left has the integer A_i written on it. When Snuke cast a spell, the following happens: Let the current number of balls be k . All the balls with k written on them disappear at the same time. Snuke's objective is to vanish all the balls by casting the spell some number of times. This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable. By the way, the integers on these balls sometimes change by themselves. There will be M such changes. In the j -th change, the integer on the X_j -th ball from the left will change into Y_j . After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are. Constraints 1 \leq N \leq 200000 1 \leq M \leq 200000 1 \leq A_i \leq N 1 \leq X_j \leq N 1 \leq Y_j \leq N Subscore In the test set worth 500 points, N \leq 200 and M \leq 200 . Input Input is given from Standard Input in the following format: N M A_1 A_2 ... A_N X_1 Y_1 X_2 Y_2 : X_M Y_M Output Print M lines. The j -th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable. Sample Input 1 5 3 1 1 3 4 5 1 2 2 5 5 4 Sample Output 1 0 1 1 After the first change, the integers on the balls become 2 , 1 , 3 , 4 , 5 , from left to right. Here, all the balls can be vanished by casting the spell five times. Thus, no modification is necessary. After the second change, the integers on the balls become 2 , 5 , 3 , 4 , 5 , from left to right. In this case, at least one modification must be made. One optimal solution is to modify the integer on the fifth ball from the left to 2 , and cast the spell four times. After the third change, the integers on the balls become 2 , 5 , 3 , 4 , 4 , from left to right. Also in this case, at least one modification must be made. One optimal solution is to modify the integer on the third ball from the left to 2 , and cast the spell three times. Sample Input 2 4 4 4 4 4 4 4 1 3 1 1 1 2 1 Sample Output 2 0 1 2 3 Sample Input 3 10 10 8 7 2 9 10 6 6 5 5 4 8 1 6 3 6 2 7 10 9 7 9 9 2 4 8 1 1 8 7 7 Sample Output 3 1 0 1 2 2 3 3 3 3 2 | 35,381 |
Score : 1500 points Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits. We have a board divided into N horizontal rows and N vertical columns of square cells. The cell at the i -th row from the top and the j -th column from the left is called Cell (i,j) . Each cell is either empty or occupied by an obstacle. Also, each empty cell has a digit written on it. If A_{i,j}= 1 , 2 , ..., or 9 , Cell (i,j) is empty and the digit A_{i,j} is written on it. If A_{i,j}= # , Cell (i,j) is occupied by an obstacle. Cell Y is reachable from cell X when the following conditions are all met: Cells X and Y are different. Cells X and Y are both empty. One can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell. Consider all pairs of cells (X,Y) such that cell Y is reachable from cell X . Find the sum of the products of the digits written on cell X and cell Y for all of those pairs. Constraints 1 \leq N \leq 1500 A_{i,j} is one of the following characters: 1 , 2 , ... 9 and # . Input Input is given from Standard Input in the following format: N A_{1,1}A_{1,2}...A_{1,N} A_{2,1}A_{2,2}...A_{2,N} : A_{N,1}A_{N,2}...A_{N,N} Output Print the sum of the products of the digits written on cell X and cell Y for all pairs (X,Y) such that cell Y is reachable from cell X . Sample Input 1 2 11 11 Sample Output 1 5 There are five pairs of cells (X,Y) such that cell Y is reachable from cell X , as follows: X=(1,1) , Y=(1,2) X=(1,1) , Y=(2,1) X=(1,1) , Y=(2,2) X=(1,2) , Y=(2,2) X=(2,1) , Y=(2,2) The product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5 . Sample Input 2 4 1111 11#1 1#11 1111 Sample Output 2 47 Sample Input 3 10 76##63##3# 8445669721 75#9542133 3#285##445 749632##89 2458##9515 5952578#77 1#3#44196# 4355#99#1# #298#63587 Sample Output 3 36065 Sample Input 4 10 4177143673 7######### 5#1716155# 6#4#####5# 2#3#597#6# 6#9#8#3#5# 5#2#899#9# 1#6#####6# 6#5359657# 5######### Sample Output 4 6525 | 35,382 |
Score : 800 points Problem Statement There are N towns in Snuke Kingdom, conveniently numbered 1 through N . Town 1 is the capital. Each town in the kingdom has a Teleporter , a facility that instantly transports a person to another place. The destination of the Teleporter of town i is town a_i ( 1â€a_iâ€N ). It is guaranteed that one can get to the capital from any town by using the Teleporters some number of times . King Snuke loves the integer K . The selfish king wants to change the destination of the Teleporters so that the following holds: Starting from any town, one will be at the capital after using the Teleporters exactly K times in total. Find the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire. Constraints 2â€Nâ€10^5 1â€a_iâ€N One can get to the capital from any town by using the Teleporters some number of times. 1â€Kâ€10^9 Input The input is given from Standard Input in the following format: N K a_1 a_2 ... a_N Output Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire. Sample Input 1 3 1 2 3 1 Sample Output 1 2 Change the destinations of the Teleporters to a = (1,1,1) . Sample Input 2 4 2 1 1 2 2 Sample Output 2 0 There is no need to change the destinations of the Teleporters, since the king's desire is already satisfied. Sample Input 3 8 2 4 1 2 3 1 2 3 4 Sample Output 3 3 For example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4) . | 35,383 |
Problem Statement "Rooks Game" is a single-player game and uses a chessboard which has $N \times N$ grid and $M$ rook pieces. A rook moves through any number of unoccupied squares horizontally or vertically. When a rook can attack another rook, it can capture the rook and move to the square which was occupied. Note that, in Rooks Game, we don't distinguish between white and black, in other words, every rook can capture any of other rooks. Initially, there are $M$ rooks on the board. In each move, a rook captures another rook. The player repeats captures until any rook cannot be captured. There are two types of goal of this game. One is to minimize the number of captured rooks, and the other is to maximize it. In this problem, you are requested to calculate the minimum and maximum values of the number of captured rooks. Input The input consists of a single test case in the format below. $N$ $M$ $x_{1}$ $y_{1}$ $\vdots$ $x_{M}$ $y_{M}$ The first line contains two integers $N$ and $M$ which are the size of the chessboard and the number of rooks, respectively ($1 \le N, M \le 1000$). Each of the following $M$ lines gives the position of each rook. The $i$-th line with $x_{i}$ and $y_{i}$ means that the $i$-th rook is in the $x_{i}$-th column and $y_{i}$-th row ($1 \le x_{i}, y_{i} \le N$). You can assume any two rooks are not in the same place. Output Output the minimum and maximum values of the number of captured rooks separated by a single space. Examples Input Output 8 3 1 1 1 8 8 8 1 2 8 4 1 1 1 8 8 8 8 1 2 3 5 5 1 1 2 2 3 3 4 4 5 5 0 0 100 1 100 100 0 0 10 12 1 2 1 4 1 6 3 6 5 6 10 7 8 7 6 7 4 7 2 7 7 3 9 5 7 8 | 35,384 |
Bit Mask A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0, 1, ..., n-1$ th flag corresponds to 1 (ON) or 0 (OFF). The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1. On the other hand, a mask is a special bit sequence which can be used to set specified bits of a given bit sequence to ON/OFF. It can also be used to extract/exclude a bit sequence based on a specified pattern. Given a sequence of bits with 64 flags which represent a state, perform the following operations using a set of pre-defined masks. Note that each flag of the bits is initialized by OFF. test(i): Print 1 if $i$-th flag is ON, otherwise 0 set(m): Set flags specified by mask $m$ to ON clear(m): Set flags specified by mask $m$ to OFF flip(m): Inverse flags specified by mask $m$ all(m): Print 1 if all flags specified by mask $m$ are ON, otherwise 0 any(m): Print 1 if at least one flag specified by mask $m$ is ON, otherwise 0 none(m): Print 1 if all flags specified by mask $m$ are OFF, otherwise 0 count(m): Print the number of flags specifed by mask $m$ with ON val(m): Print the decimal value of the state specified by mask $m$ Input The input is given in the following format. $n$ $mask_0$ $mask_1$ : $mask_{n-1}$ $q$ $query_1$ $query_2$ : $query_q$ $n$ represents the number of masks. $mask_i$ represents state of $i$-th mask and is given in the following format: $k$ $b_0$ $b_1$ ... $b_k$ $k$ is the number of ON in the bits. The following $k$ integers $b_j$ show that $b_j$-th bit is ON. $query_i$ represents $i$-th query and is given in the following format: 0 $i$ or 1 $m$ or 2 $m$ or 3 $m$ or 4 $m$ or 5 $m$ or 6 $m$ or 7 $m$ or 8 $m$ The first digit 0 , 1 ,..., 8 represents the operation test(i), set(m), clear(m), flip(m), all(m), any(m), none(m), count(m) or val(m) respectively. Output Print the result in a line for each test, all, any, none, count and val operation. Constraints $1 \leq n \leq 10$ $1 \leq k \leq 64$ $1 \leq q \leq 200,000$ $0 \leq i < 64$ $0 \leq m < n$ Sample Input 1 3 3 0 1 3 1 3 3 0 1 2 8 1 0 2 1 3 1 4 2 5 2 6 2 7 2 8 2 Sample Output 1 0 1 0 2 3 | 35,385 |
Cross Points of a Circe and a Line For given a circle $c$ and a line $l$, print the coordinates of the cross points of them. Input The input is given in the following format. $cx\; cy\; r$ $q$ $Line_1$ $Line_2$ : $Line_q$ In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given. In the following $q$ lines, as queries, $Line_i$ are given ($1 \leq i \leq q$) in the following format. $x_1\; y_1\; x_2\; y_2$ Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers. Output For each query, print the coordinates of the cross points in the following rules. If there is one cross point, print two coordinates with the same values. Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first. The output values should be in a decimal fraction with an error less than 0.000001. Constraints $p1$ and $p2$ are different The circle and line have at least one cross point $1 \leq q \leq 1,000$ $-10,000 \leq cx, cy, x1, y1, x2, y2 \leq 10,000$ $1 \leq r \leq 10,000$ Sample Input and Output Sample Input 2 1 1 2 0 1 4 1 3 0 3 3 Sample Output 1.00000000 1.00000000 3.00000000 1.00000000 3.00000000 1.00000000 3.00000000 1.00000000 | 35,386 |
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Score : 600 points Problem Statement There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i . When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable. Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line. Choose a robot and activate it. This operation cannot be done when there is a robot moving. While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively. How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353 , since it can be enormous. Constraints 1 \leq N \leq 2 \times 10^5 -10^9 \leq X_i \leq 10^9 1 \leq D_i \leq 10^9 X_i \neq X_j (i \neq j) All values in input are integers. Input Input is given from Standard Input in the following format: N X_1 D_1 : X_N D_N Output Print the number of possible sets of robots remaining on the number line, modulo 998244353 . Sample Input 1 2 1 5 3 3 Sample Output 1 3 There are three possible sets of robots remaining on the number line: \{1, 2\} , \{1\} , and \{\} . These can be achieved as follows: If Takahashi activates nothing, the robots \{1, 2\} will remain. If Takahashi activates Robot 1 , it will activate Robot 2 while moving, after which there will be no robots on the number line. This state can also be reached by activating Robot 2 and then Robot 1 . If Takahashi activates Robot 2 and finishes doing the operation, the robot \{1\} will remain. Sample Input 2 3 6 5 -1 10 3 3 Sample Output 2 5 There are five possible sets of robots remaining on the number line: \{1, 2, 3\} , \{1, 2\} , \{2\} , \{2, 3\} , and \{\} . Sample Input 3 4 7 10 -10 3 4 3 -4 3 Sample Output 3 16 None of the robots influences others. Sample Input 4 20 -8 1 26 4 0 5 9 1 19 4 22 20 28 27 11 8 -3 20 -25 17 10 4 -18 27 24 28 -11 19 2 27 -2 18 -1 12 -24 29 31 29 29 7 Sample Output 4 110 Remember to print the count modulo 998244353 . | 35,388 |
Generic Poker You have a deck of N à M cards. Each card in the deck has a rank. The range of ranks is 1 through M , and the deck includes N cards of each rank. We denote a card with rank m by m here. You can draw a hand of L cards at random from the deck. If the hand matches the given pattern, some bonus will be rewarded. A pattern is described as follows. hand_pattern = card_pattern 1 ' ' card_pattern 2 ' ' ... ' ' card_pattern L card_pattern = '*' | var_plus var_plus = variable | var_plus '+' variable = 'a' | 'b' | 'c' hand_pattern A hand matches the hand_pattern if each card_pattern in the hand_pattern matches with a distinct card in the hand. card_pattern If the card_pattern is an asterisk ('*'), it matches any card. Characters 'a', 'b', and 'c' denote variables and all the occurrences of the same variable match cards of the same rank. A card_pattern with a variable followed by plus ('+') characters matches a card whose rank is the sum of the rank corresponding to the variable and the number of plus characters. You can assume that, when a hand_pattern includes a card_pattern with a variable followed by some number of plus characters, it also includes card_patterns with that variable and all smaller numbers (including zero) of plus characters. For example, if 'a+++' appears in a hand_pattern, card_patterns 'a', 'a+', and 'a++' also appear in the hand_pattern. There is no restriction on which ranks different variables mean. For example, 'a' and 'b' may or may not match cards of the same rank. We show some example hand_patterns. The pattern a * b a b matches the hand: 3 3 10 10 9 with 'a's and 'b's meaning 3 and 10 (or 10 and 3), respectively. This pattern also matches the following hand. 3 3 3 3 9 In this case, both 'a's and 'b's mean 3. The pattern a a+ a++ a+++ a++++ matches the following hand. 4 5 6 7 8 In this case, 'a' should mean 4. Your mission is to write a program that computes the probability that a hand randomly drawn from the deck matches the given hand_pattern. Input The input is a sequence of datasets. Each dataset is formatted as follows. N M L card_pattern 1 card_pattern 2 ... card_pattern L The first line consists of three positive integers N , M , and L . N indicates the number of cards in each rank, M indicates the number of ranks, and L indicates the number of cards in a hand. N , M , and L are constrained as follows. 1 †N †7 1 †M †60 1 †L †7 L †N à M The second line describes a hand_pattern. The end of the input is indicated by a line containing three zeros separated by a single space. Output For each dataset, output a line containing a decimal fraction which means the probability of a hand matching the hand_pattern. The output should not contain an error greater than 10 â8 . No other characters should be contained in the output. Sample Input 1 1 1 a 3 3 4 a+ * a * 2 2 3 a a b 2 2 3 * * * 2 2 3 * b b 2 2 2 a a 2 3 3 a a+ a++ 2 6 6 a a+ a++ b b+ b++ 4 13 5 a a * * * 4 13 5 a a b b * 4 13 5 a a a * * 4 13 5 a a+ a++ a+++ a++++ 4 13 5 * * * * * 4 13 5 a a a b b 4 13 5 a a a a * 7 60 7 a b a b c c * 7 60 7 * * * * * * * 7 60 7 a a+ a++ a+++ a++++ a+++++ a++++++ 1 14 4 b a+ a a 0 0 0 Output for the Sample Input 1.0000000000 0.8809523810 1.0000000000 1.0000000000 1.0000000000 0.3333333333 0.4000000000 0.1212121212 0.4929171669 0.0492196879 0.0228091236 0.0035460338 1.0000000000 0.0014405762 0.0002400960 0.0002967709 1.0000000000 0.0000001022 0.0000000000 | 35,389 |
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Score : 700 points Problem Statement You are given two sequences a and b , both of length 2N . The i -th elements in a and b are a_i and b_i , respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N . The beauty of a pair (s,t) is calculated as follows: Let X=0 . For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i , and increment X by b_i otherwise. The beauty of (s,t) is the final value of X . You will be given Q queries. Process them in order. In the i -th query, update the value of a_{p_i} to x_i , and the value of b_{p_i} to y_i . Then, find the maximum possible beauty of a pair of balanced sequences of parentheses. In this problem, only the sequences below are defined to be balanced sequences of parentheses. An empty string The concatenation of ( , s , ) in this order, where s is a balanced sequence of parentheses The concatenation of s , t in this order, where s and t are balanced sequences of parentheses Constraints 1 \leq N,Q \leq 10^{5} -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9} 1 \leq p_i \leq 2N All input values are integers. Partial Scores In the test set worth 200 points, N \leq 5 and Q \leq 10 . In the test set worth 300 points, Q = 1 . Input Input is given from Standard Input in the following format: N Q a_1 a_2 ... a_{2N} b_1 b_2 ... b_{2N} p_1 x_1 y_1 : p_Q x_Q y_Q Output Print Q lines. The i -th line should contain the response to the i -th query. Sample Input 1 2 2 1 1 7 3 4 2 3 3 2 4 6 3 2 5 Sample Output 1 15 15 The first query updates a and b to a=(1,4,7,3),b=(4,6,3,3) . The maximum possible beauty is 15 for (s,t) =( ()() , ()() ) . The second query updates a and b to a=(1,4,2,3),b=(4,6,5,3) . The maximum possible beauty is 15 for (s,t) =( ()() , (()) ) . Sample Input 2 7 7 34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29 46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17 7 27 34 12 -2 22 4 -50 -12 3 -32 15 8 -7 23 3 -30 11 4 -2 23 Sample Output 2 311 312 260 286 296 292 327 | 35,392 |
Problem D: Rotation Estimation Mr. Nod is an astrologist and has defined a new constellation. He took two photos of the constellation to foretell a future of his friend. The constellation consists of n stars. The shape of the constellation in these photos are the same, but the angle of them are different because these photos were taken on a different day. He foretells a future by the difference of the angle of them. Your job is to write a program to calculate the difference of the angle of two constellation. Input The input is a sequence of datasets. Each dataset is given in the following format: n x 1,1 y 1,1 ... x 1, n y 1, n x 2,1 y 2,1 ... x 2, n y 2, n The first line of each dataset contains a positive integers n ( n †1,000). The next n lines contain two real numbers x 1, i and y 1, i (| x 1, i |, | y 1, i | †100), where ( x 1, i , y 1, i ) denotes the coordinates of the i -th star of the constellation in the first photo. The next n lines contain two real numbers x 2, i and y 2, i (| x 2, i |, | y 2, i | †100), where ( x 2, i , y 2, i ) denotes the coordinates of the i -th star of the constellation in the second photo. Note that the ordering of the stars does not matter for the sameness. It is guaranteed that distance between every pair of stars in each photo is larger than 10 -5 . The input is terminated in case of n = 0. This is not part of any datasets and thus should not be processed. Output For each dataset, you should print a non-negative real number which is the difference of the angle of the constellation in the first photo and in the second photo. The difference should be in radian, and should not be negative. If there are two or more solutions, you should print the smallest one. The difference may be printed with any number of digits after decimal point, provided the absolute error does not exceed 10 -7 . No extra space or character is allowed. Sample Input 3 0.0 0.0 1.0 1.0 0.0 1.0 3.0 3.0 2.0 2.0 3.0 2.0 0 Output for the Sample Input 3.14159265359 | 35,393 |
Score : 100 points Problem Statement You are given four digits N_1, N_2, N_3 and N_4 . Determine if these can be arranged into the sequence of digits " 1974 ". Constraints 0 \leq N_1, N_2, N_3, N_4 \leq 9 N_1, N_2, N_3 and N_4 are integers. Input Input is given from Standard Input in the following format: N_1 N_2 N_3 N_4 Output If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits " 1974 ", print YES ; if they cannot, print NO . Sample Input 1 1 7 9 4 Sample Output 1 YES We can get 1974 by swapping N_2 and N_3 . Sample Input 2 1 9 7 4 Sample Output 2 YES We already have 1974 before doing anything. Sample Input 3 1 2 9 1 Sample Output 3 NO Sample Input 4 4 9 0 8 Sample Output 4 NO | 35,394 |
Multi-ending Story You are a programmer who loves bishojo games (a sub-genre of dating simulation games). A game, which is titled "I * C * P * C!" and was released yesterday, has arrived to you just now. This game has multiple endings. When you complete all of those endings, you can get a special figure of the main heroine, Sakuya. So, you want to hurry and play the game! But, let's calm down a bit and think how to complete all of the endings in the shortest time first. In fact, you have a special skill that allows you to know the structure of branching points of games. By using the skill, you have found out that all of the branching points in this game are to select two choices "Yes" or "No", and once a different choice is taken the branched stories flow to different endings; they won't converge any more, like a binary tree. You also noticed that it takes exactly one minute to proceed the game from a branching point to another branching point or to an ending. In addition, you can assume it only takes negligible time to return to the beginning of the game (``reset'') and to play from the beginning to the first branching point. The game has an additional feature called "Quick Save", which can significantly reduce the playing time for completion. The feature allows you to record the point where you are currently playing and return there at any time later. You can record any number of times, but you can hold only the last recorded point. That is, when you use Quick Save, you overwrite the previous record. If you want to return to the overwritten point, you must play the game from the beginning once again. Well, let's estimate how long it will take for completing all of the endings in the shortest time. Input A data set is given in the following format. The first line of the data set contains one integer N ( 2 \leq N \leq 500{,}000 ), which denotes the number of the endings in this game. The following N-1 lines describe the branching points. The i -th line describes the branching point of ID number i and contains two integers Yes_i and No_i ( i + 1 \leq Yes_i, No_i \leq N ), which denote the ID numbers of the next branching points when you select Yes or No respectively. Yes_i = N means that you can reach an ending if you select Yes, and so for No_i = N . The branching point with ID 1 is the first branching point. The branching points with ID between 2 and N-1 (inclusive) appear exactly once in Yes_i 's and No_i 's. Output Print the shortest time in a line. Sample Input 1 4 2 3 4 4 4 4 Output for the Sample Input 1 6 Sample Input 2 5 5 2 3 5 5 4 5 5 Output for the Sample Input 2 8 | 35,395 |
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¥ååœ¢åŒ 1è¡ç®ã§ã¯ M (è¡æ°:瞊ã®åžæ°) ãš N (åæ°:暪ã®åžæ°) ãäžããããã 2è¡ç®ãã M è¡ãé·ã N ã®æååã1è¡ãã€äžããããã i çªç®ã®æååã® j æåç®ã¯ i è¡ j åç®ã®åžã®ç¶æ
ãè¡šããåæåã¯'-'ã'x'ããããã¯'o'ã®ããããã§ããã空åžã'-'ãäŒæ©äžããããçåŸã座ãåžã'x'ããã以å€ã®çåŸã座ã£ãŠããåžã'o'ãšããã å¶çŽ 0<M †100 0<N †100 åºååœ¢åŒ æ¡ä»¶ã«ãã£ãŠAåã座ããåžã®åæ°ã1è¡ã§åºåãããæåŸã«æ¹è¡ãå¿ããªãããšã å
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¥åäŸ3 3 5 ----- ----- ----- åºåäŸ3 10 å
¥åäŸ4 4 6 o-oxoo oo-ooo oooxo- o-ooox åºåäŸ4 0 | 35,398 |
Problem F: Line Puzzle ããã°ã©ãã³ã°ã§ããºã«ã解ããŠã¿ããã n à n ã®æ°åãæ Œåç¶ã«äžŠãã§ãããæ°åã®ããã€ãã¯äžžã§å²ãŸããŠãããããããèµ·ç¹ãšåŒã¶ããšã«ãããããºã«ã®ã«ãŒã«ã¯ä»¥äžã®ãšããã§ããïŒ åèµ·ç¹ãã瞊ã»æšªã«é²ãïŒæ¬ã®ç·ãåŒãïŒæãã«ã¯åŒããªãïŒã éã£ãæ°åã®åãèµ·ç¹ã®æ°åãšåãã«ãªãããã«ç·ã䌞ã°ãã ç·ã¯æåããããŠã¯ãããªãã ç·ã¯ãã§ã«åŒãããæ°åãéãããšã¯ã§ããªãïŒç·ã¯äº€å·®ããŠã¯ãããªãïŒã ç·ã¯ïŒå以äžã®èµ·ç¹ãéãããšã¯ã§ããªãã äžå³ã«ç€ºãããã«ãããºã«ã®ãŽãŒã«ã¯ãã¹ãŠã®èµ·ç¹ã䜿ãããã¹ãŠã®æ°åã«ç·ãåŒãããšã§ããã ããªãã®ä»äºã¯ãããºã«ã解ãããã°ã©ã ãäœæããããšã§ããã ãã ããã®åé¡ã§ã¯ãäžããããããºã«ã解ãããã®ãã©ãããå€å®ããã ãã§ããã Input å
¥åã¯è€æ°ã®ããŒã¿ã»ãããããªããåããŒã¿ã»ããã®åœ¢åŒã¯ä»¥äžã®ãšããã§ããïŒ n n à n ã®æ°å n à n ã®æ°åãäžããããããºã«ã瀺ããèµ·ç¹ã®æ°åã¯è² ã®æ°ãšããŠäžããããã n ã 0 ã®ãšãå
¥åã®çµããã瀺ãã n 㯠3 ä»¥äž 8 以äžãèµ·ç¹ä»¥å€ã®æ°å㯠1 ä»¥äž 50 以äžãèµ·ç¹ã¯ -50 ä»¥äž -1 以äžã§ãããšä»®å®ããŠããããŸããå
¥åãããããºã«ã®æ§è³ªãšããŠä»¥äžã®ããšãä»®å®ããŠããïŒ äžããããããºã«ã®åè¡ãååã«ã¯æäœã§ãïŒã€ã®èµ·ç¹ãããã èµ·ç¹ã®åæ°ã¯ãå
šäœã®æ°åã®åæ° ( n à n ) ã® 20 % ãã 40 % çšåºŠã§ããã Output åããŒã¿ã»ããã«å¯ŸããŠãããºã«ã解ãããã®ã§ããã° "YES" ããããã§ãªããã° "NO" ãšïŒè¡ã«åºåããã Sample Input 3 -3 1 1 2 -4 1 2 1 -1 3 -4 1 1 1 1 -6 1 -5 3 4 -8 6 -2 1 2 -7 -2 1 1 -1 1 1 1 1 1 -5 6 2 2 3 -7 3 2 1 -10 1 1 3 2 2 6 5 2 -6 1 3 4 -23 2 2 5 3 3 -6 2 3 7 -7 2 3 2 -5 -13 6 2 2 3 -7 3 2 1 -10 1 1 3 2 2 6 5 2 -6 1 3 4 -23 2 2 5 3 3 -6 2 3 7 -7 2 3 2 -5 -12 0 Output for the Sample Input YES NO NO YES NO | 35,399 |
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