Split (1)

train · 39.1k rows

task stringlengths 0 154k	__index_level_0__ int64 0 39.2k
Zero AND Subsets 非負整数の多重集合 a_1,a_2,..,a_N が与えられます。この集合の空でない部分集合であって、値のbitwiseANDが 0 になるものはいくつありますか。答えを 10^9+7 で割った余りを求めてください。入力 N a_1 a_2...a_N 出力答えを 10^9+7 で割った余りを出力せよ。制約 1 \leq N \leq 10^5 0 \leq a_i \leq 2^{20}-1 入力例 6 8 6 9 1 2 1 出力例 51	38,175
Is it a Right Triangle? Write a program which judges wheather given length of three side form a right triangle. Print " YES " if the given sides (integers) form a right triangle, " NO " if not so. Input Input consists of several data sets. In the first line, the number of data set, N is given. Then, N lines follow, each line corresponds to a data set. A data set consists of three integers separated by a single space. Constraints 1 ≤ length of the side ≤ 1,000 N ≤ 1,000 Output For each data set, print " YES " or " NO ". Sample Input 3 4 3 5 4 3 6 8 8 8 Output for the Sample Input YES NO NO	38,176
Problem I: Revenge of Voronoi A discrete Voronoi diagram is a derivation of a Voronoi diagram. It is represented as a set of pixels. Each of the generatrices lies on the center of some pixel. Each pixel belongs to the generatrix nearest from the center of the pixel in the sense of Manhattan distance. The Manhattan distance d between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by the following formula: d = \| x 1 - x 2 \| + \| y 1 - y 2 \| Your task is to find a set of generatrices which generates a given discrete Voronoi diagram. In the given diagram, each generatrix is given a unique lowercase letter as its identifier, and each pixel is represented by the identifier of the generatrix the pixel belongs to. If a pixel has multiple generatrices at the same distance from its center, it belongs to the generatrix with the most preceding identifier among them (i.e. the smallest character code). Input The input consists of multiple test cases. Each test case begins with a line containing two integers W (1 ≤ W ≤ 32) and H (1 ≤ H ≤ 32), which denote the width and height of the discrete Voronoi diagram. The following H lines, each of which consists of W letters, give one discrete Voronoi diagram. Each letter represents one pixel. The end of input is indicated by a line with two zeros. This is not a part of any test cases. Output For each test case, print the case number and the coordinates of generatrices as shown in the sample output. Each generatrix line should consist of its identifier, x -coordinate, and y -coordinate. Generatrices should be printed in alphabetical order of the identifiers. Each coordinate is zero-based where (0, 0) indicates the center of the top-left corner pixel of the diagram. You may assume that every test case has at least one solution. If there are multiple solutions, any one is acceptable. Print a blank line after every test case including the last one. Sample Input 4 3 ooxx ooxx ooxx 4 1 null 4 4 aabb aabb ccdd ccdd 0 0 Output for the Sample Input Case 1: o 0 0 x 2 0 Case 2: l 2 0 n 0 0 u 1 0 Case 3: a 0 0 b 2 0 c 0 2 d 2 2	38,177
Score : 100 points Problem Statement Given is an integer N . Takahashi chooses an integer a from the positive integers not greater than N with equal probability. Find the probability that a is odd. Constraints 1 \leq N \leq 100 Input Input is given from Standard Input in the following format: N Output Print the probability that a is odd. Your output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-6} . Sample Input 1 4 Sample Output 1 0.5000000000 There are four positive integers not greater than 4 : 1 , 2 , 3 , and 4 . Among them, we have two odd numbers: 1 and 3 . Thus, the answer is \frac{2}{4} = 0.5 . Sample Input 2 5 Sample Output 2 0.6000000000 Sample Input 3 1 Sample Output 3 1.0000000000	38,178
Score : 300 points Problem Statement Every day, N passengers arrive at Takahashi Airport. The i -th passenger arrives at time T_i . Every passenger arrived at Takahashi airport travels to the city by bus. Each bus can accommodate up to C passengers. Naturally, a passenger cannot take a bus that departs earlier than the airplane arrives at the airport. Also, a passenger will get angry if he/she is still unable to take a bus K units of time after the arrival of the airplane. For that reason, it is necessary to arrange buses so that the i -th passenger can take a bus departing at time between T_i and T_i + K (inclusive). When setting the departure times for buses under this condition, find the minimum required number of buses. Here, the departure time for each bus does not need to be an integer, and there may be multiple buses that depart at the same time. Constraints 2 \leq N \leq 100000 1 \leq C \leq 10^9 1 \leq K \leq 10^9 1 \leq T_i \leq 10^9 C , K and T_i are integers. Input The input is given from Standard Input in the following format: N C K T_1 T_2 : T_N Output Print the minimum required number of buses. Sample Input 1 5 3 5 1 2 3 6 12 Sample Output 1 3 For example, the following three buses are enough: A bus departing at time 4.5 , that carries the passengers arriving at time 2 and 3 . A bus departing at time 6 , that carries the passengers arriving at time 1 and 6 . A bus departing at time 12 , that carries the passenger arriving at time 12 . Sample Input 2 6 3 3 7 6 2 8 10 6 Sample Output 2 3	38,179
Score : 400 points Problem Statement We have a large square grid with H rows and W columns. Iroha is now standing in the top-left cell. She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell. However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells. Find the number of ways she can travel to the bottom-right cell. Since this number can be extremely large, print the number modulo 10^9+7 . Constraints 1 ≦ H, W ≦ 100,000 1 ≦ A < H 1 ≦ B < W Input The input is given from Standard Input in the following format: H W A B Output Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7 . Sample Input 1 2 3 1 1 Sample Output 1 2 We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right". Sample Input 2 10 7 3 4 Sample Output 2 3570 There are 12 forbidden cells. Sample Input 3 100000 100000 99999 99999 Sample Output 3 1 Sample Input 4 100000 100000 44444 55555 Sample Output 4 738162020	38,180
Problem G: Captain Q′s Treasure You got an old map, which turned out to be drawn by the infamous pirate “Captain Q”. It shows the locations of a lot of treasure chests buried in an island. The map is divided into square sections, each of which has a digit on it or has no digit. The digit represents the number of chests in its 9 neighboring sections (the section itself and its 8 neighbors). You may assume that there is at most one chest in each section. Although you have the map, you can't determine the sections where the chests are buried. Even the total number of chests buried in the island is unknown. However, it is possible to calculate the minimum number of chests buried in the island. Your mission in this problem is to write a program that calculates it. Input The input is a sequence of datasets. Each dataset is formatted as follows. h w map The first line of a dataset consists of two positive integers h and w . h is the height of the map and w is the width of the map. You may assume 1≤ h ≤15 and 1≤ w ≤15. The following h lines give the map. Each line consists of w characters and corresponds to a horizontal strip of the map. Each of the characters in the line represents the state of a section as follows. ‘.’: The section is not a part of the island (water). No chest is here. ‘’: The section is a part of the island, and the number of chests in its 9 neighbors is not known. ‘0’-‘9’: The section is a part of the island, and the digit represents the number of chests in its 9 neighbors. You may assume that the map is not self-contradicting, i.e., there is at least one arrangement of chests. You may also assume the number of sections with digits is at least one and at most 15. A line containing two zeros indicates the end of the input. Output For each dataset, output a line that contains the minimum number of chests. The output should not contain any other character. Sample Input 5 6 2.2** ..... ..2... ..... 2.2* 6 5 .2. .... .... ..2.. .... .2. 5 6 .1111. ... 33.... *...0 .2*. 6 9 ....1.... ...1.1... ....1.... .1....1. 1.1**1.1 .1....1. 9 9 ********* 4444* ********* 4444* ********* 4444* ********* 444 ******* 0 0 Output for the Sample Input 6 5 5 6 23	38,181
社員旅行 Problem Statement あなたの会社には n 人の社員が存在する． m 個の社員 (a_i,b_i) の組について， a_i は b_i の上司である．社員 x が社員 y の実質的な上司であるとは，次のうち少なくとも一方が成り立つことをいう． x が y の上司である． y の実質的な上司である社員 z が存在して， x は z の上司である．あなたの会社で，自分自身が自分の実質的な上司であるような社員は存在しない．あなたの会社では社員が全員参加する社員旅行が計画されている．全社員の要求により，旅館での部屋割りは「よい部屋割り」でなければならない．ある部屋割りが「よい部屋割り」であるとは以下の両方が満たされることをいう．各社員はどこかの部屋に割り振られる．社員 x と社員 y が同じ部屋に割り振られているとき， x は y の実質的な上司でない．幹事の社員は非常に優秀なので，「よい部屋割り」でかつ必要な部屋の数が最小になるように部屋割りを行った．しかし残念なことに予算が不足している．どうしても必要な部屋の数を減らさなければならないらしい．そこで，人事部で働くあなたは上司-部下の関係を一つだけ解消することによって，「よい部屋割り」を得るために必要な部屋の数を減らすことにした．さて，どの関係を解消すればよいのだろう？ Input 入力は以下の形式に従う．与えられる数は全て整数である． n m a_1 b_1 ... a_m b_m Constraints 2≦n≦10^5 1≦m≦2 \times 10^5 1≦a_i<b_i≦n i \neq j ならば (a_i, b_i) \neq (a_j, b_j) Output 次を満たすような i を昇順に1行ずつ出力せよ．「 a_i が b_i の上司である」という関係を解消したとき，「よい部屋割り」を得るために必要な部屋の数を減らすことができる．そのような i が存在しない場合は-1を1行に出力せよ． Sample Input 1 5 4 1 2 2 3 3 4 3 5 Output for the Sample Input 1 1 2	38,182
Problem E: 足し算ゲームねこのファーブルは足し算を用いた簡単なゲームを思いつき、同じくねこで友達のオードリーと一緒にやってみることにした。ゲームのルールは次のようなものである。まず最初に、適当な正の整数を選び、そこからスタートする。各プレーヤーは、その数のうち隣り合う2つの桁を選択して和を計算し、もとの2つの数字と置き換える。たとえば、「1234」の十の位と百の位を選ぶと、次の数は「154」となる。「5555」の十の位と百の位を選んだ場合は「5105」となる。このような操作を数が1桁になるまで交互に繰り返し、操作ができなくなったプレーヤーが負けとなる。ゲーム開始時の整数の値が与えられる。先攻であるファーブルと後攻であるオードリーがいずれも最適な戦略を取るとき、どちらが勝つのかを判定するプログラムを作成せよ。 Input 入力は、ゲーム開始時の数を表す1000桁以下の正の整数が1つ書かれた1行のみからなる。なお、最上位の桁は0ではない。 Output ファーブルが勝つなら "Fabre wins."、オードリーが勝つなら "Audrey wins." と1行に出力せよ。最後にピリオドをつける必要があることに注意すること。 Notes on Submission 上記形式で複数のデータセットが与えられます。入力データの 1 行目にデータセットの数が与えられます。各データセットに対する出力を上記形式で順番に出力するプログラムを作成して下さい。 Sample Input 3 1234 5555 9 Output for the Sample Input Audrey wins. Fabre wins. Audrey wins.	38,183
Score : 300 points Problem Statement A programming competition site AtCode provides algorithmic problems. Each problem is allocated a score based on its difficulty. Currently, for each integer i between 1 and D (inclusive), there are p_i problems with a score of 100i points. These p_1 + … + p_D problems are all of the problems available on AtCode. A user of AtCode has a value called total score . The total score of a user is the sum of the following two elements: Base score: the sum of the scores of all problems solved by the user. Perfect bonuses: when a user solves all problems with a score of 100i points, he/she earns the perfect bonus of c_i points, aside from the base score (1 ≤ i ≤ D) . Takahashi, who is the new user of AtCode, has not solved any problem. His objective is to have a total score of G or more points. At least how many problems does he need to solve for this objective? Constraints 1 ≤ D ≤ 10 1 ≤ p_i ≤ 100 100 ≤ c_i ≤ 10^6 100 ≤ G All values in input are integers. c_i and G are all multiples of 100 . It is possible to have a total score of G or more points. Input Input is given from Standard Input in the following format: D G p_1 c_1 : p_D c_D Output Print the minimum number of problems that needs to be solved in order to have a total score of G or more points. Note that this objective is always achievable (see Constraints). Sample Input 1 2 700 3 500 5 800 Sample Output 1 3 In this case, there are three problems each with 100 points and five problems each with 200 points. The perfect bonus for solving all the 100 -point problems is 500 points, and the perfect bonus for solving all the 200 -point problems is 800 points. Takahashi's objective is to have a total score of 700 points or more. One way to achieve this objective is to solve four 200 -point problems and earn a base score of 800 points. However, if we solve three 100 -point problems, we can earn the perfect bonus of 500 points in addition to the base score of 300 points, for a total score of 800 points, and we can achieve the objective with fewer problems. Sample Input 2 2 2000 3 500 5 800 Sample Output 2 7 This case is similar to Sample Input 1, but the Takahashi's objective this time is 2000 points or more. In this case, we inevitably need to solve all five 200 -point problems, and by solving two 100 -point problems additionally we have the total score of 2000 points. Sample Input 3 2 400 3 500 5 800 Sample Output 3 2 This case is again similar to Sample Input 1, but the Takahashi's objective this time is 400 points or more. In this case, we only need to solve two 200 -point problems to achieve the objective. Sample Input 4 5 25000 20 1000 40 1000 50 1000 30 1000 1 1000 Sample Output 4 66 There is only one 500 -point problem, but the perfect bonus can be earned even in such a case.	38,184
Score : 2200 points Problem Statement We have two indistinguishable pieces placed on a number line. Both pieces are initially at coordinate 0 . (They can occupy the same position.) We can do the following two kinds of operations: Choose a piece and move it to the right (the positive direction) by 1 . Move the piece with the smaller coordinate to the position of the piece with the greater coordinate. If two pieces already occupy the same position, nothing happens, but it still counts as doing one operation. We want to do a total of N operations of these kinds in some order so that one of the pieces will be at coordinate A and the other at coordinate B . Find the number of ways to move the pieces to achieve it. The answer can be enormous, so compute the count modulo 998244353 . Two ways to move the pieces are considered different if and only if there exists an integer i ( 1 \leq i \leq N ) such that the set of the coordinates occupied by the pieces after the i -th operation is different in those two ways. Constraints 1 \leq N \leq 10^7 0 \leq A \leq B \leq N All values in input are integers. Input Input is given from Standard Input in the following format: N A B Output Print the number of ways to move the pieces to achieve our objective, modulo 998244353 . Sample Input 1 5 1 3 Sample Output 1 4 Shown below are the four ways to move the pieces, where (x,y) represents the state where the two pieces are at coordinates x and y . (0,0)→(0,0)→(0,1)→(0,2)→(0,3)→(1,3) (0,0)→(0,0)→(0,1)→(0,2)→(1,2)→(1,3) (0,0)→(0,0)→(0,1)→(1,1)→(1,2)→(1,3) (0,0)→(0,1)→(1,1)→(1,1)→(1,2)→(1,3) Sample Input 2 10 0 0 Sample Output 2 1 Sample Input 3 10 4 6 Sample Output 3 197 Sample Input 4 1000000 100000 200000 Sample Output 4 758840509	38,185
Problem A: How I Wonder What You Are! One of the questions children often ask is "How many stars are there in the sky?" Under ideal conditions, even with the naked eye, nearly eight thousands are observable in the northern hemisphere. With a decent telescope, you may find many more, but, as the sight field will be limited, you may find much less at a time. Children may ask the same questions to their parents on a planet of some solar system billions of light-years away from the Earth. Their telescopes are similar to ours with circular sight fields, but alien kids have many eyes and can look into different directions at a time through many telescopes. Given a set of positions of stars, a set of telescopes and the directions they are looking to, your task is to count up how many stars can be seen through these telescopes. Input The input consists of one or more datasets. The number of datasets is less than 50. Each dataset describes stars and the parameters of the telescopes used. The first line of a dataset contains a positive integer n not exceeding 500, meaning the number of stars. Each of the n lines following it contains three decimal fractions, s x , s y , and s z . They give the position ( s x , s y , s z ) of the star described in Euclidean coordinates. You may assume -1000 ≤ s x ≤ 1000, -1000 ≤ s y ≤ 1000, -1000 ≤ s z ≤ 1000 and ( s x , s y , s z ) ≠ (0, 0, 0). Then comes a line containing a positive integer m not exceeding 50, meaning the number of telescopes. Each of the following m lines contains four decimal fractions, t x , t y , t z , and φ , describing a telescope. The first three numbers represent the direction of the telescope. All the telescopes are at the origin of the coordinate system (0, 0, 0) (we ignore the size of the planet). The three numbers give the point ( t x , t y , t z ) which can be seen in the center of the sight through the telescope. You may assume -1000 ≤ t x ≤ 1000, -1000 ≤ t y ≤ 1000, -1000 ≤ t z ≤ 1000 and ( t x , t y , t z ) ≠ (0, 0, 0). The fourth number φ (0 ≤ φ ≤ π /2) gives the angular radius, in radians, of the sight field of the telescope. Let us defie that θ i,j is the angle between the direction of the i -th star and the center direction of the j -th telescope and φ j is the angular radius of the sight field of the j -th telescope. The i -th star is observable through the j -th telescope if and only if θ i,j is less than . You may assume that \| θ i,j - φ j \| > 0.00000001 for all pairs of i and j . Figure 1: Direction and angular radius of a telescope The end of the input is indicated with a line containing a single zero. Output For each dataset, one line containing an integer meaning the number of stars observable through the telescopes should be output. No other characters should be contained in the output. Note that stars that can be seen through more than one telescope should not be counted twice or more. Sample Input 3 100 0 500 -500.243 -200.1 -300.5 0 300 200 2 1 1 1 0.65 -1 0 0 1.57 3 1 0 0 0 1 0 0 0 1 4 1 -1 -1 0.9553 -1 1 -1 0.9554 -1 -1 1 0.9553 -1 1 -1 0.9554 3 1 0 0 0 1 0 0 0 1 4 1 -1 -1 0.9553 -1 1 -1 0.9553 -1 -1 1 0.9553 -1 1 -1 0.9553 0 Output for the Sample Input 2 1 0	38,186
今年も，全国プログラミング選手権大会の時期がやってきた．全国大会の参加権を賭けた地区大会は， 2 n チームが1 対1 の勝ち残り式トーナメント方式で対決する．トーナメント表にはチーム番号 0, . . . 2 n − 1 が割り振られており，1 回戦から n 回戦までの対決手順は次の通りである． 1 回戦では，（チーム番号が l のチーム）と（チーム番号が l + 1 のチーム）が対決する．( l ≡ 0 (mod 2)) i + 1 回戦( 1 ≤ i < n ) では，「チーム番号が l 以上 l + 2 i 未満のチームのうち， i 回戦までの対決で 1 回も負けていないチーム」と「チーム番号が l + 2 i 以上 l + 2 i+1 未満のチームのうち， i 回戦までの対決で一回も負けていないチーム」が対決する．( l ≡ 0 (mod 2 i +1 )) n 回戦まで終わると，各チームの順位は 2 n − (そのチームが勝った回数) 位で確定する．なお，この対決には引き分けが存在しないため，対決したチームのいずれか一方が勝ち，もう一方が負ける．晴れて地区大会の代表に選ばれた私達は，他の地区大会の結果をマネージャーに調べてもらうことにした．ここで調べてもらった結果が「マネージャーから受け取った順位表」であった．「マネージャーから受け取った順位表」をより詳細に説明すると，長さ 2 n の数列で i ( 0 ≤ i ≤ 2 n − 1 ) 番目の要素にチーム番号 i のチームの順位が書かれているものである．だが，「マネージャーから受け取った順位表」には同じ順位が大量に並んでいた！トーナメントのルール上，同じ順位が大量に並ぶなんてありえないはずだ．そこで，「マネージャーから受け取った順位表」を「無矛盾な順位表」にするために順位を変更するチーム数の最小値を計算してどのくらい順位表が間違っているかをマネージャーに教えてあげよう．「無矛盾な順位表」とは，順位が確定したトーナメントの結果として起こりうる順位表のことを表す． Input 入力には，「マネージャーから受け取った順位表」が以下の形式で与えられる． n m a 0 a 1 . . . a m b 0 b 1 . . . b m−1 1 行目は n, m の2 個の整数からなり， 2 n は「地区大会の参加チーム数」， m は「『マネージャーから受け取った順位表』で連続した順位が並んでいる区間の個数」を表す． 2 行目は a i (0 ≤ i ≤ m) の m + 1 個の整数からなり，各 a i は「『マネージャーから受け取った順位表』で連続した順位が並んでいる区間の区切り位置」を表す． 3 行目は b i (0 ≤ i < m) の m 個の整数からなり，各2 b i は「『マネージャーから受け取った順位表』におけるチーム番号が a i 以上 a i+1 未満のチームの順位」を表す． Constraints 1 ≤ n ≤ 30 1 ≤ m ≤ 10,000 0 = a 0 < a 1 ≤ . . . ≤ a m−1 < a m = 2 n 0 ≤ b i ≤ n Output 「マネージャーから受け取った順位表」を「無矛盾な順位表」にするために順位を変更するチーム数の最小値を1 行に出力せよ． Sample Input 1 1 1 0 2 1 Output for the Sample Input 1 1 参加チーム数が2 の「無矛盾な順位表」は，{"チーム番号 0 のチームの順位", "チーム番号 1 のチームの順位"} として {1, 2} と {2, 1} の2 通りがある．順位表 {2, 2} を「無矛盾な順位表」に修正するためには，いずれかのチームの順位を 1 に変更しなければならない． Sample Input 2 2 3 0 1 2 4 0 1 2 Output for the Sample Input 2 2 Sample Input 3 2 3 0 1 3 4 0 2 1 Output for the Sample Input 3 0 Sample Input 4 4 5 0 1 2 4 8 16 0 1 2 3 4 Output for the Sample Input 4 10	38,187
問題 2: 投票 (Vote) 問題 20XX年に東京で世界的なスポーツ大会が開かれることになった．プログラミングコンテストはスポーツとして世界で楽しまれており，競技として採用される可能性がある．採用される競技を決める審査委員会について調べたところ，次のようなことが分かった．審査委員会のために，候補となる N 個の競技を面白い方から順番に並べたリストが作成された．リストの上から i 番目には i 番目に面白い競技が書かれている．それを競技 i とする．さらに競技 i の開催に必要な費用 A i が書かれている．また，審査委員会は委員 1 から委員 M までの M 人の委員で構成されている．委員 j は自分の審査基準 B j をもっており，開催に必要な費用が B j 以下の競技のうち最も面白いものに 1 票を投票した．どの委員の審査基準に対しても，少なくとも 1 つの競技は開催に必要な費用が審査基準以下であった．したがって，委員は全員 1 票を投票した．最も多く票を獲得した競技は 1 つだけであった．競技のリストと委員の情報が与えられたとき，最も多く票を獲得した競技の番号を求めるプログラムを作成せよ．入力入力は 1 + N + M 行からなる． 1 行目には整数 N, M (1 ≤ N ≤ 1000，1 ≤ M ≤ 1000) が書かれており，それぞれ競技の数，委員の数を表す．続く N 行のうちの i 行目 (1 ≤ i ≤ N) には整数 A i (1 ≤ A i ≤ 1000) が書かれており，競技 i の開催に必要な費用 A i を表す．続く M 行のうちの j 行目 (1 ≤ j ≤ M) には整数 B j (1 ≤ B j ≤ 1000) が書かれており，委員 j の審査基準 B j を表す．与えられる入力データにおいては，どの委員も必ず 1 票を投票し，最も多く票を獲得した競技は 1 つであることが保証されている．出力最も多く票を獲得した競技の番号を 1 行で出力せよ．入出力例入力例 1 4 3 5 3 1 4 4 3 2 出力例 1 2 入出力例 1 では，競技は 4 つあり，委員は 3 人いる．リストの 4 つの競技にかかる費用はそれぞれ 5, 3, 1, 4 である．委員 1 の審査基準は 4 である．費用が 4 以下の競技のうち最も面白いものは競技 2 である．委員 2 の審査基準は 3 である．費用が 3 以下の競技のうち最も面白いものは競技 2 である．委員 3 の審査基準は 2 である．費用が 2 以下の競技のうち最も面白いものは競技 3 である．よって，競技 2 が 2 票，競技 3 が 1 票を獲得する．最も多く票を獲得した競技は競技 2 であるので，2 を出力する．入力例 2 6 6 3 1 4 1 5 9 2 6 5 3 5 9 出力例 2 1 入出力例 2 では，競技 1 が 5 票，競技 2 が 1 票を獲得する．最も多く票を獲得した競技は競技 1 なので，1 を出力する．問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	38,188
ルパン四世怪盗「ルパン四世」は会津藩士を末裔とする美女「富士峰子」より、会津若松市に会津藩が残した軍資金が眠っていることを聞かされる。ルパンの長年の仲間である「石川越ェ門」の報告によれば、軍資金は千両箱に収められいくつかの蔵に保管されている。蔵に見張りはいないが厳重に施錠されている。しかし、越ェ門は彼が父から伝授された秘伝「鋼鉄斬り」の技を繰り出せば瞬時に蔵を破れるという。残った問題は千両箱の運搬だ。体力のないルパンと越ェ門は千両箱を一つも持てない。そこで、頼りになる男「無限大介」に運搬を頼んだ。すべての千両箱を運び出すために、ルパンは以下のような計画を立案した。まず、ルパンの運転で最初の蔵へ行き、越ェ門と大介を降ろす。越ェ門が蔵を破る大介がすべての千両箱を運び出すその千両箱を持ったままルパンが決めた次の蔵へ向かうこれを繰り返し、最後の蔵まで破り千両箱を運び出す。その間にルパンはヘリコプターを準備し最後の蔵で二人と千両箱を運び上げ脱出する。大介はどんなに重いものも運搬できるが、荷物の重さに応じて移動速度は遅くなる。ルパンは、このことを考慮して蔵を破る順番を決めなければならない。ルパンに代わって、最初の蔵を破ってから最後の蔵に辿りつくまでの移動時間が最小となるような蔵を破る順番を出力するプログラムを作成してください。ただし、蔵はすべて鶴ヶ城からまっすぐ北に走る通りに面している。蔵の数は高々 15 個であり、城からの距離は高々 10000 メートル以下である。千両箱の重さはいずれもひとつ 20 キログラムである。それぞれの蔵に収められている千両箱の個数は 10000 個以下である。蔵から蔵への移動は、通りに沿って地下に設置されている地下道を使う。大介は w キログラムの荷物を運ぶのに、分速 2,000／(70 + w ) メートルで移動する。入力データは、それぞれの蔵について蔵の番号（100 以下の整数）と城からの距離（メートル）とその蔵に保管されている千両箱の個数が与えられる。 Input 入力は以下の形式で与えられます。 n s 1 d 1 v 1 s 2 d 2 v 2 : s n d n v n 1 行目に蔵の個数 n （ n ≤ 15）、続く n 行に第 i の蔵の情報が与えられます。蔵の情報として、蔵の番号 s i (1 ≤ s i ≤ 100)、城からの距離 d i (1 ≤ d i ≤ 10000)、千両箱の数 v i (1 ≤ v i ≤ 10000) が１行に与えられます。 Output 蔵を破る順番を１行に出力してください。蔵の番号を空白で区切ってください。 Sample Input 1 2 1 100 1 2 200 2 Output for the Sample Input 1 1 2 Sample Input 2 3 11 100 1 13 200 20 12 300 3 Output for the Sample Input 2 11 12 13 Sample Input 3 5 13 199 1 51 1000 1 37 350 10 27 300 2 99 200 1000 Output for the Sample Input 3 51 37 27 13 99	38,189
Problem D: International Party Isaac H. Ives is attending an international student party (maybe for girl-hunting). Students there enjoy talking in groups with excellent foods and drinks. However, since students come to the party from all over the world, groups may not have a language spoken by all students of the group. In such groups, some student(s) need to work as interpreters, but intervals caused by interpretation make their talking less exciting. Needless to say, students want exciting talks. To have talking exciting as much as possible, Isaac proposed the following rule: the number of languages used in talking should be as little as possible, and not exceed five. Many students agreed with his proposal, but it is not easy for them to find languages each student should speak. So he calls you for help. Your task is to write a program that shows the minimum set of languages to make talking possible, given lists of languages each student speaks. Input The input consists of a series of data sets. The first line of each data set contains two integers N (1 ≤ N ≤ 30) and M (2 ≤ M ≤ 20) separated by a blank, which represent the numbers of languages and students respectively. The following N lines contain language names, one name per line. The following M lines describe students in the group. The i -th line consists of an integer K i that indicates the number of languages the i -th student speaks, and K i language names separated by a single space. Each language name consists of up to twenty alphabetic letters. A line that contains two zeros indicates the end of input and is not part of a data set. Output Print a line that contains the minimum number L of languages to be spoken, followed by L language names in any order. Each language name should be printed in a separate line. In case two or more sets of the same size is possible, you may print any one of them. If it is impossible for the group to enjoy talking with not more than five languages, you should print a single line that contains “Impossible” (without quotes). Print an empty line between data sets. Sample Input 3 4 English French Japanese 1 English 2 French English 2 Japanese English 1 Japanese 2 2 English Japanese 1 English 1 Japanese 6 7 English Dutch German French Italian Spanish 1 English 2 English Dutch 2 Dutch German 2 German French 2 French Italian 2 Italian Spanish 1 Spanish 0 0 Output for the Sample Input 2 English Japanese Impossible Impossible	38,190
Score : 2000 points Problem Statement There is a bridge that connects the left and right banks of a river. There are 2 N doors placed at different positions on this bridge, painted in some colors. The colors of the doors are represented by integers from 1 through N . For each k ( 1 \leq k \leq N ), there are exactly two doors painted in Color k . Snuke decides to cross the bridge from the left bank to the right bank. He will keep on walking to the right, but the following event will happen while doing so: At the moment Snuke touches a door painted in Color k ( 1 \leq k \leq N ), he teleports to the right side of the other door painted in Color k . It can be shown that he will eventually get to the right bank. For each i ( 1 \leq i \leq 2 N - 1 ), the section between the i -th and (i + 1) -th doors from the left will be referred to as Section i . After crossing the bridge, Snuke recorded whether or not he walked through Section i , for each i ( 1 \leq i \leq 2 N - 1 ). This record is given to you as a string s of length 2 N - 1 . For each i ( 1 \leq i \leq 2 N - 1 ), if Snuke walked through Section i , the i -th character in s is 1 ; otherwise, the i -th character is 0 . Figure: A possible arrangement of doors for Sample Input 3 Determine if there exists an arrangement of doors that is consistent with the record. If it exists, construct one such arrangement. Constraints 1 \leq N \leq 10^5 \|s\| = 2 N - 1 s consists of 0 and 1 . Input Input is given from Standard Input in the following format: N s Output If there is no arrangement of doors that is consistent with the record, print No . If there exists such an arrangement, print Yes in the first line, then print one such arrangement in the second line, in the following format: c_1 c_2 ... c_{2 N} Here, for each i ( 1 \leq i \leq 2 N ), c_i is the color of the i -th door from the left. Sample Input 1 2 010 Sample Output 1 Yes 1 1 2 2 Sample Input 2 2 001 Sample Output 2 No Sample Input 3 3 10110 Sample Output 3 Yes 1 3 2 1 2 3 The figure below is identical to the one in the statement. Sample Input 4 3 10101 Sample Output 4 No Sample Input 5 6 00111011100 Sample Output 5 Yes 1 6 1 2 3 4 4 2 3 5 6 5	38,191
Score : 300 points Problem Statement There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0 -th step. He can climb up one or two steps at a time. However, the treads of the a_1 -th, a_2 -th, a_3 -th, \ldots , a_M -th steps are broken, so it is dangerous to set foot on those steps. How many are there to climb up to the top step, that is, the N -th step, without setting foot on the broken steps? Find the count modulo 1\ 000\ 000\ 007 . Constraints 1 \leq N \leq 10^5 0 \leq M \leq N-1 1 \leq a_1 < a_2 < ... < a_M \leq N-1 Input Input is given from Standard Input in the following format: N M a_1 a_2 . . . a_M Output Print the number of ways to climb up the stairs under the condition, modulo 1\ 000\ 000\ 007 . Sample Input 1 6 1 3 Sample Output 1 4 There are four ways to climb up the stairs, as follows: 0 \to 1 \to 2 \to 4 \to 5 \to 6 0 \to 1 \to 2 \to 4 \to 6 0 \to 2 \to 4 \to 5 \to 6 0 \to 2 \to 4 \to 6 Sample Input 2 10 2 4 5 Sample Output 2 0 There may be no way to climb up the stairs without setting foot on the broken steps. Sample Input 3 100 5 1 23 45 67 89 Sample Output 3 608200469 Be sure to print the count modulo 1\ 000\ 000\ 007 .	38,192
Problem H: Co-occurrence Search A huge amount of information is being heaped on WWW. Albeit it is not well-organized, users can browse WWW as an unbounded source of up-to-date information, instead of consulting established but a little out-of-date encyclopedia. However, you can further exploit WWW by learning more about keyword search algorithms. For example, if you want to get information on recent comparison between Windows and UNIX, you may expect to get relevant description out of a big bunch of Web texts, by extracting texts that contain both keywords "Windows" and "UNIX" close together. Here we have a simplified version of this co-occurrence keyword search problem, where the text and keywords are replaced by a string and key characters, respectively. A character string S of length n (1 ≤ n ≤ 1,000,000) and a set K of k distinct key characters a 1 , ..., a k (1 ≤ k ≤ 50) are given. Find every shortest substring of S that contains all of the key characters a 1 , ..., a k . Input The input is a text file which contains only printable characters (ASCII codes 21 to 7E in hexadecimal) and newlines. No white space such as space or tab appears in the input. The text is a sequence of the shortest string search problems described above. Each problem consists of character string S i and key character set K i ( i = 1, 2, ..., p ). Every S i and K i is followed by an empty line. However, any single newline between successive lines in a string should be ignored; that is, newlines are not part of the string. For various technical reasons, every line consists of at most 72 characters. Each key character set is given in a single line. The input is terminated by consecutive empty lines; p is not given explicitly. Output All of p problems should be solved and their answers should be output in order. However, it is not requested to print all of the shortest substrings if more than one substring is found in a problem, since found substrings may be too much to check them all. Only the number of the substrings together with their representative is requested instead. That is, for each problem i , the number of the shortest substrings should be output followed by the first (or the leftmost) shortest substring s i 1 , obeying the following format: the number of the shortest substrings for the i-th problem empty line the first line of s i1 the second line of s i1 ... the last line of s i1 empty line for the substring termination where each line of the shortest substring s i 1 except for the last line should consist of exactly 72 characters and the last line (or the single line if the substring is shorter than or equal to 72 characters, of course) should not exceed 72 characters. If there is no such substring for a problem, the output will be a 0 followed by an empty line; no more successive empty line should be output because there is no substring to be terminated. Sample Input Thefirstexampleistrivial. mfv AhugeamountofinformationisbeingheapedonWWW.Albeititisnot well-organized,userscanbrowseWWWasanunboundedsourceof up-to-dateinformation,insteadofconsultingestablishedbutalittle out-of-dateencyclopedia.However,youcanfurtherexploitWWWby learningmoreaboutkeywordsearchalgorithms.Forexample,ifyou wanttogetinformationonrecentcomparisonbetweenWindowsandUNIX, youmayexpecttogetrelevantdescriptionoutofabigbunchofWeb texts,byextractingtextsthatcontainbothkeywords"Windows"and"UNIX" closetogether. bWn 3.1415926535897932384626433832795028841971693993751058209749445923078164 pi Wagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky Weary ASCIIcharacterssuchas+,,[,#,<,},_arenotexcludedinagivenstringas thisexampleillustratesbyitself.Youshouldnotforgetthem.Onemorefact youshouldnoticeisthatuppercaselettersandlowercaselettersare distinguishedinthisproblem.Don'tidentify"g"and"G",forexmaple. However,weareafraidthatthisexamplegivesyoutoomuchhint! ![GsC_l ETAONRISHDLFCMUGYPWBVKXJQZ ABCDEFGHIJKLMNOPQRSTUVWXYZ Output for the Sample Input 1 firstexampleistriv 7 nWWW.Alb 0 1 Wagner,Bach,Beethoven,Chopin,Brahms,Hindemith,Ives,Suk,Mozart,Stravinsky 1 CIIcharacterssuchas+,,[,#,<,},_arenotexcludedinagivenstringasthisexampl eillustratesbyitself.Youshouldnotforgetthem.Onemorefactyoushouldnoticeis thatuppercaselettersandlowercaselettersaredistinguishedinthisproblem.Don 'tidentify"g"and"G",forexmaple.However,weareafraidthatthisexamplegivesyo utoomuchhint! 1 ETAONRISHDLFCMUGYPWBVKXJQZ	38,193
Pipe Fitter and the Fierce Dogs You, a proud pipe fitter of ICPC (International Community for Pipe Connection), undertake a new task. The area in which you will take charge of piping work is a rectangular shape with $W$ blocks from west to east and $H$ blocks from north to south. We refer to the block at the $i$-th from west and the $j$-th from north as $(i, j)$. The westernmost and northernmost block is $(1, 1)$, and the easternmost and southernmost block is $(W,H)$. To make the area good scenery, the block $(i, j)$ has exactly one house if and only if both of $i$ and $j$ are odd numbers. Your task is to construct a water pipe network in the area such that every house in the area is supplied water through the network. A water pipe network consists of pipelines. A pipeline is made by connecting one or more pipes, and a pipeline with l pipes is constructed as follows: choose a first house, and connect the house to an underground water source with a special pipe . choose an $i$-th house ($2 \leq i \leq l$), and connect the $i$-th house to the ($i - 1$)-th house with a common pipe . In this case, there is a condition to choose a next $i$-th house because the area is slope land. Let $(x, y)$ be the block of the ($i - 1$)-th house. An $i$-th house must be located at either $(x - 2, y + 2)$, $(x, y + 2)$, or $(x + 2, y + 2)$. A common pipe connecting two houses must be located at $(x - 1, y + 1)$, $(x, y + 1)$, or $(x + 1, y + 1)$, respectively. In addition, you should notice the followings when you construct several pipelines: For each house, exactly one pipeline is through the house. Multiple pipes can be located at one block. In your task, common pipes are common, so you can use any number of common pipes. On the other hand, special pipes are special, so the number of available special pipes in this task is restricted under ICPC regulation. Besides the restriction of available special pipes, there is another factor obstructing your pipe work: fierce dogs. Some of the blocks which do not contain a house seem to be home of fierce dogs. Each dog always stays at his/her home block. Since several dogs must not live at the same block as their home, you can assume each block is home of only one dog, or not home of any dogs. The figure below is an example of a water pipe network in a 5 $\times$ 5 area with 4 special pipes. This corresponds to the first sample. Locating a common pipe at a no-dog block costs 1 unit time, but locating a common pipe at a dog-living block costs 2 unit time because you have to fight against the fierce dog. Note that when you locate multiple pipes at the same block, each pipe-locating costs 1 unit time for no-dog blocks and 2 for dog-living blocks, respectively. By the way, special pipes are very special, so locating a special pipe costs 0 unit time. You, a proud pipe fitter, want to accomplish this task as soon as possible. Fortunately, you get a list of blocks which are home of dogs. You have frequently participated in programming contests before being a pipe fitter. Hence, you decide to make a program determining whether or not you can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, and if so, computing the minimum total time cost to construct it. Input The input consists of a single test case. $W$ $H$ $K$ $N$ $x_1$ $y_1$ $x_2$ $y_2$ ... $x_N$ $y_N$ All numbers in a test case are integers. The first line contains three integers $W$, $H$, and $K$. $W$ and $H$ represent the size of the rectangle area. $W$ is the number of blocks from west to east ($1 \leq W < 10,000$), and $H$ is the number of blocks from north to south ($1 \leq H < 10,000$). $W$ and $H$ must be odd numbers. $K$ is the number of special pipes that you can use in this task ($1 \leq K \leq 100,000,000$). The second line has an integer $N$ ($0 \leq N \leq 100,000$), which is the number of dogs in the area. Each of the following $N$ lines contains two integers $x_i$ and $y_i$, which indicates home of the $i$-th fierce dog is the block $(x_i, y_i)$. These numbers satisfy the following conditions: $1 \leq x_i \leq W, 1 \leq y_i \leq H$. At least one of $x_i$ and $y_i$ is even number. $i \ne j$ implies $(x_i, y_i) \ne (x_j, y_j)$. That is, two or more dogs are not in the same block. Output If we can construct a water pipe network such that every house is supplied water through the network with a restricted number of special pipes, print the minimum total time cost to construct it. If not, print -1. Sample Input 1 5 5 4 6 3 2 4 2 5 2 1 4 3 4 5 4 Output for the Sample Input 1 6 Sample Input 2 5 3 1 0 Output for the Sample Input 2 -1 Sample Input 3 9 5 100 5 2 1 1 2 3 4 4 3 2 2 Output for the Sample Input 3 0 Sample Input 4 5 5 3 4 1 2 5 2 1 4 5 4 Output for the Sample Input 4 8 Sample Input 5 9 5 5 10 2 1 2 2 3 2 5 2 8 2 4 3 2 4 3 4 5 4 8 4 Output for the Sample Input 5 10	38,194
Fractional Knapsack Problem You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 \le i \le N$) has weight $w_i$ and value $v_i$ for the weight. When you put some items into the knapsack, the following conditions must be satisfied: The total value of the items is as large as possible. The total weight of the selected items is at most $W$. You can break some items if you want. If you put $w'$($0 \le w' \le w_i$) of item $i$, its value becomes $\displaystyle v_i \times \frac{w'}{w_i}.$ Find the maximum total value of items in the knapsack. Input $N$ $W$ $v_1$ $w_1$ $v_2$ $w_2$ : $v_N$ $w_N$ The first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given. Output Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$. Constraints $1 \le N \le 10^5$ $1 \le W \le 10^9$ $1 \le v_i \le 10^9 (1 \le i \le N)$ $1 \le w_i \le 10^9 (1 \le i \le N)$ Sample Input 1 3 50 60 10 100 20 120 30 Sample Output 1 240 When you put 10 of item $1$, 20 of item $2$ and 20 of item $3$, the total value is maximized. Sample Input 2 3 50 60 13 100 23 120 33 Sample Output 2 210.90909091 When you put 13 of item $1$, 23 of item $2$ and 14 of item $3$, the total value is maximized. Note some outputs can be a real number. Sample Input 3 1 100 100000 100000 Sample Output 3 100	38,195
Score: 300 points Problem Statement M-kun is a student in Aoki High School, where a year is divided into N terms. There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows: For the first through (K-1) -th terms: not given. For each of the K -th through N -th terms: the multiplication of the scores in the last K exams, including the exam in the graded term. M-kun scored A_i in the exam at the end of the i -th term. For each i such that K+1 \leq i \leq N , determine whether his grade for the i -th term is strictly greater than the grade for the (i-1) -th term. Constraints 2 \leq N \leq 200000 1 \leq K \leq N-1 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 K A_1 A_2 A_3 \ldots A_N Output Print the answer in N-K lines. The i -th line should contain Yes if the grade for the (K+i) -th term is greater than the grade for the (K+i-1) -th term, and No otherwise. Sample Input 1 5 3 96 98 95 100 20 Sample Output 1 Yes No His grade for each term is computed as follows: 3 -rd term: (96 \times 98 \times 95) = 893760 4 -th term: (98 \times 95 \times 100) = 931000 5 -th term: (95 \times 100 \times 20) = 190000 Sample Input 2 3 2 1001 869120 1001 Sample Output 2 No Note that the output should be No if the grade for the 3 -rd term is equal to the grade for the 2 -nd term. Sample Input 3 15 7 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 Sample Output 3 Yes Yes No Yes Yes No Yes Yes	38,196
Score : 300 points Problem Statement The problem set at CODE FESTIVAL 20XX Finals consists of N problems. The score allocated to the i -th (1≦i≦N) problem is i points. Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve. As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him. Determine the set of problems that should be solved. Constraints 1≦N≦10^7 Partial Score 200 points will be awarded for passing the test set satisfying 1≦N≦1000 . Additional 100 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 Output Among the sets of problems with the total score of N , find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line. If there exists more than one such set, any of them will be accepted. Sample Input 1 4 Sample Output 1 1 3 Solving only the 4 -th problem will also result in the total score of 4 points, but solving the 1 -st and 3 -rd problems will lower the highest score of a solved problem. Sample Input 2 7 Sample Output 2 1 2 4 The set \{3,4\} will also be accepted. Sample Input 3 1 Sample Output 3 1	38,197
Longest Increasing Subsequence For a given sequence A = {a 0 , a 1 , ... , a n-1 } , find the length of the longest increasing subsequnece (LIS) in A . An increasing subsequence of A is defined by a subsequence {a i 0 , a i 1 , ... , a i k } where 0 ≤ i 0 < i 1 < ... < i k < n and a i 0 < a i 1 < ... < a i k . Input n a 0 a 1 : a n-1 In the first line, an integer n is given. In the next n lines, elements of A are given. Output The length of the longest increasing subsequence of A . Constraints 1 ≤ n ≤ 100000 0 ≤ a i ≤ 10 9 Sample Input 1 5 5 1 3 2 4 Sample Output 1 3 Sample Input 2 3 1 1 1 Sample Output 2 1	38,198
Score : 100 points Problem Statement A Hitachi string is a concatenation of one or more copies of the string hi . For example, hi and hihi are Hitachi strings, while ha and hii are not. Given a string S , determine whether S is a Hitachi string. Constraints The length of S is between 1 and 10 (inclusive). S is a string consisting of lowercase English letters. Input Input is given from Standard Input in the following format: S Output If S is a Hitachi string, print Yes ; otherwise, print No . Sample Input 1 hihi Sample Output 1 Yes hihi is the concatenation of two copies of hi , so it is a Hitachi string. Sample Input 2 hi Sample Output 2 Yes Sample Input 3 ha Sample Output 3 No	38,199
D: スキャナー / Scanner 問題文ここに $N$ 枚の紙がある。あなたは $3$ 台のスキャナーを並列に用いることで、全ての紙をスキャンしたいと考えている。それぞれの紙はスキャンにかかる時間が決まっており、 $i$ 番目の紙をスキャンするのにかかる時間は $T_i$ である。紙をスキャンする順番は任意であるが、$1$ 台のスキャナーで複数の紙を同時にスキャンすることはできない。全ての紙のスキャンが終了し、スキャンを行っているスキャナーがなくなるまでにかかる時間を最小化しなさい。入力 $N$ $T_1$ $T_2$ $T_3$ $\vdots$ $T_N$ 制約 $1 \leq N \leq 50$ $1 \leq T_i \leq 50$ 入力は全て整数出力答えを $1$ 行で出力してください．サンプルサンプル入力1 4 1 1 1 1 サンプル出力1 2 サンプル入力2 9 15 20 27 4 10 7 34 30 36 サンプル出力2 61 サンプル入力3 6 20 18 46 16 9 48 サンプル出力3 55	38,201
テニスジョウ君とヤエさんは昼休みにテニスをします。ただし、昼休みは時間が限られているので、短い時間で終わるように、得点について以下の３つのルールで行います。相手が３点以下のときに先に５点とれば勝ち。４対４の同点になったときは、その直後に連続して２点とった方が勝ち。４対４の後に双方が１点ずつとったときは引き分け。以下の図は、ジョウ君とヤエさんの試合で起こり得るすべての状況を表しています。丸の中の左の数がジョウ君の得点、右がヤエさんの得点です。Ａと書いた矢印はジョウ君が１点とったことを、Ｂと書いた矢印はヤエさんが１点とったことを表します。ジョウ君とヤエさんの得点が与えられたとき、試合開始からその得点状況になるまでに、上の図で通り得るすべての経路を列挙するプログラムを作成してください。入力入力は１つのデータセットからなる。入力データは以下の形式で与えられる。 j y j (0 ≤ j ≤ 6) がジョウ君の得点、 y (0 ≤ y ≤ 6) がヤエさんの得点である。ただし、 j と y がともに 0 であることはない。また、 j が 6 のときは y は 4、 y が 6 のときは j は 4 である。出力上の図で、試合開始（0-0と書かれた丸）から与えられた得点が書かれた丸までのすべての経路を出力する。経路は図の矢印に添えられた英字(A,B)の列で表し、辞書式順序（英和辞書で単語が並んでいる順番）になるように並べる。１つの経路を１行に出力する。経路の前後には空白を出力しない。入出力例入力例1 2 2 出力例1 AABB ABAB ABBA BAAB BABA BBAA 入力例2 5 1 出力例2 AAAABA AAABAA AABAAA ABAAAA BAAAAA	38,202
Score : 100 points Problem Statement You are given an integer N . Consider an infinite N -ary tree as shown below: Figure: an infinite N -ary tree for the case N = 3 As shown in the figure, each vertex is indexed with a unique positive integer, and for every positive integer there is a vertex indexed with it. The root of the tree has the index 1 . For the remaining vertices, vertices in the upper row have smaller indices than those in the lower row. Among the vertices in the same row, a vertex that is more to the left has a smaller index. Regarding this tree, process Q queries. The i -th query is as follows: Find the index of the lowest common ancestor (see Notes) of Vertex v_i and w_i . Notes In a rooted tree, the lowest common ancestor (LCA) of Vertex v and w is the farthest vertex from the root that is an ancestor of both Vertex v and w . Here, a vertex is considered to be an ancestor of itself. For example, in the tree shown in Problem Statement, the LCA of Vertex 5 and 7 is Vertex 2 , the LCA of Vertex 8 and 11 is Vertex 1 , and the LCA of Vertex 3 and 9 is Vertex 3 . Constraints 1 ≤ N ≤ 10^9 1 ≤ Q ≤ 10^5 1 ≤ v_i < w_i ≤ 10^9 Input Input is given from Standard Input in the following format: N Q v_1 w_1 : v_Q w_Q Output Print Q lines. The i -th line (1 ≤ i ≤ Q) must contain the index of the lowest common ancestor of Vertex v_i and w_i . Sample Input 1 3 3 5 7 8 11 3 9 Sample Output 1 2 1 3 The queries in this case correspond to the examples shown in Notes. Sample Input 2 100000 2 1 2 3 4 Sample Output 2 1 1	38,203
Score : 200 points Problem Statement You have written N problems to hold programming contests. The i -th problem will have a score of P_i points if used in a contest. With these problems, you would like to hold as many contests as possible under the following condition: A contest has three problems. The first problem has a score not greater than A points, the second has a score between A + 1 and B points (inclusive), and the third has a score not less than B + 1 points. The same problem should not be used in multiple contests. At most how many contests can be held? Constraints 3 \leq N \leq 100 1 \leq P_i \leq 20 ( 1 \leq i \leq N ) 1 \leq A < B < 20 All values in input are integers. Input Input is given from Standard Input in the following format: N A B P_1 P_2 ... P_N Output Print the answer. Sample Input 1 7 5 15 1 10 16 2 7 20 12 Sample Output 1 2 Two contests can be held by putting the first, second, third problems and the fourth, fifth, sixth problems together. Sample Input 2 8 3 8 5 5 5 10 10 10 15 20 Sample Output 2 0 No contest can be held, because there is no problem with a score of A = 3 or less. Sample Input 3 3 5 6 5 6 10 Sample Output 3 1	38,204
Problem F: RabbitLunch うさぎは昼食ににんじんとキウイを1 個ずつ食べる. うさぎはとても個性的なので, 食べるにんじんの種類もキウイの種類も同じであるような, 異なる2 匹のうさぎが存在してはならない. にんじんは $M$ 種類ある. $i$ 種類目のにんじんは $m_i$ 個ある. キウイは $N$ 種類ある. $i$ 種類目のキウイは $n_i$ 個ある. 最大何匹のうさぎが昼食をとれるか求めよ. $m_i$ と $n_i$ は次の漸化式を用いて生成せよ. $m_0 = m0$ $m_{i+1} = (m_i * 58 + md )$ mod $(N + 1)$ $n_0 = n0$ $n_{i+1} = (n_i * 58 + nd )$ mod $(M + 1)$ Constraints $M$ will be between 1 and 2,500,000, inclusive. $N$ will be between 1 and 2,500,000, inclusive. $m0$ and $md$ will be between 0 and $N$, inclusive. $n0$ and $nd$ will be between 0 and $M$, inclusive. Input 入力は以下の形式で与えられる: $M$ $N$ $m0$ $md$ $n0$ $nd$ Output 昼食をとれるうさぎの匹数の最大値を表す整数を 1 行に出力せよ. Sample Input 1 2 3 1 3 1 0 Sample Output 1 2 Sample Input 2 5 8 1 2 3 4 Sample Output 2 19	38,205
Problem A Secret of Chocolate Poles Wendy, the master of a chocolate shop, is thinking of displaying poles of chocolate disks in the showcase. She can use three kinds of chocolate disks: white thin disks, dark thin disks, and dark thick disks. The thin disks are $1$ cm thick, and the thick disks are $k$ cm thick. Disks will be piled in glass cylinders. Each pole should satisfy the following conditions for her secret mission, which we cannot tell. A pole should consist of at least one disk. The total thickness of disks in a pole should be less than or equal to $l$ cm. The top disk and the bottom disk of a pole should be dark. A disk directly upon a white disk should be dark and vice versa. As examples, six side views of poles are drawn in Figure A.1. These are the only possible side views she can make when $l = 5$ and $k = 3$. Figure A.1. Six chocolate poles corresponding to Sample Input 1 Your task is to count the number of distinct side views she can make for given $l$ and $k$ to help her accomplish her secret mission. Input The input consists of a single test case in the following format. $l$ $k$ Here, the maximum possible total thickness of disks in a pole is $l$ cm, and the thickness of the thick disks is $k$ cm. $l$ and $k$ are integers satisfying $1 \leq l \leq 100$ and $2 \leq k \leq 10$. Output Output the number of possible distinct patterns. Sample Input 1 5 3 Sample Output 1 6 Sample Input 2 9 10 Sample Output 2 5 Sample Input 3 10 10 Sample Output 3 6 Sample Input 4 20 5 Sample Output 4 86 Sample Input 5 100 2 Sample Output 5 3626169232670	38,207
Problem L: The Return of FizzBuzz ICPC World Finals 7日目いよいよ明日はICPC World Finalsの本番である。ティー氏はあるオンラインジャッジ(Aru Online Judge)で練習をすることにした。問題一覧を眺めているとFizzBuzzという問題が目についた。この問題は、FizzBuzzゲームで得られる発言のn文字目から20文字を出力するというものだ。 …ふぅ。あっという間に解けてしまった。これでは簡単すぎた。入力と出力を逆にした問題を作ってみることにしよう。問題 FizzBuzzとは、1以上の整数を順に、以下のルールに従って発言していくゲームである。 3で割り切れる時には「Fizz」 5で割り切れる時には「Buzz」 3と5の両方で割り切れる時には「FizzBuzz」それ以外の時はその数字ゲームの進行状況を以下に示す。 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, … 得られた発言を結合することで得られる（無限長の）文字列をFizzBuzz Stringと呼ぶ。ある文字列$s$が与えられる。 $s$がFizzBuzz Stringの部分文字列として出現するかを判定し、出現する場合には最初に出現するインデックスを求めよ。入力 n s 1 s 2 … s n 入力は複数のテストケースからなる。 1行目にテストケース数$n$が与えられる。 2行目から$ n+1 $行目は各テストケースに対応し、文字列$ s_{i} $が1行で与えられる。出力 $i$番目の文字列$ s_{i} $について、 $ s_{i} $がFizzBuzz Stringの部分文字列として出現する場合には最初に出現するインデックスを(1-indexで)、出現しない場合には"-1"を$i$行目に出力せよ。制約 $ 1 \leq n \leq 20 $ 文字列は文字$ \{ 0,1,\cdots,8,9 ,\mbox{F},\mbox{B},\mbox{i},\mbox{u},\mbox{z} \} (1 \leq i \leq n) $からなる。文字列の長さは1以上15以下である。入出力例入力1 6 78Fizz 98FizzBuzz101 FizzBu izzFiz 111111111111111 123456789 出力1 16 304 18 -1 7703703700 7795884765 入力例は6つのテストケースからなる。それぞれ以下の発言に対応する。 …, Buzz, Fizz, 7, 8, Fizz, Buzz, … …, Fizz, 97, 98, Fizz, Buzz, 101, Fizz, … …, 7, 8, Fizz, Buzz, 11, 12, … 存在しない …, 1111111109, FizzBuzz, 1111111111, 1111111112, Fizz, 1111111114, … …, 1123456787, Fizz, 1123456789, Buzz, Fizz, …	38,208
Score : 1100 points Problem Statement We will call a string that can be obtained by concatenating two equal strings an even string. For example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not. For a non-empty string S , we will define f(S) as the shortest even string that can be obtained by appending one or more characters to the end of S . For example, f( abaaba )= abaababaab . It can be shown that f(S) is uniquely determined for a non-empty string S . You are given an even string S consisting of lowercase English letters. For each letter in the lowercase English alphabet, find the number of its occurrences from the l -th character through the r -th character of f^{10^{100}} (S) . Here, f^{10^{100}} (S) is the string f(f(f( ... f(S) ... ))) obtained by applying f to S 10^{100} times. Constraints 2 \leq \|S\| \leq 2\times 10^5 1 \leq l \leq r \leq 10^{18} S is an even string consisting of lowercase English letters. l and r are integers. Input Input is given from Standard Input in the following format: S l r Output Print 26 integers in a line with spaces in between. The i -th integer should be the number of the occurrences of the i -th letter in the lowercase English alphabet from the l -th character through the r -th character of f^{10^{100}} (S) . Sample Input 1 abaaba 6 10 Sample Output 1 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Since f( abaaba )= abaababaab , the first ten characters in f^{10^{100}}(S) is also abaababaab . Thus, the sixth through the tenth characters are abaab . In this string, a appears three times, b appears twice and no other letters appear, and thus the output should be 3 and 2 followed by twenty-four 0 s. Sample Input 2 xx 1 1000000000000000000 Sample Output 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000000000000000 0 0 Sample Input 3 vgxgpuamkvgxgvgxgpuamkvgxg 1 1000000000000000000 Sample Output 3 87167725689669676 0 0 0 0 0 282080685775825810 0 0 0 87167725689669676 0 87167725689669676 0 0 87167725689669676 0 0 0 0 87167725689669676 141040342887912905 0 141040342887912905 0 0	38,209
Score : 700 points Problem Statement N hotels are located on a straight line. The coordinate of the i -th hotel (1 \leq i \leq N) is x_i . Tak the traveler has the following two personal principles: He never travels a distance of more than L in a single day. He never sleeps in the open. That is, he must stay at a hotel at the end of a day. You are given Q queries. The j -th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j . For each query, find the minimum number of days that Tak needs to travel from the a_j -th hotel to the b_j -th hotel following his principles. It is guaranteed that he can always travel from the a_j -th hotel to the b_j -th hotel, in any given input. Constraints 2 \leq N \leq 10^5 1 \leq L \leq 10^9 1 \leq Q \leq 10^5 1 \leq x_i < x_2 < ... < x_N \leq 10^9 x_{i+1} - x_i \leq L 1 \leq a_j,b_j \leq N a_j \neq b_j N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers. Partial Score 200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3 . Input The input is given from Standard Input in the following format: N x_1 x_2 ... x_N L Q a_1 b_1 a_2 b_2 : a_Q b_Q Output Print Q lines. The j -th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j -th hotel to the b_j -th hotel. Sample Input 1 9 1 3 6 13 15 18 19 29 31 10 4 1 8 7 3 6 7 8 5 Sample Output 1 4 2 1 2 For the 1 -st query, he can travel from the 1 -st hotel to the 8 -th hotel in 4 days, as follows: Day 1 : Travel from the 1 -st hotel to the 2 -nd hotel. The distance traveled is 2 . Day 2 : Travel from the 2 -nd hotel to the 4 -th hotel. The distance traveled is 10 . Day 3 : Travel from the 4 -th hotel to the 7 -th hotel. The distance traveled is 6 . Day 4 : Travel from the 7 -th hotel to the 8 -th hotel. The distance traveled is 10 .	38,210
Problem I: Pythagoraslope Alice, your girlfriend, is a student at an art school. She is in the final year, and now working hard to build a facture for fulfilling the requirement to graduate. Her work is a large pinball with many straight slopes. Before starting to build, she has made several plans, but is unsure if they work as expected. So she asked you, a professional programmer, for help. You have modeled this situation by a two dimensional plane with some line segments on it. In this model, there is gravitation downward, i.e., in the decreasing direction of y -coordinate. Your task is to write a program that simulates the pinball, and compute the last position where the ball crosses the x -axis. You may assume coefficient of restitution between the slopes and the ball is 0, i.e., when the ball collides a slope, it instantly loses the velocity component orthogonal to the slope. And since her pinball is so large, you may also assume that the volume of the ball is negligible. Input The input consists of multiple data sets. Each data set is given in the format below. N g x y x 1,1 y 1,1 x 1,2 y 1,2 ... x N ,1 y N ,1 x N ,2 y N ,2 where N ( N ≤ 100) is the number of slopes, g is gravity acceleration, and ( x , y ) is the initial position of the ball. Each of the following N lines represents a slope, which is a line segment between ( x i ,1 , y i ,1 ) and ( x i ,2 , y i ,2 ). You may assume that: all coordinates are more than or equal to 1, and less than or equal to 10,000; x i ,1 ≠ x i ,2 and y i ,1 ≠ y i ,2 for all 1 ≤ i ≤ N ; no two line segments cross each other; extending or shrinking a slope by the length of 0.0001 does not change the ball’s trail, that is, do not change the set of slopes where the ball passes; the ball never collides to a slope at the angle of 90 ± 0.0001 degrees from the slope; and the initial position of the ball never lies on any slope. The end of the input is indicated by a line containing a single zero. This is not a part of the data sets, and you must not process it. Output For each data set, output the x -coordinate of the final crossing point of the ball’s trail and the x -axis. Your program may print any number of digits after the decimal point, but the output must not contain an error greater than 10 -4 (= 0.0001). Sample Input 3 1 120 1000 100 100 180 20 170 10 270 30 270 40 400 20 0 Output for the Sample Input 403.87458314	38,211
Score : 200 points Problem Statement In the beginning, Takahashi has A cookies, and Aoki has B cookies. They will perform the following operation alternately, starting from Takahashi: If the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person. Find the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total. Constraints 1 \leq A,B \leq 10^9 1 \leq K \leq 100 A,B and K are integers. Input Input is given from Standard Input in the following format: A B K Output Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total. Sample Input 1 5 4 2 Sample Output 1 5 3 The process will go as follows: In the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively. Takahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively. Aoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively. Sample Input 2 3 3 3 Sample Output 2 1 3 Sample Input 3 314159265 358979323 84 Sample Output 3 448759046 224379523	38,212
Score : 2200 points Problem Statement You are given positions (X_i, Y_i) of N enemy rooks on an infinite chessboard. No two rooks attack each other (at most one rook per row or column). You're going to replace one rook with a king and then move the king repeatedly to beat as many rooks as possible. You can't enter a cell that is being attacked by a rook. Additionally, you can't move diagonally to an empty cell (but you can beat a rook diagonally). (So this king moves like a superpawn that beats diagonally in 4 directions and moves horizontally/vertically in 4 directions.) For each rook, consider replacing it with a king, and find the minimum possible number of moves needed to beat the maximum possible number of rooks. Constraints 2 \leq N \leq 200\,000 1 \leq X_i, Y_i \leq 10^6 X_i \neq X_j Y_i \neq Y_j All values in input are integers. Input Input is given from Standard Input in the following format. N X_1 Y_1 X_2 Y_2 \vdots X_N Y_N Output Print N lines. The i -th line is for scenario of replacing the rook at (X_i, Y_i) with your king. This line should contain one integer: the minimum number of moves to beat M_i rooks where M_i denotes the maximum possible number of beaten rooks in this scenario (in infinite time). Sample Input 1 6 1 8 6 10 2 7 4 4 9 3 5 1 Sample Output 1 5 0 7 5 0 0 See the drawing below. If we replace rook 3 with a king, we can beat at most two other rooks. The red path is one of optimal sequences of moves: beat rook 1, then keep going down and right until you can beat rook 4. There are 7 steps and that's the third number in the output. x-coordinate increases from left to right, while y increases bottom to top. Starting from rook 2, 5 or 6, we can't beat any other rook. The optimal number of moves is 0. Sample Input 2 5 5 5 100 100 70 20 81 70 800 1 Sample Output 2 985 985 1065 1034 0 Sample Input 3 10 2 5 4 4 13 12 12 13 14 17 17 19 22 22 16 18 19 27 25 26 Sample Output 3 2 2 9 9 3 3 24 5 0 25	38,213
Problem Statement You are given a list of $N$ intervals. The $i$-th interval is $[l_i, r_i)$, which denotes a range of numbers greater than or equal to $l_i$ and strictly less than $r_i$. In this task, you consider the following two numbers: The minimum integer $x$ such that you can select $x$ intervals from the given $N$ intervals so that the union of the selected intervals is $[0, L)$. The minimum integer $y$ such that for all possible combinations of $y$ intervals from the given $N$ interval, it does cover $[0, L)$. We ask you to write a program to compute these two numbers. Input The input consists of a single test case formatted as follows. $N$ $L$ $l_1$ $r_1$ $l_2$ $r_2$ $\vdots$ $l_N$ $r_N$ The first line contains two integers $N$ ($1 \leq N \leq 2 \times 10^5$) and $L$ ($1 \leq L \leq 10^{12}$), where $N$ is the number of intervals and $L$ is the length of range to be covered, respectively. The $i$-th of the following $N$ lines contains two integers $l_i$ and $r_i$ ($0 \leq l_i < r_i \leq L$), representing the range of the $i$-th interval $[l_i, r_i)$. You can assume that the union of all the $N$ intervals is $[0, L)$ Output Output two integers $x$ and $y$ mentioned in the problem statement, separated by a single space, in a line. Examples Input Output 3 3 0 2 1 3 1 2 2 3 2 4 0 4 0 4 1 1 5 4 0 2 2 4 0 3 1 3 3 4 2 4	38,214
小数位の和 a , b , n は、いずれも正の整数であるとします。分数 a / b の小数第 i 位の数を f(i) とします (0 ≤ f(i) ≤ 9)。このとき、 i = 1 から n までの f(i) の和を s とします。 s = f(1) + f(2) + ... + f(n) a , b , n を読み込んで、 s を出力して終了するプログラムを作成してください。 Input 入力は複数のデータセットからなります。各データセットとして、3 つの整数 a (1 ≤ a ≤ 1000), b (1 ≤ b ≤ 10000), n (1 ≤ n ≤ 100) が空白区切りで１行に与えられます。データセットの数は 100 を超えません。 Output データセットごとに、 s を１行に出力します。 Sample Input 1 2 3 2 3 4 5 4 3 4 3 2 Output for the Sample Input 5 24 7 6	38,215
Min-Max For given three integers $a, b, c$, print the minimum value and the maximum value. Input The input is given in the following format. $a \; b \; c\;$ Three integers $a, b, c$ are given in a line. Output Print the minimum and maximum values separated by a space in a line. Constraints $-1,000,000,000 \leq a, b, c \leq 1,000,000,000$ Sample Input 1 4 5 3 Sample Output 1 3 5	38,216
床ヒデヨ博士の家の床には正方形のタイルが敷きつめられています。芸術に造詣が深いヒデヨ博士は、赤、黄、青の塗料を使ってタイルに色を塗ることにしました。はじめに部屋の適当なタイルをひとつ選び、以下の方法で色を塗っていきます。タイルを塗る色を、赤（図の番号１）、黄（図の番号２）、青（図の番号３）の順に変えていき、青の次はまた赤から始める。すでに色を塗った領域の隣に正方形を追加し、そこに色を塗る。それらを合わせた領域が長方形になるようにする。正方形を追加する方向は、東、北、西、南の順に変えていき、南の次はまた東から始める（図では、上方向が北、右方向が東である）。最初に赤く塗ったタイルから東西方向に$x$個、南北方向に$y$個移動したところにあるタイルは、何色に塗られているでしょうか。ただし、東の方向を$x$の正の方向、北の方向を$y$の正の方向とします。 $x$と$y$を入力し、タイルの色を出力するプログラムを作成せよ。入力入力は以下の形式で与えられる。 $x$ $y$ １行に$x$と$y$ ($-10^6 \leq x,y \leq 10^6$)が与えられる。出力タイルの色が赤のとき1、黄のとき2、青のとき3を１行に出力する。入出力例入力例１ 0 0 出力例１ 1 入力例２ -4 5 出力例２ 2 入力例３ 8 -14 出力例３ 3	38,217
博士の暗号博士 : ?D-C'KOPUA ピーター : どうしたんですか、デビッド博士? わけのわからないことを叫ぶのにはもう慣れましたが、今日は文章にすらなっていませんよ。博士 : ほれ。ピーター : なんですか? この表は......ああ、予選の問題にこんなのがありました。表を使って文字を置き換えると文字数が減るんですよね。まさか予選と本選で同じ問題を出して手を抜こうって気じゃないでしょうね。博士 : 逆じゃよ。ピーター : 逆? なるほど、今度は短くした文字列を元に戻そうって問題ですか。ということは「?D-C'KOPUA」の文字を、この表を使って「文字」から「符号」に置きかえるんですね......できましたよ。 11111 00011 11101 00010 11110 01010 01110 01111 10100 00000 博士 : うむ。次はこれじゃ。ピーター : そうそう、こんな表もありましたね。これを逆に使うんだから「符号」から「文字」に置き換えればいいんですね。でも、最初は「11111」ですが表にありませんよ? 博士 : そういうときは、もっと短くするか、後ろとつなげるかしてみるのだよ。ピーター : じゃあ短くして......あ、「111」ならあります。じゃあ最初は「P」ですね。そうすると残りは「11」ですが、これはぴったり合うのがないから次の「00011」から 1 文字借りて「110」にすればいいんですね。博士 : そうそう。つまり「E」だね。ピーター : それで残るのが「0011」なので、これも次から借りて「00111」にして「T」と......。全部できました。最後の「0000」は捨てちゃえばいいんですよね? 博士 : そうじゃ、よろしい。次はこれじゃ。 ?D-C'?-C'-LMGZN?FNJKN- WEYN?P'QMRWLPZLKKTPOVRGDI 博士 : さらにこれじゃ。 ?P'QNPY?IXX?IXXK.BI -G?R'RPP'RPOVWDMW?SWUVG'-LCMGQ 博士 : 仕上げにこうじゃ。 ?P'QMDUEQ GADKOQ ?SWUVG'-LCMG?X?IGX,PUL.?UL.VNQQI ピーター : しっかし面倒だなあ。博士、今度は自分でプログラムを作って下さいよ。ということで、博士のかわりに、上の文章を置き換えるプログラムを作成してください。 Input 複数のデータセットが与えられます。各データセットとして、１つの文字列（表に含まれる文字からなる 200 文字以下の文字列）が１行に与えられます。入力の終わりまで処理してください。データセットの数は 200 を超えません。 Output 各データセットごとに、変換後の文字列を１行に出力してください。 Sample Input ?D-C'KOPUA Output for the Sample Input PETER POTTER	38,218
城壁 (Rampart) 歴史学者である JOI 教授は，かつて存在した IOI 王国について研究している．過去の調査によると，IOI 王国は縦 H 行，横 W 列のマスに区切られた長方形の形をしていた．IOI 王国の首都は，防衛のために城壁で囲われていた． IOI 王国の首都を囲う城壁は次のような形をしている．城壁には大きさと呼ばれる値が定まっている．大きさ s ( s ≥ 3) の城壁とは， s × s の正方形の領域から外周以外の ( s − 2) × ( s − 2) の正方形の領域を除いたものである．調査によると，首都を囲う城壁の大きさは L 以上であった．また，IOI 王国のいくつかのマスには城壁が存在しなかったことがわかっている． JOI 教授は，さらなる研究のために，城壁としてありうるものが何通りあるかを知りたい．課題 IOI 王国の大きさと，城壁の大きさの最小値，城壁が存在しなかったことが分かっているマスの情報が与えられたとき，城壁としてありうるものは何通りあるかを求めるプログラムを作成せよ．入力標準入力から以下のデータを読み込め． 1 行目には，整数 H , W , L , P が空白を区切りとして書かれている．これは，IOI 王国は縦 H 行，横 W 列のマスに区切られた長方形の形をしており，城壁の大きさは L 以上であり，城壁が存在しなかったことがわかっているマスが P マス存在することを表す．続く P 行のうちの i 行目 (1 ≤ i ≤ P ) には，整数 A i , B i が空白を区切りとして書かれている．これは，IOI 王国の上から A i 行目，左から B i 列目のマスには城壁が存在しなかったことがわかっていることを表す．出力標準出力に，城壁としてありうるものは何通りあるかを表す整数を 1 行で出力せよ. 制限すべての入力データは以下の条件を満たす． 1 ≤ H ≤ 4 000． 1 ≤ W ≤ 4 000． 3 ≤ L ≤ H かつ 3 ≤ L ≤ W ． 0 ≤ P ≤ 100 000． 1 ≤ A i ≤ H (1 ≤ i ≤ P )． 1 ≤ B i ≤ W (1 ≤ i ≤ P )． ( A i , B i ) ≠ ( A j , B j ) (1 ≤ i < j ≤ P )．入出力例入力例 1 5 5 3 2 2 2 4 3 出力例 1 4 この入力例の場合，城壁としてありうるものは以下の 4 通りが考えられる．ただし，× で示したマスは城壁が存在しなかったことがわかっているマスである．入力例 2 7 8 4 3 2 2 3 7 6 5 出力例 2 13 入力例 3 4000 4000 1234 4 1161 3028 596 1892 3731 2606 702 1530 出力例 3 7050792912 問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	38,219
I: Palindrome Compliment 問題文小池くんはチームメイトをよく褒めます。彼はチームメイトである松崎くんを文字列 $S$ で褒めます。その形式は以下の条件を満たします。 $Hoge, Zaki, O$ は小文字アルファベットのみからなる文字列 $S = Hoge + Zaki + Hoge + O$ ($+$ は文字列の結合を表す) $S$ は回文小池くんは$Hoge$の長さを$N$としたときに、松崎くんの褒め方が何通りあるのか気になりました。 3人目のチームメンバーにしてred coderであるあなたは小池くんの代わりに答えを計算することになりました。文字列 $Zaki, O$ と整数 $N$ が与えられるので、ありえる組み合わせの数を求めてください．なお、答えは非常に大きくなる可能性があるので、$10^9 + 7$ で割った余りを出力してください。制約 $Zaki$ と $O$ は小文字アルファベットからなる文字列 $1 \leq \|Zaki\| \leq 10^5$ $1 \leq \|O\| \leq 10^5$ $1 \leq N \leq 10^9$ 入力入力は以下の形式で標準入力から与えられます。 $Zaki$ $O$ $N$ 出力答えを1行に出力してください。入出力例入力例1 zaki o 4 出力例1 0 入力例2 aab aa 3 出力例2 26 入力例3 aaa aaaa 3 出力例3 1	38,220
Problem B: Equals are Equals Mr. Simpson got up with a slight feeling of tiredness. It was the start of another day of hard work. A bunch of papers were waiting for his inspection on his desk in his office. The papers contained his students' answers to questions in his Math class, but the answers looked as if they were just stains of ink. His headache came from the ``creativity'' of his students. They provided him a variety of ways to answer each problem. He has his own answer to each problem, which is correct, of course, and the best from his aesthetic point of view. Some of his students wrote algebraic expressions equivalent to the expected answer, but many of them look quite different from Mr. Simpson's answer in terms of their literal forms. Some wrote algebraic expressions not equivalent to his answer, but they look quite similar to it. Only a few of the students' answers were exactly the same as his. It is his duty to check if each expression is mathematically equivalent to the answer he has prepared. This is to prevent expressions that are equivalent to his from being marked as ``incorrect'', even if they are not acceptable to his aesthetic moral. He had now spent five days checking the expressions. Suddenly, he stood up and yelled, ``I've had enough! I must call for help.'' Your job is to write a program to help Mr. Simpson to judge if each answer is equivalent to the ``correct'' one. Algebraic expressions written on the papers are multi-variable polynomials over variable symbols a , b ,..., z with integer coefficients, e.g., ( a + b 2 )( a - b 2 ), ax 2 +2 bx + c and ( x 2 +5 x + 4)( x 2 + 5 x + 6) + 1. Mr. Simpson will input every answer expression as it is written on the papers; he promises you that an algebraic expression he inputs is a sequence of terms separated by additive operators ` + ' and ` - ', representing the sum of the terms with those operators, if any; a term is a juxtaposition of multiplicands, representing their product; and a multiplicand is either (a) a non-negative integer as a digit sequence in decimal, (b) a variable symbol (one of the lowercase letters ` a ' to ` z '), possibly followed by a symbol ` ^ ' and a non-zero digit, which represents the power of that variable, or (c) a parenthesized algebraic expression, recursively. Note that the operator ` + ' or ` - ' appears only as a binary operator and not as a unary operator to specify the sing of its operand. He says that he will put one or more space characters before an integer if it immediately follows another integer or a digit following the symbol ` ^ '. He also says he may put spaces here and there in an expression as an attempt to make it readable, but he will never put a space between two consecutive digits of an integer. He remarks that the expressions are not so complicated, and that any expression, having its ` - 's replaced with ` + 's, if any, would have no variable raised to its 10th power, nor coefficient more than a billion, even if it is fully expanded into a form of a sum of products of coefficients and powered variables. Input The input to your program is a sequence of blocks of lines. A block consists of lines, each containing an expression, and a terminating line. After the last block, there is another terminating line. A terminating line is a line solely consisting of a period symbol. The first expression of a block is one prepared by Mr. Simpson; all that follow in a block are answers by the students. An expression consists of lowercase letters, digits, operators ` + ', ` - ' and ` ^ ', parentheses ` ( ' and ` ) ', and spaces. A line containing an expression has no more than 80 characters. Output Your program should produce a line solely consisting of `` yes '' or `` no '' for each answer by the students corresponding to whether or not it is mathematically equivalent to the expected answer. Your program should produce a line solely containing a period symbol after each block. Sample Input a+b+c (a+b)+c a- (b-c)+2 . 4ab (a - b) (0-b+a) - 1a ^ 2 - b ^ 2 2 b 2 a . 108 a 2 2 3 3 3 a 4 a^1 27 . . Output for the Sample Input yes no . no yes . yes yes .	38,221
ゴルフクロセは超一流の腕を持ったバトルプログラマーであり，プログラミングコンテスト界隈でその名を知らぬ者はいない．アルゴリズム，データマイニング，ハッキング，AI，……ありとあらゆる大会を総なめにしてきた．そんなクロセが次の目標に据えた競技は，「コードゴルフ」である．コードゴルフとは，与えられた問題に対し正答を返すプログラムの「ソースコードの短さ」を競う競技である．コードゴルフにおいては，異なるプログラミング言語間で公平な比較が難しいため，使用言語が限定されることが多い．クロセが次に狙っている大会「ICPC (International Competition of Program Compactness)」では，「AJAGOL」と呼ばれるプログラミング言語のみが使用できるルールとなっている．コードを1バイトでも短くするため，クロセが初めに注目したのは，「定数宣言」の短縮だった． AJAGOLはいにしえの36bitアーキテクチャに最適化して設計された伝統ある言語である．整数を表現するために36bit符号無し整数型が用意されており，$0$ 以上 $2^{36}-1$ 以下の整数を扱うことができる．さて，AJAGOLの定数は通常，数字[0-9]を任意の個数用いた十進数で宣言される．また，演算子として以下の表の演算子を用いることができる．優先順位演算子結合性意味 1 ( , ) - 括弧 2 ^ 右結合冪乗: a^b := $a^b$ 3 * 左結合乗算: ab := $a \times b$ 3 / 左結合除算: a/b := $ \lfloor a \div b \rfloor$ 4 + 左結合加算: a+b := $a + b$ 4 - 左結合減算: a-b := $a - b$ ここで，優先順位の値が小さい演算ほど優先的に計算され，同じ値のときには結合性に従った順序で計算される．例えば " 2^2^3+8/32 " という計算式は，2^2^3+8/32 = 2^8+8/32 = 256+8/32 = 256+22 = 256+4 = 260 という順序で計算される．また，演算途中の値が $[0, 2^{36}-1]$ に収まらない計算やゼロ除算，ゼロのゼロ乗は，AJAGOLでは実行時エラーとなるため避ける必要がある．例えば " 2^36-100 "，" 1111/0 "，" (2-2)^0 " などは実行時エラーとなる．超一流のバトルプログラマーであるクロセは，これらの演算子を用いることにより，通常よりも短い定数宣言が可能であることを見抜いた．例えば，117649は言わずと知れた $7^6$ であるが，AJAGOLの冪乗演算子を用いることで " 7^6 " と3バイトで書くことができる．これは通常の " 117649 " という宣言で必要となる6バイトよりも3バイト短い．よって，AJAGOLによるコードゴルフでは，117649を定数として用いたい場合には " 7^6 " と宣言するのが基本となる．定数宣言の短縮はコードゴルフにおいて最も基本的なテクニックの1つであるが，あくまで小手先のテクニックとも言える．このようなところに多大な時間を掛けていては，本質的なコードの短縮に時間を割けなくなってしまう．そこでクロセは，非負整数を十進数で入力したとき，それを表現するAJAGOL定数宣言として最も短いものを調べることにした． Input 入力は複数のデータセットからなる．各データセットは整数 $N$ ($0 \leq N \leq 2^{36}-1$) を含む1行で与えられる．入力の終了は $-1$ のみを含む1行で表される． Output 各データセットに対し，与えられた整数 $N$ を表現する最も短いAJAGOL定数宣言の長さを1行で出力せよ． Sample Input 117649 1 125000 1610612736 68719476636 -1 Output for Sample Input 3 1 4 6 11	38,222
Problem B: Carrot Tour うさぎがある国を旅行している. この国には1 から n の番号がついた n 個の都市があり, うさぎは今都市1にいる. 都市 i は座標平面上の1 点( x i , y i ) とみなす. うさぎは以下の条件をみたすように旅をする. 移動経路は折れ線であり, その各部分は異なる2 都市を結ぶ線分でなければならない. 移動経路の全長は r 以下でなければならない. 経路のうち重なった部分も, 通った回数分数える. 移動する方向が変わるとき, 曲がる角度は θ 以下でなければならない. 最初の移動方向に制限はない. うさぎがある都市から別の都市へ移動をすると, 移動先の都市でニンジンを1 本もらえる. 同じ都市を複数回訪れることは可能であり, 訪れるたびにニンジンをもらえる. うさぎがこの旅で手に入れることのできるニンジンの本数の最大値を求めよ. Input 入力の一行目には一つの整数 n が, 二行目には二つの実数 r , θ がスペースで区切られて与えられる. 1 ≤ n ≤ 20 0 < r < 10 4 0° < θ < 180° 続く n 行には, 整数 x i , y i がスペースで区切られて与えられる -10 000 ≤ x i , y i ≤ 10 000 r , θ を±10 −3 以内で変化させても答えは変わらない. どの2 つの都市の位置も異なる. Output うさぎがこの旅で手に入れることのできるニンジンの本数の最大値を一行に出力せよ. Sample Input 1 5 100.1 90.1 0 0 0 10 5 5 10 0 10 10 Sample Output 1 10	38,223
Score : 500 points Problem Statement You are given a tree with N vertices and N-1 edges. The vertices are numbered 1 to N , and the i -th edge connects Vertex a_i and b_i . You have coloring materials of K colors. For each vertex in the tree, you will choose one of the K colors to paint it, so that the following condition is satisfied: If the distance between two different vertices x and y is less than or equal to two, x and y have different colors. How many ways are there to paint the tree? Find the count modulo 1\ 000\ 000\ 007 . What is tree? A tree is a kind of graph. For detail, please see: Wikipedia "Tree (graph theory)"	38,224
Score : 100 points Problem Statement You are given two integers A and B as the input. Output the value of A + B . However, if A + B is 10 or greater, output error instead. Constraints A and B are integers. 1 ≤ A, B ≤ 9 Input Input is given from Standard Input in the following format: A B Output If A + B is 10 or greater, print the string error (case-sensitive); otherwise, print the value of A + B . Sample Input 1 6 3 Sample Output 1 9 Sample Input 2 6 4 Sample Output 2 error	38,225
Problem J: The Incubator サラリーマンの朝は早い。エリートコースを進み一流企業に入社して新人という肩書きからも卒業する頃、僕に下った辞令は未開の惑星における営業活動だった。辺鄙な土地での不便な生活を強いられているが、一応は左遷でなく栄転であり、その証拠に給料もぐんと上がっている - こんな場所では金なんて使いようもないのだけど。近年僕たちが直面している宇宙規模のエネルギー不足に対応するため、特定の生物種の個体から莫大なエネルギーを生成するテクノロジーが開発された。その特定の生物種というのが、この辺鄙な惑星の固有種なのだ。この生物が絶滅しないように保護しつつ、適度にエネルギーを回収していくのが僕の仕事だ。エネルギーの回収は、いくつかのステップからなる。まずは、エネルギーの回収に使用する個体を選別する。個体によって得られるエネルギーの量は大きく異なるのだ。次に、選別された見込みのある個体に、インキュベーションという特別な処理を行う。インキュベートされた個体は膨大なエネルギーの源となる何かをを絶えず蓄えたり吐き出したりするので、個体にできるだけ多くのエネルギーの源となる何かが蓄えられている瞬間を狙って、円環の理に導く。するとお待ちかねのエネルギーが手に入る、という仕組みだ。エリートサラリーマンに課せられるノルマは厳しい。しかし、僕にとって数十万のインキュベートされた個体を管理するのは朝飯前だ。今日は月末なので本社に月報を提出しなければならないが、今月はとても良い個体に遭遇したこともあって、過去最高の成績になりそうだ。と喜んでいたのも束の間、最後の最後でひどいミスをやらかしてしまった。SQL文を打ち間違えて、今月の成果を記録しているデータベースのテーブル 1 つをまるごとふっ飛ばしてしまったのだ。あれがなければ、今月の成果は全く無しということになってしまう。降格、左遷、あるいは解雇もありえるかもしれない。最後の頼みの綱は、作業のたびにこまめにつけていたログファイルだ。僕はいつも、個体をインキュベートするたびに一意な整数の番号を振り、インキュベートされた個体たちの番号を 1 つの配列に保存している。僕の営業活動は、次のような行動からなる。個体をインキュベートし、その個体に番号 x を割り当て、その個体の番号を配列の末尾に追加する。配列の n 番目の番号が示す個体を円環の理に導く。番号 x の個体を円環の理に導く。残念ながら僕は最大 lim 体の個体しか管理できない。個体をインキュベートしたとき、もしインキュベート済みの個体が lim を超えたならば、昔にインキュベートした個体から順に lim 以下になるまで円環の理に導く。僕はこれら 4 つの営業活動を行うたびに、欠かさずログファイルに記入している。しかし、4 の活動だけはログファイルに一切記入していない。そうしても特に曖昧なところは残らないためだ。いつも僕は、個体の番号の配列の操作を愚直に行なっている。しかし今度ばかりは、愚直に操作しながらログファイルを走査していては間に合いそうにない。月報の提出期限は 5 時間後に迫っている。そこで、君たちにお願いがあるんだ。ログファイルから僕の営業活動を再現するプログラムを書いてほしい。もし書いてくれたら、お礼に君たちの願い事を何でも 1 つ叶えてあげよう。何だって構わない。どんな願いことだって叶えてあげられるよ。 Input 入力は複数のケースからなる。各ケースは以下のフォーマットで与えられる。ここには入力のフォーマットを書く。 q lim query 0 x 0 . . . query q-1 x q-1 query i が0の時、インキュベートした個体に x i の番号を割り当てたことを表す。 query i が1の時、配列の x i 番目の番号が示す個体を円環の理に導く。 query i が2の時、その時点で配列に含まれている中で x i 番目の個体の番号を出力する query i が3の時、番号が x i の個体を円環の理に導く。 q = 0 かつ lim = 0の時入力の終わりを表す。 lim は32bit signed integerで表すことができる正の整数である。すべてのクエリーについて、 x i は0以上の整数で32bit signed integerで表すことができる。 0のクエリーについて、 x i は32bit signed integerの範囲に収まる非負整数で表される。 1,2のクエリーについて、 x i の値は1以上の整数である。また存在しない配列の番号が指定されることはない 3のクエリーについて、存在しない個体番号が入力に含まれることはない。また一度消去された個体の番号が値が同じテストケース内で、別の個体に割り当てられることはない。ジャッジデータは次の2つのうち少なくとも片方を満たす。 1 ≤ q ≤ 400,000 かつテストケースの数が5個以下 1 ≤ q ≤ 10,000 かつテストケースの数は50個以下 Output 入力のクエリーが2の場合、x番目の個体番号を出力する各ケースの最後には"end"を出力する Sample input 22 5 0 0 0 1 0 2 0 3 0 4 2 1 2 2 2 3 2 4 2 5 0 5 2 1 0 6 2 2 3 3 2 2 2 2 1 2 2 2 2 1 2 2 2 3 30 5 0 383594529 1 1 0 868094164 0 708344471 0 4102559 0 944076771 0 320398558 1 1 0 949521499 0 1035499529 0 585547493 0 915496840 0 721553343 0 405934659 0 814301872 1 1 2 3 0 919753364 1 1 0 69231610 2 2 0 373477673 0 842917649 0 961543702 0 907959899 2 1 2 2 2 3 2 4 2 5 30 5 0 726736645 0 1 0 344304573 0 241734870 3 726736645 1 3 2 1 0 586879203 2 3 0 511883046 0 481344051 0 154183395 0 435126242 0 185906768 1 1 0 383123551 0 20253038 1 5 2 1 2 2 0 163044554 3 435126242 0 105612613 0 725050544 0 559442328 2 1 2 2 2 3 2 4 2 5 0 0 Sample output 0 1 2 3 4 1 3 4 4 5 2 5 6 end 405934659 405934659 69231610 373477673 842917649 961543702 907959899 end 1 586879203 154183395 435126242 383123551 163044554 105612613 725050544 559442328 end The University of Aizu Programming Contest 2011 Summer 原案: Tomoya Sakai 問題文: Takashi Tayama	38,226
Score : 1200 points Problem Statement We have N boxes numbered 1 to N , and M balls numbered 1 to M . Currently, Ball i is in Box A_i . You can do the following operation: Choose a box containing two or more balls, pick up one of the balls from that box, and put it into another box. Since the balls are very easy to break, you cannot move Ball i more than C_i times in total. Within this limit, you can do the operation any number of times. Your objective is to have Ball i in Box B_i for every i ( 1 \leq i \leq M ). Determine whether this objective is achievable. If it is, also find the minimum number of operations required to achieve it. Constraints 1 \leq N \leq 10^5 1 \leq M \leq 10^5 1 \leq A_i,B_i \leq N 1 \leq C_i \leq 10^5 In the situation where the objective is achieved, every box contains one or more balls. That is, for every i ( 1 \leq i \leq N ), there exists j such that B_j=i . 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 \vdots A_M B_M C_M Output If the objective is unachievable, print -1 ; if it is achievable, print the minimum number of operations required to achieve it. Sample Input 1 3 3 1 2 1 2 1 1 1 3 2 Sample Output 1 3 We can achieve the objective in three operations, as follows: Pick up Ball 1 from Box 1 and put it into Box 2 . Pick up Ball 2 from Box 2 and put it into Box 1 . Pick up Ball 3 from Box 1 and put it into Box 3 . Sample Input 2 2 2 1 2 1 2 1 1 Sample Output 2 -1 Sample Input 3 5 5 1 2 1 2 1 1 1 3 2 4 5 1 5 4 1 Sample Output 3 6 Sample Input 4 1 1 1 1 1 Sample Output 4 0	38,227
Common-Prime Sort You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6, 4, 2, 3, 7] can be sorted using the following steps. Step 0: 6 4 2 3 7 (given sequence) Step 1: 2 4 6 3 7 (elements 6 and 2 swapped) Step 2: 2 6 4 3 7 (elements 4 and 6 swapped) Step 3: 2 3 4 6 7 (elements 6 and 3 swapped) Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name "Coprime sort" to this approach and are now examining if a given sequence is coprime-sortable. Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number. Input The input is given in the following format. $N$ $a_1$ $a_2$ $...$ $a_N$ The first line provides the number of elements included in the sequence $N$ ($2 \leq N \leq 10^5$). The second line provides an array of integers $a_i$ ($2 \leq a_i \leq 10^5$) that constitute the sequence. Output Output " 1 " if the sequence is coprime-sortable in increasing order, or " 0 " otherwise. Sample Input 1 5 6 4 2 3 7 Sample Output 1 1 Sample Input 2 7 2 9 6 5 6 7 3 Sample Output 2 0	38,229
勉強を開始した時刻と終了した時刻の情報を基に、1日で勉強した時間の合計が t 以上であるかをチェックし、達していない場合は足りない時間を求めるプログラムを作成します。時間は1時間を1単位とし、分や秒は考えないものとします。時刻は24時間表記で1時間単位で表します。 1日の勉強の目標時間と、実際に勉強した時間の情報（勉強の回数 n 、それぞれの勉強の開始時刻 s と終了時刻 f ）を入力とし、勉強時間の合計が目標に達しているかを調べ、達していれば "OK" を、達していない場合は足りない時間を出力するプログラムを作成してください。ただし、それぞれ行った勉強時間は重複しません。例：目標時間勉強した時間判定 10時間 6時〜11時＝ 5時間 12時〜15時＝ 3時間 18時〜22時＝ 4時間 OK 14時間 6時〜11時＝ 5時間 13時〜20時＝ 7時間 2時間不足入力複数のデータセットの並びが与えられます。入力の終わりはゼロひとつの行で示されます。各データセットは以下の形式で与えられます。 t n s 1 f 1 s 2 f 2 : s n f n １行目に１日の目標時間 t (0 ≤ t ≤ 22)、２行目に勉強の回数 n (1 ≤ n ≤ 10)が与えられます。続く n 行に i 回目の勉強の開始時刻 s i と終了時刻 f (6 ≤ s i , f i ≤ 22) が与えられます。データセットの数は 100 を超えません。出力データセットごとに、OK または足りない時間を１行に出力します。入力例 10 3 6 11 12 15 18 22 14 2 6 11 13 20 0 出力例 OK 2	38,230
たしざんひきざん (Calculation Training) square1001 君は E869120 君に、誕生日プレゼントとして二つの数字 $A$ と $B$ をプレゼントしました。 E869120 君はこの二つの数字を使って、計算トレーニングをすることにしました。具体的には、E869120君は次の操作をちょうど $N$ 回これらの数に行います。奇数回目の操作のとき、$A$ を $A-B$ で置き換える偶数回目の操作のとき、$B$ を $A+B$ で置き換える E869120君が $N$ 回の操作をした後、$A$ と $B$ の値がそれぞれいくつになっているか求めてください。入力入力は以下の形式で標準入力から与えられる。 $N$ $A$ $B$ 出力 E869120君が $N$ 回の操作をした後の $A$ と $B$ の値を、この順に空白区切りで出力してください。ただし、最後には改行を入れること。制約 $1 \leq N \leq 1000000000000000000 \ (= 10^{18})$ $1 \leq A \leq 1000000000 \ (= 10^9)$ $1 \leq B \leq 1000000000 \ (= 10^9)$ 入力は全て整数である。入力例1 3 3 4 出力例1 -4 3 $(A, B)$ の値は $(3,4) → (-1,4) → (-1,3) → (-4,3)$ と変化します。入力例2 8 6 9 出力例2 3 -6	38,231
Score : 400 points Problem Statement We have a tree with N vertices numbered 1 to N . The i -th edge in the tree connects Vertex u_i and Vertex v_i , and its length is w_i . Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied: For any two vertices painted in the same color, the distance between them is an even number. Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem. Constraints All values in input are integers. 1 \leq N \leq 10^5 1 \leq u_i < v_i \leq N 1 \leq w_i \leq 10^9 Input Input is given from Standard Input in the following format: N u_1 v_1 w_1 u_2 v_2 w_2 . . . u_{N - 1} v_{N - 1} w_{N - 1} Output Print a coloring of the vertices that satisfies the condition, in N lines. The i -th line should contain 0 if Vertex i is painted white and 1 if it is painted black. If there are multiple colorings that satisfy the condition, any of them will be accepted. Sample Input 1 3 1 2 2 2 3 1 Sample Output 1 0 0 1 Sample Input 2 5 2 5 2 2 3 10 1 3 8 3 4 2 Sample Output 2 1 0 1 0 1	38,232
Problem H: Hogemon Get Problem がっちょ君は人気のゲームHogemon Getに熱中している。がっちょ君が住んでいる会津国はそれぞれ1から N の番号がついている N 個の町からなる。また、会津国には M 本の道があり、すべての道は異なる2つの町を結んでいる。がっちょ君は道を双方向に移動することができるが、道以外を通って、ある町から別の町に行くことはできない。 Hogemon Getでは、町 i でボールを d i 個入手することができる。ただし、ある町で再びボールを入手するためには、最後にその町でボールを入手してから15分以上経過している必要がある。なお、がっちょ君は町1、町 N を含むすべての町を何度でも訪れることができる。がっちょ君は最初、町1にいて、町 N に R 分以内で移動しなければならない。つまり、 R 分後に町 N にいる必要がある。がっちょ君は移動の際に、最大でいくつのボールを入手することができるだろうか。 Input 入力は以下の形式で与えられる。 N M R d 1 d 2 ... d N a 1 b 1 c 1 a 2 b 2 c 2 ... a M b M c M 入力はすべて整数である。 1行目に町の個数 N ,道の本数 M ,制限時間 R が空白区切りで与えられる。 2行目に町 i ( i =1,2,..., N )に訪れることで入手することができるボールの個数 d i が空白区切りで与えられる。 3行目から M +2行目に道 j ( j =1,2,..., M )の情報 a j , b j , c j が空白区切りで与えられる。 j 番目の道は町 a j と町 b j の間を c j 分で移動できることを表す。 Constraints 3 ≤ N ≤ 30 N -1 ≤ M ≤ min( N ×( N -1)/2, 300) 10 ≤ R ≤ 1000 0 ≤ d i ≤ 10 d 1 = d N = 0 1 ≤ a j < b j ≤ N 5 ≤ c j ≤ 100 町1から町 N へは R 分以内で移動できることが保証されているある2つの町の組に対して2本以上の道があることはない Output 町1から町 N へ R 分以内に移動するまでに入手することができる最大のボールの個数を1行で出力せよ。 Sample Input 1 5 4 40 0 1 1 1 0 1 2 5 2 3 5 3 4 5 4 5 5 Sample Output 1 6 経過時間(分) 町の番号ボールの数(個) 0 1 0 5 2 1 10 3 2 15 4 3 20 3 3 25 2 4 30 3 5 35 4 6 40 5 6 ※経過時間20分の町3では最後に町3でボールを入手してから15分経過していないのでボールを入手することができない。 Sample Input 2 4 3 100 0 3 1 0 1 2 5 2 3 30 3 4 5 Sample Output 2 16 経過時間(分) 町の番号ボールの数(個) 0 1 0 5 2 3 20 2 6 35 2 9 50 2 12 65 2 15 95 3 16 100 4 16 Sample Input 3 5 4 50 0 1 1 10 0 1 2 10 2 3 10 2 4 10 4 5 10 Sample Output 3 22	38,233
Problem C: Craftsman Takeshi, a famous craftsman, accepts many offers from all over Japan. However, the tools which he is using now has become already too old. So he is planning to buy new tools and to replace the old ones before next use of the tools. Some offers may incur him monetary cost, if the offer requires the tools to be replaced. Thus, it is not necessarily best to accept all the orders he has received. Now, you are one of his disciples. Your task is to calculate the set of orders to be accepted, that maximizes his earning for a given list of orders and prices of tools. His earning may shift up and down due to sale income and replacement cost. He always purchases tools from his friend's shop. The shop discounts prices for some pairs of items when the pair is purchased at the same time. You have to take the discount into account. The total price to pay may be not equal to the simple sum of individual prices. You may assume that all the tools at the shop are tough enough. Takeshi can complete all orders with replaced tools at this time. Thus you have to buy at most one tool for each kind of tool. Input The input conforms to the following format: N M P X 1 K 1 I 1,1 ... I 1, K 1 ... X N K N I N ,1 ... I N , K N Y 1 ... Y M J 1,1 J 1,2 D 1 ... J P ,1 J P ,2 D P where N , M , P are the numbers of orders, tools sold in the shop and pairs of discountable items, respectively. The following N lines specify the details of orders. X i is an integer indicating the compensation for the i -th order, and K i is the number of tools required to complete the order. The remaining part of each line describes the tools required for completing the order. Tools are specified by integers from 1 through M . The next M lines are the price list at the shop of Takeshi's friend. An integer Y i represents the price of the i -th tool. The last P lines of each test case represent the pairs of items to be discounted. When Takeshi buys the J i ,1 -th and the J i ,2 -th tool at the same time, he has to pay only D i yen, instead of the sum of their individual prices. It is guaranteed that no tool appears more than once in the discount list, and that max{ Y i , Y j } < D i,j < Y i + Y j for every discount prices, where D i,j is the discount price of i -th and j -th tools bought at the same time. Also it is guaranteed that 1 ≤ N ≤ 100, 2 ≤ M ≤ 100, 1 ≤ K i ≤ 100, 1 ≤ P ≤ M /2 and 1 ≤ X i , Y i ≤ 1000. Output Output the maximum possible earning of Takeshi to the standard output. Sample Input and Output Input #1 3 4 2 100 2 1 2 100 1 3 100 1 4 20 20 50 150 1 2 30 3 4 180 Output #1 120 Input #2 1 2 1 100 1 2 20 40 1 2 51 Output #2 60	38,234
Score : 1100 points Problem Statement You are given a directed graph with N vertices and M edges. The vertices are numbered 1, 2, ..., N , and the edges are numbered 1, 2, ..., M . Edge i points from Vertex a_i to Vertex b_i . For each edge, determine whether the reversion of that edge would change the number of the strongly connected components in the graph. Here, the reversion of Edge i means deleting Edge i and then adding a new edge that points from Vertex b_i to Vertex a_i . Constraints 2 \leq N \leq 1000 1 \leq M \leq 200,000 1 \leq a_i, b_i \leq N a_i \neq b_i If i \neq j , then a_i \neq a_j or b_i \neq b_j . Input Input is given from Standard Input in the following format: N M a_1 b_1 a_2 b_2 : a_M b_M Output Print M lines. In the i -th line, if the reversion of Edge i would change the number of the strongly connected components in the graph, print diff ; if it would not, print same . Sample Input 1 3 3 1 2 1 3 2 3 Sample Output 1 same diff same The number of the strongly connected components is 3 without reversion of edges, but it will become 1 if Edge 2 is reversed. Sample Input 2 2 2 1 2 2 1 Sample Output 2 diff diff Reversion of an edge may result in multiple edges in the graph. Sample Input 3 5 9 3 2 3 1 4 1 4 2 3 5 5 3 3 4 1 2 2 5 Sample Output 3 same same same same same diff diff diff diff	38,235
問題文世の中の少女たちはキュゥべえと契約し願いを叶えてもらい，それとひきかえに魔法少女となる．使う魔法の形・効果は願いに強く影響を受ける．魔法少女さやかちゃんは最近キュゥべえと契約した新米魔法少女である．さやかの願いは「事故のため指が動かなくなり，音楽を演奏するのを諦めていた男の子を助けること」であったので，作る魔方陣は音符が輪の上に並んだ形をしている．さやかは N 個の音符を持っており，それらを輪の上に並べることによって魔方陣を作る．音符をどのような順番で並べるかは彼女の自由である．魔方陣を作るために精神力が消費され，その量は音符の配置によって以下のように決まる．まず， M 個の正の整数からなる音楽的美しさ S_1,\ ...,\ S_M が定められている，各音符は音程を持っており，音程は 1 から M の整数 K_1,\ ...,\ K_N で表される．音程が a,\ b\ (a≤b) であるような 2 つの音符の間の反発力とは， [(S_a\ +\ ...\ +\ S_b) / L] で定められる量である．ここで， L は入力で与えられる定数であり，実数 x に対して [x] は x を越えない最大の整数を表すものとする．さやかの消費する精神力は，各2つの隣り合う音符 ( N 組存在する) の間の反発力の合計値である．例えば音楽的美しさがそれぞれ \{100,\ 200,\ 300,\ 400,\ 500\} で，音程が \{1,\ 3,\ 5,\ 4\} である音符をこの順番で並べて魔方陣を作った時，消費される精神力は 37\ (=[(100+200+300)/99]+[(300+400+500)/99]+[(500+400)/99]+[(400+300+200+100)/99]) となる．使うべき音符の音程の組み合わせと各音程の音楽的美しさが与えられるので，消費される精神力の最小値を求めよ．入力形式入力は以下の形式で与えられる． N\ M\ L\\ K_1\ K_2\ …\ K_N\\ S_1\ S_2\ …\ S_M N はさやかの持っている音符の数， M は音楽的美しさの値の個数， L は反発力を定めるのに使われる定数である． K_i は音符の音程を表し， S_j は音楽的美しさを表す．出力形式消費される精神力の最小値を 1 行に出力せよ．制約 3 ≤ N ≤ 2,000 1 ≤ M ≤ 10 5 1 ≤ L ≤ 10 5 1 ≤ K_i ≤ M 1 ≤ S_j ≤ 10 5 入力値は全て整数である．入出力例入力例 1 4 5 99 1 4 5 3 100 200 300 400 500 出力例1 37 入力例 2 3 1 99 1 1 1 100 出力例 2 3 Problem Setter: Flat35	38,236
Score : 100 points Problem Statement There are H rows and W columns of white square cells. You will choose h of the rows and w of the columns, and paint all of the cells contained in those rows or columns. How many white cells will remain? It can be proved that this count does not depend on what rows and columns are chosen. Constraints All values in input are integers. 1 \leq H, W \leq 20 1 \leq h \leq H 1 \leq w \leq W Input Input is given from Standard Input in the following format: H W h w Output Print the number of white cells that will remain. Sample Input 1 3 2 2 1 Sample Output 1 1 There are 3 rows and 2 columns of cells. When two rows and one column are chosen and painted in black, there is always one white cell that remains. Sample Input 2 5 5 2 3 Sample Output 2 6 Sample Input 3 2 4 2 4 Sample Output 3 0	38,237
Daruma Otoshi You are playing a variant of a game called "Daruma Otoshi (Dharma Block Striking)". At the start of a game, several wooden blocks of the same size but with varying weights are stacked on top of each other, forming a tower. Another block symbolizing Dharma is placed atop. You have a wooden hammer with its head thicker than the height of a block, but not twice that. You can choose any two adjacent blocks, except Dharma on the top, differing at most 1 in their weight, and push both of them out of the stack with a single blow of your hammer. The blocks above the removed ones then fall straight down, without collapsing the tower. You cannot hit a block pair with weight difference of 2 or more, for that makes too hard to push out blocks while keeping the balance of the tower. There is no chance in hitting three blocks out at a time, for that would require superhuman accuracy. The goal of the game is to remove as many blocks as you can. Your task is to decide the number of blocks that can be removed by repeating the blows in an optimal order. Figure D1. Striking out two blocks at a time In the above figure, with a stack of four blocks weighing 1, 2, 3, and 1, in this order from the bottom, you can hit middle two blocks, weighing 2 and 3, out from the stack. The blocks above will then fall down, and two blocks weighing 1 and the Dharma block will remain. You can then push out the remaining pair of weight-1 blocks after that. Input The input consists of multiple datasets. The number of datasets is at most 50. Each dataset is in the following format. n w 1 w 2 … w n n is the number of blocks, except Dharma on the top. n is a positive integer not exceeding 300. w i gives the weight of the i -th block counted from the bottom. w i is an integer between 1 and 1000, inclusive. The end of the input is indicated by a line containing a zero. Output For each dataset, output in a line the maximum number of blocks you can remove. Sample Input 4 1 2 3 4 4 1 2 3 1 5 5 1 2 3 6 14 8 7 1 4 3 5 4 1 6 8 10 4 6 5 5 1 3 5 1 3 0 Output for the Sample Input 4 4 2 12 0	38,238
Score : 600 points Problem Statement We have a tree with N vertices numbered 1 to N . The i -th edge in this tree connects Vertex a_i and b_i . Additionally, each vertex is painted in a color, and the color of Vertex i is c_i . Here, the color of each vertex is represented by an integer between 1 and N (inclusive). The same integer corresponds to the same color; different integers correspond to different colors. For each k=1, 2, ..., N , solve the following problem: Find the number of simple paths that visit a vertex painted in the color k one or more times. Note: The simple paths from Vertex u to v and from v to u are not distinguished. Constraints 1 \leq N \leq 2 \times 10^5 1 \leq c_i \leq N 1 \leq a_i,b_i \leq N The given graph is a tree. All values in input are integers. Input Input is given from Standard Input in the following format: N c_1 c_2 ... c_N a_1 b_1 : a_{N-1} b_{N-1} Output Print the answers for k = 1, 2, ..., N in order, each in its own line. Sample Input 1 3 1 2 1 1 2 2 3 Sample Output 1 5 4 0 Let P_{i,j} denote the simple path connecting Vertex i and j . There are 5 simple paths that visit a vertex painted in the color 1 one or more times: P_{1,1}\,,\, P_{1,2}\,,\, P_{1,3}\,,\, P_{2,3}\,,\, P_{3,3} There are 4 simple paths that visit a vertex painted in the color 2 one or more times: P_{1,2}\,,\, P_{1,3}\,,\, P_{2,2}\,,\, P_{2,3} There are no simple paths that visit a vertex painted in the color 3 one or more times. Sample Input 2 1 1 Sample Output 2 1 Sample Input 3 2 1 2 1 2 Sample Output 3 2 2 Sample Input 4 5 1 2 3 4 5 1 2 2 3 3 4 3 5 Sample Output 4 5 8 10 5 5 Sample Input 5 8 2 7 2 5 4 1 7 5 3 1 1 2 2 7 4 5 5 6 6 8 7 8 Sample Output 5 18 15 0 14 23 0 23 0	38,240
Score : 1200 points Problem Statement Snuke loves flags. Snuke is placing N flags on a line. The i -th flag can be placed at either coordinate x_i or coordinate y_i . Snuke thinks that the flags look nicer when the smallest distance between two of them, d , is larger. Find the maximum possible value of d . Constraints 2 ≤ N ≤ 10^{4} 1 ≤ x_i, y_i ≤ 10^{9} x_i and y_i are integers. Input The input is given from Standard Input in the following format: N x_1 y_1 : x_N y_N Output Print the answer. Sample Input 1 3 1 3 2 5 1 9 Sample Output 1 4 The optimal solution is to place the first flag at coordinate 1 , the second flag at coordinate 5 and the third flag at coordinate 9 . The smallest distance between two of the flags is 4 in this case. Sample Input 2 5 2 2 2 2 2 2 2 2 2 2 Sample Output 2 0 There can be more than one flag at the same position. Sample Input 3 22 93 6440 78 6647 862 11 8306 9689 798 99 801 521 188 206 6079 971 4559 209 50 94 92 6270 5403 560 803 83 1855 99 42 504 75 484 629 11 92 122 3359 37 28 16 648 14 11 269 Sample Output 3 17	38,241
Unable Count I would, if I could, If I couldn't how could I? I couldn't, without I could, could I? Could you, without you could, could ye? Could ye? could ye? Could you, without you could, could ye? It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues? Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n , to count all the integers that cannot be represented by a formula of the form a * i + b * j , where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows: 2 = 21 + 50, 4 = 22 + 50, 5 = 20 + 51, 6 = 23 + 50, 7 = 21 + 51. Input The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space . The integers n , a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros. Output For each input line except the last one, your program should write out a line that contains only the result of the count. Sample Input 10 2 3 10 2 5 100 5 25 0 0 0 Output for the Sample Input 1 2 80	38,242
G: 回文部分列 (Palindromic Subsequences) 問題英小文字のみからなる文字列 S が与えられるので、この文字列 S の連続とは限らない部分列であって、回文であるものは何種類あるかを求めてください。ここで、 S の連続とは限らない部分列とは、元の文字列 S から 1 文字以上 \|S\| 文字以下を任意に選択し (選択するそれぞれの文字の位置は非連続でも良い)、それらを元の順番通りに連結させてできた文字列のことを指します。この問題において、空文字列は部分列として認められないことに注意してください。また、文字列 X が回文であるとは、元の文字列 X と、 X を反転した文字列 X’ が等しいことを指します。さらに、異なる部分列のとりかたの結果同じ回文が生成されたとしても、それは重複して数えないことに注意してください。例えば S = acpc である場合、 2 文字目のみからなる部分列と、 4 文字目のみからなる部分列はどちらも回文 c ですが、これは複数回数えず、合わせて一度だけ数えることとします。答えは非常に大きくなることがあるので、 1,000,000,007 で割った余りを出力してください。入力形式 S 制約 1 \leq \|S\| \leq 2,000 S に含まれる文字は英小文字のみである出力形式答えを 1,000,000,007 で割った余りを 1 行で出力してください。入力例1 acpc 出力例1 5 文字列 acpc の連続とは限らない部分列であって回文であるものは、 a , c , cc , cpc , p の 5 種類です。部分列の種類数を数えることに注意してください。入力例2 z 出力例2 1 条件を満たす部分列は z のみです。空文字列は部分列として認められないことに注意してください。入力例3 madokamagica 出力例3 28	38,243
Balls and Boxes 10 Balls Boxes Any way At most one ball At least one ball Distinguishable Distinguishable 1 2 3 Indistinguishable Distinguishable 4 5 6 Distinguishable Indistinguishable 7 8 9 Indistinguishable Indistinguishable 10 11 12 Problem You have $n$ balls and $k$ boxes. You want to put these balls into the boxes. Find the number of ways to put the balls under the following conditions: Each ball is not distinguished from the other. Each box is not distinguished from the other. Each ball can go into only one box and no one remains outside of the boxes. Each box can contain an arbitrary number of balls (including zero). Note that you must print this count modulo $10^9+7$. Input $n$ $k$ The first line will contain two integers $n$ and $k$. Output Print the number of ways modulo $10^9+7$ in a line. Constraints $1 \le n \le 1000$ $1 \le k \le 1000$ Sample Input 1 5 3 Sample Output 1 5 Sample Input 2 10 5 Sample Output 2 30 Sample Input 3 100 100 Sample Output 3 190569292	38,244
Score : 500 points Problem Statement Jumbo Takahashi will play golf on an infinite two-dimensional grid. The ball is initially at the origin (0, 0) , and the goal is a grid point (a point with integer coordinates) (X, Y) . In one stroke, Jumbo Takahashi can perform the following operation: Choose a grid point whose Manhattan distance from the current position of the ball is K , and send the ball to that point. The game is finished when the ball reaches the goal, and the score will be the number of strokes so far. Jumbo Takahashi wants to finish the game with the lowest score possible. Determine if the game can be finished. If the answer is yes, find one way to bring the ball to the goal with the lowest score possible. What is Manhattan distance? The Manhattan distance between two points (x_1, y_1) and (x_2, y_2) is defined as \|x_1-x_2\|+\|y_1-y_2\| .	38,247
Deque For a dynamic array $A = \{a_0, a_1, ...\}$ of integers, perform a sequence of the following operations: push($d$, $x$): Add element $x$ at the begining of $A$, if $d = 0$. Add element $x$ at the end of $A$, if $d = 1$. randomAccess($p$): Print element $a_p$. pop($d$): Delete the first element of $A$, if $d = 0$. Delete the last element of $A$, if $d = 1$. $A$ is a 0-origin array and it is empty in the initial state. Input The input is given in the following format. $q$ $query_1$ $query_2$ : $query_q$ Each query $query_i$ is given by 0 $d$ $x$ or 1 $p$ or 2 $d$ where the first digits 0 , 1 and 2 represent push, randomAccess and pop operations respectively. randomAccess and pop operations will not be given for an empty array. Output For each randomAccess, print $a_p$ in a line. Constraints $1 \leq q \leq 400,000$ $0 \leq p < $ the size of $A$ $-1,000,000,000 \leq x \leq 1,000,000,000$ Sample Input 1 11 0 0 1 0 0 2 0 1 3 1 0 1 1 1 2 2 0 2 1 0 0 4 1 0 1 1 Sample Output 1 2 1 3 4 1	38,249
Score : 500 points Problem Statement We have N logs of lengths A_1,A_2,\cdots A_N . We can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0<t<L) , it becomes two logs of lengths t and L-t . Find the shortest possible length of the longest log after at most K cuts, and print it after rounding up to an integer. Constraints 1 \leq N \leq 2 \times 10^5 0 \leq K \leq 10^9 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 K A_1 A_2 \cdots A_N Output Print an integer representing the answer. Sample Input 1 2 3 7 9 Sample Output 1 4 First, we will cut the log of length 7 at a point whose distance from an end of the log is 3.5 , resulting in two logs of length 3.5 each. Next, we will cut the log of length 9 at a point whose distance from an end of the log is 3 , resulting in two logs of length 3 and 6 . Lastly, we will cut the log of length 6 at a point whose distance from an end of the log is 3.3 , resulting in two logs of length 3.3 and 2.7 . In this case, the longest length of a log will be 3.5 , which is the shortest possible result. After rounding up to an integer, the output should be 4 . Sample Input 2 3 0 3 4 5 Sample Output 2 5 Sample Input 3 10 10 158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202 Sample Output 3 292638192	38,250
C: 短絡評価問題直大くんと北大くんはゲームをしています。北大くんは、まず以下の BNF で表される論理式を生成します。 <formula> ::= <or-expr> <or-expr> ::= <and-expr> \| <or-expr> "\|" <and-expr> <and-expr> ::= <term> \| <and-expr> "&" <term> <term> ::= "(" <or-expr> ")" \| "?" & は論理積を、 \| は論理和を表し、 & の方が \| より先に評価されます。直大くんは、この論理式を（文字列として見て）左から読んでいき、 ? を見つけたとき以下の行動をします。その ? を 0 にしても 1 にしても論理式の評価結果が変わらないことが確定しているなら、何もせず読み進める。そうでないなら、北大くんに 1 円払い、その ? を 0 または 1 に書き換える。論理式は以下のように評価されます。いわゆる普通の論理式です。 (0 & ?) == 0 (1 & 0) == 0 (1 & 1) == 1 (0 \| 0) == 0 (0 \| 1) == 1 (1 \| ?) == 1 直大くんが論理式の評価結果を確定させるために支払う必要がある最小金額はいくらでしょう？評価結果を 0 にする場合と 1 にする場合でそれぞれ求めてください。入力形式上の BNF に従う論理式が一行で与えられます。制約論理式の長さは 2\times 10^5 を超えない。出力形式評価結果を 0 、 1 にするために必要な最小金額を空白区切りで出力してください。入力例1 ?&?\|?&?\|?&? 出力例1 3 2 0 にしたい場合は 0 0 0 で書き換えて 0&?\|0&?\|0&? とし、 1 にしたい場合は 1 1 で書き換えて 1&1\|?&?\|?&? とするのが最適です。入力例2 ?&?&?\|?&?&? 出力例2 2 3 それぞれ 0&?&?\|0&?&? 、 1&1&1\|?&?&? となります。入力例3 (?\|?\|?)&?&?&?&?\|?&?\|?&? 出力例3 4 4	38,251
Score : 200 points Problem Statement An integer N is a multiple of 9 if and only if the sum of the digits in the decimal representation of N is a multiple of 9 . Determine whether N is a multiple of 9 . Constraints 0 \leq N < 10^{200000} N is an integer. Input Input is given from Standard Input in the following format: N Output If N is a multiple of 9 , print Yes ; otherwise, print No . Sample Input 1 123456789 Sample Output 1 Yes The sum of these digits is 1+2+3+4+5+6+7+8+9=45 , which is a multiple of 9 , so 123456789 is a multiple of 9 . Sample Input 2 0 Sample Output 2 Yes Sample Input 3 31415926535897932384626433832795028841971693993751058209749445923078164062862089986280 Sample Output 3 No	38,252
Problem D: AABABCAC Problem 文字列$s$,$t$が与えられる。最初、文字列集合$A=${$s$},$B=\phi$とする。このとき、次の操作をできるだけたくさん行いたい。操作 step1 全ての $u ∊ A$ について、以下の処理を行う。 $u$の全ての部分列(連続でなくてもよい)から、$t$と等しいものを任意に1つ選ぶ。選んだ部分列の$u$に対応するインデックスをそれぞれ$z_1$, $z_2$, …, $z_{\|t\|}$とする(ただし1 $\le$ $z_1$ $\lt$ $z_2$ $\lt$ … $\lt$ $z_{\|t\|}$ $\le$ $\|u\|$)。そのような部分列がなければ操作を終了する。選んだ部分列の文字$u_{z_1}$, $u_{z_2}$, …, $u_{z_{\|t\|}}$でもとの文字列を分割し、それらを$B$に追加する。例えば、$u=$"abcdcd", $t=$"ac"の場合は次の2通りの分割の方法が考えられる。 $u$の1番目の文字と3番目の文字を選んだ場合、""と"b"と"dcd"に分割される。 $u$の1番目の文字と5番目の文字を選んだ場合、""と"bcd"と"d"に分割される。 step2 $A$を$B$に置き換え、$B$を空にする。操作回数を1増やす。部分列の例 "abac"の部分列は、 { "" , "a" , "b" , "c" , "aa" ,"ab" , "ac" , "ba" , "bc" , "aac" , "aba" , "abc" , "bac" , "abac" } である。 "a"は"abac"の1文字目、または3文字目を抜き出すことによってできた部分列である。 "ac"は"abac"の1文字目と4文字目、または3文字目と4文字目を抜き出すことによってできた部分列である。 Input 入力は以下の形式で与えられる。 $s$ $t$ 1行目に文字列$s$,2行目に文字列$t$が与えられる。 Constraints 入力は以下の条件を満たす。 1 $\le$ $\|t\|$ $\le$ $\|s\|$ $\le$ $10^5$ 文字列$s$,$t$に含まれる文字はアルファベットの大文字または小文字 Output 操作回数の最大値を出力せよ。 Sample Input 1 AABABCAC A Sample Output 1 2 1回目の操作は、$A=${ "AABABCAC" }で始まる。 step1では、$u=$"AABABCAC"に対して、例えば4番目の文字を$t$と等しい部分列として選び、"AAB"と"BCAC"に分割し、それらを$B$に追加する。 step2では、$A$を$B$に置き換え、$B$を空にし、操作回数は1となる。 2回目の操作は、$A=${ "AAB" , "BCAC" }で始まる。 step1では、$u=$"AAB"に対して、例えば1番目の文字を$t$と等しい部分列として選び、""と"AB"に分割し、それらを$B$に追加する。次に$u=$"BCAC"に対して、3番目の文字を$t$と等しい部分列として選び、"BC"と"C"に分割し、それらを$B$に追加する。 step2では、$A$を$B$に置き換え、$B$を空にし、操作回数は2となる。 3回目の操作は、$A=${ "" , "AB" , "BC" , "C" }で始まる。 step1では、$u=$""に対して、$t$と等しい部分列が存在しないため、ここで操作を終了する。この例の場合、3回目の操作ではstep1で操作が終了したため、操作回数は2となる。 Sample Input 2 abaabbabaabaabbabbabaabbab ab Sample Output 2 3 Sample Input 3 AbCdEfG aBcDeFg Sample Output 3 0	38,253
Score : 1200 points Problem Statement There are N apartments along a number line, numbered 1 through N . Apartment i is located at coordinate X_i . Also, the office of AtCoder Inc. is located at coordinate S . Every employee of AtCoder lives in one of the N apartments. There are P_i employees who are living in Apartment i . All employees of AtCoder are now leaving the office all together. Since they are tired from work, they would like to get home by the company's bus. AtCoder owns only one bus, but it can accommodate all the employees. This bus will leave coordinate S with all the employees and move according to the following rule: Everyone on the bus casts a vote on which direction the bus should proceed, positive or negative. (The bus is autonomous and has no driver.) Each person has one vote, and abstaining from voting is not allowed. Then, the bus moves a distance of 1 in the direction with the greater number of votes. If a tie occurs, the bus moves in the negative direction. If there is an apartment at the coordinate of the bus after the move, all the employees who live there get off. Repeat the operation above as long as there is one or more employees on the bus. For a specific example, see Sample Input 1. The bus takes one seconds to travel a distance of 1 . The time required to vote and get off the bus is ignorable. Every employee will vote so that he himself/she herself can get off the bus at the earliest possible time. Strictly speaking, when a vote is taking place, each employee see which direction results in the earlier arrival at his/her apartment, assuming that all the employees follow the same strategy in the future. Based on this information, each employee makes the optimal choice, but if either direction results in the arrival at the same time, he/she casts a vote to the negative direction. Find the time the bus will take from departure to arrival at the last employees' apartment. It can be proved that, given the positions of the apartments, the numbers of employees living in each apartment and the initial position of the bus, the future movement of the bus is uniquely determined, and the process will end in a finite time. Constraints 1 \leq N \leq 10^5 1 \leq S \leq 10^9 1 \leq X_1 < X_2 < ... < X_N \leq 10^9 X_i \neq S ( 1 \leq i \leq N ) 1 \leq P_i \leq 10^9 ( 1 \leq i \leq N ) All values in input are integers. Input Input is given from Standard Input in the following format: N S X_1 P_1 X_2 P_2 : X_N P_N Output Print the number of seconds the bus will take from departure to arrival at the last employees' apartment. Sample Input 1 3 2 1 3 3 4 4 2 Sample Output 1 4 Assume that the bus moves in the negative direction first. Then, the coordinate of the bus changes from 2 to 1 , and the employees living in Apartment 1 get off. The movement of the bus after that is obvious: it just continues moving in the positive direction. Thus, if the bus moves in the negative direction first, the coordinate of the bus changes as 2 → 1 → 2 → 3 → 4 from departure. The time it takes to get home for the employees living in Apartment 1 , 2 , 3 are 1 , 3 , 4 seconds, respectively. Next, assume that the bus moves in the positive direction first. Then, the coordinate of the bus changes from 2 to 3 , and the employees living in Apartment 2 get off. Afterwards, the bus starts heading to Apartment 1 , because there are more employees living in Apartment 1 than in Apartment 3 . Then, after arriving at Apartment 1 , the bus heads to Apartment 3 . Thus, if the bus moves in the positive direction first, the coordinate of the bus changes as 2 → 3 → 2 → 1 → 2 → 3 → 4 from departure. The time it takes to get home for the employees living in Apartment 1 , 2 , 3 are 3 , 1 , 6 seconds, respectively. Therefore, in the beginning, the employees living in Apartment 1 or 3 will try to move the bus in the negative direction. On the other hand, the employees living in Apartment 2 will try to move the bus in the positive direction in the beginning. There are a total of 3 + 2 = 5 employees living in Apartment 1 and 3 combined, which is more than those living in Apartment 2 , which is 4 . Thus, the bus will move in the negative direction first, and the coordinate of the bus will change as 2 → 1 → 2 → 3 → 4 from departure. Sample Input 2 6 4 1 10 2 1000 3 100000 5 1000000 6 10000 7 100 Sample Output 2 21 Since the numbers of employees living in different apartments are literally off by a digit, the bus consistently head to the apartment where the most number of employees on the bus lives. Sample Input 3 15 409904902 94198000 15017 117995501 7656764 275583856 313263626 284496300 356635175 324233841 607 360631781 148 472103717 5224 497641071 34695 522945827 816241 554305668 32 623788284 22832 667409501 124410641 876731548 12078 904557302 291749534 918215789 5 Sample Output 3 2397671583	38,254
Problem A: Unreliable Messengers The King of a little Kingdom on a little island in the Pacific Ocean frequently has childish ideas. One day he said, “You shall make use of a message relaying game when you inform me of something.” In response to the King’s statement, six servants were selected as messengers whose names were Mr. J, Miss C, Mr. E, Mr. A, Dr. P, and Mr. M. They had to relay a message to the next messenger until the message got to the King. Messages addressed to the King consist of digits (‘0’-‘9’) and alphabet characters (‘a’-‘z’, ‘A’-‘Z’). Capital and small letters are distinguished in messages. For example, “ke3E9Aa” is a message. Contrary to King’s expectations, he always received wrong messages, because each messenger changed messages a bit before passing them to the next messenger. Since it irritated the King, he told you who are the Minister of the Science and Technology Agency of the Kingdom, “We don’t want such a wrong message any more. You shall develop software to correct it!” In response to the King’s new statement, you analyzed the messengers’ mistakes with all technologies in the Kingdom, and acquired the following features of mistakes of each messenger. A surprising point was that each messenger made the same mistake whenever relaying a message. The following facts were observed. Mr. J rotates all characters of the message to the left by one. For example, he transforms “aB23d” to “B23da”. Miss C rotates all characters of the message to the right by one. For example, she transforms “aB23d” to “daB23”. Mr. E swaps the left half of the message with the right half. If the message has an odd number of characters, the middle one does not move. For example, he transforms “e3ac” to “ace3”, and “aB23d” to “3d2aB”. Mr. A reverses the message. For example, he transforms “aB23d” to “d32Ba”. Dr. P increments by one all the digits in the message. If a digit is ‘9’, it becomes ‘0’. The alphabet characters do not change. For example, he transforms “aB23d” to “aB34d”, and “e9ac” to “e0ac”. Mr. M decrements by one all the digits in the message. If a digit is ‘0’, it becomes ‘9’. The alphabet characters do not change. For example, he transforms “aB23d” to “aB12d”, and “e0ac” to “e9ac”. The software you must develop is to infer the original message from the final message, given the order of the messengers. For example, if the order of the messengers is A -> J -> M -> P and the message given to the King is “aB23d”, what is the original message? According to the features of the messengers’ mistakes, the sequence leading to the final message is A J M P “32Bad” --> “daB23” --> “aB23d” --> “aB12d” --> “aB23d”. As a result, the original message should be “32Bad”. Input The input format is as follows. n The order of messengers The message given to the King . . . The order of messengers The message given to the King The first line of the input contains a positive integer n, which denotes the number of data sets. Each data set is a pair of the order of messengers and the message given to the King. The number of messengers relaying a message is between 1 and 6 inclusive. The same person may not appear more than once in the order of messengers. The length of a message is between 1 and 25 inclusive. Output The inferred messages are printed each on a separate line. Sample Input 5 AJMP aB23d E 86AE AM 6 JPEM WaEaETC302Q CP rTurnAGundam1isdefferentf Output for the Sample Input 32Bad AE86 7 EC302QTWaEa TurnAGundam0isdefferentfr	38,255
Score : 700 points Problem Statement N problems are proposed for an upcoming contest. Problem i has an initial integer score of A_i points. M judges are about to vote for problems they like. Each judge will choose exactly V problems, independently from the other judges, and increase the score of each chosen problem by 1 . After all M judges cast their vote, the problems will be sorted in non-increasing order of score, and the first P problems will be chosen for the problemset. Problems with the same score can be ordered arbitrarily, this order is decided by the chief judge. How many problems out of the given N have a chance to be chosen for the problemset? Constraints 2 \le N \le 10^5 1 \le M \le 10^9 1 \le V \le N - 1 1 \le P \le N - 1 0 \le A_i \le 10^9 Input Input is given from Standard Input in the following format: N M V P A_1 A_2 ... A_N Output Print the number of problems that have a chance to be chosen for the problemset. Sample Input 1 6 1 2 2 2 1 1 3 0 2 Sample Output 1 5 If the only judge votes for problems 2 and 5 , the scores will be 2 2 1 3 1 2 . The problemset will consist of problem 4 and one of problems 1 , 2 , or 6 . If the only judge votes for problems 3 and 4 , the scores will be 2 1 2 4 0 2 . The problemset will consist of problem 4 and one of problems 1 , 3 , or 6 . Thus, problems 1 , 2 , 3 , 4 , and 6 have a chance to be chosen for the problemset. On the contrary, there is no way for problem 5 to be chosen. Sample Input 2 6 1 5 2 2 1 1 3 0 2 Sample Output 2 3 Only problems 1 , 4 , and 6 have a chance to be chosen. Sample Input 3 10 4 8 5 7 2 3 6 1 6 5 4 6 5 Sample Output 3 8	38,256
Score : 900 points Problem Statement There are N squares in a row. The squares are numbered 1, 2, ..., N from left to right. You have two pieces, initially placed on square A and B , respectively. You will be asked to process Q queries of the following kind, in the order received: Given an integer x_i , move one of the two pieces of your choice to square x_i . Here, it takes you one second to move a piece one square. That is, the time it takes to move a piece from square X to Y is \|X-Y\| seconds. Your objective is to process all the queries in the shortest possible time. You may only move the pieces in response to queries, and you may not move both pieces at the same time. Also, it is not allowed to rearrange the order in which queries are given. It is, however, allowed to have both pieces in the same square at the same time. Constraints 1 ≤ N, Q ≤ 200,000 1 ≤ A, B ≤ N 1 ≤ x_i ≤ N Input Input is given from Standard Input in the following format: N Q A B x_1 x_2 ... x_Q Output Let the shortest possible time to process all the queries be X seconds. Print X . Sample Input 1 8 3 1 8 3 5 1 Sample Output 1 7 All the queries can be processed in seven seconds, by: moving the piece at square 1 to 3 moving the piece at square 8 to 5 moving the piece at square 3 to 1 Sample Input 2 9 2 1 9 5 1 Sample Output 2 4 The piece at square 9 should be moved first. Sample Input 3 9 2 1 9 5 9 Sample Output 3 4 The piece at square 1 should be moved first. Sample Input 4 11 16 8 1 1 1 5 1 11 4 5 2 5 3 3 3 5 5 6 7 Sample Output 4 21	38,257
図書整理数の表わし方には色々な種類があり、私たちが普段使っている 10 進数は一つの代表的なものでしかありません。コンピュータ関連の知識がある人には、2 進数、16 進数あたりはとても身近なものです。 N さんは司書資格を活かして司書の仕事に就きました。最初の仕事は図書整理です。この図書館では、一冊ごとに一貫して番号が与えられており、それに従って本を整理しています。この図書館では本の番号をマイナス十進数で表すことになっています。マイナス十進数は、 a n a n−1 a n−2 ... a 2 a 1 a 0 (各 a i は 0~9 の数字) と表記する方法であり、この数は次の数を表します。 a n ×(−10) n + a n−1 ×(−10) n−1 + ... + a 2 ×(−10) 2 + a 1 ×(−10) 1 + a 0 ×(−10) 0 たとえば、マイナス十進数の 2156 は、以下のとおり十進数の-1944 に対応しています。 2×(-10) 3 + 1×(-10) 2 + 5×(-10) 1 + 6×(-10) 0 = 2×(-1000) + 1×(100) + 5×(-10) + 6×(1) = -2000 + 100 - 50 + 6 = -1944 十進数の番号をマイナス十進数に直すのは大変なので、N さんは大変不自由な思いをしています。本の番号を入力とし、この番号のマイナス十進数表記を出力するプログラムを作成してください。 Input 複数のデータセットの並びが入力として与えられます。入力の終わりはゼロひとつの行で示されます。各データセットとして、本の番号を表す整数 A (-2 31 ≤ A < 2 31 ) が１行に与えられます。データセットの数は 1200 を超えません。 Output 入力データセットごとに、番号のマイナス十進数表記を１行に出力します。 Sample Input 9 10 -10 -1944 -305432133 0 Output for the Sample Input 9 190 10 2156 1715573947	38,258
Problem E: SAT-EN-3 彼女は悩んでいた。成績が良くないのだ。両親に無理を言って全寮制の学校に入学したものの、彼女の才能は一向に開花することはなかった。あるいは才能など元々なかったのかもしれないが、それはできるだけ考えたくない可能性だった。そこで彼女が頼ったのは、インターネット上で見つけた怪しげな脳力トレーニングの教材だった。SAT-EN-3 (SATisifiability problem for Enhancement of Neuron: version 3) と銘打つその学習メソッドによると、充足可能性問題のようなもののインスタンスをひたすら手で解くことによって、計算力が向上し、引いては論理的思考力・直感力・想像力も豊かになり、部活動でも活躍できて恋愛もうまくいくのだという。さすがに最後の2つは眉唾ものじゃないかな、と彼女は思ったが、ソロバンや百マス計算のような例もあることだ。暗算が得意になったら儲けものかな、ぐらいの気楽さで、彼女はこの教材に取り組んでみることにした。 SAT-EN-3では、加法標準形で表される論理式の各変数に適切に割り当て、論理式の値を真にすることができるかどうか判定しなければならない。ちなみに、1つ以上の変数 (または、その否定) の論理積を節 (clause) と呼び、いくつかの節の論理和で表される論理式のみが加法標準形に従っている。一般に充足可能性問題といえば論理式は乗法標準形で表されるが、SAT-EN-3では加法標準形であることに注意せよ。彼女はしばらく SAT-EN-3 の問題集に取り組もうとして、ふと思い直した。問題集にお金を払うぐらいなら、プログラミングが得意な親友にパフェでもご馳走して、 SAT-EN-3 の問題を生成し、解くプログラムを書いてもらおう。そうすれば問題も解答もいくらでも手にはいるじゃないか。こうして彼女の親友であるあなたは、SAT-EN-3を解くプログラムを書くことになったのである。 Input 入力は複数のケースからなる。各ケースは以下のフォーマットで与えられる。 expression 入力の終わりは "#" からなる行によって与えられる expression は以下のBNFに従う。ここでは文字列リテラルを""を用いて囲んでいる。実際の入力に""は含まれない。また入力には余計な空白は含まれていない。 <expression> ::= "("<clause>")" \| "("<clause>")\|("<expression>")" <clause> ::= <literal>"&"<literal>"&"<literal> <literal> ::= <variable> \| "~"<variable> <variable> ::= [a-z]\|[A-z] expression の長さは500文字を超えない。テストケースの数は1100個を超えない。 Output 与えられた式を満たす変数の割り当てが存在するのならばyesを、そうでなければnoを出力せよ。 Sample input (B&B&f)\|(~d&~i&i)\|(~v&i&~V)\|(~g&~e&o)\|(~f&d&~v)\|(d&~i&o)\|(g&i&~B)\|(~i&f&d)\|(e&~i&~V)\|(~v&f&~d) (S&X&~X) # Sample output yes no The University of Aizu Programming Contest 2011 Summer 原案: Tomoya Sakai 問題文: Takashi Tayama	38,259
E: Broccoli or Cauliflower Problem The input is a rooted tree T = (V, E) with n vertices. Note that n is odd and the vertex with index 1 is the root of T . In addition, we give a label G or W for each vertex. Let T_v = (U, F) be a subtree of T such that U is defined as following. U = $\{$ u \in V \ \ \| \ \ u $\text{ is the descendant of }$ v $\}$ We call T_v a subtree of v . We consider the following operation and perform operations q times. Let v be a vertex. If a vertex u \in U has the label G , then we change the label of u G to W . Otherwise, we change the label of u W to G . After each operation, output “broccoli” if the number of vertices with the label G is greater than W . Otherwise, output “cauliflower”. Input format An input is the following format. n q p_2 ... p_n c_1 ... c_n v_1 $\vdots$ v_q In line 1 , there are two integers n and q , where n is the number of vertices in T and q is the number of queries. Note that n is odd. In line 2 , there are n - 1 integers p_2 to p_n . p_i represents the parent of a vertex v_i . In line 3 , there are n characters c_1 to c_n . c_i represents the label of v_i . Finally, in line j + 3 , there is an integer v_j . We perform the operation for T_{v_j} . Constraints 1 \leq n \leq 100,000 ( n is odd. ) 1 \leq q \leq 100,000 1 \leq p_i < i （ 2 \leq i \leq n ） c_j is G or W . ( 1 \leq j \leq n ) 1 \leq v_i \leq n （ 1 \leq i \leq q ） Output format An output consists q lines and output “broccoli” or “cauliflower” in each line. Input example 1 7 4 1 1 2 2 3 3 G G W W W G G 2 1 3 4 Output example 1 broccoli cauliflower cauliflower broccoli Input example 2 17 18 1 1 1 3 1 4 2 4 3 6 10 9 3 4 5 15 W W W W W W W W G W G G W G W W W 6 7 1 9 14 6 4 5 3 7 8 13 9 6 14 12 9 13 Output example 2 cauliflower cauliflower broccoli broccoli broccoli broccoli broccoli broccoli broccoli cauliflower cauliflower cauliflower cauliflower cauliflower broccoli cauliflower cauliflower cauliflower	38,260
柴犬の数イヅア公園には、夕方になると柴犬と散歩する人たちがたくさん来ます。柴犬には毛の色によって赤柴、黒柴、白柴、胡麻柴という種類があります。柴犬がたくさんいるとうれしいトモエちゃんは、それぞれの毛色の柴犬が何頭いるかがんばって数えましたが、まだ足し算ができないので柴犬が全部で何頭いるかわかりません。それぞれの毛色の柴犬の数が与えられたときに、柴犬の総数を計算するプログラムを作成せよ。入力入力は以下の形式で与えられる。 $R$ $B$ $W$ $G$ １行に赤柴の数$R$ ($1 \leq R \leq 100$)、黒柴の数$B$ ($1 \leq B \leq 100$)、白柴の数$W$ ($1 \leq W \leq 100$)、胡麻柴の数$G$ ($1 \leq G \leq 100$)が与えられる。出力柴犬の総数を１行に出力する。入出力例入力例１ 4 2 1 1 出力例１ 8 入力例２ 22 18 34 36 出力例２ 110	38,261
Beautiful Currency KM country has N kinds of coins and each coin has its value a_i . The king of the country, Kita_masa, thought that the current currency system is poor, and he decided to make it beautiful by changing the values of some (possibly no) coins. A currency system is called beautiful if each coin has an integer value and the ( i +1)-th smallest value is divisible by the i -th smallest value for all i ( 1 \leq i \leq N-1 ). For example, the set {1, 5, 10, 50, 100, 500} is considered as a beautiful system, while the set {1, 5, 10, 25, 50, 100} is NOT, because 25 is not divisible by 10 . Since changing the currency system may confuse citizens, the king, Kita_masa, wants to minimize the maximum value of the confusion ratios. Here, the confusion ratio for the change in the i -th coin is defined as \|a_i - b_i\| / a_i , where a_i and b_i is the value of i -th coin before and after the structure changes, respectively. Note that Kita_masa can change the value of each existing coin, but he cannot introduce new coins nor eliminate existing coins. After the modification, the values of two or more coins may coincide. Input Each dataset contains two lines. The first line contains a single integer, N , and the second line contains N integers, {a_i} . You may assume the following constraints: 1 \leq N \leq 20 1 \leq a_1 \lt a_2 \lt... \lt a_N \lt 10^5 Output Output one number that represents the minimum of the maximum value of the confusion ratios. The value may be printed with an arbitrary number of decimal digits, but may not contain an absolute error greater than or equal to 10^{-8} . Sample Input 1 3 6 11 12 Output for the Sample Input 1 0.090909090909 Sample Input 2 3 6 11 24 Output for the Sample Input 2 0.090909090909 Sample Input 3 3 6 11 30 Output for the Sample Input 3 0.166666666667	38,262
Problem A: Plants Problem がっちょ君は横 W 個×縦 H 個のマスで区切られた畑を所有している。 x 列目 y 行目のマスをマス (x, y) と呼ぶことにする。いくつかのマスの土地には高さ0cmの植物が1本だけ植えてあり、その他のマスの土地には何も植えられていない。がっちょ君はある時刻に畑に肥料をまく。肥料がまかれたマスに植物が植えられているとき、その植物の高さが1cm伸びる。植物が植えられていないときは、何もおこらない。植物が伸びるのにかかる時間はとても短いので無視できる。がっちょ君は同じ時刻に複数のマスに肥料をまくことができる。ただし、同じ時刻に同じマスに2度以上肥料をまくことはない。がっちょ君が肥料をまいた記録が与えられたとき、時刻 T 時点での畑の植物の高さの和を計算せよ。 Input 入力は以下の形式で与えられる。 W H T p x 0 y 0 t 0 x 1 y 1 t 1 ... x p−1 y p−1 t p−1 s 0,0 s 1,0 … s W−1,0 s 0,1 s 1,1 … s W−1,1 ... s 0,H−1 s 1,H−1 … s W−1,H−1 1行目に畑の横幅 W 、畑の縦幅 H 、時刻 T が与えられる。がっちょ君は時刻 T までに肥料をまきおえる。 2行目にがっちょ君が肥料をまいた回数 p が与えられる。 3行目から2+ p 行目までに与えられる３つの整数は、がっちょ君が時刻 t i にマス( x i , y i )に肥料をまいたことを表す。 3+ p 行目から2+ p + H 行目までは、最初の畑のそれぞれのマスに植物が植えられているかどうかを表す W × H 個の整数が与えられる。 s j,k が1のときマス( j , k )に高さ0cmの植物が1本だけ植えられていることを表し、 s j,k が0のときマス( j , k )に植物は1本も植えられていないことを表す。 Constraints 1 ≤ W , H , T ≤ 50 0 ≤ p ≤ min( W × H × T , 50) 0 ≤ x i < W 0 ≤ y i < H 0 ≤ t i < T s j,k = 0または1 Output 時刻 T での畑の植物の高さの和を1行に出力せよ。 Sample Input 1 3 3 3 5 2 0 0 0 1 0 1 1 1 1 2 1 2 2 0 0 0 0 0 1 0 0 0 0 Sample Output 1 1 Sample Input 2 2 3 4 2 0 0 0 1 1 3 1 0 0 0 0 0 Sample Output 2 1 Sample Input 3 3 8 6 6 0 4 3 2 5 3 0 2 3 2 2 5 1 1 3 2 2 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 Sample Output 3 4 Sample Input 4 8 3 3 7 0 1 1 5 1 0 4 0 2 3 2 0 3 1 1 3 0 1 5 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 Sample Output 4 4	38,263
Problem H: Round Table You are the owner of a restaurant, and you are serving for N customers seating in a round table. You will distribute M menus to them. Each customer receiving a menu will make the order of plates, and then pass the menu to the customer on the right unless he or she has not make the order. The customer i takes L i unit time for the ordering. Your job is to write a program to calculate the minimum time until all customers to call their orders, so you can improve your business performance. Input The input consists of a sequence of positive integers. The first line of the input contains two positive integers N ( N ≤ 50,000) and M ( M ≤ N ). The second line contains N positive integers L 1 , L 2 ,..., L N ( L i ≤ 600). Output Output the minimum possible time required for them to finish ordering. Sample Input and Output Input #1 3 2 1 5 10 Output #1 10 Input #2 4 2 1 2 3 4 Output #2 5	38,264
Presentation You are a researcher investigating algorithms on binary trees. Binary tree is a data structure composed of branch nodes and leaf nodes. Every branch nodes have left child and right child, and each child is either a branch node or a leaf node. The root of a binary tree is the branch node which has no parent. You are preparing for your presentation and you have to make a figure of binary trees using a software. You have already made a figure corresponding to a binary tree which is composed of one branch node and two leaf nodes (Figure 1.) However, suddenly the function of your software to create a figure was broken. You are very upset because in five hours you have to make the presentation in front of large audience. You decided to make the figure of the binary trees using only copy function, shrink function and paste function of the presentation tool. That is, you can do only following two types of operations. Copy the current figure to the clipboard. The figure copied to the clipboard before is removed. Paste the copied figure (with shrinking, if needed), putting the root of the pasted figure on a leaf node of the current figure. You can paste the copied figure multiple times. Moreover, you decided to make the figure using the minimum number of paste operations because paste operation is very time cosuming. Now, your job is to calculate the minimum possible number of paste operations to produce the target figure. Figure 1: initial state For example, the answer for the instance of sample 1(Figure 4) is 3, because you can produce the target figure by following operations and this is minimum. Figure 2: intermediate 1 Figure 3: intermediate 2 Figure 4: Goal Input The input is a line which indicates a binary tree. The grammar of the expression is given by the following BNF. <tree> ::= <leaf> \| "(" <tree> <tree> ")" <leaf> ::= "()" Every input obeys this syntax. You can assume that every tree in the input has at least 1 branch node, and that it has no more than 10^5 branch nodes. Output A line containing the minimum possible number of paste operations to make the given binary tree. Sample Input 1 ((()())(((()())(()()))())) Output for the Sample Input 1 3 Sample Input 2 (((()())(()()))(()())) Output for the Sample Input 2 4 Sample Input 3 ((()(()()))((()(()()))())) Output for the Sample Input 3 3 Sample Input 4 (()()) Output for the Sample Input 4 0	38,265
Space Coconut Crab 宇宙ヤシガニ English text is not available in this practice contest. ケン・マリンブルーは，宇宙ヤシガニを求めて全銀河を旅するスペースハンターである．宇宙ヤシガニは，宇宙最大とされる甲殻類であり，成長後の体長は 400 メートル以上，足を広げれば 1,000 メートル以上にもなると言われている．既に多数の人々が宇宙ヤシガニを目撃しているが，誰一人として捕らえることに成功していない．ケンは，長期間の調査によって，宇宙ヤシガニの生態に関する重要な事実を解明した．宇宙ヤシガニは，驚くべきことに，相転移航法と呼ばれる最新のワープ技術と同等のことを行い，通常空間と超空間の間を往来しながら生きていた．さらに，宇宙ヤシガニが超空間から通常空間にワープアウトするまでには長い時間がかかり，またワープアウトしてからしばらくは超空間に移動できないことも突き止めた．そこで，ケンはついに宇宙ヤシガニの捕獲に乗り出すことにした．戦略は次のとおりである．はじめに，宇宙ヤシガニが通常空間から超空間に突入する際のエネルギーを観測する．このエネルギーを e とするとき，宇宙ヤシガニが超空間からワープアウトする座標 ( x , y , z ) は以下の条件を満たすことがわかっている． x , y , z はいずれも非負の整数である． x + y 2 + z 3 = e である．上記の条件の下で x + y + z の値を最小にする．これらの条件だけでは座標が一意に決まるとは限らないが， x + y + z の最小値を m としたときに，ワープアウトする座標が平面 x + y + z = m 上にあることは確かである．そこで，この平面上に十分な大きさのバリアを張る．すると，宇宙ヤシガニはバリアの張られたところにワープアウトすることになる．バリアの影響を受けた宇宙ヤシガニは身動きがとれなくなる．そこをケンの操作する最新鋭宇宙船であるウェポン・ブレーカー号で捕獲しようという段取りである．バリアは一度しか張ることができないため，失敗するわけにはいかない．そこでケンは，任務の遂行にあたって計算機の助けを借りることにした．あなたの仕事は，宇宙ヤシガニが超空間に突入する際のエネルギーが与えられたときに，バリアを張るべき平面 x + y + z = m を求めるプログラムを書くことである．用意されたテストケースの全てに対して正しい結果を出力したとき，あなたのプログラムは受け入れられるであろう． Input 入力は複数のデータセットで構成される．各データセットは 1 行のみからなり，1 つの正の整数 e ( e ≦ 1,000,000) が含まれる．これは，宇宙ヤシガニが超空間に突入した際のエネルギーを表す．入力は e = 0 の時に終了し，これはデータセットには含まれない． Output 各データセットについて， m の値を 1 行に出力しなさい．出力には他の文字を含めてはならない． Sample Input 1 2 4 27 300 1250 0 Output for the Sample Input 1 2 2 3 18 44	38,266
Red Dragonfly It’s still hot every day, but September has already come. It’s autumn according to the calendar. Looking around, I see two red dragonflies at rest on the wall in front of me. It’s autumn indeed. When two red dragonflies’ positional information as measured from the end of the wall is given, make a program to calculate the distance between their heads. Input The input is given in the following format. $x_1$ $x_2$ The input line provides dragonflies’ head positions $x_1$ and $x_2$ ($0 \leq x_1, x_2 \leq 100$) as integers. Output Output the distance between the two red dragonflies in a line. Sample Input 1 20 30 Sample Output 1 10 Sample Input 2 50 25 Sample Output 2 25 Sample Input 3 25 25 Sample output 3 0	38,267
Problem E: The Genome Database of All Space Life In 2300, the Life Science Division of Federal Republic of Space starts a very ambitious project to complete the genome sequencing of all living creatures in the entire universe and develop the genomic database of all space life. Thanks to scientific research over many years, it has been known that the genome of any species consists of at most 26 kinds of molecules, denoted by English capital letters ( i.e. A to Z ). What will be stored into the database are plain strings consisting of English capital letters. In general, however, the genome sequences of space life include frequent repetitions and can be awfully long. So, for efficient utilization of storage, we compress N -times repetitions of a letter sequence seq into N ( seq ) , where N is a natural number greater than or equal to two and the length of seq is at least one. When seq consists of just one letter c , we may omit parentheses and write Nc . For example, a fragment of a genome sequence: ABABABABXYXYXYABABABABXYXYXYCCCCCCCCCC can be compressed into: 4(AB)XYXYXYABABABABXYXYXYCCCCCCCCCC by replacing the first occurrence of ABABABAB with its compressed form. Similarly, by replacing the following repetitions of XY , AB , and C , we get: 4(AB)3(XY)4(AB)3(XY)10C Since C is a single letter, parentheses are omitted in this compressed representation. Finally, we have: 2(4(AB)3(XY))10C by compressing the repetitions of 4(AB)3(XY) . As you may notice from this example, parentheses can be nested. Your mission is to write a program that uncompress compressed genome sequences. Input The input consists of multiple lines, each of which contains a character string s and an integer i separated by a single space. The character string s , in the aforementioned manner, represents a genome sequence. You may assume that the length of s is between 1 and 100, inclusive. However, of course, the genome sequence represented by s may be much, much, and much longer than 100. You may also assume that each natural number in s representing the number of repetitions is at most 1,000. The integer i is at least zero and at most one million. A line containing two zeros separated by a space follows the last input line and indicates the end of the input. Output For each input line, your program should print a line containing the i -th letter in the genome sequence that s represents. If the genome sequence is too short to have the i -th element, it should just print a zero. No other characters should be printed in the output lines. Note that in this problem the index number begins from zero rather than one and therefore the initial letter of a sequence is its zeroth element. Sample Input ABC 3 ABC 0 2(4(AB)3(XY))10C 30 1000(1000(1000(1000(1000(1000(NM)))))) 999999 0 0 Output for the Sample Input 0 A C M	38,268
Cube Dividing Pablo Cubarson is a well-known cubism artist. He is producing a new piece of work using a cuboid which consists of $A \times B \times C$ unit cubes. He plans to make a beautiful shape by removing $N$ units cubes from the cuboid. When he is about to begin the work, he has noticed that by the removal the cuboid may be divided into several parts disconnected to each other. It is against his aesthetics to divide a cuboid. So he wants to know how many parts are created in his plan. Your task is to calculate the number of connected components in the cuboid after removing the $N$ cubes. Two cubes are connected if they share one face. Input The input consists of a single test case. The test case is formatted as follows: $A$ $B$ $C$ $N$ $X_1$ $Y_1$ $Z_1$ ... $X_N$ $Y_N$ $Z_N$ The first line contains four integers $A$, $B$, $C$ and $N$. $A$, $B$ and $C$ ($1 \leq A,B,C \leq 10^6$) denote the size of the cuboid $-$ the cuboid has an $A$ unit width from left to right and a $B$ unit height from bottom to top, and a $C$ unit depth from front to back. $N$ ($0 \leq N \leq 20,000, N \leq A \times B \times C - 1$) denotes the number of the cubes removed in the Cubarson's plan. Each of the following $N$ lines contains three integers $X_i$ ($0 \leq X_i \leq A-1$), $Y_i$ ($0 \leq Y_i \leq B-1$) and $Z_i$ ($0 \leq Z_i \leq C - 1$). They denote that the cube located at the $X_i$-th position from the left, the $Y_i$-th from the bottom and the $Z_i$-th from the front will be removed in the plan. You may assume the given positions are distinct. Output Print the number of the connected components in the cuboid after removing the specified cubes. Sample Input 1 2 2 2 4 0 0 0 1 1 0 1 0 1 0 1 1 Output for the Sample Input 1 4 Sample Input 2 3 3 3 1 1 1 1 Output for the Sample Input 2 1 Sample Input 3 1 1 3 2 0 0 0 0 0 2 Output for the Sample Input 3 1	38,269
Score : 700 points Problem Statement There is a tree with N vertices, numbered 1 through N . The i -th of the N-1 edges connects vertices a_i and b_i . Currently, there are A_i stones placed on vertex i . Determine whether it is possible to remove all the stones from the vertices by repeatedly performing the following operation: Select a pair of different leaves. Then, remove exactly one stone from every vertex on the path between those two vertices. Here, a leaf is a vertex of the tree whose degree is 1 , and the selected leaves themselves are also considered as vertices on the path connecting them. Note that the operation cannot be performed if there is a vertex with no stone on the path. Constraints 2 ≦ N ≦ 10^5 1 ≦ a_i,b_i ≦ N 0 ≦ A_i ≦ 10^9 The given graph is a tree. Input The input is given from Standard Input in the following format: N A_1 A_2 … A_N a_1 b_1 : a_{N-1} b_{N-1} Output If it is possible to remove all the stones from the vertices, print YES . Otherwise, print NO . Sample Input 1 5 1 2 1 1 2 2 4 5 2 3 2 1 3 Sample Output 1 YES All the stones can be removed, as follows: Select vertices 4 and 5 . Then, there is one stone remaining on each vertex except 4 . Select vertices 1 and 5 . Then, there is no stone on any vertex. Sample Input 2 3 1 2 1 1 2 2 3 Sample Output 2 NO Sample Input 3 6 3 2 2 2 2 2 1 2 2 3 1 4 1 5 4 6 Sample Output 3 YES	38,270
Sum of 4 Integers Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality: a + b + c + d = n For example, for n = 35, we have 4 different combinations of ( a, b, c, d ): ( 8, 9, 9, 9 ), ( 9, 8, 9, 9 ), ( 9, 9, 8, 9 ), and ( 9, 9, 9, 8 ). Input The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50. Output Print the number of combination in a line. Sample Input 35 1 Output for the Sample Input 4 4	38,271
F: 赤黒そーるじぇむ / Red-Black Soul Gem 問題ほむちゃんは、そーるじぇむを赤色や黒色に変化させたり、異なる 2 つのそーるじぇむ間を魔法の糸で接続したりする不思議な力を持っています。この力を使うことで、ほむちゃんは、そーるじぇむによる魔方陣を作ることができます。ほむちゃんは、 1 から N で番号付けられた N 個のそーるじぇむがあるとき、以下の条件が成り立つ異なる魔方陣がいくつあるのか気になりました。どの 2 つのそーるじぇむ間も、高々 1 回しか接続されない。すべてのそーるじぇむの色が、赤色か黒色のいずれかになっている。任意のそーるじぇむに対して、自身の色と異なる色のそーるじぇむのうち、少なくとも 1 つと接続されている。このとき、魔方陣はそーるじぇむを頂点とし、魔法の糸を辺とするグラフとみなすことができます。ここで、そのグラフは連結でなくてもよいことに注意してください。ほむちゃんは計算が苦手なので、代わりにあなたが高速なプログラムを作って異なる魔方陣の数を計算してあげましょう。しかし、その数は非常に多いことが予想されるので、ある素数 M で割った余りを求めることにします。なお、ある魔方陣 G と H が異なるとは、あるそーるじぇむ v について G と H でその色が異なる、もしくはあるそーるじぇむの組 u , v が G と H の一方でのみ接続されていることを指します。入力形式 N M 制約 2 \leq N \leq 2,000 10^8 \leq M \leq 10^9 + 7 M は素数であることが保証される出力形式条件を満たすグラフの個数を M で割った余りを整数で 1 行に出力してください。入力例1 3 310779401 出力例1 12 例えば、以下のような魔方陣は条件を満たします。入力例2 7 566666561 出力例2 98638848 例えば、以下のような魔方陣は条件を満たします。入力例3 1010 1000000007 出力例3 862232855 M で割った余りを出力することに注意してください。	38,272
薄氷渡り問題冬の寒いある日，JOI太郎君は広場にはった薄氷を割って遊ぶことにした．広場は長方形で，東西方向に m 個，南北方向に n 個，つまり， m × n の区画に区切られている．また，薄氷が有る区画と無い区画がある． JOI太郎君は，次のルールにしたがって，薄氷を割りながら区画を移動することにした．薄氷があるどの区画からも薄氷を割り始めることができる．東西南北のいずれかの方向に隣接し，まだ割られていない薄氷のある区画に移動できる．移動した先の区画の薄氷をかならず割る． JOI太郎君が薄氷を割りながら移動できる区画数の最大値を求めるプログラムを作成せよ．ただし， 1 ≤ m ≤ 90，1 ≤ n ≤ 90 である．与えられる入力データでは，移動方法は20万通りを超えない．入力入力は複数のデータセットからなる．各データセットは以下の形式で与えられる．入力はn+2行ある． 1 行目には整数 m が書かれている． 2 行目には整数 n が書かれている． 3 行目から n+2 行目までの各行には、0 もしくは 1 が，空白で区切られて m 個書かれており，各区画に薄氷があるか否かを表している．北から i 番目，西からj番目の区画を (i,j) と記述することにすると (1 ≤ i ≤ n, 1 ≤ j ≤ m)，第 i+2 行目の j 番目の値は，区画 (i,j) に薄氷が存在する場合は 1 となり，区画 (i,j) に薄氷が存在しない場合は 0 となる． m, n がともに 0 のとき入力の終了を示す. データセットの数は 5 を超えない．出力データセットごとに, 移動できる区画数の最大値を１行に出力せよ．入出力例入力例 3 3 1 1 0 1 0 1 1 1 0 5 3 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 出力例 5 5 1つ目の入力例に対して，最大値を与える移動方法の例 2つ目の入力例に対して，最大値を与える移動方法の例 2つ目の入力例に対して，最大値を与えない移動方法の例上記問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	38,273
Set Difference Find the difference of two sets $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}\}$, $A - B$. Input The input is given in the following format. $n$ $a_0 \; a_1 \; ... \; a_{n-1}$ $m$ $b_0 \; b_1 \; ... \; b_{m-1}$ Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set. Output Print elements in the difference in ascending order. Print an element in a line. Constraints $1 \leq n, m \leq 200,000$ $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$ $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$ Sample Input 1 5 1 2 3 5 8 2 2 5 Sample Output 1 1 3 8	38,274
Score : 400 points Problem Statement Given is a rooted tree with N vertices numbered 1 to N . The root is Vertex 1 , and the i -th edge (1 \leq i \leq N - 1) connects Vertex a_i and b_i . Each of the vertices has a counter installed. Initially, the counters on all the vertices have the value 0 . Now, the following Q operations will be performed: Operation j (1 \leq j \leq Q) : Increment by x_j the counter on every vertex contained in the subtree rooted at Vertex p_j . Find the value of the counter on each vertex after all operations. Constraints 2 \leq N \leq 2 \times 10^5 1 \leq Q \leq 2 \times 10^5 1 \leq a_i < b_i \leq N 1 \leq p_j \leq N 1 \leq x_j \leq 10^4 The given graph is a tree. All values in input are integers. Input Input is given from Standard Input in the following format: N Q a_1 b_1 : a_{N-1} b_{N-1} p_1 x_1 : p_Q x_Q Output Print the values of the counters on Vertex 1, 2, \ldots, N after all operations, in this order, with spaces in between. Sample Input 1 4 3 1 2 2 3 2 4 2 10 1 100 3 1 Sample Output 1 100 110 111 110 The tree in this input is as follows: Each operation changes the values of the counters on the vertices as follows: Operation 1 : Increment by 10 the counter on every vertex contained in the subtree rooted at Vertex 2 , that is, Vertex 2, 3, 4 . The values of the counters on Vertex 1, 2, 3, 4 are now 0, 10, 10, 10 , respectively. Operation 2 : Increment by 100 the counter on every vertex contained in the subtree rooted at Vertex 1 , that is, Vertex 1, 2, 3, 4 . The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 110, 110 , respectively. Operation 3 : Increment by 1 the counter on every vertex contained in the subtree rooted at Vertex 3 , that is, Vertex 3 . The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 111, 110 , respectively. Sample Input 2 6 2 1 2 1 3 2 4 3 6 2 5 1 10 1 10 Sample Output 2 20 20 20 20 20 20	38,275
Score : 200 points Problem Statement You are given a string S consisting of lowercase English letters. Find the lexicographically (alphabetically) smallest lowercase English letter that does not occur in S . If every lowercase English letter occurs in S , print None instead. Constraints 1 \leq \|S\| \leq 10^5 ( \|S\| is the length of string S .) S consists of lowercase English letters. Input Input is given from Standard Input in the following format: S Output Print the lexicographically smallest lowercase English letter that does not occur in S . If every lowercase English letter occurs in S , print None instead. Sample Input 1 atcoderregularcontest Sample Output 1 b The string atcoderregularcontest contains a , but does not contain b . Sample Input 2 abcdefghijklmnopqrstuvwxyz Sample Output 2 None This string contains every lowercase English letter. Sample Input 3 fajsonlslfepbjtsaayxbymeskptcumtwrmkkinjxnnucagfrg Sample Output 3 d	38,276
G: Computer Onesan / コンピュータおねえさんある日，おねえさんは，子供たちに組合せの数え方について教えてあげることになりました．そこで，おねえさんは，次のような問題を解いてみることにしました．縦幅 1 ，横幅 1 の正方形を縦幅 N ，横幅 M の長方形に敷き詰めたときに，長方形の左上の頂点から右下の頂点への通り方が何通りあるかを数える敷き詰めた正方形の辺の上しか通れないそれぞれの通り方は，同じ場所を1度しか通らない図1に， N = 2, M = 2 の場合の全ての通り方を示します．図1では，全部で12通りの通り方を示しており，その経路は赤い太線で表しています．図1: N = 2, M = 2 の場合の全ての通り方この問題では， N と M が少し大きくなるだけで，組合せの数が爆発的に増加してしまい，手で数えるのがとても難しくなってしまいます．そこで，おねえさんは，自分の頭脳をロボットに移植し，25万年をかけて，10 x 10 の場合の組合せの数を数える計画を立てました．「10 x 10 なんて計算するとおねえさん死んじゃう！やめて！」止める子供たちをよそに，おねえさんは，計算を開始します．おねえさんは，そこまでしてでも，子供たちに組合せ爆発のすごさを教えてあげたいのです．おねえさんの熱意に心打たれたプログラマーのあなたは，この問題を解くプログラムを書いてあげることにしました．といっても，いきなり 10 x 10 を計算するプログラムを作るのは難しいので，手始めに M が小さい場合のプログラムを書くことにしました． Input 入力は，1行に， N と M が半角スペースで与えられます． N は長方形の縦の幅で，1 <= N <= 100を満たします． M は長方形の横の幅で，1 <= M <= 2を満たします． Output 入力に対する通り方の数を1行に出力してください．ただし，答えが非常に大きくなる場合があるので，1,000,000で割った余りを出力してください． Sample Input 1 1 1 Sample Output 1 2 Sample Input 2 1 2 Sample Output 2 4 Sample Input 3 2 1 Sample Output 3 4 Sample Input 4 2 2 Sample Output 4 12 Sample Input 5 3 2 Sample Output 5 38	38,277
Problem J: Billion Million Thousand A linguist, Nodvic Natharus Damenhof (commonly called Dr. Usoperant ), invented an artificial language Usoperant in 2007. The word usoperant means ‘one which tires’. Damenhof’s goal was to create a complex and pedantic language that would remind many difficulties in universal communications. Talking in Usoperant, you should remember the importance of choosing your words in many conversations. For example of the complexity, you may be confused by the way to say large numbers. Usoperant has some words that indicate exponential numbers in decimal, described as 10 p where p is a positive integer. In terms of English, those words might include thousand for 10 3 (1,000), million for 10 6 (1,000,000), and undecillion for 10 36 (1,000,000,000,000,000,000,000,000,000,000,000,000). You can concatinate those words to express larger numbers. When two words w 1 and w 2 mean numbers 10 p 1 and 10 p 2 respectively, a concatinated word w 1 w 2 means 10 p 1 + p 2 . Using the above examples in English (actually the following examples are incorrect in English), you can say 10 9 by millionthousand , 10 12 by millionmillion and 10 39 by undecillionthousand . Note that there can be multiple different expressions for a certain number. For example, 10 9 can also be expressed by thousandthousandthousand . It is also possible to insert separators between the adjacent components like million-thousand and thousand-thousand-thousand . In this problem, you are given a few of such words, their representing digits and an expression of a certain number in Usoperant. Your task is to write a program to calculate the length of the shortest expression which represents the same number as the given expression. The expressions in the input do not contain any separators like millionthousand . In case of ambiguity, the expressions should be interpreted as the largest number among possibles. The resultant expressions should always contain separators like million-thousand , so we can distinguish, for example, x - x (a concatinated word of two x 's) and xx (just a single word). The separators should not be counted in the length. Input The input consists of multiple test cases. Each test case begins with a line including an integer N (1 ≤ N ≤ 100). The integer N indicates the number of words in the dictionary of exponential numbers. The following N lines give the words in the dictionary. Each line contains a word w i and an integer p i (1 ≤ i ≤ N , 1 ≤ p i ≤ 10), specifying that the word w i expresses an exponential number 10 p i in Usoperant. Each w i consists of at most 100 alphabetical letters. Then a line which contains an expression of a number in Usoperant follows. The expression consists of at most 200 alphabetical letters. The end of the input is indicated by a line which contains only a single 0. Output For each test case, print a line which contains the case number and the length of the shortest expression which represents the same number as the given expression in the input. Sample Input 3 billion 9 million 6 thousand 3 billionmillionthousand 3 oku 8 sen 3 man 4 okusenman 2 nico 2 video 4 niconicovideo 6 abcd 1 efgh 2 abcde 4 fgh 6 y 8 yy 10 abcdefgh 0 Output for the Sample Input Case 1: 14 Case 2: 9 Case 3: 10 Case 4: 2 Note: In the fourth case, the word abcdefgh can be separated as abcd-efgh (representing 10 3 ) and abcde-fgh (representing 10 10 ), and by the rule described in the problem statement, this word should be interpreted as 10 10 . As this number can be expressed by yy , the length of the shortest expression is two (as in the sample output). The existence of y - y (representing 10 16 ) is not a problem here, because we can distinguish yy and y - y as long as we always use separators.	38,279
Score : 300 points Problem Statement Given is a string S of length N-1 . Each character in S is < or > . A sequence of N non-negative integers, a_1,a_2,\cdots,a_N , is said to be good when the following condition is satisfied for all i ( 1 \leq i \leq N-1 ): If S_i= < : a_i<a_{i+1} If S_i= > : a_i>a_{i+1} Find the minimum possible sum of the elements of a good sequence of N non-negative integers. Constraints 2 \leq N \leq 5 \times 10^5 S is a string of length N-1 consisting of < and > . Input Input is given from Standard Input in the following format: S Output Find the minimum possible sum of the elements of a good sequence of N non-negative integers. Sample Input 1 <>> Sample Output 1 3 a=(0,2,1,0) is a good sequence whose sum is 3 . There is no good sequence whose sum is less than 3 . Sample Input 2 <>>><<><<<<<>>>< Sample Output 2 28	38,280
Score : 200 points Problem Statement Takahashi has two positive integers A and B . It is known that A plus B equals N . Find the minimum possible value of "the sum of the digits of A " plus "the sum of the digits of B " (in base 10 ). Constraints 2 ≤ N ≤ 10^5 N is an integer. Input Input is given from Standard Input in the following format: N Output Print the minimum possible value of "the sum of the digits of A " plus "the sum of the digits of B ". Sample Input 1 15 Sample Output 1 6 When A=2 and B=13 , the sums of their digits are 2 and 4 , which minimizes the value in question. Sample Input 2 100000 Sample Output 2 10	38,282
Problem I: Coin and Die Problem 表と裏のあるコインと $1$ から $N$ までの目があるサイコロがある。Gachoくんはこれらを用いて以下のゲームをして遊ぶことにした。ゲームは最初に得点が $0$ の状態から始まり、以下の手順で進められる。サイコロを $1$ 回振り、そのとき出た目の数を得点に加算する現在の得点が $K$ 以上ならゲームクリアとなりゲームを終了する現在の得点が $K$ 未満ならコインを投げ表が出れば1.に戻り、裏が出ればゲームオーバーとなりゲームを終了するコインは投げると $A\%$の確率で表になり、 $(100-A)\%$の確率で裏になる。また、サイコロは振ると、それぞれの目が等確率で出現する。このとき、一度のゲームでGachoくんがゲームクリアすることができる確率を求めよ。求める確率を互いに素な整数 $P, Q$ を用いて $\frac{P}{Q}$ と表したとき、 $R \times Q \equiv P\bmod 998244353$ となる $0$ 以上 $998244352$ 以下の整数 $R$ を出力せよ。この問題の制約下で、このような $R$ は必ず一意に存在する。 Input 入力は以下の形式で与えられる。 $N$ $K$ $A$ $N, K, A$ が空白区切りで一行に与えられる。 Constraints 入力は以下の条件を満たす。 $1 \leq N \leq 10^5 $ $1 \leq K \leq 10^5 $ $1 \leq A \leq 99 $ 入力はすべて整数 Output ゲームをクリアすることができる確率を互いに素な整数 $P, Q$を用いて $\frac{P}{Q}$ と表したとき、$R \times Q\equiv P\bmod 998244353$ となる $0$ 以上 $998244352$ 以下の整数 $R$ を出力せよ。 Sample Input 1 1 1 50 Sample Output 1 1 Sample Input 2 2 2 10 Sample Output 2 648858830 Sample Input 3 6 10 99 Sample Output 3 650893870	38,283

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