task stringlengths 0 154k | __index_level_0__ int64 0 39.2k |
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Score : 200 points Problem Statement There are N positive integers written on a blackboard: A_1, ..., A_N . Snuke can perform the following operation when all integers on the blackboard are even: Replace each integer X on the blackboard by X divided by 2 . Find the maximum possible number of operations that Snuke can perform. Constraints 1 \leq N \leq 200 1 \leq A_i \leq 10^9 Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the maximum possible number of operations that Snuke can perform. Sample Input 1 3 8 12 40 Sample Output 1 2 Initially, [8, 12, 40] are written on the blackboard. Since all those integers are even, Snuke can perform the operation. After the operation is performed once, [4, 6, 20] are written on the blackboard. Since all those integers are again even, he can perform the operation. After the operation is performed twice, [2, 3, 10] are written on the blackboard. Now, there is an odd number 3 on the blackboard, so he cannot perform the operation any more. Thus, Snuke can perform the operation at most twice. Sample Input 2 4 5 6 8 10 Sample Output 2 0 Since there is an odd number 5 on the blackboard already in the beginning, Snuke cannot perform the operation at all. Sample Input 3 6 382253568 723152896 37802240 379425024 404894720 471526144 Sample Output 3 8 | 37,120 |
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Problem C: Verbal Arithmetic Let's think about verbal arithmetic. The material of this puzzle is a summation of non-negative integers represented in a decimal format, for example, as follows. 905 + 125 = 1030 In verbal arithmetic, every digit appearing in the equation is masked with an alphabetic character. A problem which has the above equation as one of its answers, for example, is the following. ACM + IBM = ICPC Solving this puzzle means finding possible digit assignments to the alphabetic characters in the verbal equation. The rules of this puzzle are the following. Each integer in the equation is expressed in terms of one or more digits '0'-'9', but all the digits are masked with some alphabetic characters 'A'-'Z'. The same alphabetic character appearing in multiple places of the equation masks the same digit. Moreover, all appearances of the same digit are masked with a single alphabetic character. That is, different alphabetic characters mean different digits. The most significant digit must not be '0', except when a zero is expressed as a single digit '0'. That is, expressing numbers as "00" or "0123" is not permitted. There are 4 different digit assignments for the verbal equation above as shown in the following table. Mask A B C I M P Case 1 9 2 0 1 5 3 Case 2 9 3 0 1 5 4 Case 3 9 6 0 1 5 7 Case 4 9 7 0 1 5 8 Your job is to write a program which solves this puzzle. Input The input consists of a number of datasets. The end of the input is indicated by a line containing a zero. The number of datasets is no more than 100. Each dataset is formatted as follows. N STRING 1 STRING 2 ... STRING N The first line of a dataset contains an integer N which is the number of integers appearing in the equation. Each of the following N lines contains a string composed of uppercase alphabetic characters 'A'-'Z' which mean masked digits. Each dataset expresses the following equation. STRING 1 + STRING 2 + ... + STRING N -1 = STRING N The integer N is greater than 2 and less than 13. The length of STRING i is greater than 0 and less than 9. The number of different alphabetic characters appearing in each dataset is greater than 0 and less than 11. Output For each dataset, output a single line containing the number of different digit assignments that satisfy the equation. The output must not contain any superfluous characters. Sample Input 3 ACM IBM ICPC 3 GAME BEST GAMER 4 A B C AB 3 A B CD 3 ONE TWO THREE 3 TWO THREE FIVE 3 MOV POP DIV 9 A B C D E F G H IJ 0 Output for the Sample Input 4 1 8 30 0 0 0 40320 | 37,122 |
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Binary Search Tree III Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II. insert $k$: Insert a node containing $k$ as key into $T$. find $k$: Report whether $T$ has a node containing $k$. delete $k$: Delete a node containing $k$. print : Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively. The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases: If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$). If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent. If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key. Input In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given. Output For each find $k$ operation, print " yes " if $T$ has a node containing $k$, " no " if not. In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key Constraints The number of operations $\leq 500,000$ The number of print operations $\leq 10$. $-2,000,000,000 \leq key \leq 2,000,000,000$ The height of the binary tree does not exceed 100 if you employ the above pseudo code. The keys in the binary search tree are all different. Sample Input 1 18 insert 8 insert 2 insert 3 insert 7 insert 22 insert 1 find 1 find 2 find 3 find 4 find 5 find 6 find 7 find 8 print delete 3 delete 7 print Sample Output 1 yes yes yes no no no yes yes 1 2 3 7 8 22 8 2 1 3 7 22 1 2 8 22 8 2 1 22 Reference Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press. | 37,124 |
Score : 600 points Problem Statement Snuke is introducing a robot arm with the following properties to his factory: The robot arm consists of m sections and m+1 joints . The sections are numbered 1 , 2 , ..., m , and the joints are numbered 0 , 1 , ..., m . Section i connects Joint i-1 and Joint i . The length of Section i is d_i . For each section, its mode can be specified individually. There are four modes: L , R , D and U . The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i) ): (x_0, y_0) = (0, 0) . If the mode of Section i is L , (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}) . If the mode of Section i is R , (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}) . If the mode of Section i is D , (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}) . If the mode of Section i is U , (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}) . Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j) . Constraints All values in input are integers. 1 \leq N \leq 1000 -10^9 \leq X_i \leq 10^9 -10^9 \leq Y_i \leq 10^9 Partial Score In the test cases worth 300 points, -10 \leq X_i \leq 10 and -10 \leq Y_i \leq 10 hold. Input Input is given from Standard Input in the following format: N X_1 Y_1 X_2 Y_2 : X_N Y_N Output If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print -1 . m d_1 d_2 ... d_m w_1 w_2 : w_N m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers. w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j) . The i -th character of w_j should be one of the letters L , R , D and U , representing the mode of Section i . Sample Input 1 3 -1 0 0 3 2 -1 Sample Output 1 2 1 2 RL UU DR In the given way to bring Joint m of the robot arm to each (X_j, Y_j) , the positions of the joints will be as follows: To (X_1, Y_1) = (-1, 0) : First, the position of Joint 0 is (x_0, y_0) = (0, 0) . As the mode of Section 1 is R , the position of Joint 1 is (x_1, y_1) = (1, 0) . Then, as the mode of Section 2 is L , the position of Joint 2 is (x_2, y_2) = (-1, 0) . To (X_2, Y_2) = (0, 3) : (x_0, y_0) = (0, 0), (x_1, y_1) = (0, 1), (x_2, y_2) = (0, 3) . To (X_3, Y_3) = (2, -1) : (x_0, y_0) = (0, 0), (x_1, y_1) = (0, -1), (x_2, y_2) = (2, -1) . Sample Input 2 5 0 0 1 0 2 0 3 0 4 0 Sample Output 2 -1 Sample Input 3 2 1 1 1 1 Sample Output 3 2 1 1 RU UR There may be duplicated points among (X_j, Y_j) . Sample Input 4 3 -7 -3 7 3 -3 -7 Sample Output 4 5 3 1 4 1 5 LRDUL RDULR DULRD | 37,125 |
Problem I: Intersection of Two Prisms Suppose that P 1 is an infinite-height prism whose axis is parallel to the z -axis, and P 2 is also an infinite-height prism whose axis is parallel to the y -axis. P 1 is defined by the polygon C 1 which is the cross section of P 1 and the xy -plane, and P 2 is also defined by the polygon C 2 which is the cross section of P 2 and the x z-plane. Figure I.1 shows two cross sections which appear as the first dataset in the sample input, and Figure I.2 shows the relationship between the prisms and their cross sections. Figure I.1: Cross sections of Prisms Figure I.2: Prisms and their cross sections Figure I.3: Intersection of two prisms Figure I.3 shows the intersection of two prisms in Figure I.2, namely, P 1 and P 2 . Write a program which calculates the volume of the intersection of two prisms. Input The input is a sequence of datasets. The number of datasets is less than 200. Each dataset is formatted as follows. m n x 11 y 11 x 12 y 12 . . . x 1 m y 1 m x 21 z 21 x 22 z 22 . . . x 2 n z 2 n m and n are integers (3 †m †100, 3 †n †100) which represent the numbers of the vertices of the polygons, C 1 and C 2 , respectively. x 1 i , y 1 i , x 2 j and z 2 j are integers between -100 and 100, inclusive. ( x 1 i , y 1 i ) and ( x 2 j , z 2 j ) mean the i -th and j -th vertices' positions of C 1 and C 2 respectively. The sequences of these vertex positions are given in the counterclockwise order either on the xy -plane or the xz -plane as in Figure I.1. You may assume that all the polygons are convex , that is, all the interior angles of the polygons are less than 180 degrees. You may also assume that all the polygons are simple , that is, each polygon's boundary does not cross nor touch itself. The end of the input is indicated by a line containing two zeros. Output For each dataset, output the volume of the intersection of the two prisms, P 1 and P 2 , with a decimal representation in a line. None of the output values may have an error greater than 0.001. The output should not contain any other extra characters. Sample Input 4 3 7 2 3 3 0 2 3 1 4 2 0 1 8 1 4 4 30 2 30 12 2 12 2 2 15 2 30 8 13 14 2 8 8 5 13 5 21 7 21 9 18 15 11 15 6 10 6 8 8 5 10 12 5 9 15 6 20 10 18 12 3 3 5 5 10 3 10 10 20 8 10 15 10 8 4 4 -98 99 -99 -99 99 -98 99 97 -99 99 -98 -98 99 -99 96 99 0 0 Output for the Sample Input 4.708333333333333 1680.0000000000005 491.1500000000007 0.0 7600258.4847715655 | 37,126 |
A - Breadth-First Search by Foxpower Problem Statement Fox Ciel went to JAG Kingdom by bicycle, but she forgot a place where she parked her bicycle. So she needs to search it from a bicycle-parking area before returning home. The parking area is formed as a unweighted rooted tree $T$ with $n$ vertices, numbered $1$ through $n$. Each vertex has a space for parking one or more bicycles. Ciel thought that she parked her bicycle near the vertex $1$, so she decided to search it from there by the breadth-first search. That is, she searches it at the vertices in the increasing order of their distances from the vertex $1$. If multiple vertices have the same distance, she gives priority to the vertices in the order of searching at their parents. If multiple vertices have the same parent, she searches at the vertex with minimum number at first. Unlike a computer, she can't go to a next vertex by random access. Thus, if she goes to the vertex $j$ after the vertex $i$, she needs to walk the distance between the vertices $i$ and $j$. BFS by fox power perhaps takes a long time, so she asks you to calculate the total moving distance in the worst case starting from the vertex $1$. Input The input is formatted as follows. $n$ $p_2$ $p_3$ $p_4$ $\cdots$ $p_n$ The first line contains an integer $n$ ($1 \le n \le 10^5$), which is the number of vertices on the unweighted rooted tree $T$. The second line contains $n-1$ integers $p_i$ ($1 \le p_i < i$), which are the parent of the vertex $i$. The vertex $1$ is a root node, so $p_1$ does not exist. Output Print the total moving distance in the worst case in one line. Sample Input 1 4 1 1 2 Output for the Sample Input 1 6 Sample Input 2 4 1 1 3 Output for the Sample Input 2 4 Sample Input 3 11 1 1 3 3 2 4 1 3 2 9 Output for the Sample Input 3 25 | 37,127 |
Score : 700 points Problem Statement We have an integer sequence of length N : A_0,A_1,\cdots,A_{N-1} . Find the following sum ( \mathrm{lcm}(a, b) denotes the least common multiple of a and b ): \sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j) Since the answer may be enormous, compute it modulo 998244353 . Constraints 1 \leq N \leq 200000 1 \leq A_i \leq 1000000 All values in input are integers. Input Input is given from Standard Input in the following format: N A_0\ A_1\ \cdots\ A_{N-1} Output Print the sum modulo 998244353 . Sample Input 1 3 2 4 6 Sample Output 1 22 \mathrm{lcm}(2,4)+\mathrm{lcm}(2,6)+\mathrm{lcm}(4,6)=4+6+12=22 . Sample Input 2 8 1 2 3 4 6 8 12 12 Sample Output 2 313 Sample Input 3 10 356822 296174 484500 710640 518322 888250 259161 609120 592348 713644 Sample Output 3 353891724 | 37,128 |
Problem D Wall Clocks You are the manager of a chocolate sales team. Your team customarily takes tea breaks every two hours, during which varieties of new chocolate products of your company are served. Everyone looks forward to the tea breaks so much that they frequently give a glance at a wall clock. Recently, your team has moved to a new office. You have just arranged desks in the office. One team member asked you to hang a clock on the wall in front of her desk so that she will not be late for tea breaks. Naturally, everyone seconded her. You decided to provide an enough number of clocks to be hung in the field of view of everyone. Your team members will be satisfied if they have at least one clock (regardless of the orientation of the clock) in their view, or, more precisely, within 45 degrees left and 45 degrees right (both ends inclusive) from the facing directions of their seats. In order to buy as few clocks as possible, you should write a program that calculates the minimum number of clocks needed to meet everyone's demand. The office room is rectangular aligned to north-south and east-west directions. As the walls are tall enough, you can hang clocks even above the door and can assume one's eyesight is not blocked by other members or furniture. You can also assume that each clock is a point (of size zero), and so you can hang a clock even on a corner of the room. For example, assume that there are two members. If they are sitting facing each other at positions shown in Figure D.1(A), you need to provide two clocks as they see distinct sections of the wall. If their seats are arranged as shown in Figure D.1(B), their fields of view have a common point on the wall. Thus, you can meet their demands by hanging a single clock at the point. In Figure D.1(C), their fields of view have a common wall section. You can meet their demands with a single clock by hanging it anywhere in the section. Arrangements (A), (B), and (C) in Figure D.1 correspond to Sample Input 1, 2, and 3, respectively. Input The input consists of a single test case, formatted as follows. $n$ $w$ $d$ $x_1$ $y_1$ $f_1$ ... $x_n$ $y_n$ $f_n$ Figure D.1. Arrangements of seats and clocks. Gray area indicates field of view. All numbers in the test case are integers. The first line contains the number of team members $n$ $(1 \leq n \leq 1,000)$ and the size of the office room $w$ and $d$ $(2 \leq w, d \leq 100,000)$. The office room has its width $w$ east-west, and depth $d$ north-south. Each of the following $n$ lines indicates the position and the orientation of the seat of a team member. Each member has a seat at a distinct position $(x_i, y_i)$ facing the direction $f_i$, for $i = 1, ..., n$. Here $1 \leq x_i \leq w - 1, 1 \leq y_i \leq d - 1$, and $f_i$ is one of N , E , W , and S , meaning north, east, west, and south, respectively. The position $(x, y)$ means $x$ distant from the west wall and $y$ distant from the south wall. Output Print the minimum number of clocks needed. Sample Input 1 2 10 6 4 4 E 6 4 W Sample Output 1 2 Sample Input 2 2 10 6 2 4 E 6 4 W Sample Output 2 1 Sample Input 3 2 10 6 3 2 S 6 4 W Sample Output 3 1 Sample Input 4 6 10 6 1 5 N 7 1 N 8 2 E 9 1 S 4 4 S 3 3 W Sample Output 4 3 Sample Input 5 4 10 6 4 3 W 2 4 N 4 4 W 3 3 S Sample Output 5 2 Sample Input 6 4 100000 40000 25000 25000 S 20000 30000 S 75000 25000 S 80000 30000 S Sample Output 6 1 | 37,129 |
Score : 300 points Problem Statement You've come to your favorite store Infinitesco to buy some ice tea. The store sells ice tea in bottles of different volumes at different costs. Specifically, a 0.25 -liter bottle costs Q yen, a 0.5 -liter bottle costs H yen, a 1 -liter bottle costs S yen, and a 2 -liter bottle costs D yen. The store has an infinite supply of bottles of each type. You want to buy exactly N liters of ice tea. How many yen do you have to spend? Constraints 1 \leq Q, H, S, D \leq 10^8 1 \leq N \leq 10^9 All input values are integers. Input Input is given from Standard Input in the following format: Q H S D N Output Print the smallest number of yen you have to spend to buy exactly N liters of ice tea. Sample Input 1 20 30 70 90 3 Sample Output 1 150 Buy one 2 -liter bottle and two 0.5 -liter bottles. You'll get 3 liters for 90 + 30 + 30 = 150 yen. Sample Input 2 10000 1000 100 10 1 Sample Output 2 100 Even though a 2 -liter bottle costs just 10 yen, you need only 1 liter. Thus, you have to buy a 1 -liter bottle for 100 yen. Sample Input 3 10 100 1000 10000 1 Sample Output 3 40 Now it's better to buy four 0.25 -liter bottles for 10 + 10 + 10 + 10 = 40 yen. Sample Input 4 12345678 87654321 12345678 87654321 123456789 Sample Output 4 1524157763907942 | 37,130 |
Set: Delete For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique . insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation. find($x$): Report the number of $x$ in $S$ (0 or 1). delete($x$): Delete $x$ from $S$. Input The input is given in the following format. $q$ $query_1$ $query_2$ : $query_q$ Each query $query_i$ is given by 0 $x$ or 1 $x$ or 2 $x$ where the first digits 0 , 1 and 2 represent insert, find and delete operations respectively. Output For each insert operation, print the number of elements in $S$. For each find operation, print the number of specified elements in $S$. Constraints $1 \leq q \leq 200,000$ $0 \leq x \leq 1,000,000,000$ Sample Input 1 8 0 1 0 2 0 3 2 2 1 1 1 2 1 3 0 2 Sample Output 1 1 2 3 1 0 1 3 | 37,131 |
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Problem C. Santa's Gift Santa is going to pack gifts into a bag for a family. There are $N$ kinds of gifts. The size and the price of the $i$-th gift ($1 \leq i \leq N$) are $s_i$ and $p_i$, respectively. The size of the bag is $C$, thus Santa can pack gifts so that the total size of the gifts does not exceed $C$. Children are unhappy if they are given multiple items of the same kind gift, so Santa has to choose at most one gift of the same kind per child. In addition, if a child did not receive a gift that the other children in the same family receive, he/she will complain about that. Hence Santa must distribute gifts fairly to all the children of a family, by giving the same set of gifts to each child. In other words, for a family with $k$ children, Santa must pack zero or $k$ items for each kind of gifts. Santa gives one bag to one family, therefore, the total size of the gifts for each family does not exceed $C$. Santa wants to maximize the total price of packed items for a family but does not know the number of children in the family he is going to visit yet. The number seems at most $M$. To prepare all the possible cases, calculate the maximum total price of items for a family with $k$ children for each $1 \leq k \leq M$. Input The input consists of a single test case in the following format. $C$ $N$ $M$ $s_1$ $p_1$ $...$ $s_N$ $p_N$ The first line contains three integers $C$, $N$ and $M$, where $C$ ($1 \leq C \leq 10^4$) is the size of the bag, $N$ ($1 \leq N \leq 10^4$) is the number of kinds of the gifts, and $M$ ($1 \leq M \leq 10^4$) is the maximum number of children in the family. The $i$-th line of the following $N$ lines contains two integers $s_i$ and $p_i$ ($1 \leq s_i, p_i \leq 10^4$), where $s_i$ and $p_i$ are the size and the price of the $i$-th gift, respectively. Output The output should consist of $M$ lines. In the $k$-th line, print the maximum total price of gifts for a family with $k$ children. Examples Sample Input 1 6 3 2 1 2 2 10 3 5 Output for Sample Input 1 17 24 Sample Input 2 200 5 5 31 41 59 26 53 58 97 93 23 84 Output for Sample Input 2 235 284 375 336 420 Sample Input 3 1 1 2 1 1 Output for Sample Input 3 1 0 Sample Input 4 2 2 2 1 1 2 100 Output for Sample Input 4 100 2 | 37,133 |
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Problem G: Painting Problem é·ã$N$ã®æ°å$X$ãäžãããããåæç¶æ
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šãŠ$0$ã§ãããå ããŠã$M$åã®æŽæ°ã®ãã¢$(A_i, B_i)$ãäžãããããåãã¢ã«å¯Ÿã以äžã®æäœãè¡ããæçµçãªæ°å$X$ãåºåããã æŽæ°$j$ $(1 \le j \le N)$ã«å¯Ÿãã$(A_i+j)$ã$B_i$ã§å²ã£ãäœãã$X_j$ã«å ããã Input å
¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ : $A_M$ $B_M$ $1$è¡ç®ã«ãäžããããæ°åã®èŠçŽ æ°$N$ããã¢ã®æ°$M$ã空çœåºåãã§äžããããã ç¶ã$M$è¡ã«ã$i$çªç®ã®ãã¢$(A_i, B_i)$ã空çœåºåãã§äžããããã Constraints å
¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã $1 \le N, M \le 10^5$ $0 \le A_i < B_i \le 10^9 (1 \le i \le M)$ äžããããå
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šãŠæŽæ°ã§ãã Output æäœåŸã®æ°åã$N$è¡ã§åºåããã$j$è¡ç®ã«$X_j$ãåºåããã Sample Input 1 5 3 1 4 3 7 0 1000 Sample Output 1 7 10 9 5 8 Sample Input 2 14 12 1 4 2 3 0 5 1 4 1 2 0 8 0 2 0 10 0 1 0 8 3 10 1 10 Sample Output 2 15 24 25 31 35 44 32 25 24 15 16 25 31 40 | 37,135 |
Score : 100 points Problem Statement You are given two integers a and b . Determine if a+b=15 or a\times b=15 or neither holds. Note that a+b=15 and a\times b=15 do not hold at the same time. Constraints 1 \leq a,b \leq 15 All values in input are integers. Input Input is given from Standard Input in the following format: a b Output If a+b=15 , print + ; if a\times b=15 , print * ; if neither holds, print x . Sample Input 1 4 11 Sample Output 1 + 4+11=15 . Sample Input 2 3 5 Sample Output 2 * 3\times 5=15 . Sample Input 3 1 1 Sample Output 3 x 1+1=2 and 1\times 1=1 , neither of which is 15 . | 37,136 |
Problem C: Champernowne Constant Champernown constant is an irrational number represented in decimal by " 0. " followed by concatenation of all positive integers in the increasing order. The first few digits of this constant are: 0.123456789101112... Your task is to write a program that outputs the K digits of Chapnernown constant starting at the N -th place for given two natural numbers K and N . Input The input has multiple lines. Each line has two positive integers N and K ( N †10 9 , K †100) separated by a space. The end of input is indicated by a line with two zeros. This line should not be processed. Output For each line, output a line that contains the K digits. Sample Input 4 5 6 7 0 0 Output for the Sample Input 45678 6789101 | 37,137 |
Score : 600 points Problem Statement We have an integer sequence A of length N , where A_1 = X, A_{i+1} = A_i + D (1 \leq i < N ) holds. Takahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others. Let S and T be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of S - T are there? Constraints -10^8 \leq X, D \leq 10^8 1 \leq N \leq 2 \times 10^5 All values in input are integers. Input Input is given from Standard Input in the following format: N X D Output Print the number of possible values of S - T . Sample Input 1 3 4 2 Sample Output 1 8 A is (4, 6, 8) . There are eight ways for (Takahashi, Aoki) to take the elements: ((), (4, 6, 8)), ((4), (6, 8)), ((6), (4, 8)), ((8), (4, 6))), ((4, 6), (8))), ((4, 8), (6))), ((6, 8), (4))) , and ((4, 6, 8), ()) . The values of S - T in these ways are -18, -10, -6, -2, 2, 6, 10 , and 18 , respectively, so there are eight possible values of S - T . Sample Input 2 2 3 -3 Sample Output 2 2 A is (3, 0) . There are two possible values of S - T : -3 and 3 . Sample Input 3 100 14 20 Sample Output 3 49805 | 37,138 |
Max Score: 350 Points Problem Statement There are N buildings along the line. The i -th building from the left is colored in color i , and its height is currently a_i meters. Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left. You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer. You cannot decrease height of buildings. Calculate the minimum cost of satisfying Chokudai's objective. Note: "Building i can see from the left" means there are no j exists that (height of building j ) ⥠(height of building i ) and j < i . Input Format N K a_1 a_2 a_3 ... a_N Output Format Print the minimum cost in one line. In the end put a line break. Constraints 1 †K †N †15 1 †a_i †10^9 Scoring Subtask 1 [ 120 points] N = K Subtask 2 [ 90 points] N †5 a_i †7 Subtask 3 [ 140 points] There are no additional constraints. Sample Input 1 5 5 3949 3774 3598 3469 3424 Sample Output 1 1541 The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953] . Sample Input 2 5 3 7 4 2 6 4 Sample Output 2 7 The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4] . | 37,139 |
Problem E: Distinct Dictionary Background èŸæžããããªãæããè
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¥åã¯ååšããªãã äžããããæååã«å«ãŸããæåã¯è±å°æåã®ã¿ã§ããã 1 †N †10 5 1 †id †N 1 †Q †10 5 1 †| S id | †10 5 (ãã ãã| s |ã¯æåå s ã®é·ããè¡šãã) Output ã¯ãšãªããšã«è§£çãäžè¡ã«åºåããã Sample Input1 3 apple app banana 9 1 1 3 1 3 2 3 3 2 1 1 2 3 1 3 2 3 3 Sample Output1 1 1 -1 -1 2 -1 Sample Input2 7 aaaab aaa aaaa aaaaaabc abbbbbc ab abbb 13 1 1 3 2 1 4 3 2 1 3 3 2 2 3 3 3 1 5 1 7 3 6 2 5 3 6 Sample Output2 1 4 3 4 7 7 | 37,140 |
Score : 1400 points Problem Statement Process the Q queries below. You are given two integers A_i and M_i . Determine whether there exists a positive integer K_i not exceeding 2 Ã 10^{18} such that A_i^{K_i} â¡ K_i (mod M_i) , and find one if it exists. Constraints 1 \leq Q \leq 100 0 \leq A_i \leq 10^9(1 \leq i \leq Q) 1 \leq M_i \leq 10^9(1 \leq i \leq Q) Inputs Input is given from Standard Input in the following format: Q A_1 M_1 : A_Q M_Q Outputs In the i -th line, print -1 if there is no integer K_i that satisfies the condition. Otherwise, print an integer K_i not exceeding 2 Ã 10^{18} such that A_i^{K_i} â¡ K_i (mod M_i) . If there are multiple solutions, any of them will be accepted. Sample Input 1 4 2 4 3 8 9 6 10 7 Sample Output 1 4 11 9 2 It can be seen that the condition is satisfied: 2^4 = 16 â¡ 4 (mod 4) , 3^{11} = 177147 â¡ 11 (mod 8) , 9^9 = 387420489 â¡ 9 (mod 6) and 10^2 = 100 â¡ 2 (mod 7) . Sample Input 2 3 177 168 2028 88772 123456789 987654321 Sample Output 2 7953 234831584 471523108231963269 | 37,141 |
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Problem D: The House of Huge Family Mr. Dango's family has an extremely huge number of members. Once it had about 100 members, and now it has as many as population of a city. It is jokingly guessed that the member might fill this planet in the near future. Mr. Dango's family, the huge family, is getting their new house. Scale of the house is as large as that of town. They all had warm and gracious personality and were close each other. However, in this year the two members of them became to hate each other. Since the two members had enormous influence in the family, they were split into two groups. They hope that the two groups don't meet each other in the new house. Though they are in the same building, they can avoid to meet each other by adjusting passageways. Now, you have a figure of room layout. Your task is written below. You have to decide the two groups each room should belong to. Besides you must make it impossible that they move from any rooms belonging to one group to any rooms belonging to the other group. All of the rooms need to belong to exactly one group. And any group has at least one room. To do the task, you can cancel building passageway. Because the house is under construction, to cancel causes some cost. You'll be given the number of rooms and information of passageway. You have to do the task by the lowest cost. Please answer the lowest cost. By characteristics of Mr. Dango's family, they move very slowly. So all passageways are escalators. Because of it, the passageways are one-way. Input The input consists of multiple datasets. Each dataset is given in the following format. n m X 1 Y 1 C 1 ... X m Y m C m All numbers in each datasets are integers. The integers in each line are separated by a space. The first line of each datasets contains two integers. n is the number of rooms in the house, m is the number of passageways in the house. Each room is indexed from 0 to n -1. Each of following m lines gives the details of the passageways in the house. Each line contains three integers. The first integer X i is an index of the room, the starting point of the passageway. The second integer Y i is an index of the room, the end point of the passageway. The third integer C i is the cost to cancel construction of the passageway. The passageways, they are escalators, are one-way. The last dataset is followed by a line containing two zeros (separated by a space). Constraints 2 †n †100 -10,000 †C i †10,000 Y 1 ... Y m can't be duplicated integer by each other. Output For each dataset, print the lowest cost in a line. You may assume that the all of integers of both the answers and the input can be represented by 32 bits signed integers. Sample input 3 2 0 1 2 1 2 1 2 1 0 1 100 2 1 0 1 0 2 1 0 1 -1 0 0 Sample output 1 100 0 -1 | 37,143 |
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Swapping Two Numbers Write a program which reads two integers x and y , and prints them in ascending order. Input The input consists of multiple datasets. Each dataset consists of two integers x and y separated by a single space. The input ends with two 0 (when both x and y are zero). Your program should not process for these terminal symbols. Output For each dataset, print x and y in ascending order in a line. Put a single space between x and y . Constraints 0 †x , y †10000 the number of datasets †3000 Sample Input 3 2 2 2 5 3 0 0 Sample Output 2 3 2 2 3 5 | 37,145 |
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㯠1 ãã m ãŸã§é çªã«çªå·ãä»ããããŠãããã®ãšããŸãã ãªãã a i ãš b i ãç·è·¯ã§ã€ãªãã£ãŠããã°ã a i ãã b i ã b i ãã a i ã®äž¡æ¹ã®ç§»åãåãæéãšæéã§å¯èœãšããŸãã ç¶ãè¡ã«åãåããã®æ° k (1 †k †200) ãäžããããŸããç¶ã k è¡ã« i çªç®ã®åãåãããäžããããŸããåååãããšããŠãåºçºé§
p i ãå°çé§
q i ãåºåããå€ã®çš®é¡ r i (0 ãŸã㯠1)ãäžããããŸãããªããåãåããã«ã¯å¿
ãçµè·¯ããããã®ãšããŸãã ããŒã¿ã»ããã®æ°ã¯ 50 ãè¶
ããªãã Output ããŒã¿ã»ããããšã«ãæå°éé¡ãããã¯æçæéãïŒè¡ã«åºåããŸãã r i ã 0 ã®æã¯æå°éé¡ãã 1 ã®æã¯æçæéãåºåããŸãã Sample Input 6 5 1 2 200 10 1 4 400 15 1 3 250 25 2 4 100 10 4 5 150 20 3 5 300 20 2 1 5 0 1 5 1 0 0 Output for the Sample Input 450 35 | 37,146 |
Problem F: Name the Crossing The city of Kyoto is well-known for its Chinese plan: streets are either North-South or East-West. Some streets are numbered, but most of them have real names. Crossings are named after the two streets crossing there, e.g. Kawaramachi-Sanjo is the crossing of Kawaramachi street and Sanjo street. But there is a problem: which name should come first? At first the order seems quite arbitrary: one says Kawaramachi-Sanjo (North-South first) but Shijo-Kawaramachi (East-West first). With some experience, one realizes that actually there seems to be an "order" on the streets, for instance in the above Shijo is "stronger" than Kawaramachi, which in turn is "stronger" than Sanjo. One can use this order to deduce the names of other crossings. You are given as input a list of known crossing names X-Y. Streets are either North-South or East-West, and only orthogonal streets may cross. As your list is very incomplete, you start by completing it using the following rule: two streets A and B have equal strength if (1) to (3) are all true: they both cross the same third street C in the input there is no street D such that D-A and B-D appear in the input there is no street E such that A-E and E-B appear in the input We use this definition to extend our strength relation: A is stronger than B, when there is a sequence A = A 1 , A 2 , ..., A n = B, with n at least 2, where, for any i in 1 .. n -1, either A i -A i +1 is an input crossing or A i and A i +1 have equal strength. Then you are asked whether some other possible crossing names X-Y are valid. You should answer affirmatively if you can infer the validity of a name, negatively if you cannot. Concretely: YES if you can infer that the two streets are orthogonal, and X is stronger than Y NO otherwise Input The input is a sequence of data sets, each of the form N Crossing 1 ... Crossing N M Question 1 ... Question M Both Crossing s and Question s are of the form X-Y where X and Y are strings of alphanumerical characters, of lengths no more than 16. There is no white space, and case matters for alphabetical characters. N and M are between 1 and 1000 inclusive, and there are no more than 200 streets in a data set. The last data set is followed by a line containing a zero. Output The output for each data set should be composed of M +1 lines, the first one containing the number of streets in the Crossing part of the input, followed by the answers to each question, either YES or NO without any spaces. Sample Input 7 Shijo-Kawaramachi Karasuma-Imadegawa Kawaramachi-Imadegawa Nishioji-Shijo Karasuma-Gojo Torimaru-Rokujo Rokujo-Karasuma 6 Shijo-Karasuma Imadegawa-Nishioji Nishioji-Gojo Shijo-Torimaru Torimaru-Gojo Shijo-Kawabata 4 1jo-Midosuji Midosuji-2jo 2jo-Omotesando Omotesando-1jo 4 Midosuji-1jo 1jo-Midosuji Midosuji-Omotesando 1jo-1jo 0 Output for the Sample Input 8 YES NO YES NO YES NO 4 YES YES NO NO | 37,147 |
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 . For each k=1, ..., N , solve the problem below: Consider writing a number on each vertex in the tree in the following manner: First, write 1 on Vertex k . Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows: Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random. Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7) . Constraints 2 \leq N \leq 2 \times 10^5 1 \leq a_i,b_i \leq N The given graph is a tree. Input Input is given from Standard Input in the following format: N a_1 b_1 : a_{N-1} b_{N-1} Output For each k=1, 2, ..., N in this order, print a line containing the answer to the problem. Sample Input 1 3 1 2 1 3 Sample Output 1 2 1 1 The graph in this input is as follows: For k=1 , there are two ways in which we can write the numbers on the vertices, as follows: Writing 1, 2, 3 on Vertex 1, 2, 3 , respectively Writing 1, 3, 2 on Vertex 1, 2, 3 , respectively Sample Input 2 2 1 2 Sample Output 2 1 1 The graph in this input is as follows: Sample Input 3 5 1 2 2 3 3 4 3 5 Sample Output 3 2 8 12 3 3 The graph in this input is as follows: Sample Input 4 8 1 2 2 3 3 4 3 5 3 6 6 7 6 8 Sample Output 4 40 280 840 120 120 504 72 72 The graph in this input is as follows: | 37,148 |
Stamp Rally ã¹ã¿ã³ãã©ãªãŒ æ¥æ¬ã¢ãã¥ãŒãºã¡ã³ãã°ã«ãŒã (Japan Amusement Group, JAG) ã§ã¯ïŒå³¶åœãæš¡ããããŒãããŒã¯ã§ã®ã€ãã³ããäŒç»ããŠããïŒ ãã®ã€ãã³ãã§ã¯ïŒåå è
ã¯æ©ãæž¡ããã³ã«æ©ããšã«æ±ºããããã¹ã¿ã³ããã¹ã¿ã³ãåž³ã«é çªã«æŒããŠããïŒ çšæãããã¹ã¿ã³ãã¯ä»¥äžã®7çš®é¡ã®ã©ããã§ããïŒ a ( ) [ ] + * ã¹ã¿ãŒããããŽãŒã«ãŸã§æ©ãæž¡ãæ©ããŠïŒæŒãããã¹ã¿ã³ãã®åãæ£ããæ°åŒã«ãªãã°ã¯ãªã¢ã§ããïŒ ãã ãæ©ãæž¡ãåãã¯æ±ºãŸã£ãŠããŠïŒéåãã«æž¡ãããšã¯ã§ããªãïŒ åãæ©ãäœåºŠãæž¡ã£ãŠããïŒæçµçã«ãŽãŒã«å°ç¹ã«å°çããã®ã§ããã°äžåºŠãŽãŒã«å°ç¹ã«çããåŸã«åŒãç¶ãã¹ã¿ã³ããéããŠãããïŒ æ£ããæ°åŒãšã¯ä»¥äžã® BNF ã§å®çŸ©ããã <expression> ã§ããïŒ <expression> ::= <term> | <expression> "+" <term> <term> ::= <factor> | <term> "*" <factor> <factor> ::= "a" | "(" <expression> ")" | "[" <expression> "]" ã¹ã¿ãŒãã»ãŽãŒã«ãšæ©ããšã®ã¹ã¿ã³ãã決ããã®ã§ïŒé¢ä¿è
ã§è©Šãã«ãã£ãŠã¿ãããªããªãã¯ãªã¢ãã人ãçŸããªãïŒ ããããããïŒãã®èšå®ã§ã¯ã¯ãªã¢ããããšãã§ããªãã®ãããããªãïŒ ã¹ã¿ãŒãã»ãŽãŒã«ãšæ©ã®æ
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¥åã¯50å以äžã®ããŒã¿ã»ãããããªãïŒåããŒã¿ã»ããã¯ä»¥äžã®åœ¢åŒã§è¡šãããïŒ n m s t a 1 b 1 c 1 ... a m b m c m ããŒã¿ã»ããã®æåã®è¡ã¯ïŒç©ºçœæå1åã§åºåããã4åã®æŽæ° n , m , s , t ãããªãïŒ n ã¯å³¶ã®æ°ã§ããïŒ 1 †n †200 ãšä»®å®ããŠããïŒ ããããã®å³¶ã«ã¯ 1 ãã n ãŸã§ã®çªå·ãä»ããããŠããïŒ m ã¯æ©ã®æ°ã§ããïŒ 1 †m †100,000 ãšä»®å®ããŠããïŒ s ã¯ã¹ã¿ãŒãã®å³¶ã®çªå·ïŒ t ã¯ãŽãŒã«ã®å³¶ã®çªå·ã§ããïŒã¹ã¿ãŒããšãŽãŒã«ãåã島ã§ããããšãããïŒ ç¶ã m è¡ã®ããããã¯ïŒç©ºçœæå1åã§åºåããã2åã®æŽæ°ãš1åã®æåãããªãïŒ a i ïŒ b i 㯠i çªç®ã®æ©ã«ãã£ãŠå³¶ a i ãã島 b i ãžæž¡ããããšãè¡šãïŒ c i 㯠i çªç®ã®æ©ã§æŒãã¹ã¿ã³ããè¡šãïŒãã2ã€ã®å³¶ã®éã«è€æ°ã®æ©ãããã£ãŠãããïŒ1ã€ã®å³¶ã®äžã§æ©ãããã£ãŠãããããããšãããïŒ å
¥åã®çµããã¯ïŒ4ã€ã®ãŒããããªã1è¡ã§ç€ºãããïŒ Output åããŒã¿ã»ããã«å¯ŸããŠïŒã¯ãªã¢ã§ãããªãã°" Yes "ãïŒã§ããªããªãã°" No "ã1è¡ã«åºåããïŒ Sample Input 4 5 1 4 1 2 ( 1 3 a 2 4 a 3 4 ) 3 2 + 4 4 1 2 1 3 ( 3 4 a 4 1 + 3 2 a 3 4 1 1 1 2 a 2 2 + 2 3 a 3 1 a 5 8 1 5 1 1 [ 1 2 ( 2 1 * 2 2 a 2 3 a 3 3 ) 3 4 ] 4 5 ) 2 14 1 1 1 2 a 1 2 ( 1 2 ) 1 2 [ 1 2 ] 1 2 + 1 2 * 2 1 a 2 1 ( 2 1 ) 2 1 [ 2 1 ] 2 1 + 2 1 * 0 0 0 0 Output for Sample Input Yes No No Yes No | 37,149 |
Score : 200 points Problem Statement We have A cards, each of which has an integer 1 written on it. Similarly, we also have B cards with 0 s and C cards with -1 s. We will pick up K among these cards. What is the maximum possible sum of the numbers written on the cards chosen? Constraints All values in input are integers. 0 \leq A, B, C 1 \leq K \leq A + B + C \leq 2 \times 10^9 Input Input is given from Standard Input in the following format: A B C K Output Print the maximum possible sum of the numbers written on the cards chosen. Sample Input 1 2 1 1 3 Sample Output 1 2 Consider picking up two cards with 1 s and one card with a 0 . In this case, the sum of the numbers written on the cards is 2 , which is the maximum possible value. Sample Input 2 1 2 3 4 Sample Output 2 0 Sample Input 3 2000000000 0 0 2000000000 Sample Output 3 2000000000 | 37,150 |
Score : 1400 points Problem Statement Sigma and Sugim are playing a game. The game is played on a graph with N vertices numbered 1 through N . The graph has N-1 red edges and N-1 blue edges, and the N-1 edges in each color forms a tree. The red edges are represented by pairs of integers (a_i, b_i) , and the blue edges are represented by pairs of integers (c_i, d_i) . Each player has his own piece. Initially, Sigma's piece is at vertex X , and Sugim's piece is at vertex Y . The game is played in turns, where turns are numbered starting from turn 1 . Sigma takes turns 1, 3, 5, ... , and Sugim takes turns 2, 4, 6, ... . In each turn, the current player either moves his piece, or does nothing. Here, Sigma can only move his piece to a vertex that is directly connected to the current vertex by a red edge. Similarly, Sugim can only move his piece to a vertex that is directly connected to the current vertex by a blue edge. When the two pieces come to the same vertex, the game ends immediately. If the game ends just after the operation in turn i , let i be the total number of turns in the game. Sigma's objective is to make the total number of turns as large as possible, while Sugim's objective is to make it as small as possible. Determine whether the game will end in a finite number of turns, assuming both players plays optimally to achieve their respective objectives. If the answer is positive, find the number of turns in the game. Constraints 2 ⊠N ⊠200,000 1 ⊠X, Y ⊠N X \neq Y 1 ⊠a_i, b_i, c_i, d_i ⊠N The N-1 edges in each color (red and blue) forms a tree. Input The input is given from Standard Input in the following format: N X Y a_1 b_1 a_2 b_2 : a_{N-1} b_{N-1} c_1 d_1 c_2 d_2 : c_{N-1} d_{N-1} Output If the game will end in a finite number of turns, print the number of turns. Otherwise, print -1 . Sample Input 1 4 1 2 1 2 1 3 1 4 2 1 2 3 1 4 Sample Output 1 4 Sample Input 2 3 3 1 1 2 2 3 1 2 2 3 Sample Output 2 4 Sample Input 3 4 1 2 1 2 3 4 2 4 1 2 3 4 1 3 Sample Output 3 2 Sample Input 4 4 2 1 1 2 3 4 2 4 1 2 3 4 1 3 Sample Output 4 -1 Sample Input 5 5 1 2 1 2 1 3 1 4 4 5 2 1 1 3 1 5 5 4 Sample Output 5 6 | 37,151 |
å®æ°æ¢çŽåæ°å å®æ°ã®ãã¡ãå°æ°éšã埪ç°ãããã®ãšæéæ¡ã®ãã®ã¯åæ°ãšããŠè¡šãããšãã§ããŸãã åæ°ã§è¡šãããšãã§ããå®æ°ãäžãããããšãããã®å®æ°ãšçããæ¢çŽåæ°ïŒãã以äžçŽåã§ããªãåæ°ïŒãåºåããããã°ã©ã ãäœæããã Input å
¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã str ïŒè¡ã«ãå€æãããå®æ°ãè¡šãæåå str ãäžãããããå®æ°ã®å€ã¯ 0 ãã倧ãããæååã¯æ°åãã.ããã(ããã)ããå«ããé·ãã 3 ä»¥äž 8 以äžã®æååã§ãããã.ãã¯å°æ°ç¹ãã(ãã¯æ°åã®åŸªç°ã®å§ãŸããã)ãã¯æ°åã®åŸªç°ã®çµããã瀺ããæŽæ°éšã«ãå°æ°éšã«ããå¿
ãïŒæ¡ä»¥äžã®æ°åãäžãããããšããããã ãã埪ç°å°æ°ãäžããããå Žåãæååã¯ä»¥äžã®æ¡ä»¶ãæºããã 埪ç°ã®å§ãŸããšçµããã®ãã¢ã¯ãå°æ°ç¹ã®å³åŽã«äžåºŠã ãçŸããã 埪ç°ã®çµããã瀺ãã)ãã¯ãæååã®æ«å°Ÿã«çŸããã 埪ç°ã®å§ãŸããšçµããã®éã«ã¯ãå¿
ãïŒæ¡ä»¥äžã®æ°åãäžããããã Output å®æ°ãæ¢çŽåæ°ã§è¡šãã圢åŒïŒååã®æŽæ°ã«ç¶ããŠã/ãåºåãã§åæ¯ã®æŽæ°ã䞊ã¹ããã®ïŒã§åºåããã Sample Input 1 0.(3) Sample Output 1 1/3 Sample Input 2 1.0 Sample Output 2 1/1 Sample Input 3 5.2(143) Sample Output 3 52091/9990 Sample Input 4 0.0739 Sample Output 4 739/10000 | 37,152 |
Bipartite Matching A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e â E has one end point in X and the other end point in Y . A matching M is a subset of edges such that each node in V appears in at most one edge in M . Given a bipartite graph, find the size of the matching which has the largest size. Input |X| |Y| |E| x 0 y 0 x 1 y 1 : x |E|-1 y |E|-1 |X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G . The vertices in X are named with the numbers 0, 1,..., |X| -1, and vertices in Y are named with the numbers 0, 1,..., |Y| -1, respectively. x i and y i are the node numbers from X and Y respectevely which represent the end-points of the i -th edge. Output Print the largest size of the matching. Constraints 1 †|X| , |Y| †100 0 †|E| †10,000 Sample Input 1 3 4 6 0 0 0 2 0 3 1 1 2 1 2 3 Sample Output 1 3 | 37,153 |
Score : 100 points Problem Statement We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions: Question 1 : Are you subscribing to Newspaper X? Question 2 : Are you subscribing to Newspaper Y? As the result, A respondents answered "yes" to Question 1 , and B respondents answered "yes" to Question 2 . What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y? Write a program to answer this question. Constraints 1 \leq N \leq 100 0 \leq A \leq N 0 \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 maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between. Sample Input 1 10 3 5 Sample Output 1 3 0 In this sample, out of the 10 respondents, 3 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y. Here, the number of respondents subscribing to both newspapers is at most 3 and at least 0 . Sample Input 2 10 7 5 Sample Output 2 5 2 In this sample, out of the 10 respondents, 7 answered they are subscribing to Newspaper X, and 5 answered they are subscribing to Newspaper Y. Here, the number of respondents subscribing to both newspapers is at most 5 and at least 2 . Sample Input 3 100 100 100 Sample Output 3 100 100 | 37,154 |
Making Lunch Boxes Taro has been hooked on making lunch boxes recently. Taro has obtained a new lunch box recipe book today, and wants to try as many of the recipes listed in the book as possible. Enough of the ingredients for all the recipes are at hand, but they all are in vacuum packs of two. If only one of them is used leaving the other, the leftover will be rotten easily, but making two of the same recipe is not interesting. Thus he decided to make a set of lunch boxes, each with different recipe, that wouldn't leave any unused ingredients. Note that the book may include recipes for different lunch boxes made of the same set of ingredients. How many lunch box recipes can Taro try today at most following his dogma? Input The input consists of at most 50 datasets, each in the following format. n m b 1,1 ... b 1, m ... b n, 1 ... b n,m The first line contains n , which is the number of recipes listed in the book, and m , which is the number of ingredients. Both n and m are positive integers and satisfy 1 †n †500, 1 †m †500 and 1 †n à m †500 . The following n lines contain the information for each recipe with the string of length m consisting of 0 or 1. b i,j implies whether the i -th recipe needs the j -th ingredient. 1 means the ingredient is needed for the recipe and 0 means not. Each line contains at least one 1. The end of the input is indicated by a line containing two zeros. Output For each dataset, output the maximum number of recipes Taro can try. Sample Input 4 3 110 101 011 110 7 1 1 1 1 1 1 1 1 4 5 10000 01000 00100 00010 6 6 111111 011000 100000 000010 100001 100100 0 0 Output for the Sample Input 3 6 0 6 | 37,155 |
Score : 1200 points Problem Statement Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N} , where 0 \leq a_i < M for each i . Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M . Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z . Constraints All values in input are integers. 1 \leq N \leq 10^5 1 \leq M \leq 10^9 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z , where Z is the largest ugliness of the N pairs. Sample Input 1 3 10 0 2 3 4 5 9 Sample Output 1 5 One solution is to form pairs (0, 5), (2, 3) and (4, 9) , with ugliness 5, 5 and 3 , respectively. Sample Input 2 2 10 1 9 1 9 Sample Output 2 0 Pairs (1, 9) and (1, 9) should be formed, with ugliness both 0 . | 37,156 |
Score : 400 points Problem Statement We have a string s consisting of lowercase English letters. Snuke can perform the following operation repeatedly: Insert a letter x to any position in s of his choice, including the beginning and end of s . Snuke's objective is to turn s into a palindrome. Determine whether the objective is achievable. If it is achievable, find the minimum number of operations required. Notes A palindrome is a string that reads the same forward and backward. For example, a , aa , abba and abcba are palindromes, while ab , abab and abcda are not. Constraints 1 \leq |s| \leq 10^5 s consists of lowercase English letters. Input Input is given from Standard Input in the following format: s Output If the objective is achievable, print the number of operations required. If it is not, print -1 instead. Sample Input 1 xabxa Sample Output 1 2 One solution is as follows (newly inserted x are shown in bold): xabxa â xa x bxa â xaxbxa x Sample Input 2 ab Sample Output 2 -1 No sequence of operations can turn s into a palindrome. Sample Input 3 a Sample Output 3 0 s is a palindrome already at the beginning. Sample Input 4 oxxx Sample Output 4 3 One solution is as follows: oxxx â x oxxx â x xoxxx â x xxoxxx | 37,157 |
Kagisys ããéšå±ã§ã¯ICã«ãŒããçšããŠéµãéãéãããé»åé ã·ã¹ãã ãçšããŠããã ãã®ã·ã¹ãã ã¯ä»¥äžã®ããã«åäœããã åãŠãŒã¶ãŒãæã€ICã«ãŒããæã«ããããšããã®ICã«ãŒãã®IDãã·ã¹ãã ã«æž¡ãããã ã·ã¹ãã ã¯IDãç»é²ãããŠããæãæœé ãããŠãããªãéé ããããã§ãªãã®ãªãæœé ããããããã¡ãã»ãŒãžãåºåãããã IDãç»é²ãããŠããªãå Žåã¯ãç»é²ãããŠããªããšããã¡ãã»ãŒãžãåºåããéé åã³æœé ã¯ãããªãããªãã ããŠãçŸåšã·ã¹ãã ã«ã¯Nåã®ID(U 1 , U 2 , âŠâŠ, U N )ãç»é²ãããŠãããæœé ãããŠããã MåICã«ãŒããæã«ããããããã®IDã¯ããããé çªã«T 1 , T 2 , âŠâŠ, T M ã§ãããšããã ãã®æã®ã·ã¹ãã ãã©ã®ãããªã¡ãã»ãŒãžãåºåãããæ±ããã Input å
¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã N U 1 U 2 âŠâŠ U N M T 1 T 2 âŠâŠ T M Constraints N, Mã¯æŽæ°ã§ãã 1 †N †256 U i ã¯1æå以äž10æå以äžã®å°æåè±åã®ã¿ãããªãæååã§ãã U i ã¯ãŠããŒã¯ã§ãã(i â jãªãã°U i â U j ) 1 †M †256 T i ã¯1æå以äž10æå以äžã®å°æåè±åã®ã¿ãããªãæååã§ãã Output åT 1 , T 2 , âŠâŠ, T M ã«ã€ããŠã éé ãããæã¯ã"Opened by "ã®åŸã«ç¶ããŠIDãã æœé ãããæã¯ã"Closed by "ã®åŸã«ç¶ããŠIDãã IDãç»é²ãããŠããªããã®ã ã£ãå Žåã¯"Unknown "ã®åŸã«ç¶ããŠIDã ãããã1è¡ã«åºåããã åæç¶æ
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ã§ããã Sample Input 1 4 abcd efgh ijkl mnop 5 abcd abcc efgh abcd mnop Output for the Sample Input 1 Opened by abcd Unknown abcc Closed by efgh Opened by abcd Closed by mnop Sample Input 2 2 a abcdefghij 9 c bcdefghijk abcdefghij b a b a bcdefghijk c Output for the Sample Input 2 Unknown c Unknown bcdefghijk Opened by abcdefghij Unknown b Closed by a Unknown b Opened by a Unknown bcdefghijk Unknown c Sample Input 3 2 z x 2 z x Output for the Sample Input 3 Opened by z Closed by x | 37,158 |
Problem B: Dominoes Arrangement [0, 0] [0, 1] [1, 1] [0, 2] [1, 2] [2, 2] [0, 3] [1, 3] [2, 3] [3, 3] [0, 4] [1, 4] [2, 4] [3, 4] [4, 4] [0, 5] [1, 5] [2, 5] [3, 5] [4, 5] [5, 5] [0, 6] [1, 6] [2, 6] [3, 6] [4, 6] [5, 6] [6, 6] Consider the standard set of 28 western dominoes as shown in the above figure. Given a subset of the standard set dominoes, decide whether this subset can be arranged in a straight row in accordance with the familiar playing rule that touching ends must match. For example, the subset [1, 1], [2, 2], [1, 2] can be arranged in a row (as [1, 1] followed by [1, 2] followed by [2, 2]), while the subset [1, 1], [0, 3], [1, 4] can not be arranged in one row. Note that as in usual dominoes playing any pair [i, j] can also be treated as [j, i]. Your task is to write a program that takes as input any subset of the dominoes and output either yes (if the input subset can be arranged in one row) or no (if the input set can not be arranged in one row). Input Input file consists of pairs of lines. The first line of each pair is the number of elements N (1 †N †18) in the subset, and the second line is the elements of the subset separated by blanks, see the input sample below. The number of pairs (datasets) is less than 30. Output For each pair of lines of the input file, the corresponding output is either Yes or No, based on whether the input subset can be arranged in one line or not. Sample Input 6 13 23 14 24 15 25 10 00 01 11 02 12 22 03 13 23 33 Output for the Sample Input Yes No | 37,159 |
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ããªãïŒ Output åããŒã¿ã»ããã«ã€ããŠåºå㯠Q è¡ãããªãïŒãã®ãã¡ j è¡ç®ã«ã¯ïŒéšå± 1 ããå§ãŸãïŒæåŸã«éšå± d j ã«ããè±åºãã¿ã³ãæŒãïŒã³ã€ã³ã®åèšç²åŸææ°ãã¡ããã© e j æã§ãããããªãã¿ã³ã®æŒãæ¹ã®ç·æ°ãïŒ 10 9 +7 ã§å²ã£ãäœããåºåããïŒ Sample Input 4 9 1 2 1 1 2 2 1 3 1 1 3 2 1 3 3 2 3 1 2 3 2 1 4 1 3 4 2 8 1 5 2 5 3 5 4 5 1 1234567 2 1234567 3 1234567 4 1234567 4 8 1 2 1 1 2 1 1 2 3 3 4 3 1 4 2 2 4 1 2 4 3 2 4 3 8 1 3 2 6 3 8 4 12 1 31415926 2 53589793 3 23846 4 26433832 0 0 Output for the Sample Input 1 9 37 21 1 2469133 307629943 60012504 1 16 0 424 1 160769377 0 43581113 | 37,160 |
Simple Calculator Write a program which reads two integers a , b and an operator op , and then prints the value of a op b . The operator op is '+', '-', '*' or '/' (sum, difference, product or quotient). The division should truncate any fractional part. Input The input consists of multiple datasets. Each dataset is given in the following format. a op b The input ends with a dataset where op = '?'. Your program should not process for this dataset. Output For each dataset, print the value in a line. Constraints 0 †a , b †20000 No divisions by zero are given. Sample Input 1 1 + 2 56 - 18 13 * 2 100 / 10 27 + 81 0 ? 0 Sample Output 1 3 38 26 10 108 | 37,161 |
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¥åäŸã«å¯Ÿããåºå: 2 5 7 8 2 4 5 4 5 8 9 | 37,162 |
Score : 200 points Problem Statement Given is an integer N . Find the number of positive integers less than or equal to N that have an odd number of digits (in base ten without leading zeros). Constraints 1 \leq N \leq 10^5 Input Input is given from Standard Input in the following format: N Output Print the number of positive integers less than or equal to N that have an odd number of digits. Sample Input 1 11 Sample Output 1 9 Among the positive integers less than or equal to 11 , nine integers have an odd number of digits: 1, 2, \ldots, 9 . Sample Input 2 136 Sample Output 2 46 In addition to 1, 2, \ldots, 9 , another 37 integers also have an odd number of digits: 100, 101, \ldots, 136 . Sample Input 3 100000 Sample Output 3 90909 | 37,163 |
Score : 400 points Problem Statement We have a grid with H rows and W columns of squares. Snuke is painting these squares in colors 1 , 2 , ... , N . Here, the following conditions should be satisfied: For each i ( 1 †i †N ), there are exactly a_i squares painted in Color i . Here, a_1 + a_2 + ... + a_N = H W . For each i ( 1 †i †N ), the squares painted in Color i are 4-connected . That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i . Find a way to paint the squares so that the conditions are satisfied. It can be shown that a solution always exists. Constraints 1 †H, W †100 1 †N †H W a_i ⥠1 a_1 + a_2 + ... + a_N = H W Input Input is given from Standard Input in the following format: H W N a_1 a_2 ... a_N Output Print one way to paint the squares that satisfies the conditions. Output in the following format: c_{1 1} ... c_{1 W} : c_{H 1} ... c_{H W} Here, c_{i j} is the color of the square at the i -th row from the top and j -th column from the left. Sample Input 1 2 2 3 2 1 1 Sample Output 1 1 1 2 3 Below is an example of an invalid solution: 1 2 3 1 This is because the squares painted in Color 1 are not 4-connected. Sample Input 2 3 5 5 1 2 3 4 5 Sample Output 2 1 4 4 4 3 2 5 4 5 3 2 5 5 5 3 Sample Input 3 1 1 1 1 Sample Output 3 1 | 37,164 |
Score : 100 points Problem Statement Shichi-Go-San (literally "Seven-Five-Three") is a traditional event in a certain country to celebrate the growth of seven-, five- and three-year-old children. Takahashi is now X years old. Will his growth be celebrated in Shichi-Go-San this time? Constraints 1 †X †9 X is an integer. Input Input is given from Standard Input in the following format: X Output If Takahashi's growth will be celebrated, print YES ; if it will not, print NO . Sample Input 1 5 Sample Output 1 YES The growth of a five-year-old child will be celebrated. Sample Input 2 6 Sample Output 2 NO See you next year. | 37,165 |
Score : 100 points Problem Statement Given are two strings S and T consisting of lowercase English letters. Concatenate T and S in this order, without space in between, and print the resulting string. Constraints S and T are strings consisting of lowercase English letters. The lengths of S and T are between 1 and 100 (inclusive). Input Input is given from Standard Input in the following format: S T Output Print the resulting string. Sample Input 1 oder atc Sample Output 1 atcoder When S = oder and T = atc , concatenating T and S in this order results in atcoder . Sample Input 2 humu humu Sample Output 2 humuhumu | 37,166 |
You are practicing a juggle that involves in a number of square tiles. They all look the same in their size, but actually there are three different kinds of the tiles, A, B and X. The kind of a tile can be distinguishable by its mass. All the tiles of the same kind have exactly the same mass. The mass of type A tiles is within the range [mA1, mA2] . The mass of type B tiles is similarly within the range [mB1, mB2] . You donât know the exact numbers for type A and B. The mass of type X tiles is exactly mX . You have just got one big object consists of the tiles. The tiles are arranged in an H \times W grid. All the adjacent tiles are glued together on the edges. Some cells in the H \times W grid can be empty. You wanted to balance the object on a pole. You started to wonder the center of gravity of the object, then. You cannot put the object on a pole if the center of gravity is on an empty cell. The center of gravity of each single square tile is at the center of the square. The center of gravity of an object which combines two objects with masses m_{1} and m_{2} is the point dividing the line segment between those centers in the ratio m_{2} : m_{1} internally. Your task is to write a program that computes the probability that the center of gravity of the big object is actually on the object, not on a hole in the object. Although the exact mass is unknown for tile A and B, the probability follows the continuous uniform distribution within the range mentioned above. You can assume the distribution is independent between A and B. Input The input is formatted as follows. H W mA1 mA2 mB1 mB2 mX M_{1,1}M_{1,2}...M_{1,W} M_{2,1}M_{2,2}...M_{2,W} : : M_{H,1}M_{H,2}...M_{H,W} The first line of the input contains two integers H and W ( 1 \leq H, W \leq 50 ) separated by a space, where H and W are the numbers of rows and columns of given matrix. The second line of the input contains five integers mA1 , mA2 , mB1 , mB2 and mX ( 1 \leq mA1 \lt mA2 \leq 100 , 1 \leq mB1 \lt mB2 \leq 100 and 1 \leq mX \leq 100 ) separated by a space. The following H lines, each consisting of W characters, denote given matrix. In those H lines, A , B and X denote a piece of type A, type B and type X respectively, and . denotes empty cell to place no piece. There are no other characters in those H lines. Of the cell at i -th row in j -th column, the coordinate of the left top corner is (i, j) , and the coordinate of the right bottom corner is (i+1, j+1) . You may assume that given matrix has at least one A , B and X each and all pieces are connected on at least one edge. Also, you may assume that the probability that the x-coordinate of the center of gravity of the object is an integer is equal to zero and the probability that the y-coordinate of the center of gravity of the object is an integer is equal to zero. Output Print the probability that the center of gravity of the object is on the object. The output should not contain an error greater than 10^{-8} . Sample Input 1 3 3 2 4 1 2 1 XAX B.B XAX Output for the Sample Input 1 0.0000000000000 Sample Input 2 4 2 1 100 1 100 50 AX XB BA XB Output for the Sample Input 2 1.0 Sample Input 3 2 3 1 2 3 4 2 X.B AXX Output for the Sample Input 3 0.500 Sample Input 4 10 10 1 100 1 100 1 AXXXXXXXXX X........X X........X X..XXXXXXX X........X XXXXXX...X X........X X......X.X X......X.X XXXXXXXXXB Output for the Sample Input 4 0.4930639462354 Sample Input 5 25 38 42 99 40 89 3 ...........X...............X.......... ...........XXX..........XXXX.......... ...........XXXXX.......XXXX........... ............XXXXXXXXXXXXXXX........... ............XXXXXXXXXXXXXXX........... ............XXXXXXXXXXXXXX............ .............XXXXXXXXXXXXX............ ............XXXXXXXXXXXXXXX........... ...........XXXXXXXXXXXXXXXXX.......... .......X...XXXXXXXXXXXXXXXXX...X...... .......XX.XXXXXXXXXXXXXXXXXX..XX...... ........XXXXXXXXXXXXXXXXXXXX.XX....... ..........XXXXXXXXXXXXXXXXXXXX........ .........XXXXX..XXXXXXXX..XXXXX....... .......XXXXXX....XXXXX....XXXXXX...... ......XXXXXXXX...XXXXX..XXXXXXXX.X.... ....XXXXXXX..X...XXXXX..X..XXXXXXXX... ..BBBXXXXXX.....XXXXXXX......XXXAAAA.. ...BBBXXXX......XXXXXXX........AAA.... ..BBBB.........XXXXXXXXX........AAA... ...............XXXXXXXXX.............. ..............XXXXXXXXXX.............. ..............XXXXXXXXXX.............. ...............XXXXXXXX............... ...............XXXXXXXX............... Output for the Sample Input 5 0.9418222212582 | 37,167 |
Score : 200 points Problem Statement Snuke has N integers. Among them, the smallest is A , and the largest is B . We are interested in the sum of those N integers. How many different possible sums there are? Constraints 1 †N,A,B †10^9 A and B are integers. Input Input is given from Standard Input in the following format: N A B Output Print the number of the different possible sums. Sample Input 1 4 4 6 Sample Output 1 5 There are five possible sums: 18=4+4+4+6 , 19=4+4+5+6 , 20=4+5+5+6 , 21=4+5+6+6 and 22=4+6+6+6 . Sample Input 2 5 4 3 Sample Output 2 0 Sample Input 3 1 7 10 Sample Output 3 0 Sample Input 4 1 3 3 Sample Output 4 1 | 37,168 |
Problem J: Merry Christmas International Christmas Present Company (ICPC) is a company to employ Santa and deliver presents on Christmas. Many parents request ICPC to deliver presents to their children at specified time of December 24. Although same Santa can deliver two or more presents, because it takes time to move between houses, two or more Santa might be needed to finish all the requests on time. Employing Santa needs much money, so the president of ICPC employed you, a great program- mer, to optimize delivery schedule. Your task is to write a program to calculate the minimum number of Santa necessary to finish the given requests on time. Because each Santa has been well trained and can conceal himself in the town, you can put the initial position of each Santa anywhere. Input The input consists of several datasets. Each dataset is formatted as follows. N M L u 1 v 1 d 1 u 2 v 2 d 2 . . . u M v M d M p 1 t 1 p 2 t 2 . . . p L t L The first line of a dataset contains three integer, N , M and L (1 †N †100, 0 †M †1000, 1 †L †1000) each indicates the number of houses, roads and requests respectively. The following M lines describe the road network. The i -th line contains three integers, u i , v i , and d i (0 †u i < v i †N - 1, 1 †d i †100) which means that there is a road connecting houses u i and v i with d i length. Each road is bidirectional. There is at most one road between same pair of houses. Whole network might be disconnected. The next L lines describe the requests. The i -th line contains two integers, p i and t i (0 †p i †N - 1, 0 †t i †10 8 ) which means that there is a delivery request to house p i on time t i . There is at most one request for same place and time. You can assume that time taken other than movement can be neglectable, and every Santa has the same speed, one unit distance per unit time. The end of the input is indicated by a line containing three zeros separated by a space, and you should not process this as a test case. Output Print the minimum number of Santa necessary to finish all the requests on time. Sample Input 3 2 3 0 1 10 1 2 10 0 0 1 10 2 0 3 2 4 0 1 10 1 2 10 0 0 1 10 2 20 0 40 10 10 10 0 1 39 2 3 48 3 5 20 4 8 43 3 9 10 8 9 40 3 4 5 5 7 20 1 7 93 1 3 20 0 0 1 100000000 2 100 3 543 4 500 5 400 6 300 7 200 8 100 9 100 0 0 0 Output for the Sample Input 2 1 4 | 37,169 |
Estimating the Flood Risk Mr. Boat is the owner of a vast extent of land. As many typhoons have struck Japan this year, he became concerned of flood risk of his estate and he wants to know the average altitude of his land. The land is too vast to measure the altitude at many spots. As no steep slopes are in the estate, he thought that it would be enough to measure the altitudes at only a limited number of sites and then approximate the altitudes of the rest based on them. Multiple approximations might be possible based on the same measurement results, in which case he wants to know the worst case, that is, one giving the lowest average altitude. Mr. Boatâs estate, which has a rectangular shape, is divided into grid-aligned rectangular areas of the same size. Altitude measurements have been carried out in some of these areas, and the measurement results are now at hand. The altitudes of the remaining areas are to be approximated on the assumption that altitudes of two adjoining areas sharing an edge differ at most 1. In the first sample given below, the land is divided into 5 Ã 4 areas. The altitudes of the areas at (1, 1) and (5, 4) are measured 10 and 3, respectively. In this case, the altitudes of all the areas are uniquely determined on the assumption that altitudes of adjoining areas differ at most 1. In the second sample, there are multiple possibilities, among which one that gives the lowest average altitude should be considered. In the third sample, no altitude assignments satisfy the assumption on altitude differences. Your job is to write a program that approximates the average altitude of his estate. To be precise, the program should compute the total of approximated and measured altitudes of all the mesh-divided areas. If two or more different approximations are possible, the program should compute the total with the severest approximation, that is, one giving the lowest total of the altitudes. Input The input consists of a single test case of the following format. $w$ $d$ $n$ $x_1$ $y_1$ $z_1$ . . . $x_n$ $y_n$ $z_n$ Here, $w$, $d$, and $n$ are integers between $1$ and $50$, inclusive. $w$ and $d$ are the numbers of areas in the two sides of the land. $n$ is the number of areas where altitudes are measured. The $i$-th line of the following $n$ lines contains three integers, $x_i$, $y_i$, and $z_i$ satisfying $1 \leq x_i \leq w$, $1 \leq y_i \leq d$, and $â100 \leq z_i \leq 100$. They mean that the altitude of the area at $(x_i , y_i)$ was measured to be $z_i$. At most one measurement result is given for the same area, i.e., for $i \ne j$, $(x_i, y_i) \ne (x_j , y_j)$. Output If all the unmeasured areas can be assigned their altitudes without any conflicts with the measured altitudes assuming that two adjoining areas have the altitude difference of at most 1, output an integer that is the total of the measured or approximated altitudes of all the areas. If more than one such altitude assignment is possible, output the minimum altitude total among the possible assignments. If no altitude assignments satisfy the altitude difference assumption, output No . Sample Input 1 5 4 2 1 1 10 5 4 3 Sample Output 1 130 Sample Input 2 5 4 3 2 2 0 4 3 0 5 1 2 Sample Output 2 -14 Sample Input 3 3 3 2 1 1 8 3 3 3 Sample Output 3 No Sample Input 4 2 2 1 1 1 -100 Sample Output 4 -404 | 37,171 |
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Problem D: Fissure Puzzle Easy Problem $N \times N$åã®ãã¹ããæãã°ãªããããããæåãã¹ãŠã®ãã¹ã¯çœè²ã§ããã以äžã®æé ã«åŸã£ãŠé»è²ã®ãã¹ãå¢ãããŠããã äžããå¶æ°çªç®ãã€ãå·Šããå¶æ°çªç®ã§ãããã¹ã®äžã§ãçœè²ã®ãã¹ã1ã€éžã¶ãéžãã ãã¹ã¯é»è²ã«å€åãããããã«ããã®ãã¹ã®äžäžå·Šå³ããããã®æ¹åã«ã€ããŠãé£æ¥ããŠããçœè²ã®ãã¹ãé£éçã«é»è²ã«å€åããããã®é£éã¯ãã®æ¹åã«çœè²ã®ãã¹ãååšããªããªããŸã§ç¶ãã(以äžã«äŸã瀺ã) â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ â¡â¡â¡â¡â¡â¡â¡â¡â¡ âäžãã4çªç®ãå·Šãã6çªç®ãéžã¶ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â â â â â â â â â â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ âäžãã2çªç®ãå·Šãã2çªç®ãéžã¶ â¡â â¡â¡â¡â â¡â¡â¡ â â â â â â â¡â¡â¡ â¡â â¡â¡â¡â â¡â¡â¡ â â â â â â â â â â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ â¡â¡â¡â¡â¡â â¡â¡â¡ âäžãã6çªç®ãå·Šãã8çªç®ãéžã¶ â¡â â¡â¡â¡â â¡â¡â¡ â â â â â â â¡â¡â¡ â¡â â¡â¡â¡â â¡â¡â¡ â â â â â â â â â â¡â¡â¡â¡â¡â â¡â â¡ â¡â¡â¡â¡â¡â â â â â¡â¡â¡â¡â¡â â¡â â¡ â¡â¡â¡â¡â¡â â¡â â¡ â¡â¡â¡â¡â¡â â¡â â¡ ããªãã¯äžãã$i$çªç®ã§å·Šãã$j$çªç®ã®ãã¹ã®è²ã$A_{i,j}$ã§ããã°ãªãããäœãããããã¹ãéžã¶æå°ã®åæ°ãæ±ããã Input å
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¥åãšãããã®äœçœ®ã§é¬ŒãããããåãèŠãããåŠããå€å®ããããã°ã©ã ãäœæããŠãã ããã ãªãã鬌ãããããåãèŠããå Žåã«ã¯ DangerãèŠããªãå Žåã«ã¯ Safe ãšåºåããŠãã ããã鬌ãšãããåã®äœçœ®ãçµãã ç·åäžã«å£ãããå Žåã«ã¯èŠããªããã®ãšãã鬌ããããåãå£ã®äžã«ã¯ããªããã®ãšããŸãã Input è€æ°ã®ããŒã¿ã»ãããäžããããŸããåããŒã¿ã»ããã¯ä»¥äžã®åœ¢åŒã§äžããããŸãã n wx 1 wy 1 r 1 wx 2 wy 2 r 2 : wx n wy n r n m tx 1 ty 1 sx 1 sy 1 tx 2 ty 2 sx 2 sy 2 : tx m ty m sx m sy m 1 è¡ç®ã«åç圢ã®å£ã®æ° n (0 †n †100)ãç¶ã n è¡ã«å£ i ã®äžå¿ã®åº§æšãè¡šãæŽæ° wx i , wy i (0 †wx i , wy i †255) ãšååŸãè¡šãæŽæ° r i (1 †r i †255) ãäžããããŸãã ç¶ãè¡ã«ãããåãšé¬Œã®äœçœ®æ
å ±ã®åæ° m (m †100)ãç¶ã m è¡ã«äœçœ®æ
å ± i ã®ãããåã®äœçœ®ã®åº§æšãè¡šãæŽæ° tx i , ty i (0 †tx i , ty i †255) ãšé¬Œã®äœçœ®ã®åº§æšãè¡šãæŽæ° sx i , sy i (0 †sx i , sy i †255) ãäžããããŸãã ãŸããåç圢ã®å£ã®äžéšã ããå
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ããŸããã Output åããŒã¿ã»ããã«ã€ããŠãäœçœ®æ
å ± i ã®å€å®çµæ Danger ãŸã㯠Safe ã i è¡ç®ã«åºåããŠãã ããã Sample Input 3 6 6 3 19 7 4 21 8 1 6 5 4 2 11 12 4 2 11 11 9 2 11 14 3 20 5 17 9 20 5 20 10 20 5 0 Output for the Sample Input Safe Safe Danger Safe Danger Safe | 37,174 |
Score : 900 points Problem Statement Given are a permutation p_1, p_2, \dots, p_N of (1, 2, ..., N) and an integer K . Maroon performs the following operation for i = 1, 2, \dots, N - K + 1 in this order: Shuffle p_i, p_{i + 1}, \dots, p_{i + K - 1} uniformly randomly. Find the expected value of the inversion number of the sequence after all the operations are performed, and print it modulo 998244353 . More specifically, from the constraints of this problem, it can be proved that the expected value is always a rational number, which can be represented as an irreducible fraction \frac{P}{Q} , and that the integer R that satisfies R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353 is uniquely determined. Print this R . Here, the inversion number of a sequence a_1, a_2, \dots, a_N is defined to be the number of ordered pairs (i, j) that satisfy i < j, a_i > a_j . Constraints 2 \leq N \leq 200,000 2 \leq K \leq N (p_1, p_2, \dots, p_N) is a permutation of (1, 2, \dots, N) . All values in input are integers. Input Input is given from Standard Input in the following format: N K p_1 p_2 ... p_N Output Print the expected value modulo 998244353 . Sample Input 1 3 2 1 2 3 Sample Output 1 1 The final sequence is one of (1, 2, 3) , (2, 1, 3) , (1, 3, 2) , (2, 3, 1) , each with probability \frac{1}{4} . Their inversion numbers are 0, 1, 1, 2 respectively, so the expected value is 1 . Sample Input 2 10 3 1 8 4 9 2 3 7 10 5 6 Sample Output 2 164091855 | 37,175 |
ã€ã«ãããŒã·ã§ã³ (Illumination) åé¡æ JOI æ°ã¯ïŒèªå®
ã®æ·å°ã« N æ¬ã®æšãææããŠããïŒãããã®æšã¯äžåã«äžŠãã§ããïŒé ã« 1 ãã N ãŸã§ã®æŽæ°ã§çªå·ãä»ããããŠããïŒ ãã®å¬ïŒJOI æ°ã¯ããã€ãã®æšãéžãã§ïŒã€ã«ãããŒã·ã§ã³ã食ãä»ããããšã«ããïŒã€ã«ãããŒã·ã§ã³ã«ã¯ çŸãã ãšåŒã°ããå€ãå®ãŸã£ãŠããïŒæš i ã«ã€ã«ãããŒã·ã§ã³ã食ãä»ããå Žåã®çŸãã㯠A_i ã§ããïŒ JOI æ°ã¯ïŒããŸãã«è¿ã 2 ã€ã®æšã®äž¡æ¹ã«ã€ã«ãããŒã·ã§ã³ã食ãä»ããŠããŸããšïŒç©ããããå Žåãããããšã«æ°ãã€ããïŒå
·äœçã«ã¯ïŒ j = 1, 2, ..., M ã«å¯ŸããŠïŒæš L_j , L_j + 1 , ... , R_j ã®ãã¡ 2 ã€ä»¥äžã«ã€ã«ãããŒã·ã§ã³ã食ãä»ããã¹ãã§ã¯ãªããšããããšãå€æããïŒ ãã®æ¡ä»¶ã«åŸã£ãŠã€ã«ãããŒã·ã§ã³ã食ãä»ãããšãã®ïŒçŸããã®åèšã®æ倧å€ãæ±ããïŒ å¶çŽ 1 ⊠N ⊠200000 (= 2Ã10^5) 1 ⊠M ⊠200000 (= 2Ã10^5) 1 ⊠A_i ⊠1000000000 (= 10^9) ( 1 ⊠i ⊠N ) 1 ⊠L_j ⊠R_j ⊠N ( 1 ⊠j ⊠M ) å
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å ±ãªãªã³ããã¯æ¥æ¬å§å¡äŒäœ ã第 18 åæ¥æ¬æ
å ±ãªãªã³ãã㯠JOI 2018/2019 äºéžç«¶æ課é¡ã | 37,176 |
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å·ã幎ãæãæ¥ããŸãã¯ãpre-meijiããïŒè¡ã«åºåããŠãã ããã Sample Input 2005 9 3 1868 12 2 1868 9 7 Output for the Sample Input heisei 17 9 3 meiji 1 12 2 pre-meiji | 37,177 |
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æãšæ¯ã¹ãŠæ°Žéæéã¯ã©ã®ãããç¯çŽã§ããã®ã§ããããã ä»æã®äœ¿çšæ°Žé w [m 3 ] ãå
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æã®æ°Žéæéã§ãã 4280 åãšæ¯èŒããŠãã©ã®ãããæ°Žéæéãç¯çŽã§ããããåºåããããã°ã©ã ãäœæããŠãã ããã ãªããæ°Žéæéã¯æ¬¡ã®ããã«èšç®ãããŸãã (æ°Žéæé) = (åºæ¬æé) + (æ°Žéã«ããæé) æ°Žéã«ããæéã¯äžè¡šã®ããã«äœ¿çšéã«å¿ããŠèšç®ãããŸãã 段é æ°Žé æé 第 1 段éæé 10 [m 3 ] ãŸã§ åºæ¬æé 1150 å 第 2 段éæé 10 [m 3 ] è¶
é 20 [m 3 ] ãŸã§ 1 [m 3 ] ããã 125 å 第 3 段éæé 20 [m 3 ] è¶
é 30 [m 3 ] ãŸã§ 1 [m 3 ] ããã 140 å 第 4 段éæé 30 [m 3 ] è¶
éå 1 [m 3 ] ããã 160 å äŸãã°ã䜿çšæ°Žé 40 [m 3 ] ã®å Žåã¯ã åºæ¬æé 1150 å(第 1 段é) + 10 [m 3 ] à 125 å(第 2 段é) + 10 [m 3 ] à 140 å(第 3 段é) + 10 [m 3 ] à 160 å(第 4 段é) = 5400 å ãšãªããŸãã Input è€æ°ã®ããŒã¿ã»ããã®äžŠã³ãå
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æã®æ°Žéæéãšã®å·®ã1è¡ã«åºåããŸãã Sample Input 29 40 0 -1 Output for the Sample Input 620 -1120 3130 | 37,178 |
Standard Deviation You have final scores of an examination for n students. Calculate standard deviation of the scores s 1 , s 2 ... s n . The variance α 2 is defined by α 2 = (â n i =1 (s i - m) 2 )/n where m is an average of s i . The standard deviation of the scores is the square root of their variance. Input The input consists of multiple datasets. Each dataset is given in the following format: n s 1 s 2 ... s n The input ends with single zero for n . Output For each dataset, print the standard deviation in a line. The output should not contain an absolute error greater than 10 -4 . Constraints n †1000 0 †s i †100 Sample Input 5 70 80 100 90 20 3 80 80 80 0 Sample Output 27.85677655 0.00000000 | 37,179 |
Sum Source Detection JAG members began a game with integers. The game consists of $N + M + 1$ players: $N$ open number holders, $M$ secret number holders, and one answerer, you. In the preparation, an integer $K$ is told to all $N + M + 1$ players. $N + M$ number holders choose their own integers per person under the following restrictions: Each holder owns a positive integer. The sum of all the integers equals $K$. Every integer owned by secret number holders is strictly less than any integers owned by open number holders. After the choices, $N$ open number holders show their integers $O_1, ..., O_N$ to the answerer while secret number holders do not. The game has $Q$ rounds. At the beginning of each round, $M$ secret number holders can change their numbers under the above restrictions, while open number holders cannot. Then $N + M$ number holders select part of members among them arbitrary, calculate the sum $X$ of the integers owned by the selected members, and tell $X$ to the answerer. For each round, the answerer tries to identify the definitely selected open number holders from the information $K$, $X$, and $O_1, ..., O_N$: The answerer will get points per actually selected open number holder in the answer. On the other hand, if the answer contains at least one non-selected member, you lose your points got in the round. Thus, the answerer, you, must answer only the open number holders such that the holders are definitely selected. Your task in this problem is to write a program to determine all the open number holders whose integers are necessary to the sum for each round in order to maximize your points. Input The input consists of a single test case formatted as follows. $N$ $M$ $K$ $Q$ $O_1$ ... $O_N$ $X_1$ ... $X_Q$ The first line consists of four integers $N, M, K,$ and $Q$. $N$ and $M$ are the numbers of open number holders and secret number holders respectively ($1 \leq N, 0 \leq M, N + M \leq 40$). $K$ is an integer ($1 \leq K \leq 200,000$). $Q$ is the number of rounds of the game ($1 \leq Q \leq 10,000$). The second line contains $N$ integers $O_1, ..., O_N$, as the $i$-th open number holder owns $O_i$ ($1 \leq O_1 \leq ... \leq O_N \leq K$). The third line indicates $Q$ integers $X_1, ..., X_Q$ ($0 \leq X_i \leq K$). $X_i$ is the sum of the integers owned by the selected members in the $i$-th round. It is guaranteed that there is at least one way to compose $X_i$. In other words, you can assume that there is at least one integer sequence $S_1, ..., S_M$, which represents integers owned by secret number holders, satisfying the followings: $0 < S_j < O_1$ for $1 \leq j \leq M$. Note that $O_1 = min_{1\leq k \leq N}O_k$ holds. $\sum_{j=1}^N O_j + \sum_{k=1}^M S_k = K$. There is at least one pair of subsets $U \subseteq \{1,...,N\}$ and $V \subseteq \{1, ..., M\}$ such that $\sum_{j\in U} O_j + \sum_{k\in V}S_k = X_i$ holds. Output On each sum $X_i$, print the indices of the open number holders whose integers are required to make up $X_i$. The output for each sum has to be printed in one line, in ascending order, and separated by a single space. If there is no open number holder whose integer is certainly used for $X_i$, print $-1$ in one line. Sample Input 1 2 2 23 2 7 10 9 10 Output for Sample Input 1 1 -1 The first sum 9 can be achieved only by the first open number holder's 7 plus 2 of a secret number holder. In this case, secret number holders have 2 and 4. The second open number holder's 10 is a candidate for the second sum 10. The first open holder's 7 plus 3 is also possible one, as secret number holders have two 3s. Sample Input 2 1 1 100 3 51 49 51 100 Output for Sample Input 2 -1 1 1 The only secret number holder owns 49. The output for the first sum is $-1$ because the open number holder's 51 is not selected. Sample Input 3 2 1 58152 4 575 57500 575 57577 77 0 Output for Sample Input 3 1 2 -1 -1 In this case, the only secret number holder definitely has 77. The output for the last sum 0 is -1 because no integer of open number holders is needed to form 0. Sample Input 4 3 2 1500 1 99 300 1000 99 Output for Sample Input 4 1 The only way to compose 99 is to select the first open number holder only; secret number holders have two integers between 1 and 98, while the sum of them must be 101. Sample Input 5 3 2 20 19 3 3 11 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 Output for Sample Input 5 -1 -1 -1 -1 -1 -1 1 2 1 2 1 2 3 3 3 3 3 3 3 1 2 3 1 2 3 1 2 3 The numbers owned by the two secret number holders are 1 and 2. At least one open number holder's 3 is required to compose 5 and 6 respectively, but it is impossible to determine the definitely selected open number holder(s). On the other hand, 7 needs the two open number holders who both own 3. | 37,180 |
Score : 1300 points Problem Statement One day, AtCoDeer the deer found a simple graph (that is, a graph without self-loops and multiple edges) with N vertices and M edges, and brought it home. The vertices are numbered 1 through N and mutually distinguishable, and the edges are represented by (a_i,b_i) (1âŠiâŠM) . He is painting each edge in the graph in one of the K colors of his paint cans. As he has enough supply of paint, the same color can be used to paint more than one edge. The graph is made of a special material, and has a strange property. He can choose a simple cycle (that is, a cycle with no repeated vertex), and perform a circular shift of the colors along the chosen cycle. More formally, let e_1 , e_2 , ... , e_a be the edges along a cycle in order, then he can perform the following simultaneously: paint e_2 in the current color of e_1 , paint e_3 in the current color of e_2 , ... , paint e_a in the current color of e_{a-1} , and paint e_1 in the current color of e_{a} . Figure 1 : An example of a circular shift Two ways to paint the edges, A and B , are considered the same if A can be transformed into B by performing a finite number of circular shifts. Find the number of ways to paint the edges. Since this number can be extremely large, print the answer modulo 10^9+7 . Constraints 1âŠNâŠ50 1âŠMâŠ100 1âŠKâŠ100 1âŠa_i,b_iâŠN (1âŠiâŠM) The graph has neither self-loops nor multiple edges. Input The input is given from Standard Input in the following format: N M K a_1 b_1 a_2 b_2 : a_M b_M Output Print the number of ways to paint the edges, modulo 10^9+7 . Sample Input 1 4 4 2 1 2 2 3 3 1 3 4 Sample Output 1 8 Sample Input 2 5 2 3 1 2 4 5 Sample Output 2 9 Sample Input 3 11 12 48 3 1 8 2 4 9 5 4 1 6 2 9 8 3 10 8 4 10 8 6 11 7 1 8 Sample Output 3 569519295 | 37,181 |
Problem J: No Story Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer L , how many pairs of positive integers a , b ( a †b ) such that LCM( a , b ) = L are there? Here, LCM( a , b ) stands for the least common multiple of a and b . Input For each dataset, an integer L is given in a line. Input terminates when L = 0. Output For each dataset, output the number of pairs of a and b . Constraints 1 †L †10 12 Sample Input 12 9 2 0 Output for the Sample Input 8 3 2 | 37,182 |
A: Attack the Moles ICPC ã§è¯ãæ瞟ãåããã«ã¯ä¿®è¡ãæ¬ ãããªãïŒããã㯠ICPC ã§åã¡ããã®ã§ïŒä»æ¥ãä¿®è¡ãããããšã«ããïŒ ä»æ¥ã®ä¿®è¡ã¯ïŒãããããããäœåãè¡ã£ãŠïŒåå°ç¥çµãšèšæ¶åãé«ããããšãããã®ã§ããïŒåºãŠãããããã次ã
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å ±ããã¹ãŠèšé²ãïŒã³ã³ãã¥ãŒã¿ã§è§£æãè¡ãããšã«ããïŒ ããããå©ãã«ã¯ïŒãããã®åºçŸäœçœ®ã«æãåãããåŸïŒãããã®åºãŠããã¿ã€ãã³ã°ã«ãŽã£ããåãããŠããããå©ããªããã°ãªããªãïŒããããããŸãå©ãããšïŒãã®ãããã«å¿ããŠãã€ã³ããåŸãããšãåºæ¥ãïŒããããå©ãåäœã¯äžç¬ã§è¡ãããšãåºæ¥ããïŒæã移åãããéãã«ã¯éçãããïŒãããã¯ããããå©ãã«ããã£ãŠå·Šå³äž¡æ¹ã®æãçšããããšãã§ããïŒå·Šæãšå³æã¯ç¬ç«ã«åããããšãå¯èœã§ãããïŒå·Šæã¯åžžã«å³æãã座æšãå°ããäœçœ®ã«ååšããªããã°ãªããªãïŒãã®ãããªæ¡ä»¶äžã§ïŒæ倧ã§ã©ãã ãã®ãã€ã³ããåŸããããã調ã¹ããïŒ Input N V X Left X Right X 1 T 1 P 1 ... X N T N P N N ã¯åºãŠãããããã®æ°ïŒ V ã¯æã移åãããããæ倧ã®éãïŒ X Left , X Right ã¯ããããïŒå·ŠæïŒå³æã®åæäœçœ®ã®åº§æšã§ããïŒ X i , T i , P i ã¯ããããïŒ i çªç®ã®ãããã®ïŒåºçŸããäœçœ®ã®åº§æšïŒã²ãŒã éå§ããåºçŸãŸã§ã®æéïŒå©ããéã«åŸããããã€ã³ãã§ããïŒ 1 †N †3,000ïŒ1 †V †10,000ïŒ1 †X Left < X Right †100,000ïŒ1 †X 1 †X 2 †... †X N †100,000ïŒ1 †T i †100,000ïŒ1 †P i †100,000 ãæºããïŒ( X i , T i ) ãšããŠåäžã®çµã¯è€æ°åçŸããªãïŒ Output ããããåŸãããæ倧ã®ãã€ã³ãã 1 è¡ã«åºåããïŒ Sample Input 1 3 10 150 250 100 20 123 201 10 67 202 10 45 Sample Output 1 190 Sample Input 2 1 7 20 90 55 5 73 Sample Output 2 73 Sample Input 3 10 2 1000 2000 400 300 1 600 200 1 700 800 1 700 500 1 900 600 1 1000 700 1 1300 900 1 1400 400 1 1500 1000 1 2000 100 1 Sample Output 3 10 | 37,183 |
Score : 500 points Problem Statement Seisu-ya , a store specializing in non-negative integers, sells N non-negative integers. The i -th integer is A_i and has a utility of B_i . There may be multiple equal integers with different utilities. Takahashi will buy some integers in this store. He can buy a combination of integers whose bitwise OR is less than or equal to K . He wants the sum of utilities of purchased integers to be as large as possible. Find the maximum possible sum of utilities of purchased integers. Constraints 1 \leq N \leq 10^5 0 \leq K < 2^{30} 0 \leq A_i < 2^{30}(1\leq i\leq N) 1 \leq B_i \leq 10^9(1\leq i\leq N) All input values are integers. Inputs Input is given from Standard Input in the following format: N K A_1 B_1 : A_N B_N Outputs Print the maximum possible sum of utilities of purchased integers. Sample Input 1 3 5 3 3 4 4 2 5 Sample Output 1 8 Buy 2 and 3 to achieve the maximum possible total utility, 8 . Sample Input 2 3 6 3 3 4 4 2 5 Sample Output 2 9 Buy 2 and 4 to achieve the maximum possible total utility, 9 . Sample Input 3 7 14 10 5 7 4 11 4 9 8 3 6 6 2 8 9 Sample Output 3 32 | 37,184 |
String Crossing Problem N åã®æåå{ S 1 , S 2 , ..., S N } ãäžããããã ç¶ã㊠Q åã®ã¯ãšãªãäžããããã ã¯ãšãªã®çš®é¡ã¯ä»¥äžã®2ã€ã§ããã a , b , c , d ãå
¥åãã S a ã® b æåç®ããã® substring ã S c ã® d -1æåãŸã§ã® substring ã®åŸã«ç¹ããããããæ°ãã S c ãšããã å
ã® S c ã® d æåç®ããã® substring ã S a ã® b -1æåãŸã§ã® substring ã®åŸã«ç¹ããããããæ°ãã S a ãšããã a , b , c ãå
¥åãã S a ã® b æåç®ã c ã«å€æŽããã äŸãã° S 1 ="abcd", S 2 ="efgh"ããã ã¯ãšãªã®çš®é¡ã1㧠a =1, b =2, c =2, d =3ã®ãšã a - -> bcd X ef - -> gh S 1 ="agh", S 2 ="efbcd"ãšãªãã å
šãŠã®ã¯ãšãªãåŠçããåŸã®æåå S 1 ãã S N ãå
šãŠåºåããã Input å
¥åã¯ä»¥äžã®åœ¢åŒã§äžããããã N Q S 1 S 2 ... S N query 1 query 2 ... query Q å query ã¯æ¬¡ã®ããããã§ããã 1 a b c d or 2 a b c Constraints 1 †N †10 5 1 †Q †10 5 N åã®æååã®é·ãã®åèšã¯2Ã10 6 ãè¶ããªãã æåå S i ã¯å
šãŠè±å°æåã§ããããšãä¿èšŒãããã ã¯ãšãªã®çš®é¡ã1ã®ãšã a â c 1 †b †| S a | 1 †d †| S c | ã¯ãšãªã®çš®é¡ã2ã®ãšã 1 †b †| S a | c ã¯è±å°æåã§ããããšãä¿èšŒãããã é«éãªå
¥åºåãæšå¥šããã Output åã¯ãšãªãåŠçããåŸã®æååã S 1 ãã S N ãŸã§1è¡ãã€åºåããã S 1 S 2 ... S N Sample Input 1 2 1 abcd efgh 1 1 2 2 3 Sample Output 1 agh efbcd Sample Input 2 2 3 abcd efgh 1 1 2 2 3 2 1 3 x 2 2 4 x Sample Output 2 agx efbxd Sample Input 3 10 10 sjcvpauokb fmeaowomscy sepeqqfcosrjmonfsv zapc aromazjzqoeiqswvcaf clifpa dusudcz qeqdzdtdzlkhc gkpsjvdvadmf xrtyxnkolluagwxp 1 4 4 6 3 1 7 1 8 1 2 2 6 o 1 4 4 3 7 2 1 2 i 1 6 3 3 2 1 6 5 1 9 2 10 9 j 1 2 2 7 3 2 3 2 b Sample Output 3 sicvpauoeqqifpa fqdzdtdzlkhc sb zapfcosrjmonfsv aromazjzqoeiqswvcaf clepkb qemeaooomscy dusudcz gkpsjvdvadmf xrtyxnkojluagwxp | 37,185 |
倱ãããæ° æã¯3xxx幎ãé«åºŠã«çºéããææã¯åæ»æãè¿ããŠãããæŽå²å®¶ãã¡ã¯ãã®ç¶æ³ãæéããããšéå»ã®å¡æºãåŠã¶ããšã«ããã泚ç®ããã®ã¯ã³ã³ãã¥ãŒã¿åµäžæã®å€©æãæ®ããè³æã§ããããã®è³æã«ã¯èšç®åŒãæžãããŠãããã®èšç®çµæãç¥ãããã®ã ããæ®å¿µãªãããã®äžéšã®æåãèããŠèªããªããªã£ãŠãããä»æ¹ããªãã®ã§èšç®çµæãšããŠããããæã倧ããæ°ãæ±ããããšã«ããã èšç®åŒã¯2é²æ°ã§æžãããŠãããæŒç®ã¯è¶³ãç®ã»åŒãç®ã»æãç®ã®3çš®é¡ã§ãããæ¬åŒ§ãçšããããŠãããæ¬åŒ§å
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èŠãããã <expression> ::= <number> | <expression> <operation> <expression> | ( <expression> <operation> <expression> ) <number> ::= <digit> | <number> <digit> <operation> ::= + | - | * <digit> ::= 0 | 1 åœæã®ã³ã³ãã¥ãŒã¿ã®èšç®èœåã®éçã«ãããæ°åã¯0ä»¥äž 2 10 æªæºã®æŽæ°ã§ããèšç®äžããã®ç¯å²ãåºãããšã¯ãªãããã ãèšç®ã¯æ¬åŒ§å
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ã«è¡ãããã以å€ã®å Žåã¯å·Šããé ã«èšç®ããã Input å
¥åã¯1è¡ãããªãã解èªãã¹ãæ°åŒã1ã€äžãããããæ°åŒã¯1æå以äž100æå以äžã§ããã1ã€ã®æ°åŒã«ã€ããŠæ倧5æåãèªããªããªã£ãŠããŠãã.ãã§è¡šçŸãããŠãããäžããããæ°åŒã«å«ãŸããæåã¯01+-*().ã®ããããã§ããã Constraints æ°åŒã¯1æå以äž100æåä»¥äž æ¹è¡ãé€ããã¹ãŠã®æåã¯01+-*().ã®ãããã .ã®åæ°ã¯5åä»¥äž Output å
ã®æ°åŒãšããŠèãããããã®ã®å
ãèšç®çµæãæ倧ãšãªããã®ãæ±ããèšç®çµæã10é²æ³ã§åºåãããèªããªããªã£ãŠããæåãã©ã®ããã«åããŠãå
ã®æ°åŒãšèãããããã®ãäœããªããšãã¯-1ãåºåããã Sample Input 1 000 Output for the Sample Input 1 0 Sample Input 2 0.0 Output for the Sample Input 2 2 Sample Input 3 ... Output for the Sample Input 3 7 Sample Input 4 (1.1) Output for the Sample Input 4 2 Sample Input 5 0-1. Output for the Sample Input 5 -1 | 37,186 |
Score : 100 points Problem Statement On the Planet AtCoder, there are four types of bases: A , C , G and T . A bonds with T , and C bonds with G . You are given a letter b as input, which is A , C , G or T . Write a program that prints the letter representing the base that bonds with the base b . Constraints b is one of the letters A , C , G and T . Input Input is given from Standard Input in the following format: b Output Print the letter representing the base that bonds with the base b . Sample Input 1 A Sample Output 1 T Sample Input 2 G Sample Output 2 C | 37,187 |
Playoff by all the teams The Minato Mirai Football Association hosts its annual championship as a single round-robin tournament, in which each team plays a single match against all the others. Unlike many other round-robin tournaments of football, matches never result in a draw in this tournament. When the regular time match is a tie, overtime is played, and, when it is a tie again, a penalty shootout is played to decide the winner. If two or more teams won the most number of matches in the round-robin, a playoff is conducted among them to decide the champion. However, if the number of teams is an odd number, it is possible that all the teams may have the same number of wins and losses, in which case all the teams participate in the playoff, called a "full playoff" here. Now, some of the tournament matches have already been played and we know their results. Whether or not a full playoff will be required may depend on the results of the remaining matches. Write a program that computes the number of win/loss combination patterns of the remaining matches that lead to a full playoff. The first datatset of the Sample Input represents the results of the first three matches in a round-robin tournament of five teams, shown in the following table. In the table, gray cells indicate the matches not played yet. Team 1 Team 2 Team 3 Team 4 Team 5 Team 1 lost lost Team 2 lost Team 3 won Team 4 won Team 5 won In this case, all the teams win the same number of matches with only two win/loss combination patterns of the remaining matches, which lead to a full playoff, as shown below. In the two tables, the differences are indicated in light yellow. Team 1 Team 2 Team 3 Team 4 Team 5 Team 1 won won lost lost Team 2 lost lost won won Team 3 lost won won lost Team 4 won lost lost won Team 5 won lost won lost Team 1 Team 2 Team 3 Team 4 Team 5 Team 1 won won lost lost Team 2 lost lost won won Team 3 lost won lost won Team 4 won lost won lost Team 5 won lost lost won Input The input consists of multiple datasets, each in the following format. n m x 1 y 1 ... x m y m n is an odd integer, 3, 5, 7, or 9, indicating the number of teams participating in the tournament. m is a positive integer less than n ( n â1)/2, which is the number of matches already finished. x i and y i give the result of the i -th match that has already taken place, indicating that team x i defeated team y i . Each of x i and y i is an integer 1 through n which indicates the team number. No team plays against itself, that is, for any i , x i â y i . The match result of the same team pair appears at most once. That is, if i â j , then ( x i , y i ) â ( x j , y j ) and ( x i , y i ) â ( y j , x j ) hold. The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 100. Output For each dataset, output a single line containing one integer which indicates the number of possible future win/loss patterns that a full playoff will be required. Sample Input 5 3 3 2 4 1 5 1 3 1 1 2 3 2 1 2 3 2 5 4 4 1 4 2 5 1 5 2 5 3 4 1 4 2 5 1 5 4 3 2 4 1 5 1 5 2 9 11 6 1 6 4 7 2 7 3 7 4 8 2 8 3 8 4 9 1 9 3 9 5 9 10 6 1 6 4 7 2 7 3 7 4 8 2 8 3 8 4 9 1 9 3 5 6 4 3 2 1 5 1 2 4 1 3 2 3 9 1 1 2 0 Output for the Sample Input 2 1 0 0 1 0 0 16 0 1615040 | 37,188 |
Shopping You are now in a bookshop with your friend Alice to buy a book, "The Winning Strategy for the Programming Koshien Contest,â just released today. As you definitely want to buy it, you are planning to borrow some money from Alice in case the amount you have falls short of the price. If the amount you receive from Alice still fails to meet the price, you have to abandon buying the book this time. Write a program to calculate the minimum amount of money you need to borrow from Alice given the following three items of data: the money you and Alice have now and the price of the book. Input The input is given in the following format. m f b A line containing the three amounts of money is given: the amount you have with you now m (0 †m †10000), the money Alice has now f (0 †f †10000) and the price of the book b (100 †b †20000). Output Output a line suggesting the minimum amount of money you need to borrow from Alice. Output "NA" if all the money Alice has with him now is not a sufficient amount for you to buy the book. Sample Input 1 1000 3000 3000 Sample Output 1 2000 Sample Input 2 5000 3000 4500 Sample Output 2 0 Sample Input 3 500 1000 2000 Sample Output 3 NA | 37,189 |
Score : 300 points Problem Statement We have a string X , which has an even number of characters. Half the characters are S , and the other half are T . Takahashi, who hates the string ST , will perform the following operation 10^{10000} times: Among the occurrences of ST in X as (contiguous) substrings, remove the leftmost one. If there is no occurrence, do nothing. Find the eventual length of X . Constraints 2 ⊠|X| ⊠200,000 The length of X is even. Half the characters in X are S , and the other half are T . Partial Scores In test cases worth 200 points, |X| ⊠200 . Input The input is given from Standard Input in the following format: X Output Print the eventual length of X . Sample Input 1 TSTTSS Sample Output 1 4 In the 1 -st operation, the 2 -nd and 3 -rd characters of TSTTSS are removed. X becomes TTSS , and since it does not contain ST anymore, nothing is done in the remaining 10^{10000}-1 operations. Thus, the answer is 4 . Sample Input 2 SSTTST Sample Output 2 0 X will eventually become an empty string: SSTTST â STST â ST â ``. Sample Input 3 TSSTTTSS Sample Output 3 4 X will become: TSSTTTSS â TSTTSS â TTSS . | 37,190 |
Score : 200 points Problem Statement Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank. The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.) Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time? Constraints 101 \le X \le 10^{18} All values in input are integers. Input Input is given from Standard Input in the following format: X Output Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time. Sample Input 1 103 Sample Output 1 3 The balance after one year is 101 yen. The balance after two years is 102 yen. The balance after three years is 103 yen. Thus, it takes three years for the balance to reach 103 yen or above. Sample Input 2 1000000000000000000 Sample Output 2 3760 Sample Input 3 1333333333 Sample Output 3 1706 | 37,191 |
ABC Gene æåå ABC ã§è¡šãããéºäŒåé
åããããããªãã¯æ¬¡ã®æäœãäœåãè¡ãããã®éºäŒåé
åãæžãæããŠããããšãã§ããã æå A ïŒ B ïŒ C ã®ãã¡ 1 ã€ãéžã¶ãããã x ãšãããéºäŒåé
åã«å«ãŸãããã¹ãŠã® x ããããã ABC ãžåæã«çœ®ãæããã A ïŒ B ïŒ C ã ããããªãæåå S ãäžãããããéºäŒåé
åã S ã«äžèŽããããããå€å®ããã Constraints 1 †|S| †5,000 S 㯠A ïŒ B ïŒ C ã ããããªãã Input Format å
¥åã¯ä»¥äžã®åœ¢åŒã§æšæºå
¥åããäžããããã S Output Format éºäŒåé
åã S ã«äžèŽããããããªãã° Yes ããäžèŽãããããªããªãã° No ãäžè¡ã«åºåããã Sample Input 1 ABC Sample Output 1 Yes éºäŒåé
åã¯ã¯ãããã ABC ã§ããã Sample Input 2 AABCC Sample Output 2 Yes B ãéžãã§æäœãè¡ããš ABC â AABCC ãšãªãã Sample Input 3 AABCABC Sample Output 3 No äŸãã°ã C ãéžãã§æäœãè¡ã£ãŠã AABCC â AABCABC ãšã¯ãªããªãããã¹ãŠã® C ããããã ABC ãžåæã«çœ®ãæããã®ã§ãå®é㯠AABCC â AABABCABC ãšãªãã | 37,192 |
What is the Number in my Mind ? Let us enjoy a number guess game. A number containing L digits is in my mind (where 4 <= L <= 10). You should guess what number it is. It is composed of any of the following ten digits: "0","1","2","3","4","5","6","7","8", and "9". No digits appear twice in the number. For example, when L = 4, "1234" is a legitimate candidate but "1123" is not (since "1" appears twice). The number may begin with "0", and a number "05678" should be distinct from a number "5678", for example. If you and your computer cannot see through my mind by telepathy, a group of hints will be needed in order for you to identify the number in my mind. A hint is a triple of numbers named try , hit , and blow . The try is a number containing L decimal digits. No digits appear twice in the try , and this number may also begin with "0". The hit value indicates the count of digits that the try and the number in my mind have in common, and that are exactly in the same position. The blow value indicates the count of digits that the try and the number in my mind have in common, but that are NOT in the same position. They are arranged in one line as follows. try hit blow For example, if L = 4 and the number in my mind is 9876 , then the following is an example of hint-set consisting of legitimate hints. 7360 0 2 2507 0 1 9713 1 1 9678 2 2 The above hint-set should be sufficient for you to guess the number and the answer should be 9876 . In contrast, the following hint-set is not sufficient to guess the number. 7360 0 2 9713 1 1 9678 2 2 No number is consistent with the following hint-set. 9678 2 2 1234 2 2 Answers for last two hint-sets should be NO . Your job is to write a program identifying the numbers in my mind using given hint-sets. Input The input consists of multiple hint-sets as follows. Each of them corresponds to a number in my mind. < HINT-SET 1 > < HINT-SET 2 > . . . < HINT-SET i > . . . < HINT-SET n > A <HINT-SET i > is composed of one header line in the following format ( L and H should be separated by a single space character.): L H and H lines of hints in the following format (1 <= j <= H ) : TRY 1 HIT 1 BLOW 1 TRY 2 HIT 2 BLOW 2 . . . TRY j HIT j BLOW j . . . TRY H HIT H BLOW H L indicates the number of digits of the number in my mind and TRY j . HIT j and BLOW j indicate hit and blow values between the TRY j and the number in my mind. (They are separated by a single space character.) The end of the input is indicated by a header line with L = 0 and H = 0. Output For each hint-set, the answer should be printed, each in a separate line. If you can successfully identify the number for a given hint-set, the answer should be the number. If you cannot identify the number, the answer should be NO . Sample Input 6 4 160348 0 4 913286 2 3 431289 3 1 671283 3 3 10 8 3827690415 2 8 0482691573 1 9 1924730586 3 7 1378490256 1 9 6297830541 1 9 4829531706 3 7 4621570983 1 9 9820147536 6 4 4 4 2713 0 3 1247 2 0 1230 1 1 1387 2 1 6 5 605743 0 4 593026 2 2 792456 1 2 143052 1 3 093614 3 3 5 2 12345 5 0 67890 0 5 0 0 Output for the Sample Input 637281 7820914536 3287 NO NO | 37,193 |
Score : 100 points Problem Statement In some other world, today is December D -th. Write a program that prints Christmas if D = 25 , Christmas Eve if D = 24 , Christmas Eve Eve if D = 23 and Christmas Eve Eve Eve if D = 22 . Constraints 22 \leq D \leq 25 D is an integer. Input Input is given from Standard Input in the following format: D Output Print the specified string (case-sensitive). Sample Input 1 25 Sample Output 1 Christmas Sample Input 2 22 Sample Output 2 Christmas Eve Eve Eve Be sure to print spaces between the words. | 37,194 |
Score : 1700 points Problem Statement There are two rooted trees, each with N vertices. The vertices of each tree are numbered 1 through N . In the first tree, the parent of Vertex i is Vertex A_i . Here, A_i=-1 if Vertex i is the root of the first tree. In the second tree, the parent of Vertex i is Vertex B_i . Here, B_i=-1 if Vertex i is the root of the second tree. Snuke would like to construct an integer sequence of length N , X_1 , X_2 , ... , X_N , that satisfies the following condition: For each vertex on each tree, let the indices of its descendants including itself be a_1 , a_2 , ... , a_k . Then, abs(X_{a_1} + X_{a_2} + ... + X_{a_k})=1 holds. Determine whether it is possible to construct such a sequence. If the answer is possible, find one such sequence. Constraints 1 \leq N \leq 10^5 1 \leq A_i \leq N , if Vertex i is not the root in the first tree. A_i = -1 , if Vertex i is the root in the first tree. 1 \leq B_i \leq N , if Vertex i is not the root in the second tree. B_i = -1 , if Vertex i is the root in the second tree. Input corresponds to valid rooted trees. Input Input is given from Standard Input in the following format: N A_1 A_2 .. A_N B_1 B_2 .. B_N Output If it is not possible to construct an integer sequence that satisfies the condition, print IMPOSSIBLE . If it is possible, print POSSIBLE in the first line. Then, in the second line, print X_1 , X_2 , ... , X_N , an integer sequence that satisfies the condition. Sample Input 1 5 3 3 4 -1 4 4 4 1 -1 1 Sample Output 1 POSSIBLE 1 -1 -1 3 -1 For example, the indices of the descendants of Vertex 3 of the first tree including itself, is 3,1,2 . It can be seen that the sample output holds abs(X_3+X_1+X_2)=abs((-1)+(1)+(-1))=abs(-1)=1 . Similarly, the condition is also satisfied for other vertices. Sample Input 2 6 -1 5 1 5 1 3 6 5 5 3 -1 3 Sample Output 2 IMPOSSIBLE In this case, constructing a sequence that satisfies the condition is IMPOSSIBLE . Sample Input 3 8 2 7 1 2 2 1 -1 4 4 -1 4 7 4 4 2 4 Sample Output 3 POSSIBLE 1 2 -1 0 -1 1 0 -1 | 37,196 |
Fast Forwarding Mr. Anderson frequently rents video tapes of his favorite classic films. Watching the films so many times, he has learned the precise start times of his favorite scenes in all such films. He now wants to find how to wind the tape to watch his favorite scene as quickly as possible on his video player. When the [play] button is pressed, the film starts at the normal playback speed. The video player has two buttons to control the playback speed: The [3x] button triples the speed, while the [1/3x] button reduces the speed to one third. These speed control buttons, however, do not take effect on the instance they are pressed. Exactly one second after playback starts and every second thereafter, the states of these speed control buttons are checked. If the [3x] button is pressed on the timing of the check, the playback speed becomes three times the current speed. If the [1/3x] button is pressed, the playback speed becomes one third of the current speed, unless it is already the normal speed. For instance, assume that his favorite scene starts at 19 seconds from the start of the film. When the [3x] button is on at one second and at two seconds after the playback starts, and the [1/3x] button is on at three seconds and at five seconds after the start, the desired scene can be watched in the normal speed five seconds after starting the playback, as depicted in the following chart. Your task is to compute the shortest possible time period after the playback starts until the desired scene starts. The playback of the scene, of course, should be in the normal speed. Input The input consists of a single test case of the following format. $t$ The given single integer $t$ ($0 \leq t < 2^{50}$) is the start time of the target scene. Output Print an integer that is the minimum possible time in seconds before he can start watching the target scene in the normal speed. Sample Input 1 19 Sample Output 1 5 Sample Input 2 13 Sample Output 2 5 Sample Input 3 123456789098765 Sample Output 3 85 Sample Input 4 51 Sample Output 4 11 Sample Input 5 0 Sample Output 5 0 Sample Input 6 3 Sample Output 6 3 Sample Input 7 4 Sample Output 7 2 | 37,197 |
Score : 1800 points Problem Statement For a sequence S of positive integers and positive integers k and l , S is said to belong to level (k,l) when one of the following conditions is satisfied: The length of S is 1 , and its only element is k . There exist sequences T_1,T_2,...,T_m ( m \geq l ) belonging to level (k-1,l) such that the concatenation of T_1,T_2,...,T_m in this order coincides with S . Note that the second condition has no effect when k=1 , that is, a sequence belongs to level (1,l) only if the first condition is satisfied. Given are a sequence of positive integers A_1,A_2,...,A_N and a positive integer L . Find the number of subsequences A_i,A_{i+1},...,A_j ( 1 \leq i \leq j \leq N ) that satisfy the following condition: There exists a positive integer K such that the sequence A_i,A_{i+1},...,A_j belongs to level (K,L) . Constraints 1 \leq N \leq 2 \times 10^5 2 \leq L \leq N 1 \leq A_i \leq 10^9 Input Input is given from Standard Input in the following format: N L A_1 A_2 ... A_N Output Print the number of subsequences A_i,A_{i+1},...,A_j ( 1 \leq i \leq j \leq N ) that satisfy the condition. Sample Input 1 9 3 2 1 1 1 1 1 1 2 3 Sample Output 1 22 For example, both of the sequences (1,1,1) and (2) belong to level (2,3) , so the sequence (2,1,1,1,1,1,1) belong to level (3,3) . Sample Input 2 9 2 2 1 1 1 1 1 1 2 3 Sample Output 2 41 Sample Input 3 15 3 4 3 2 1 1 1 2 3 2 2 1 1 1 2 2 Sample Output 3 31 | 37,198 |
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Counting Characters Write a program which counts and reports the number of each alphabetical letter. Ignore the case of characters. Input A sentence in English is given in several lines. Output Prints the number of alphabetical letters in the following format: a : The number of 'a' b : The number of 'b' c : The number of 'c' . . z : The number of 'z' Constraints The number of characters in the sentence < 1200 Sample Input This is a pen. Sample Output a : 1 b : 0 c : 0 d : 0 e : 1 f : 0 g : 0 h : 1 i : 2 j : 0 k : 0 l : 0 m : 0 n : 1 o : 0 p : 1 q : 0 r : 0 s : 2 t : 1 u : 0 v : 0 w : 0 x : 0 y : 0 z : 0 | 37,200 |
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Score : 100 points Problem Statement Given is an integer x that is greater than or equal to 0 , and less than or equal to 1 . Output 1 if x is equal to 0 , or 0 if x is equal to 1 . Constraints 0 \leq x \leq 1 x is an integer Input Input is given from Standard Input in the following format: x Output Print 1 if x is equal to 0 , or 0 if x is equal to 1 . Sample Input 1 1 Sample Output 1 0 Sample Input 2 0 Sample Output 2 1 | 37,204 |
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¥åã¯ä»¥äžã®æ¡ä»¶ãæºããã $2 \leq n \leq 10^4$ $n-1 \leq m \leq min(\frac{n \times (n - 1)}{2}, 10^4)$ $0 \leq a_i, b_i \leq n - 1 (a_i â b_i)$ $1 \leq c_i \leq 10^6$ $0 \leq d_i \leq 10^6$ Output ãã£ããæã®æå°å€ãå®æ°ã§1è¡ã«åºåããããã ãã$10^{-5}$ãè¶
ãã誀差ãå«ãã§ã¯ãªããªãã Sample Input 1 4 5 0 2 22 13 0 3 15 25 1 2 3 3 1 3 28 5 2 3 5 22 Sample Output 1 0.36000 éä¿¡ã±ãŒãã«$0$ãšéä¿¡ã±ãŒãã«$3$ãåãé€ããšããã£ããæã¯$(\frac{13 + 5}{22 + 28}) = 0.36$ãšãªããããããã£ããæã®æå°å€ãšãªãã Sample Input 2 5 6 0 1 22 33 0 2 43 11 0 3 92 10 1 3 50 12 2 3 88 2 3 4 58 89 Sample Output 2 0.06667 Sample Input 3 2 1 0 1 1 1 Sample Output 3 0 | 37,205 |
Problem Statement Alice is a private teacher. One of her job is to prepare the learning materials for her student. Now, as part of the materials, she is drawing a Venn diagram between two sets $A$ and $B$. Venn diagram is a diagram which illustrates the relationships among one or more sets. For example, a Venn diagram between two sets $A$ and $B$ is drawn as illustrated below. The rectangle corresponds to the universal set $U$. The two circles in the rectangle correspond to two sets $A$ and $B$, respectively. The intersection of the two circles corresponds to the intersection of the two sets, i.e. $A \cap B$. Fig: Venn diagram between two sets Alice, the mathematics personified, came up with a special condition to make her Venn diagram more beautiful. Her condition is that the area of each part of her Venn diagram is equal to the number of elements in its corresponding set. In other words, one circle must have the area equal to $|A|$, the other circle must have the area equal to $|B|$, and their intersection must have the area equal to $|A \cap B|$. Here, $|X|$ denotes the number of elements in a set $X$. Alice already drew a rectangle, but has been having a trouble figuring out where to draw the rest, two circles, because she cannot even stand with a small error human would make. As an old friend of Alice's, your task is to help her by writing a program to determine the centers and radii of two circles so that they satisfy the above condition. Input The input is a sequence of datasets. The number of datasets is not more than $300$. Each dataset is formatted as follows. $U_W$ $U_H$ $|A|$ $|B|$ $|A \cap B|$ The first two integers $U_W$ and $U_H$ ($1 \le U_W, U_H \le 100$) denote the width and height of the rectangle which corresponds to the universal set $U$, respectively. The next three integers $|A|$, $|B|$ and $|A \cap B|$ ($1 \le |A|, |B| \le 10{,}000$ and $0 \le |A \cap B| \le \min\{|A|,|B|\}$) denote the numbers of elements of the set $A$, $B$ and $A \cap B$, respectively. The input is terminated by five zeroes. You may assume that, even if $U_W$ and $U_H$ would vary within $\pm 0.01$, it would not change whether you can draw two circles under the Alice's condition. Output For each dataset, output the centers and radii of the two circles that satisfy the Alice's condition as follows: $X_A$ $Y_A$ $R_A$ $X_B$ $Y_B$ $R_B$ $X_A$ and $Y_A$ are the coordinates of the center of the circle which corresponds to the set $A$. $R_A$ is the radius of the circle which corresponds to the set $A$. $X_B$, $Y_B$ and $R_B$ are the values for the set B. These values must be separated by a space. If it is impossible to satisfy the condition, output: impossible The area of each part must not have an absolute error greater than $0.0001$. Also, the two circles must stay inside the rectangle with a margin of $0.0001$ for error, or more precisely, all of the following four conditions must be satisfied: $X_A - R_A \ge -0.0001$ $X_A + R_A \le U_W + 0.0001$ $Y_A - R_A \ge -0.0001$ $Y_A + R_A \le U_H + 0.0001$ The same conditions must hold for $X_B$, $Y_B$ and $R_B$. Sample Input 10 5 1 1 0 10 5 2 2 1 10 10 70 70 20 0 0 0 0 0 Output for the Sample Input 1 1 0.564189584 3 1 0.564189584 1 1 0.797884561 1.644647246 1 0.797884561 impossible | 37,206 |
Problem G: Dice ãµã€ã³ãïŒå
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¥åã«å¯Ÿãããåãµã€ã³ãããã¹ãŠåçŽã§ãããŸã§ã®æçææ°ãæ±ããã Sample Input 1 3 3 4o. 4o. 4o. Sample Output 1 ïŒ åãµã€ã³ãã西æ¹åã«ç§»åããã°ããã Sample Input 2 4 4 4o.. .o3. .o.. .5.. Sample Output2 3 1è¡ç®ã®ã«ãããµã€ã³ãã西æ¹å 2è¡ç®ã®ã«ãããµã€ã³ããæ±æ¹å 3è¡ç®ã®ã«ãããµã€ã³ããåæ¹åã«ç§»åããã°ããã Sample Input 3 6 10 1xxxxxxxxx o.......o. xxxx.xxxx4 xoxx.xxxx. x....3xx.. x..xxxxx.. Sample Output 3 34 | 37,207 |
Score : 600 points Problem Statement You are given an integer sequence A of length N and an integer K . You will perform the following operation on this sequence Q times: Choose a contiguous subsequence of length K , then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like). Let X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible. Find the smallest possible value of X-Y when the Q operations are performed optimally. Constraints 1 \leq N \leq 2000 1 \leq K \leq N 1 \leq Q \leq N-K+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 Q A_1 A_2 ... A_N Output Print the smallest possible value of X-Y . Sample Input 1 5 3 2 4 3 1 5 2 Sample Output 1 1 In the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1 . Thus, the first operation removes A_3=1 and now we have A=(4,3,5,2) . In the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2 . In this case, the largest element removed is 2 , and the smallest is 1 , so their difference is 2-1=1 . Sample Input 2 10 1 6 1 1 2 3 5 8 13 21 34 55 Sample Output 2 7 Sample Input 3 11 7 5 24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784 Sample Output 3 451211184 | 37,208 |
Score : 100 points Problem Statement Given is a lowercase English letter C that is not z . Print the letter that follows C in alphabetical order. Constraints C is a lowercase English letter that is not z . Input Input is given from Standard Input in the following format: C Output Print the letter that follows C in alphabetical order. Sample Input 1 a Sample Output 1 b a is followed by b . Sample Input 2 y Sample Output 2 z y is followed by z . | 37,210 |
Problem B: Independent Research Problem åã¯å€äŒã¿ã®èªç±ç 究ã®ããŒããšããŠãçãç©èŠ³å¯ãéžæããçãç©èŠ³å¯ãããã賌å
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Problem D: åã®åéã¯å°ãã åã«ã¯ãããããã®åéããããã©ã®åéãããšãŠãå°ããã åã¯ãããåéãšäžç·ã«åºããããäœäººãã®åéããªã¥ãã¯ã«å
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¥ã£ãŠããåéã®çµã¿åããã¯äœéãèãããããããã®ç·æ°ã1,000,000,007 ã§å²ã£ãäœããåºåããããªã1,000,000,007 ã¯çŽ æ°ã§ããã ã誰ããªã¥ãã¯ã«å
¥ã£ãŠããªãããïŒéããšããŠæ°ããããšã«æ³šæããã Sample Input 1 4 8 1 2 7 9 Sample Output 1 2 Sample Input 2 4 25 20 15 20 15 Sample Output 2 4 Sample Input 3 6 37 5 9 13 18 26 33 Sample Output 3 6 | 37,212 |
Score : 500 points Problem Statement There is an apple tree that bears apples of N colors. The N colors of these apples are numbered 1 to N , and there are a_i apples of Color i . You and Lunlun the dachshund alternately perform the following operation (starting from you): Choose one or more apples from the tree and eat them. Here, the apples chosen at the same time must all have different colors. The one who eats the last apple from the tree will be declared winner. If both you and Lunlun play optimally, which will win? Constraints 1 \leq N \leq 10^5 1 \leq a_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 : a_N Output If you will win, print first ; if Lunlun will win, print second . Sample Input 1 2 1 2 Sample Output 1 first Let Color 1 be red, and Color 2 be blue. In this case, the tree bears one red apple and two blue apples. You should eat the red apple in your first turn. Lunlun is then forced to eat one of the blue apples, and you can win by eating the other in your next turn. Note that you are also allowed to eat two apples in your first turn, one red and one blue (not a winning move, though). Sample Input 2 3 100000 30000 20000 Sample Output 2 second | 37,213 |
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¥åäŸ4 5 0 5 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 åºåäŸ4 overfuro | 37,214 |
Problem G: Building Water Ways In ancient times, Romans constructed numerous water ways to supply water to cities and industrial sites. These water ways were amongst the greatest engineering feats of the ancient world. These water ways contributed to social infrastructures which improved people's quality of life. On the other hand, problems related to the water control and the water facilities are still interesting as a lot of games of water ways construction have been developed. Your task is to write a program which reads a map and computes the minimum possible cost of constructing water ways from sources to all the cities. As shown in Figure 1, the map is represented by H à W grid cells, where each cell represents source, city, flatland, or obstacle. You can construct only one water way from a source, but there are no limitations on the length of that water way and it can provide water to any number of cities located on its path. You can not construct water ways on the obstacles. Your objective is to bring water to all the city and minimize the number of cells which represent water ways. In the Figure 1, water ways are constructed in 14 cells which is the minimum cost. The water ways must satisfy the following conditions: a water way cell is adjacent to at most 2 water way cells in four cardinal points. a source cell is adjacent to at most 1 water way cell in four cardinal points. there is no path from a source to other sources through water ways. Input The input consists of multiple datasets. Each dataset consists of: H W H à W characters The integers H and W are the numbers of rows and columns of the map. H à W characters denote the cells which contain: ' P ': source ' * ': city ' . ': flatland ' # ': obstacle The end of input is indicated by a line containing two zeros separated by a space. Output For each dataset, print the minimum cost to construct the water ways. Constraints Judge data contains at most 60 data sets. 3 †H , W †10 1 †the number of sources, the number of cities †8 The map is surrounded by obstacles. Sources are not adjacent each other(on the left, right, top and bottom) There is a solution. Sample Input 3 8 ######## #P....*# ######## 10 10 ########## #P.......# #..#*....# #..#*.#.*# #.....#*.# #*.......# #..##....# #...#.P..# #P......P# ########## 0 0 Output for the Sample Input 5 14 | 37,215 |
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Score : 100 points Problem Statement You have N cups and 1 ball. The cups are arranged in a row, from left to right. You turned down all the cups, then inserted the ball into the leftmost cup. Then, you will perform the following Q operations: The i -th operation: swap the positions of the A_i -th and B_i -th cups from the left. If one of these cups contains the ball, the ball will also move. Since you are a magician, you can cast a magic described below: Magic: When the ball is contained in the i -th cup from the left, teleport the ball into the adjacent cup (that is, the (i-1) -th or (i+1) -th cup, if they exist). The magic can be cast before the first operation, between two operations, or after the last operation, but you are allowed to cast it at most once during the whole process. Find the number of cups with a possibility of containing the ball after all the operations and possibly casting the magic. Constraints 2 \leq N \leq 10^5 1 \leq Q \leq 10^5 1 \leq A_i < B_i \leq N Input The input is given from Standard Input in the following format: N Q A_1 B_1 A_2 B_2 : A_Q B_Q Output Print the number of cups with a possibility of eventually containing the ball. Sample Input 1 10 3 1 3 2 4 4 5 Sample Output 1 4 Sample Input 2 20 3 1 7 8 20 1 19 Sample Output 2 5 | 37,217 |
Score : 400 points Problem Statement Caracal is fighting with a monster. The health of the monster is H . Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens: If the monster's health is 1 , it drops to 0 . If the monster's health, X , is greater than 1 , that monster disappears. Then, two new monsters appear, each with the health of \lfloor X/2 \rfloor . ( \lfloor r \rfloor denotes the greatest integer not exceeding r .) Caracal wins when the healths of all existing monsters become 0 or below. Find the minimum number of attacks Caracal needs to make before winning. Constraints 1 \leq H \leq 10^{12} All values in input are integers. Input Input is given from Standard Input in the following format: H Output Find the minimum number of attacks Caracal needs to make before winning. Sample Input 1 2 Sample Output 1 3 When Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1 . Then, Caracal can attack each of these new monsters once and win with a total of three attacks. Sample Input 2 4 Sample Output 2 7 Sample Input 3 1000000000000 Sample Output 3 1099511627775 | 37,218 |
Parallel/Orthogonal For given two lines s1 and s2 , print "2" if they are parallel, "1" if they are orthogonal, or "0" otherwise. s1 crosses points p0 and p1 , and s2 crosses points p2 and p3 . Input The entire input looks like: q (the number of queries) 1st query 2nd query ... q th query Each query consists of integer coordinates of the points p0 , p1 , p2 , p3 in the following format: x p0 y p0 x p1 y p1 x p2 y p2 x p3 y p3 Output For each query, print "2", "1" or "0". Constraints 1 †q †1000 -10000 †x p i , y p i †10000 p0 â p1 and p2 â p3 . Sample Input 1 3 0 0 3 0 0 2 3 2 0 0 3 0 1 1 1 4 0 0 3 0 1 1 2 2 Sample Output 1 2 1 0 | 37,219 |
jfen H à W ã®ç€é¢ã§éã¶äžäººçšã²ãŒã ãããïŒãã®ã²ãŒã ã¯ããããã®ã»ã«ã« 0 ã 1 åã®ããŒã«ãããã®ã§ããã移åãããã²ãŒã ã§ããïŒããªãã¯ãã®ã²ãŒã ã§éãã§ãããïŒããŒã«ã¯éåžžã«äžžãããïŒã»ã«ããã»ã«ãžæ£ç¢ºã«ããŒã«ã移åãããã®ãé£ããããšã«æ°ã¥ããïŒããã§ããªãã¯ïŒåœä»€éãã«ããŒã«ãåãããŠããããããããäœãããšã«ããïŒããã§ïŒã»ã«ãè¡šãè¡šèšãšã㊠( y, x ) ãšããè¡šèšãçšããïŒãã㯠y è¡ç®ã® x åç®ã®ã»ã«ãè¡šãïŒ ãããããžã®åœä»€ã¯ 4 ã€ã®æŽæ° a, b, c, d ã§äžããããïŒãã㯠( a, b ) ã«ããããŒã«ã ( c, d ) ã«ç§»åããããšãè¡šãïŒãã®ãšãïŒ( a, b ) ã«ããŒã«ãååšãïŒ ( c, d ) ã«ããŒã«ãååšããªãããšãä¿èšŒãããïŒ ç€é¢ã®ç¶æ
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ã jfen èšæ³ã§è¡šããæåå 1 è¡ã§ããïŒåºåè¡ã«ã¯ä»ã®æåããã£ãŠã¯ãªããªãïŒ Sample Input b1/1b 1 1 1 2 b5/bbbbbb 2 4 1 4 b2b2b/7 1 4 2 4 # Output for Sample Input 1b/1b b2b2/bbb1bb b5b/3b3 1çªç®ã®å
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Score : 500 points Problem Statement There is a building with n rooms, numbered 1 to n . We can move from any room to any other room in the building. Let us call the following event a move : a person in some room i goes to another room j~ (i \neq j) . Initially, there was one person in each room in the building. After that, we know that there were exactly k moves happened up to now. We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible? Find the count modulo (10^9 + 7) . Constraints All values in input are integers. 3 \leq n \leq 2 \times 10^5 2 \leq k \leq 10^9 Input Input is given from Standard Input in the following format: n k Output Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7) . Sample Input 1 3 2 Sample Output 1 10 Let c_1 , c_2 , and c_3 be the number of people in Room 1 , 2 , and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3) : (0, 0, 3) (0, 1, 2) (0, 2, 1) (0, 3, 0) (1, 0, 2) (1, 1, 1) (1, 2, 0) (2, 0, 1) (2, 1, 0) (3, 0, 0) For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3 . Sample Input 2 200000 1000000000 Sample Output 2 607923868 Print the count modulo (10^9 + 7) . Sample Input 3 15 6 Sample Output 3 22583772 | 37,221 |
The Balance of the World The world should be finely balanced. Positive vs. negative, light vs. shadow, and left vs. right brackets. Your mission is to write a program that judges whether a string is balanced with respect to brackets so that we can observe the balance of the world. A string that will be given to the program may have two kinds of brackets, round (â( )â) and square (â[ ]â). A string is balanced if and only if the following conditions hold. For every left round bracket (â(â), there is a corresponding right round bracket (â)â) in the following part of the string. For every left square bracket (â[â), there is a corresponding right square bracket (â]â) in the following part of the string. For every right bracket, there is a left bracket corresponding to it. Correspondences of brackets have to be one to one, that is, a single bracket never corresponds to two or more brackets. For every pair of corresponding left and right brackets, the substring between them is balanced. Input The input consists of one or more lines, each of which being a dataset. A dataset is a string that consists of English alphabets, space characters, and two kinds of brackets, round (â( )â) and square (â[ ]â), terminated by a period. You can assume that every line has 100 characters or less. The line formed by a single period indicates the end of the input, which is not a dataset. Output For each dataset, output âyesâ if the string is balanced, or ânoâ otherwise, in a line. There may not be any extra characters in the output. Sample Input So when I die (the [first] I will see in (heaven) is a score list). [ first in ] ( first out ). Half Moon tonight (At least it is better than no Moon at all]. A rope may form )( a trail in a maze. Help( I[m being held prisoner in a fortune cookie factory)]. ([ (([( [ ] ) ( ) (( ))] )) ]). . . Output for the Sample Input yes yes no no no yes yes | 37,222 |
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