Split (1)

train · 2.1k rows

group_id stringlengths 12 18	problem_description stringlengths 85 3.02k	candidates listlengths 3 20
aoj_1111_cpp	Cyber Guardian In the good old days, the Internet was free from fears and terrorism. People did not have to worry about any cyber criminals or mad computer scientists. Today, however, you are facing atrocious crackers wherever you are, unless being disconnected. You have to protect yourselves against their attacks. Counting upon your excellent talent for software construction and strong sense of justice, you are invited to work as a cyber guardian. Your ultimate mission is to create a perfect firewall system that can completely shut out any intruders invading networks and protect children from harmful information exposed on the Net. However, it is extremely difficult and none have ever achieved it before. As the first step, instead, you are now requested to write a software simulator under much simpler assumptions. In general, a firewall system works at the entrance of a local network of an organization (e.g., a company or a university) and enforces its local administrative policy. It receives both inbound and outbound packets (note: data transmitted on the Net are divided into small segments called packets) and carefully inspects them one by one whether or not each of them is legal. The definition of the legality may vary from site to site or depend upon the local administrative policy of an organization. Your simulator should accept data representing not only received packets but also the local administrative policy. For simplicity in this problem we assume that each network packet consists of three fields: its source address, destination address, and message body. The source address specifies the computer or appliance that transmits the packet and the destination address specifies the computer or appliance to which the packet is transmitted. An address in your simulator is represented as eight digits such as 03214567 or 31415926, instead of using the standard notation of IP addresses such as 192.168.1.1. Administrative policy is described in filtering rules, each of which specifies some collection of source-destination address pairs and defines those packets with the specified address pairs either legal or illegal. Input The input consists of several data sets, each of which represents filtering rules and received packets in the following format: n m rule 1 rule 2 ... rule n packet 1 packet 2 ... packet m The first line consists of two non-negative integers n and m . If both n and m are zeros, this means the end of input. Otherwise, n lines, each representing a filtering rule, and m lines, each representing an arriving packet, follow in this order. You may assume that n and m are less than or equal to 1,024. Each rule i is in one of the following formats: permit source-pattern destination-pattern deny source-pattern destination-pattern A source-pattern or destination-pattern is a character string of length eight, where each character is either a digit ('0' to '9') or a wildcard character '?'. For instance, "1????5??" matches any address whos ...(truncated)	[ { "submission_id": "aoj_1111_10849586", "code_snippet": "#include<stdio.h>\n#include<string.h>\n#include<iostream>\n#include<algorithm>\n#include<queue>\n#include<vector>\n#include<cmath>\nconst int Max = 1111;\ntypedef long long LL;\nusing namespace std;\n\nint n,m,cnt;\nchar rule[3][Max][111];\nchar str [...
aoj_1127_cpp	Building a Space Station You are a member of the space station engineering team, and are assigned a task in the construction process of the station. You are expected to write a computer program to complete the task. The space station is made up with a number of units, called cells. All cells are sphere-shaped, but their sizes are not necessarily uniform. Each cell is fixed at its predetermined position shortly after the station is successfully put into its orbit. It is quite strange that two cells may be touching each other, or even may be overlapping. In an extreme case, a cell may be totally enclosing another one. I do not know how such arrangements are possible. All the cells must be connected, since crew members should be able to walk from any cell to any other cell. They can walk from a cell A to another cell B, if, (1) A and B are touching each other or overlapping, (2) A and B are connected by a `corridor', or (3) there is a cell C such that walking from A to C, and also from B to C are both possible. Note that the condition (3) should be interpreted transitively. You are expected to design a configuration, namely, which pairs of cells are to be connected with corridors. There is some freedom in the corridor configuration. For example, if there are three cells A, B and C, not touching nor overlapping each other, at least three plans are possible in order to connect all three cells. The first is to build corridors A-B and A-C, the second B-C and B-A, the third C-A and C-B. The cost of building a corridor is proportional to its length. Therefore, you should choose a plan with the shortest total length of the corridors. You can ignore the width of a corridor. A corridor is built between points on two cells' surfaces. It can be made arbitrarily long, but of course the shortest one is chosen. Even if two corridors A-B and C-D intersect in space, they are not considered to form a connection path between (for example) A and C. In other words, you may consider that two corridors never intersect. Input The input consists of multiple data sets. Each data set is given in the following format. n x 1 y 1 z 1 r 1 x 2 y 2 z 2 r 2 ... x n y n z n r n The first line of a data set contains an integer n , which is the number of cells. n is positive, and does not exceed 100. The following n lines are descriptions of cells. Four values in a line are x- , y- and z- coordinates of the center, and radius (called r in the rest of the problem) of the sphere, in this order. Each value is given by a decimal fraction, with 3 digits after the decimal point. Values are separated by a space character. Each of x , y , z and r is positive and is less than 100.0. The end of the input is indicated by a line containing a zero. Output For each data set, the shortest total length of the corridors should be printed, each in a separate line. The printed values should have 3 digits after the decimal point. They may not have an error greater than 0.001. Note that if no corridors ar ...(truncated)	[ { "submission_id": "aoj_1127_11065898", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\nusing ld = long double;\n\nstatic int bigint = 1e9;\nstatic ll biglong = 1e18;\nstatic ld eps = 1e-9;\n#define rep(i,s,n) for(int i=s;i<(int)(n);i++)\n#define sz(x) (int)(x).size()...
aoj_1133_cpp	Problem E: Water Tank Mr. Denjiro is a science teacher. Today he has just received a specially ordered water tank that will certainly be useful for his innovative experiments on water flow. Figure 1: The water tank The size of the tank is 100cm (Width) * 50cm (Height) * 30cm (Depth) (see Figure 1). For the experiments, he fits several partition boards inside of the tank parallel to the sideboards. The width of each board is equal to the depth of the tank, i.e. 30cm. The height of each board is less than that of the tank, i.e. 50 cm, and differs one another. The boards are so thin that he can neglect the thickness in the experiments. Figure 2: The front view of the tank The front view of the tank is shown in Figure 2. There are several faucets above the tank and he turns them on at the beginning of his experiment. The tank is initially empty. Your mission is to write a computer program to simulate water flow in the tank. Input The input consists of multiple data sets. D is the number of the data sets. D DataSet 1 DataSet 2 ... DataSet D The format of each data set ( DataSet d , 1 <= d <= D ) is as follows. N B 1 H 1 B 2 H 2 ... B N H N M F 1 A 1 F 2 A 2 ... F M A M L P 1 T 1 P 2 T 2 ... P L T L Each line in the data set contains one or two integers. N is the number of the boards he sets in the tank . B i and H i are the x -position (cm) and the height (cm) of the i -th board, where 1 <= i <= N . H i s differ from one another. You may assume the following. 0 < N < 10 , 0 < B 1 < B 2 < ... < B N < 100 , 0 < H 1 < 50 , 0 < H 2 < 50 , ..., 0 < H N < 50. M is the number of the faucets above the tank . F j and A j are the x -position (cm) and the amount of water flow (cm 3 /second) of the j -th faucet , where 1 <= j <= M . There is no faucet just above any boards . Namely, none of F j is equal to B i . You may assume the following . 0 < M <10 , 0 < F 1 < F 2 < ... < F M < 100 , 0 < A 1 < 100, 0 < A 2 < 100, ... 0 < A M < 100. L is the number of observation time and location. P k is the x -position (cm) of the k -th observation point. T k is the k -th observation time in seconds from the beginning. None of P k is equal to B i . You may assume the following . 0 < L < 10 , 0 < P 1 < 100, 0 < P 2 < 100, ..., 0 < P L < 100 , 0 < T 1 < 1000000, 0 < T 2 < 1000000, ... , 0 < T L < 1000000. Output For each data set, your program should output L lines each containing one real number which represents the height (cm) of the water level specified by the x -position P k at the time T k . Each answer may not have an error greater than 0.001. As long as this condition is satisfied, you may output any number of digits after the decimal point. After the water tank is filled to the brim, the water level at any P k is equal to the height of the tank, that is, 50 cm. Sample Input 2 5 15 40 35 20 50 45 70 30 80 10 3 20 3 60 2 65 2 6 40 4100 25 7500 10 18000 90 7000 25 15000 25 22000 5 15 40 35 20 50 45 70 30 80 10 2 60 4 75 1 3 60 6000 75 ...(truncated)	[ { "submission_id": "aoj_1133_9144865", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n#if __has_include(<atcoder/all>)\n#include <atcoder/all>\nusing namespace atcoder;\ntemplate<int mod>istream &operator>>(istream &is,static_modint<mod> &a){long long b;is>>b;a=b;return is;}\nistream &oper...
aoj_1130_cpp	Problem B: Red and Black There is a rectangular room, covered with square tiles. Each tile is colored either red or black. A man is standing on a black tile. From a tile, he can move to one of four adjacent tiles. But he can't move on red tiles, he can move only on black tiles. Write a program to count the number of black tiles which he can reach by repeating the moves described above. Input The input consists of multiple data sets. A data set starts with a line containing two positive integers W and H ; W and H are the numbers of tiles in the x - and y - directions, respectively. W and H are not more than 20. There are H more lines in the data set, each of which includes W characters. Each character represents the color of a tile as follows. '.' - a black tile '#' - a red tile '@' - a man on a black tile(appears exactly once in a data set) The end of the input is indicated by a line consisting of two zeros. Output For each data set, your program should output a line which contains the number of tiles he can reach from the initial tile (including itself). Sample Input 6 9 ....#. .....# ...... ...... ...... ...... ...... #@...# .#..#. 11 9 .#......... .#.#######. .#.#.....#. .#.#.###.#. .#.#..@#.#. .#.#####.#. .#.......#. .#########. ........... 11 6 ..#..#..#.. ..#..#..#.. ..#..#..### ..#..#..#@. ..#..#..#.. ..#..#..#.. 7 7 ..#.#.. ..#.#.. ###.### ...@... ###.### ..#.#.. ..#.#.. 0 0 Output for the Sample Input 45 59 6 13	[ { "submission_id": "aoj_1130_8840090", "code_snippet": "//会う時と+1のとき\n\n//いくつもとけるように\n//countの初期値直した　テストケース2つokおそらくいける　タリーズでwifi繋がらずまだ\n//69のaojテストケースでanswer45なのに1\n//隣接リストを用意→＠からbfs　-1でなかった点を数え上げる\n#include <iostream>\n#include <queue>\nusing namespace std;\n\nint bfs(int src, int n, int G[410][410]){ //src...
aoj_1136_cpp	Problem B: Polygonal Line Search Multiple polygonal lines are given on the xy -plane. Given a list of polygonal lines and a template, you must find out polygonal lines which have the same shape as the template. A polygonal line consists of several line segments parallel to x -axis or y -axis. It is defined by a list of xy -coordinates of vertices from the start-point to the end-point in order, and always turns 90 degrees at each vertex. A single polygonal line does not pass the same point twice. Two polygonal lines have the same shape when they fully overlap each other only with rotation and translation within xy -plane (i.e. without magnification or a flip). The vertices given in reverse order from the start-point to the end-point is the same as that given in order. Figure 1 shows examples of polygonal lines. In this figure, polygonal lines A and B have the same shape. Write a program that answers polygonal lines which have the same shape as the template. Figure 1: Polygonal lines Input The input consists of multiple datasets. The end of the input is indicated by a line which contains a zero. A dataset is given as follows. n Polygonal line 0 Polygonal line 1 Polygonal line 2 ... Polygonal line n n is the number of polygonal lines for the object of search on xy -plane. n is an integer, and 1 <= n <= 50. Polygonal line 0 indicates the template. A polygonal line is given as follows. m x 1 y 1 x 2 y 2 ... x m y m m is the number of the vertices of a polygonal line (3 <= m <= 10). x i and y i , separated by a space, are the x - and y -coordinates of a vertex, respectively (-10000 < x i < 10000, -10000 < y i < 10000). Output For each dataset in the input, your program should report numbers assigned to the polygonal lines that have the same shape as the template, in ascending order. Each number must be written in a separate line without any other characters such as leading or trailing spaces. Five continuous "+"s must be placed in a line at the end of each dataset. Sample Input 5 5 0 0 2 0 2 1 4 1 4 0 5 0 0 0 2 -1 2 -1 4 0 4 5 0 0 0 1 -2 1 -2 2 0 2 5 0 0 0 -1 2 -1 2 0 4 0 5 0 0 2 0 2 -1 4 -1 4 0 5 0 0 2 0 2 1 4 1 4 0 4 4 -60 -75 -60 -78 -42 -78 -42 -6 4 10 3 10 7 -4 7 -4 40 4 -74 66 -74 63 -92 63 -92 135 4 -12 22 -12 25 -30 25 -30 -47 4 12 -22 12 -25 30 -25 30 47 3 5 -8 5 -8 2 0 2 0 4 8 4 5 -3 -1 0 -1 0 7 -2 7 -2 16 5 -1 6 -1 3 7 3 7 5 16 5 5 0 1 0 -2 8 -2 8 0 17 0 0 Output for the Sample Input 1 3 5 +++++ 3 4 +++++ +++++	[ { "submission_id": "aoj_1136_2163060", "code_snippet": "#include <iostream>\n#include <string>\n#include <queue>\n#include <stack>\n#include <algorithm>\n#include <list>\n#include <vector>\n#include <complex>\n#include <utility>\n#include <cstdio>\n#include <cstdlib>\n#include <cstring>\n#include <cmath>\n#...
aoj_1134_cpp	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	[ { "submission_id": "aoj_1134_9634624", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long ll;\ntypedef long double ld;\ntypedef pair<ll,ll> pi;\n#define FOR(i,l,r) for(ll i=l;i<r;i++)\n#define REP(i,n) FOR(i,0,n)\n#define RFOR(i,l,r) for(ll i=r-1;i>=l;i--)\n#define RREP(i,n) R...
aoj_1128_cpp	Square Carpets Mr. Frugal bought a new house. He feels deeply in love with his new house because it has a comfortable living room in which he can put himself completely at ease. He thinks his new house is a really good buy. But, to his disappointment, the floor of its living room has some scratches on it. The floor has a rectangle shape, covered with square panels. He wants to replace all the scratched panels with flawless panels, but he cannot afford to do so. Then, he decides to cover all the scratched panels with carpets. The features of the carpets he can use are as follows. Carpets are square-shaped. Carpets may overlap each other. Carpets cannot be folded. Different sizes of carpets are available. Lengths of sides of carpets are multiples of that of the panels. The carpets must cover all the scratched panels, but must not cover any of the flawless ones. For example, if the scratched panels are as shown in Figure 1, at least 6 carpets are needed. Figure 1: Example Covering As carpets cost the same irrespective of their sizes, Mr. Frugal would like to use as few number of carpets as possible. Your job is to write a program which tells the minimum number of the carpets to cover all the scratched panels. Input The input consists of multiple data sets. As in the following, the end of the input is indicated by a line containing two zeros. DataSet 1 DataSet 2 ... DataSet n 0 0 Each data set ( DataSet i ) represents the state of a floor. The format of a data set is as follows. W H P 11 P 12 P 13 ... P 1 W P 21 P 22 P 23 ... P 2 W ... P H 1 P H 2 P H 3 ... P HW The positive integers W and H are the numbers of panels on the living room in the x- and y- direction, respectively. The values of W and H are no more than 10. The integer P yx represents the state of the panel. The value of P yx means, 0 : flawless panel (must not be covered), 1 : scratched panel (must be covered). Output For each data set, your program should output a line containing one integer which represents the minimum number of the carpets to cover all of the scratched panels. Sample Input 4 3 0 1 1 1 1 1 1 1 1 1 1 1 8 5 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 8 8 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 10 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 Output for the Sample Input 2 6 14 29	[ { "submission_id": "aoj_1128_6005812", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n//#define int long long\ntypedef long long ll;\nusing namespace std;\n#define inf 0x3f3f3f3f\n#define se second\n#define fi first\nconst int mx = 1E4;\nint n,m;\nint a[14][14];\nint dp[14][14];\nint vis[1...
aoj_1132_cpp	Problem D: Circle and Points You are given N points in the xy -plane. You have a circle of radius one and move it on the xy -plane, so as to enclose as many of the points as possible. Find how many points can be simultaneously enclosed at the maximum. A point is considered enclosed by a circle when it is inside or on the circle. Fig 1. Circle and Points Input The input consists of a series of data sets, followed by a single line only containing a single character '0', which indicates the end of the input. Each data set begins with a line containing an integer N , which indicates the number of points in the data set. It is followed by N lines describing the coordinates of the points. Each of the N lines has two decimal fractions X and Y , describing the x - and y -coordinates of a point, respectively. They are given with five digits after the decimal point. You may assume 1 <= N <= 300, 0.0 <= X <= 10.0, and 0.0 <= Y <= 10.0. No two points are closer than 0.0001. No two points in a data set are approximately at a distance of 2.0. More precisely, for any two points in a data set, the distance d between the two never satisfies 1.9999 <= d <= 2.0001. Finally, no three points in a data set are simultaneously very close to a single circle of radius one. More precisely, let P 1 , P 2 , and P 3 be any three points in a data set, and d 1 , d 2 , and d 3 the distances from an arbitrarily selected point in the xy -plane to each of them respectively. Then it never simultaneously holds that 0.9999 <= d i <= 1.0001 ( i = 1, 2, 3). Output For each data set, print a single line containing the maximum number of points in the data set that can be simultaneously enclosed by a circle of radius one. No other characters including leading and trailing spaces should be printed. Sample Input 3 6.47634 7.69628 5.16828 4.79915 6.69533 6.20378 6 7.15296 4.08328 6.50827 2.69466 5.91219 3.86661 5.29853 4.16097 6.10838 3.46039 6.34060 2.41599 8 7.90650 4.01746 4.10998 4.18354 4.67289 4.01887 6.33885 4.28388 4.98106 3.82728 5.12379 5.16473 7.84664 4.67693 4.02776 3.87990 20 6.65128 5.47490 6.42743 6.26189 6.35864 4.61611 6.59020 4.54228 4.43967 5.70059 4.38226 5.70536 5.50755 6.18163 7.41971 6.13668 6.71936 3.04496 5.61832 4.23857 5.99424 4.29328 5.60961 4.32998 6.82242 5.79683 5.44693 3.82724 6.70906 3.65736 7.89087 5.68000 6.23300 4.59530 5.92401 4.92329 6.24168 3.81389 6.22671 3.62210 0 Output for the Sample Input 2 5 5 11	[ { "submission_id": "aoj_1132_10853887", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\nconst int N = 300;\ntypedef complex <double> point;\npoint a[N];\ndouble kc[N][N];\ndouble x[N],y[N];\nint n;\nint quetgoc(int i,double r,int n){\n vector<pair<double,bool> > goc;\n for(int j=0;j<n;...
aoj_1135_cpp	Problem A: Ohgas' Fortune The Ohgas are a prestigious family based on Hachioji. The head of the family, Mr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune by depositing his money to an operation company. You are asked to help Mr. Ohga maximize his profit by operating the given money during a specified period. From a given list of possible operations, you choose an operation to deposit the given fund to. You commit on the single operation throughout the period and deposit all the fund to it. Each operation specifies an annual interest rate, whether the interest is simple or compound, and an annual operation charge. An annual operation charge is a constant not depending on the balance of the fund. The amount of interest is calculated at the end of every year, by multiplying the balance of the fund under operation by the annual interest rate, and then rounding off its fractional part. For compound interest, it is added to the balance of the fund under operation, and thus becomes a subject of interest for the following years. For simple interest, on the other hand, it is saved somewhere else and does not enter the balance of the fund under operation (i.e. it is not a subject of interest in the following years). An operation charge is then subtracted from the balance of the fund under operation. You may assume here that you can always pay the operation charge (i.e. the balance of the fund under operation is never less than the operation charge). The amount of money you obtain after the specified years of operation is called ``the final amount of fund.'' For simple interest, it is the sum of the balance of the fund under operation at the end of the final year, plus the amount of interest accumulated throughout the period. For compound interest, it is simply the balance of the fund under operation at the end of the final year. Operation companies use C, C++, Java, etc., to perform their calculations, so they pay a special attention to their interest rates. That is, in these companies, an interest rate is always an integral multiple of 0.0001220703125 and between 0.0001220703125 and 0.125 (inclusive). 0.0001220703125 is a decimal representation of 1/8192. Thus, interest rates' being its multiples means that they can be represented with no errors under the double-precision binary representation of floating-point numbers. For example, if you operate 1000000 JPY for five years with an annual, compound interest rate of 0.03125 (3.125 %) and an annual operation charge of 3000 JPY, the balance changes as follows. The balance of the fund under operation (at the beginning of year) Interest The balance of the fund under operation (at the end of year) A B = A × 0.03125 (and rounding off fractions) A + B - 3000 1000000 31250 1028250 1028250 32132 1057382 1057382 33043 1087425 1087425 33982 1118407 1118407 34950 1150357 After the five years of operation, the final amount of fund is 1150357 JPY. If the interest is simple with all othe ...(truncated)	[ { "submission_id": "aoj_1135_1862389", "code_snippet": "#include <iostream>\nusing namespace std;\nint main(){\n int a, moneyF, yearL, vary, i1, i2, i3, s, moneyB1, moneyB2, risi1, risi2, moneyto, max;\n double per;\n i1 = 0;\n cin >> a;\n while(1){\n i1++;\n if(i1>a){break;}\n ...
aoj_1140_cpp	Problem F: Cleaning Robot Here, we want to solve path planning for a mobile robot cleaning a rectangular room floor with furniture. Consider the room floor paved with square tiles whose size fits the cleaning robot (1 × 1). There are 'clean tiles' and 'dirty tiles', and the robot can change a 'dirty tile' to a 'clean tile' by visiting the tile. Also there may be some obstacles (furniture) whose size fits a tile in the room. If there is an obstacle on a tile, the robot cannot visit it. The robot moves to an adjacent tile with one move. The tile onto which the robot moves must be one of four tiles (i.e., east, west, north or south) adjacent to the tile where the robot is present. The robot may visit a tile twice or more. Your task is to write a program which computes the minimum number of moves for the robot to change all 'dirty tiles' to 'clean tiles', if ever possible. Input The input consists of multiple maps, each representing the size and arrangement of the room. A map is given in the following format. w h c 11 c 12 c 13 ... c 1 w c 21 c 22 c 23 ... c 2 w ... c h 1 c h 2 c h 3 ... c hw The integers w and h are the lengths of the two sides of the floor of the room in terms of widths of floor tiles. w and h are less than or equal to 20. The character c yx represents what is initially on the tile with coordinates ( x, y ) as follows. ' . ' : a clean tile ' * ' : a dirty tile ' x ' : a piece of furniture (obstacle) ' o ' : the robot (initial position) In the map the number of 'dirty tiles' does not exceed 10. There is only one 'robot'. The end of the input is indicated by a line containing two zeros. Output For each map, your program should output a line containing the minimum number of moves. If the map includes 'dirty tiles' which the robot cannot reach, your program should output -1. Sample Input 7 5 ....... .o.... ....... ..... ....... 15 13 .......x....... ...o...x...... .......x....... .......x....... .......x....... ............... xxxxx.....xxxxx ............... .......x....... .......x....... .......x....... ......x...... .......x....... 10 10 .......... ..o....... .......... .......... .......... .....xxxxx .....x.... .....x.*.. .....x.... .....x.... 0 0 Output for the Sample Input 8 49 -1	[ { "submission_id": "aoj_1140_10851274", "code_snippet": "// clang-format off\n//#pragma GCC optimize(\"Ofast\")\n//#pragma GCC target(\"avx\")\n#include <bits/stdc++.h>\nusing namespace std;\n#define int long long\n#define stoi stoll\n#define Endl endl\n#define itn int\n#define fi first\n#define se second\n...
aoj_1142_cpp	Problem B: Organize Your Train part II RJ Freight, a Japanese railroad company for freight operations has recently constructed exchange lines at Hazawa, Yokohama. The layout of the lines is shown in Figure B-1. Figure B-1: Layout of the exchange lines A freight train consists of 2 to 72 freight cars. There are 26 types of freight cars, which are denoted by 26 lowercase letters from "a" to "z". The cars of the same type are indistinguishable from each other, and each car's direction doesn't matter either. Thus, a string of lowercase letters of length 2 to 72 is sufficient to completely express the configuration of a train. Upon arrival at the exchange lines, a train is divided into two sub-trains at an arbitrary position (prior to entering the storage lines). Each of the sub-trains may have its direction reversed (using the reversal line). Finally, the two sub-trains are connected in either order to form the final configuration. Note that the reversal operation is optional for each of the sub-trains. For example, if the arrival configuration is "abcd", the train is split into two sub-trains of either 3:1, 2:2 or 1:3 cars. For each of the splitting, possible final configurations are as follows ("+" indicates final concatenation position): [3:1] abc+d cba+d d+abc d+cba [2:2] ab+cd ab+dc ba+cd ba+dc cd+ab cd+ba dc+ab dc+ba [1:3] a+bcd a+dcb bcd+a dcb+a Excluding duplicates, 12 distinct configurations are possible. Given an arrival configuration, answer the number of distinct configurations which can be constructed using the exchange lines described above. Input The entire input looks like the following. the number of datasets = m 1st dataset 2nd dataset ... m-th dataset Each dataset represents an arriving train, and is a string of 2 to 72 lowercase letters in an input line. Output For each dataset, output the number of possible train configurations in a line. No other characters should appear in the output. Sample Input 4 aa abba abcd abcde Output for the Sample Input 1 6 12 18	[ { "submission_id": "aoj_1142_10999336", "code_snippet": "#include <iostream>\n#include <algorithm>\n#include <string>\n#include <set>\nusing namespace std;\n\nint main() {\n int N;\n cin >> N;\n for (int i=0; i<N; ++i) {\n string word;\n set<string> S;\n cin >> word;\n f...
aoj_1131_cpp	Problem C: Unit Fraction Partition A fraction whose numerator is 1 and whose denominator is a positive integer is called a unit fraction. A representation of a positive rational number p / q as the sum of finitely many unit fractions is called a partition of p / q into unit fractions. For example, 1/2 + 1/6 is a partition of 2/3 into unit fractions. The difference in the order of addition is disregarded. For example, we do not distinguish 1/6 + 1/2 from 1/2 + 1/6. For given four positive integers p , q , a , and n , count the number of partitions of p / q into unit fractions satisfying the following two conditions. The partition is the sum of at most n many unit fractions. The product of the denominators of the unit fractions in the partition is less than or equal to a . For example, if ( p , q , a , n ) = (2,3,120,3), you should report 4 since enumerates all of the valid partitions. Input The input is a sequence of at most 1000 data sets followed by a terminator. A data set is a line containing four positive integers p , q , a , and n satisfying p , q <= 800, a <= 12000 and n <= 7. The integers are separated by a space. The terminator is composed of just one line which contains four zeros separated by a space. It is not a part of the input data but a mark for the end of the input. Output The output should be composed of lines each of which contains a single integer. No other characters should appear in the output. The output integer corresponding to a data set p , q , a , n should be the number of all partitions of p / q into at most n many unit fractions such that the product of the denominators of the unit fractions is less than or equal to a . Sample Input 2 3 120 3 2 3 300 3 2 3 299 3 2 3 12 3 2 3 12000 7 54 795 12000 7 2 3 300 1 2 1 200 5 2 4 54 2 0 0 0 0 Output for the Sample Input 4 7 6 2 42 1 0 9 3	[ { "submission_id": "aoj_1131_10848172", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\n\nint n, a;\n\nint gcd(int a, int b) {\n\tif (a%b == 0) {\n\t\treturn b;\n\t} else {\n\t\treturn gcd(b, a % b);\n\t}\n}\n\nint dfs(int p, int q, int m, int prod, int c) {\n\t// if (...
aoj_1139_cpp	Problem E: Earth Observation with a Mobile Robot Team A new type of mobile robot has been developed for environmental earth observation. It moves around on the ground, acquiring and recording various sorts of observational data using high precision sensors. Robots of this type have short range wireless communication devices and can exchange observational data with ones nearby. They also have large capacity memory units, on which they record data observed by themselves and those received from others. Figure 1 illustrates the current positions of three robots A, B, and C and the geographic coverage of their wireless devices. Each circle represents the wireless coverage of a robot, with its center representing the position of the robot. In this figure, two robots A and B are in the positions where A can transmit data to B, and vice versa. In contrast, C cannot communicate with A or B, since it is too remote from them. Still, however, once B moves towards C as in Figure 2, B and C can start communicating with each other. In this manner, B can relay observational data from A to C. Figure 3 shows another example, in which data propagate among several robots instantaneously. Figure 1: The initial configuration of three robots Figure 2: Mobile relaying Figure 3: Instantaneous relaying among multiple robots As you may notice from these examples, if a team of robots move properly, observational data quickly spread over a large number of them. Your mission is to write a program that simulates how information spreads among robots. Suppose that, regardless of data size, the time necessary for communication is negligible. Input The input consists of multiple datasets, each in the following format. N T R nickname and travel route of the first robot nickname and travel route of the second robot ... nickname and travel route of the N-th robot The first line contains three integers N , T , and R that are the number of robots, the length of the simulation period, and the maximum distance wireless signals can reach, respectively, and satisfy that 1 <= N <= 100, 1 <= T <= 1000, and 1 <= R <= 10. The nickname and travel route of each robot are given in the following format. nickname t 0 x 0 y 0 t 1 vx 1 vy 1 t 2 vx 2 vy 2 ... t k vx k vy k Nickname is a character string of length between one and eight that only contains lowercase letters. No two robots in a dataset may have the same nickname. Each of the lines following nickname contains three integers, satisfying the following conditions. 0 = t 0 < t 1 < ... < t k = T -10 <= vx 1 , vy 1 , ..., vx k , vy k <= 10 A robot moves around on a two dimensional plane. ( x 0 , y 0 ) is the location of the robot at time 0. From time t i -1 to t i (0 < i <= k ), the velocities in the x and y directions are vx i and vy i , respectively. Therefore, the travel route of a robot is piecewise linear. Note that it may self-overlap or self-intersect. You may assume that each dataset satisfies the following conditions. The distance bet ...(truncated)	[ { "submission_id": "aoj_1139_9672115", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long ll;\ntypedef vector<ll> vi;\ntypedef vector<vi> vvi;\ntypedef long double ld;\ntypedef pair<ll,ll> pi;\n#define FOR(i,l,r) for(ll i=l;i<r;i++)\n#define REP(i,n) FOR(i,0,n)\n#define ALL(A)...
aoj_1141_cpp	Problem A: Dirichlet's Theorem on Arithmetic Progressions Good evening, contestants. If a and d are relatively prime positive integers, the arithmetic sequence beginning with a and increasing by d , i.e., a , a + d , a + 2 d , a + 3 d , a + 4 d , ..., contains infinitely many prime numbers. This fact is known as Dirichlet's Theorem on Arithmetic Progressions, which had been conjectured by Johann Carl Friedrich Gauss (1777 - 1855) and was proved by Johann Peter Gustav Lejeune Dirichlet (1805 - 1859) in 1837. For example, the arithmetic sequence beginning with 2 and increasing by 3, i.e., 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, ... , contains infinitely many prime numbers 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, ... . Your mission, should you decide to accept it, is to write a program to find the n th prime number in this arithmetic sequence for given positive integers a , d , and n . As always, should you or any of your team be tired or confused, the secretary disavow any knowledge of your actions. This judge system will self-terminate in three hours. Good luck! Input The input is a sequence of datasets. A dataset is a line containing three positive integers a , d , and n separated by a space. a and d are relatively prime. You may assume a <= 9307, d <= 346, and n <= 210. The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset. Output The output should be composed of as many lines as the number of the input datasets. Each line should contain a single integer and should never contain extra characters. The output integer corresponding to a dataset a , d , n should be the n th prime number among those contained in the arithmetic sequence beginning with a and increasing by d . FYI, it is known that the result is always less than 10 6 (one million) under this input condition. Sample Input 367 186 151 179 10 203 271 37 39 103 230 1 27 104 185 253 50 85 1 1 1 9075 337 210 307 24 79 331 221 177 259 170 40 269 58 102 0 0 0 Output for the Sample Input 92809 6709 12037 103 93523 14503 2 899429 5107 412717 22699 25673	[ { "submission_id": "aoj_1141_10849693", "code_snippet": "#include<stdio.h>\n#include<math.h>\n\nint isprime(int m){\n if(m<2)\n return 0;\n for(int i=2;i<=(int)sqrt(m);i++){\n if(0==m%i)\n return 0;\n }\n return 1;\n}\n\nint main(){\n int a,b,c;\n while(scanf(\"%d%...
aoj_1138_cpp	Problem D: Traveling by Stagecoach Once upon a time, there was a traveler. He plans to travel using stagecoaches (horse wagons). His starting point and destination are fixed, but he cannot determine his route. Your job in this problem is to write a program which determines the route for him. There are several cities in the country, and a road network connecting them. If there is a road between two cities, one can travel by a stagecoach from one of them to the other. A coach ticket is needed for a coach ride. The number of horses is specified in each of the tickets. Of course, with more horses, the coach runs faster. At the starting point, the traveler has a number of coach tickets. By considering these tickets and the information on the road network, you should find the best possible route that takes him to the destination in the shortest time. The usage of coach tickets should be taken into account. The following conditions are assumed. A coach ride takes the traveler from one city to another directly connected by a road. In other words, on each arrival to a city, he must change the coach. Only one ticket can be used for a coach ride between two cities directly connected by a road. Each ticket can be used only once. The time needed for a coach ride is the distance between two cities divided by the number of horses. The time needed for the coach change should be ignored. Input The input consists of multiple datasets, each in the following format. The last dataset is followed by a line containing five zeros (separated by a space). n m p a b t 1 t 2 ... t n x 1 y 1 z 1 x 2 y 2 z 2 ... x p y p z p Every input item in a dataset is a non-negative integer. If a line contains two or more input items, they are separated by a space. n is the number of coach tickets. You can assume that the number of tickets is between 1 and 8. m is the number of cities in the network. You can assume that the number of cities is between 2 and 30. p is the number of roads between cities, which may be zero. a is the city index of the starting city. b is the city index of the destination city. a is not equal to b . You can assume that all city indices in a dataset (including the above two) are between 1 and m . The second line of a dataset gives the details of coach tickets. t i is the number of horses specified in the i -th coach ticket (1<= i <= n ). You can assume that the number of horses is between 1 and 10. The following p lines give the details of roads between cities. The i -th road connects two cities with city indices x i and y i , and has a distance z i (1<= i <= p ). You can assume that the distance is between 1 and 100. No two roads connect the same pair of cities. A road never connects a city with itself. Each road can be traveled in both directions. Output For each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces. If the traveler can reach the destination, the time needed for ...(truncated)	[ { "submission_id": "aoj_1138_10865848", "code_snippet": "#include <iostream>\n#include <algorithm>\n#include <cmath>\n#include <cstdio>\n#include <cstdlib>\n#include <cstring>\nusing namespace std;\n\nconst int INF = 0x3f3f3f3f;\nconst int MAX_N = 8;\nconst int MAX_M = 30;\n\nint N, M, P, A, B;\n\nint t[MAX...
aoj_1143_cpp	Problem C: Hexerpents of Hexwamp Hexwamp is a strange swamp, paved with regular hexagonal dimples. Hexerpents crawling in this area are serpents adapted to the environment, consisting of a chain of regular hexagonal sections. Each section fits in one dimple. Hexerpents crawl moving some of their sections from the dimples they are in to adjacent ones. To avoid breaking their bodies, sections that are adjacent to each other before the move should also be adjacent after the move. When one section moves, sections adjacent to it support the move, and thus they cannot move at that time. Any number of sections, as far as no two of them are adjacent to each other, can move at the same time. You can easily find that a hexerpent can move its sections at its either end to only up to two dimples, and can move intermediate sections to only one dimple, if any. For example, without any obstacles, a hexerpent can crawl forward twisting its body as shown in Figure C-1, left to right. In this figure, the serpent moves four of its eight sections at a time, and moves its body forward by one dimple unit after four steps of moves. Actually, they are much better in crawling sideways, like sidewinders. Figure C-1: Crawling forward Their skin is so sticky that if two sections of a serpent that are not originally adjacent come to adjacent dimples (Figure C-2), they will stick together and the serpent cannot but die. Two sections cannot fit in one dimple, of course. This restricts serpents' moves further. Sometimes, they have to make some efforts to get a food piece even when it is in the dimple next to their head. Figure C-2: Fatal case Hexwamp has rocks here and there. Each rock fits in a dimple. Hexerpents' skin does not stick to rocks, but they cannot crawl over the rocks. Although avoiding dimples with rocks restricts their moves, they know the geography so well that they can plan the fastest paths. You are appointed to take the responsibility of the head of the scientist team to carry out academic research on this swamp and the serpents. You are expected to accomplish the research, but never at the sacrifice of any casualty. Your task now is to estimate how soon a man-eating hexerpent may move its head (the first section) to the position of a scientist in the swamp. Their body sections except for the head are quite harmless and the scientist wearing high-tech anti-sticking suit can stay in the same dimple with a body section of the hexerpent. Input The input is a sequence of several datasets, and the end of the input is indicated by a line containing a single zero. The number of datasets never exceeds 10. Each dataset looks like the following. the number of sections the serpent has (= n ) x 1 y 1 x 2 y 2 ... x n y n the number of rocks the swamp has (=k) u 1 v 1 u 2 v 2 ... u k v k X Y The first line of the dataset has an integer n that indicates the number of sections the hexerpent has, which is 2 or greater and never exceeds 8. Each of the n followi ...(truncated)	[ { "submission_id": "aoj_1143_10476119", "code_snippet": "// AOJ #1143 Hexerpents of Hexwamp\n// 2025.5.12\n\n#include <bits/stdc++.h>\nusing namespace std;\nusing pii = pair<int,int>;\n\n#define gc() getchar_unlocked()\n#define pc(c) putchar_unlocked(c)\n\nint Cin() {\n\tint n = 0; int c = gc();\n\tif (c ==...
aoj_1149_cpp	Problem C: Cut the Cake Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest pâtissiers in the world. Those who are invited to his birthday party are gourmets from around the world. They are eager to see and eat his extremely creative cakes. Now a large box-shaped cake is being carried into the party. It is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination. Let us cut it into pieces with a knife and serve them to the guests attending the party. The cake looks rectangular, viewing from above (Figure C-1). As exemplified in Figure C-2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces. Each cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face. So, every piece shall be rectangular looking from above and every side face vertical. Figure C-1: The top view of the cake Figure C-2: Cutting the cake into pieces Piece sizes in Figure C-2 vary significantly and it may look unfair, but you don't have to worry. Those guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces. Of course, some prefer larger ones. Your mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece. Input The input is a sequence of datasets, each of which is of the following format. n w d p 1 s 1 ... p n s n The first line starts with an integer n that is between 0 and 100 inclusive. It is the number of cuts to be performed. The following w and d in the same line are integers between 1 and 100 inclusive. They denote the width and depth of the cake, respectively. Assume in the sequel that the cake is placed so that w and d are the lengths in the east-west and north-south directions, respectively. Each of the following n lines specifies a single cut, cutting one and only one piece into two. p i is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the i -th cut. Note that, just before the i -th cut, there exist exactly i pieces. Each piece in this stage has a unique identification number that is one of 1, 2, ..., i and is defined as follows: The earlier a piece was born, the smaller its identification number is. Of the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number. If their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer. Note that identification numbers are adjusted after each cut. s i is an integer between 1 and 1000 inclusive and specifies the starting point of the i -th cut. From the northwest corner of the piece whose identification number is p i , you can reach the starting point by traveling s i in the clockwise direction around the piece. You may as ...(truncated)	[ { "submission_id": "aoj_1149_9370376", "code_snippet": "#include <bits/stdc++.h>\n#define rep(i, n) for (int i = 0; i < (int)(n); i++)\n#define all(x) (x).begin(),(x).end()\n#define eb emplace_back\nusing namespace std;\nusing ll = long long;\nusing ld = long double;\nusing vl = vector<long long>;\nusing vv...
aoj_1151_cpp	Problem E: Twirl Around Let's think about a bar rotating clockwise as if it were a twirling baton moving on a planar surface surrounded by a polygonal wall (see Figure 1). Figure 1. A bar rotating in a polygon Initially, an end of the bar (called "end A") is at (0,0), and the other end (called "end B") is at (0, L ) where L is the length of the bar. Initially, the bar is touching the wall only at the end A. The bar turns fixing a touching point as the center. The center changes as a new point touches the wall. Your task is to calculate the coordinates of the end A when the bar has fully turned by the given count R . Figure 2. Examples of turning bars In Figure 2, some examples are shown. In cases (D) and (E), the bar is stuck prematurely (cannot rotate clockwise anymore with any point touching the wall as the center) before R rotations. In such cases, you should answer the coordinates of the end A in that (stuck) position. You can assume the following: When the bar's length L changes by ε (\|ε\| < 0.00001), the final ( x , y ) coordinates will not change more than 0.0005. Input The input consists of multiple datasets. The number of datasets is no more than 100. The end of the input is represented by "0 0 0". The format of each dataset is as follows: L R N X 1 Y 1 X 2 Y 2 ... X N Y N L is the length of the bar. The bar rotates 2π× R radians (if it is not stuck prematurely). N is the number of vertices which make the polygon. The vertices of the polygon are arranged in a counter-clockwise order. You may assume that the polygon is simple , that is, its border never crosses or touches itself. N , X i and Y i are integer numbers; R and L are decimal fractions. Ranges of those values are as follows: 1.0 ≤ L ≤ 500.0, 1.0 ≤ R ≤ 10.0, 3 ≤ N ≤ 100, -1000 ≤ X i ≤ 1000, -1000 ≤ Y i ≤ 1000, X 1 ≤ -1, Y 1 = 0, X 2 ≥ 1, Y 2 = 0. Output For each dataset, print one line containing x- and y- coordinates of the final position of the end A, separated by a space. The value may contain an error less than or equal to 0.001. You may print any number of digits after the decimal point. Sample Input 4.0 2.0 8 -1 0 5 0 5 -2 7 -2 7 0 18 0 18 6 -1 6 4.0 2.0 4 -1 0 10 0 10 12 -1 12 4.0 1.0 7 -1 0 2 0 -1 -3 -1 -8 6 -8 6 6 -1 6 4.0 2.0 6 -1 0 10 0 10 3 7 3 7 5 -1 5 5.0 2.0 6 -1 0 2 0 2 -4 6 -4 6 6 -1 6 6.0 1.0 8 -1 0 8 0 7 2 9 2 8 4 11 4 11 12 -1 12 0 0 0 Output for the Sample Input 16.0 0.0 9.999999999999998 7.4641016151377535 0.585786437626906 -5.414213562373095 8.0 0.0 6.0 0.0 9.52786404500042 4.0 Note that the above sample input corresponds to the cases in Figure 2. For convenience, in Figure 3, we will show an animation and corresponding photographic playback for the case (C). Figure 3. Animation and photographic playback for case (C)	[ { "submission_id": "aoj_1151_1380113", "code_snippet": "#include<cstdio>\n#include<cmath>\n#include<utility>\n#include<vector>\n#include<complex>\n#include<iostream>\n#include<algorithm>\n \nusing namespace std;\n \ntypedef long double Real;\ntypedef complex<Real> Point;\ntypedef complex<Real> Vector;\nty...
aoj_1145_cpp	Problem E: The Genome Database of All Space Life In 2300, the Life Science Division of Federal Republic of Space starts a very ambitious project to complete the genome sequencing of all living creatures in the entire universe and develop the genomic database of all space life. Thanks to scientific research over many years, it has been known that the genome of any species consists of at most 26 kinds of molecules, denoted by English capital letters ( i.e. A to Z ). What will be stored into the database are plain strings consisting of English capital letters. In general, however, the genome sequences of space life include frequent repetitions and can be awfully long. So, for efficient utilization of storage, we compress N -times repetitions of a letter sequence seq into N ( seq ) , where N is a natural number greater than or equal to two and the length of seq is at least one. When seq consists of just one letter c , we may omit parentheses and write Nc . For example, a fragment of a genome sequence: ABABABABXYXYXYABABABABXYXYXYCCCCCCCCCC can be compressed into: 4(AB)XYXYXYABABABABXYXYXYCCCCCCCCCC by replacing the first occurrence of ABABABAB with its compressed form. Similarly, by replacing the following repetitions of XY , AB , and C , we get: 4(AB)3(XY)4(AB)3(XY)10C Since C is a single letter, parentheses are omitted in this compressed representation. Finally, we have: 2(4(AB)3(XY))10C by compressing the repetitions of 4(AB)3(XY) . As you may notice from this example, parentheses can be nested. Your mission is to write a program that uncompress compressed genome sequences. Input The input consists of multiple lines, each of which contains a character string s and an integer i separated by a single space. The character string s , in the aforementioned manner, represents a genome sequence. You may assume that the length of s is between 1 and 100, inclusive. However, of course, the genome sequence represented by s may be much, much, and much longer than 100. You may also assume that each natural number in s representing the number of repetitions is at most 1,000. The integer i is at least zero and at most one million. A line containing two zeros separated by a space follows the last input line and indicates the end of the input. Output For each input line, your program should print a line containing the i -th letter in the genome sequence that s represents. If the genome sequence is too short to have the i -th element, it should just print a zero. No other characters should be printed in the output lines. Note that in this problem the index number begins from zero rather than one and therefore the initial letter of a sequence is its zeroth element. Sample Input ABC 3 ABC 0 2(4(AB)3(XY))10C 30 1000(1000(1000(1000(1000(1000(NM)))))) 999999 0 0 Output for the Sample Input 0 A C M	[ { "submission_id": "aoj_1145_10852720", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\n\n#define REP(i, n) for (int i = 0; i < (n); i++)\n#define int long long\n#define FOR(i, m, n) for (int i = (m); i < (n); i++)\n#define all(x) x.begin(), x.end()\nusing pii = pair<int, int>;\nconstexpr...
aoj_1144_cpp	Problem D: Curling 2.0 On Planet MM-21, after their Olympic games this year, curling is getting popular. But the rules are somewhat different from ours. The game is played on an ice game board on which a square mesh is marked. They use only a single stone. The purpose of the game is to lead the stone from the start to the goal with the minimum number of moves. Fig. D-1 shows an example of a game board. Some squares may be occupied with blocks. There are two special squares namely the start and the goal, which are not occupied with blocks. (These two squares are distinct.) Once the stone begins to move, it will proceed until it hits a block. In order to bring the stone to the goal, you may have to stop the stone by hitting it against a block, and throw again. Fig. D-1: Example of board (S: start, G: goal) The movement of the stone obeys the following rules: At the beginning, the stone stands still at the start square. The movements of the stone are restricted to x and y directions. Diagonal moves are prohibited. When the stone stands still, you can make it moving by throwing it. You may throw it to any direction unless it is blocked immediately(Fig. D-2(a)). Once thrown, the stone keeps moving to the same direction until one of the following occurs: The stone hits a block (Fig. D-2(b), (c)). The stone stops at the square next to the block it hit. The block disappears. The stone gets out of the board. The game ends in failure. The stone reaches the goal square. The stone stops there and the game ends in success. You cannot throw the stone more than 10 times in a game. If the stone does not reach the goal in 10 moves, the game ends in failure. Fig. D-2: Stone movements Under the rules, we would like to know whether the stone at the start can reach the goal and, if yes, the minimum number of moves required. With the initial configuration shown in Fig. D-1, 4 moves are required to bring the stone from the start to the goal. The route is shown in Fig. D-3(a). Notice when the stone reaches the goal, the board configuration has changed as in Fig. D-3(b). Fig. D-3: The solution for Fig. D-1 and the final board configuration Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets never exceeds 100. Each dataset is formatted as follows. the width(=w) and the height(=h) of the board First row of the board ... h-th row of the board The width and the height of the board satisfy: 2 <= w <= 20, 1 <= h <= 20. Each line consists of w decimal numbers delimited by a space. The number describes the status of the corresponding square. 0 vacant square 1 block 2 start position 3 goal position The dataset for Fig. D-1 is as follows: 6 6 1 0 0 2 1 0 1 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 Output For each dataset, print a line having a decimal integer indicating the minimum number of moves along a route from the start to the goal. If there are no such route ...(truncated)	[ { "submission_id": "aoj_1144_10883658", "code_snippet": "#include <iostream> // cout, endl, cin\n#include <string> // string, to_string, stoi\n#include <vector> // vector\n#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound\n#include <utility> // pair, make_pair\n#include <cstdio...
aoj_1155_cpp	Problem C: How can I satisfy thee? Let me count the ways... Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively. Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1. Table C-1: Truth tables of three-valued logic operators -X (XY) (X+Y) Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas). Constants: 0, 1 or 2 Variables: P, Q or R Negations: -X Conjunctions: (XY) Disjunctions: (X+Y) Note that conjunctions and disjunctions of two formulas are always parenthesized. For example, when formula (PQ) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3. Input The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, , +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF. <formula> ::= 0 \| 1 \| 2 \| P \| Q \| R \| -<formula> \| (<formula><formula>) \| (<formula>+<formula>) All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters. Finally, a line which contains only a "." (period) comes, indicating the end of the input. Output You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output. Sample Input (PQ) (--R+(PQ)) (P-P) 2 1 (-1+(((---P+Q)(--Q+---R))*(-R+-P))) . Output for the Sample Input 3 11 0 27 0 7	[ { "submission_id": "aoj_1155_4920981", "code_snippet": "#include <iostream>\n#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long ll;\nint a,b,c,ch[80],ans,A,B,C,D;\nstring s;\nint no(int n){\n if(n==0)return 2;\n if(n==1)return 1;\n return 0;\n}\nint h(int x,int y){\n if(x*y==0)retu...
aoj_1152_cpp	Problem F: Dr. Podboq or: How We Became Asymmetric After long studying how embryos of organisms become asymmetric during their development, Dr. Podboq, a famous biologist, has reached his new hypothesis. Dr. Podboq is now preparing a poster for the coming academic conference, which shows a tree representing the development process of an embryo through repeated cell divisions starting from one cell. Your job is to write a program that transforms given trees into forms satisfying some conditions so that it is easier for the audience to get the idea. A tree representing the process of cell divisions has a form described below. The starting cell is represented by a circle placed at the top. Each cell either terminates the division activity or divides into two cells. Therefore, from each circle representing a cell, there are either no branch downward, or two branches down to its two child cells. Below is an example of such a tree. Figure F-1: A tree representing a process of cell divisions According to Dr. Podboq's hypothesis, we can determine which cells have stronger or weaker asymmetricity by looking at the structure of this tree representation. First, his hypothesis defines "left-right similarity" of cells as follows: The left-right similarity of a cell that did not divide further is 0. For a cell that did divide further, we collect the partial trees starting from its child or descendant cells, and count how many kinds of structures they have. Then, the left-right similarity of the cell is defined to be the ratio of the number of structures that appear both in the right child side and the left child side. We regard two trees have the same structure if we can make them have exactly the same shape by interchanging two child cells of arbitrary cells. For example, suppose we have a tree shown below: Figure F-2: An example tree The left-right similarity of the cell A is computed as follows. First, within the descendants of the cell B, which is the left child cell of A, the following three kinds of structures appear. Notice that the rightmost structure appears three times, but when we count the number of structures, we count it only once. Figure F-3: Structures appearing within the descendants of the cell B On the other hand, within the descendants of the cell C, which is the right child cell of A, the following four kinds of structures appear. Figure F-4: Structures appearing within the descendants of the cell C Among them, the first, second, and third ones within the B side are regarded as the same structure as the second, third, and fourth ones within the C side, respectively. Therefore, there are four structures in total, and three among them are common to the left side and the right side, which means the left-right similarity of A is 3/4. Given the left-right similarity of each cell, Dr. Podboq's hypothesis says we can determine which of the cells X and Y has stronger asymmetricity by the following rules. If X and Y have different left-righ ...(truncated)	[ { "submission_id": "aoj_1152_9685131", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long ll;\ntypedef long double ld;\ntypedef pair<ll,ll> pi;\ntypedef vector<ll> vi;\n#define FOR(i,l,r) for(ll i=l;i<r;i++)\n#define REP(i,n) FOR(i,0,n)\n#define ALL(A) A.begin(),A.end()\ntempl...
aoj_1154_cpp	Problem B: Monday-Saturday Prime Factors Chief Judge's log, stardate 48642.5. We have decided to make a problem from elementary number theory. The problem looks like finding all prime factors of a positive integer, but it is not. A positive integer whose remainder divided by 7 is either 1 or 6 is called a 7 N +{1,6} number. But as it is hard to pronounce, we shall call it a Monday-Saturday number . For Monday-Saturday numbers a and b , we say a is a Monday-Saturday divisor of b if there exists a Monday-Saturday number x such that a x = b . It is easy to show that for any Monday-Saturday numbers a and b , it holds that a is a Monday-Saturday divisor of b if and only if a is a divisor of b in the usual sense. We call a Monday-Saturday number a Monday-Saturday prime if it is greater than 1 and has no Monday-Saturday divisors other than itself and 1. A Monday-Saturday number which is a prime in the usual sense is a Monday-Saturday prime but the converse does not always hold. For example, 27 is a Monday-Saturday prime although it is not a prime in the usual sense. We call a Monday-Saturday prime which is a Monday-Saturday divisor of a Monday-Saturday number a a Monday-Saturday prime factor of a . For example, 27 is one of the Monday-Saturday prime factors of 216, since 27 is a Monday-Saturday prime and 216 = 27 × 8 holds. Any Monday-Saturday number greater than 1 can be expressed as a product of one or more Monday-Saturday primes. The expression is not always unique even if differences in order are ignored. For example, 216 = 6 × 6 × 6 = 8 × 27 holds. Our contestants should write a program that outputs all Monday-Saturday prime factors of each input Monday-Saturday number. Input The input is a sequence of lines each of which contains a single Monday-Saturday number. Each Monday-Saturday number is greater than 1 and less than 300000 (three hundred thousand). The end of the input is indicated by a line containing a single digit 1. Output For each input Monday-Saturday number, it should be printed, followed by a colon `:' and the list of its Monday-Saturday prime factors on a single line. Monday-Saturday prime factors should be listed in ascending order and each should be preceded by a space. All the Monday-Saturday prime factors should be printed only once even if they divide the input Monday-Saturday number more than once. Sample Input 205920 262144 262200 279936 299998 1 Output for the Sample Input 205920: 6 8 13 15 20 22 55 99 262144: 8 262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185 279936: 6 8 27 299998: 299998	[ { "submission_id": "aoj_1154_10946380", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\n\nint next(int i) {\n return i%7 == 1 ? i+5 : i+2;\n}\n\nbool isprime(int x) {\n for(int i=6; i<x; i=next(i)) {\n if(x%i == 0) return false;\n }\n return true;\n}\n\nint main() {\n int n;\n wh...
aoj_1150_cpp	Problem D: Cliff Climbing At 17:00, special agent Jack starts to escape from the enemy camp. There is a cliff in between the camp and the nearest safety zone. Jack has to climb the almost vertical cliff by stepping his feet on the blocks that cover the cliff. The cliff has slippery blocks where Jack has to spend time to take each step. He also has to bypass some blocks that are too loose to support his weight. Your mission is to write a program that calculates the minimum time to complete climbing. Figure D-1 shows an example of cliff data that you will receive. The cliff is covered with square blocks. Jack starts cliff climbing from the ground under the cliff, by stepping his left or right foot on one of the blocks marked with 'S' at the bottom row. The numbers on the blocks are the "slippery levels". It takes t time units for him to safely put his foot on a block marked with t , where 1 ≤ t ≤ 9. He cannot put his feet on blocks marked with 'X'. He completes the climbing when he puts either of his feet on one of the blocks marked with 'T' at the top row. Figure D-1: Example of Cliff Data Jack's movement must meet the following constraints. After putting his left (or right) foot on a block, he can only move his right (or left, respectively) foot. His left foot position ( lx , ly ) and his right foot position ( rx , ry ) should satisfy lx < rx and \| lx - rx \| + \| ly - ry \| ≤ 3 . This implies that, given a position of his left foot in Figure D-2 (a), he has to place his right foot on one of the nine blocks marked with blue color. Similarly, given a position of his right foot in Figure D-2 (b), he has to place his left foot on one of the nine blocks marked with blue color. Figure D-2: Possible Placements of Feet Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset is formatted as follows: w h s(1,1) ... s(1,w) s(2,1) ... s(2,w) ... s(h,1) ... s(h,w) The integers w and h are the width and the height of the matrix data of the cliff. You may assume 2 ≤ w ≤ 30 and 5 ≤ h ≤ 60. Each of the following h lines consists of w characters delimited by a space. The character s(y, x) represents the state of the block at position ( x , y ) as follows: 'S': Jack can start cliff climbing from this block. 'T': Jack finishes climbing when he reaches this block. 'X': Jack cannot put his feet on this block. '1' - '9' ( = t ): Jack has to spend t time units to put either of his feet on this block. You can assume that it takes no time to put a foot on a block marked with 'S' or 'T'. Output For each dataset, print a line only having a decimal integer indicating the minimum time required for the cliff climbing, when Jack can complete it. Otherwise, print a line only having "-1" for the dataset. Each line should not have any characters other than these numbers. Sample Input 6 6 4 4 X X T T 4 7 8 2 X 7 3 X X X 1 8 1 2 X X X 6 1 1 2 4 4 7 S S 2 3 X X 2 10 T 1 1 X 1 X 1 X 1 1 1 X 1 ...(truncated)	[ { "submission_id": "aoj_1150_10853812", "code_snippet": "#include <iostream>\n#include <algorithm>\n#include <queue>\n#include <cstdio>\nusing namespace std;\n#define reps(i,j,k) for(int i = j ; i < k ; ++i)\n#define rep(i,j) reps(i,0,j)\n\n\nconst int ldx[] = {1,1,2,1,2,3,1,2,1};\nconst int ldy[] = {2,1,1,...
aoj_1148_cpp	Problem B: Analyzing Login/Logout Records You have a computer literacy course in your university. In the computer system, the login/logout records of all PCs in a day are stored in a file. Although students may use two or more PCs at a time, no one can log in to a PC which has been logged in by someone who has not logged out of that PC yet. You are asked to write a program that calculates the total time of a student that he/she used at least one PC in a given time period (probably in a laboratory class) based on the records in the file. The following are example login/logout records. The student 1 logged in to the PC 1 at 12:55 The student 2 logged in to the PC 4 at 13:00 The student 1 logged in to the PC 2 at 13:10 The student 1 logged out of the PC 2 at 13:20 The student 1 logged in to the PC 3 at 13:30 The student 1 logged out of the PC 1 at 13:40 The student 1 logged out of the PC 3 at 13:45 The student 1 logged in to the PC 1 at 14:20 The student 2 logged out of the PC 4 at 14:30 The student 1 logged out of the PC 1 at 14:40 For a query such as "Give usage of the student 1 between 13:00 and 14:30", your program should answer "55 minutes", that is, the sum of 45 minutes from 13:00 to 13:45 and 10 minutes from 14:20 to 14:30, as depicted in the following figure. Input The input is a sequence of a number of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets never exceeds 10. Each dataset is formatted as follows. N M r record 1 ... record r q query 1 ... query q The numbers N and M in the first line are the numbers of PCs and the students, respectively. r is the number of records. q is the number of queries. These four are integers satisfying the following. 1 ≤ N ≤ 1000, 1 ≤ M ≤ 10000, 2 ≤ r ≤ 1000, 1 ≤ q ≤ 50 Each record consists of four integers, delimited by a space, as follows. t n m s s is 0 or 1. If s is 1, this line means that the student m logged in to the PC n at time t . If s is 0, it means that the student m logged out of the PC n at time t . The time is expressed as elapsed minutes from 0:00 of the day. t , n and m satisfy the following. 540 ≤ t ≤ 1260, 1 ≤ n ≤ N , 1 ≤ m ≤ M You may assume the following about the records. Records are stored in ascending order of time t. No two records for the same PC has the same time t. No PCs are being logged in before the time of the first record nor after that of the last record in the file. Login and logout records for one PC appear alternatingly, and each of the login-logout record pairs is for the same student. Each query consists of three integers delimited by a space, as follows. t s t e m It represents "Usage of the student m between t s and t e ". t s , t e and m satisfy the following. 540 ≤ t s < t e ≤ 1260, 1 ≤ m ≤ M Output For each query, print a line having a decimal integer indicating the time of usage in minutes. Output lines should not have any character other than this number. Sample Input 4 2 10 775 1 1 1 7 ...(truncated)	[ { "submission_id": "aoj_1148_10848565", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\n\nint main(){\n\tint N,M;\n\tint r;\n\twhile( cin >> N >> M && N ){\n\t\tcin >> r;\n\t\tvector<int> imos[M];\n\t\tfor(int i = 0 ; i < M ; i++) imos[i].resize(60*24+1);\n\t\tfor(int i = 0 ; i < r ; i++)...
aoj_1160_cpp	Problem B: How Many Islands? You are given a marine area map that is a mesh of squares, each representing either a land or sea area. Figure B-1 is an example of a map. Figure B-1: A marine area map You can walk from a square land area to another if they are horizontally, vertically, or diagonally adjacent to each other on the map. Two areas are on the same island if and only if you can walk from one to the other possibly through other land areas. The marine area on the map is surrounded by the sea and therefore you cannot go outside of the area on foot. You are requested to write a program that reads the map and counts the number of islands on it. For instance, the map in Figure B-1 includes three islands. Input The input consists of a series of datasets, each being in the following format. w h c 1,1 c 1,2 ... c 1, w c 2,1 c 2,2 ... c 2, w ... c h ,1 c h ,2 ... c h , w w and h are positive integers no more than 50 that represent the width and the height of the given map, respectively. In other words, the map consists of w × h squares of the same size. w and h are separated by a single space. c i , j is either 0 or 1 and delimited by a single space. If c i , j = 0, the square that is the i -th from the left and j -th from the top on the map represents a sea area. Otherwise, that is, if c i , j = 1, it represents a land area. The end of the input is indicated by a line containing two zeros separated by a single space. Output For each dataset, output the number of the islands in a line. No extra characters should occur in the output. Sample Input 1 1 0 2 2 0 1 1 0 3 2 1 1 1 1 1 1 5 4 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 5 4 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 5 5 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 Output for the Sample Input 0 1 1 3 1 9	[ { "submission_id": "aoj_1160_11039024", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\nusing ll = long long;\n#define rep(i, n) for (int i = 0; i < (n); ++i)\n\nvector<int> dh = {1, 0, -1, 0, 1, 1, -1, -1};\nvector<int> dw = {0, 1, 0, -1, 1, -1, 1, -1};\n\nbool isInside(int h, int w, vec...
aoj_1146_cpp	Problem F Secrets in Shadows Long long ago, there were several identical columns (or cylinders) built vertically in a big open space near Yokohama (Fig. F-1). In the daytime, the shadows of the columns were moving on the ground as the sun moves in the sky. Each column was very tall so that its shadow was very long. The top view of the shadows is shown in Fig. F-2. The directions of the sun that minimizes and maximizes the widths of the shadows of the columns were said to give the important keys to the secrets of ancient treasures. Fig. F-1: Columns (or cylinders) Gig. F-2: Top view of the columns (Fig. F-1) and their shadows The width of the shadow of each column is the same as the diameter of the base disk. But the width of the whole shadow (the union of the shadows of all the columns) alters according to the direction of the sun since the shadows of some columns may overlap those of other columns. Fig. F-3 shows the direction of the sun that minimizes the width of the whole shadow for the arrangement of columns in Fig. F-2. Fig. F-3: The direction of the sun for the minimal width of the whole shadow Fig. F-4 shows the direction of the sun that maximizes the width of the whole shadow. When the whole shadow is separated into several parts (two parts in this case), the width of the whole shadow is defined as the sum of the widths of the parts. Fig. F-4: The direction of the sun for the maximal width of the whole shadow A direction of the sun is specified by an angle θ defined in Fig. F-5. For example, the east is indicated by θ = 0, the south by θ = π /2, and the west by θ = π . You may assume that the sun rises in the east ( θ = 0) and sets in the west ( θ = π ). Your job is to write a program that, given an arrangement of columns, computes two directions θ min and θ max of the sun that give the minimal width and the maximal width of the whole shadow, respectively. The position of the center of the base disk of each column is specified by its ( x , y ) coordinates. The x -axis and y -axis are parallel to the line between the east and the west and that between the north and the south, respectively. Their positive directions indicate the east and the north, respectively. You can assume that the big open space is a plane surface. Fig. F-5: The definition of the angle of the direction of the sun There may be more than one θ min or θ max for some arrangements in general, but here, you may assume that we only consider the arrangements that have unique θ min and θ max in the range 0 ≤ θ min < π , 0 ≤ θ max < π . Input The input consists of multiple datasets, followed by the last line containing a single zero. Each dataset is formatted as follows. n x 1 y 1 x 2 y 2 ... x n y n n is the number of the columns in the big open space. It is a positive integer no more than 100. x k and y k are the values of x -coordinate and y -coordinate of the center of the base disk of the k -th column ( k =1, ..., n ). They are positive integers no more than 30. They are s ...(truncated)	[ { "submission_id": "aoj_1146_10214589", "code_snippet": "#define _CRT_SECURE_NO_WARNINGS \n#include <iostream>\n#include <algorithm>\n#include <cmath>\n#include <cstring>\n#include <cassert>\n#include <vector>\ntypedef long long ll;\ntypedef long double ld;\n//typedef double ld;\ntypedef std::vector<int> Vi...
aoj_1156_cpp	Problem D: Twirling Robot Let's play a game using a robot on a rectangular board covered with a square mesh (Figure D-1). The robot is initially set at the start square in the northwest corner facing the east direction. The goal of this game is to lead the robot to the goal square in the southeast corner. Figure D-1: Example of a board The robot can execute the following five types of commands. "Straight": Keep the current direction of the robot, and move forward to the next square. "Right": Turn right with 90 degrees from the current direction, and move forward to the next square. "Back": Turn to the reverse direction, and move forward to the next square. "Left": Turn left with 90 degrees from the current direction, and move forward to the next square. "Halt": Stop at the current square to finish the game. Each square has one of these commands assigned as shown in Figure D-2. The robot executes the command assigned to the square where it resides, unless the player gives another command to be executed instead. Each time the player gives an explicit command, the player has to pay the cost that depends on the command type. Figure D-2: Example of commands assigned to squares The robot can visit the same square several times during a game. The player loses the game when the robot goes out of the board or it executes a "Halt" command before arriving at the goal square. Your task is to write a program that calculates the minimum cost to lead the robot from the start square to the goal one. Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset is formatted as follows. w h s (1,1) ... s (1, w ) s (2,1) ... s (2, w ) ... s ( h ,1) ... s ( h , w ) c 0 c 1 c 2 c 3 The integers h and w are the numbers of rows and columns of the board, respectively. You may assume 2 ≤ h ≤ 30 and 2 ≤ w ≤ 30. Each of the following h lines consists of w numbers delimited by a space. The number s ( i , j ) represents the command assigned to the square in the i -th row and the j -th column as follows. 0: "Straight" 1: "Right" 2: "Back" 3: "Left" 4: "Halt" You can assume that a "Halt" command is assigned to the goal square. Note that "Halt" commands may be assigned to other squares, too. The last line of a dataset contains four integers c 0 , c 1 , c 2 , and c 3 , delimited by a space, indicating the costs that the player has to pay when the player gives "Straight", "Right", "Back", and "Left" commands respectively. The player cannot give "Halt" commands. You can assume that all the values of c 0 , c 1 , c 2 , and c 3 are between 1 and 9, inclusive. Output For each dataset, print a line only having a decimal integer indicating the minimum cost required to lead the robot to the goal. No other characters should be on the output line. Sample Input 8 3 0 0 0 0 0 0 0 1 2 3 0 1 4 0 0 1 3 3 0 0 0 0 0 4 9 9 1 9 4 4 3 3 4 0 1 2 4 4 1 1 1 0 0 2 4 4 8 7 2 1 2 8 2 2 4 1 0 4 1 3 1 0 2 1 0 3 1 4 ...(truncated)	[ { "submission_id": "aoj_1156_10848675", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing VS = vector<string>; using LL = long long;\nusing VI = vector<int>; using VVI = vector<VI>;\nusing PII = pair<int, int>; using PLL = pair<LL, LL>;\nusing VL = vector<LL>; using ...
aoj_1157_cpp	Problem E: Roll-A-Big-Ball ACM University holds its sports day in every July. The "Roll-A-Big-Ball" is the highlight of the day. In the game, players roll a ball on a straight course drawn on the ground. There are rectangular parallelepiped blocks on the ground as obstacles, which are fixed on the ground. During the game, the ball may not collide with any blocks. The bottom point of the ball may not leave the course. To have more fun, the university wants to use the largest possible ball for the game. You must write a program that finds the largest radius of the ball that can reach the goal without colliding any obstacle block. The ball is a perfect sphere, and the ground is a plane. Each block is a rectangular parallelepiped. The four edges of its bottom rectangle are on the ground, and parallel to either x- or y-axes. The course is given as a line segment from a start point to an end point. The ball starts with its bottom point touching the start point, and goals when its bottom point touches the end point. The positions of the ball and a block can be like in Figure E-1 (a) and (b). Figure E-1: Possible positions of the ball and a block Input The input consists of a number of datasets. Each dataset is formatted as follows. N sx sy ex ey minx 1 miny 1 maxx 1 maxy 1 h 1 minx 2 miny 2 maxx 2 maxy 2 h 2 ... minx N miny N maxx N maxy N h N A dataset begins with a line with an integer N , the number of blocks (1 ≤ N ≤ 50). The next line consists of four integers, delimited by a space, indicating the start point ( sx , sy ) and the end point ( ex , ey ). The following N lines give the placement of blocks. Each line, representing a block, consists of five integers delimited by a space. These integers indicate the two vertices ( minx , miny ), ( maxx , maxy ) of the bottom surface and the height h of the block. The integers sx , sy , ex , ey , minx , miny , maxx , maxy and h satisfy the following conditions. -10000 ≤ sx , sy , ex , ey ≤ 10000 -10000 ≤ minx i < maxx i ≤ 10000 -10000 ≤ miny i < maxy i ≤ 10000 1 ≤ h i ≤ 1000 The last dataset is followed by a line with a single zero in it. Output For each dataset, output a separate line containing the largest radius. You may assume that the largest radius never exceeds 1000 for each dataset. If there are any blocks on the course line, the largest radius is defined to be zero. The value may contain an error less than or equal to 0.001. You may print any number of digits after the decimal point. Sample Input 2 -40 -40 100 30 -100 -100 -50 -30 1 30 -70 90 -30 10 2 -4 -4 10 3 -10 -10 -5 -3 1 3 -7 9 -3 1 2 -40 -40 100 30 -100 -100 -50 -30 3 30 -70 90 -30 10 2 -400 -400 1000 300 -800 -800 -500 -300 7 300 -700 900 -300 20 3 20 70 150 70 0 0 50 50 4 40 100 60 120 8 130 80 200 200 1 3 20 70 150 70 0 0 50 50 4 40 100 60 120 10 130 80 200 200 1 3 20 70 150 70 0 0 50 50 10 40 100 60 120 10 130 80 200 200 3 1 2 4 8 8 0 0 10 10 1 1 1 4 9 9 2 2 7 7 1 0 Output for the Sample Input 30 1 18.16666666667 717.7 ...(truncated)	[ { "submission_id": "aoj_1157_10849696", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\ndouble EPS = 1e-9;\ntypedef complex<double> P;\n\nstruct L : public vector<P> {\n L(const P &a, const P &b) {\n push_back(a); push_back(b);\n }\n};\ndouble cross(const P& a, const P& b) {\n retur...
aoj_1159_cpp	Problem A: Next Mayor One of the oddest traditions of the town of Gameston may be that even the town mayor of the next term is chosen according to the result of a game. When the expiration of the term of the mayor approaches, at least three candidates, including the mayor of the time, play a game of pebbles, and the winner will be the next mayor. The rule of the game of pebbles is as follows. In what follows, n is the number of participating candidates. Requisites A round table, a bowl, and plenty of pebbles. Start of the Game A number of pebbles are put into the bowl; the number is decided by the Administration Commission using some secret stochastic process. All the candidates, numbered from 0 to n -1 sit around the round table, in a counterclockwise order. Initially, the bowl is handed to the serving mayor at the time, who is numbered 0. Game Steps When a candidate is handed the bowl and if any pebbles are in it, one pebble is taken out of the bowl and is kept, together with those already at hand, if any. If no pebbles are left in the bowl, the candidate puts all the kept pebbles, if any, into the bowl. Then, in either case, the bowl is handed to the next candidate to the right. This step is repeated until the winner is decided. End of the Game When a candidate takes the last pebble in the bowl, and no other candidates keep any pebbles, the game ends and that candidate with all the pebbles is the winner. A math teacher of Gameston High, through his analysis, concluded that this game will always end within a finite number of steps, although the number of required steps can be very large. Input The input is a sequence of datasets. Each dataset is a line containing two integers n and p separated by a single space. The integer n is the number of the candidates including the current mayor, and the integer p is the total number of the pebbles initially put in the bowl. You may assume 3 ≤ n ≤ 50 and 2 ≤ p ≤ 50. With the settings given in the input datasets, the game will end within 1000000 (one million) steps. The end of the input is indicated by a line containing two zeros separated by a single space. Output The output should be composed of lines corresponding to input datasets in the same order, each line of which containing the candidate number of the winner. No other characters should appear in the output. Sample Input 3 2 3 3 3 50 10 29 31 32 50 2 50 50 0 0 Output for the Sample Input 1 0 1 5 30 1 13	[ { "submission_id": "aoj_1159_10851347", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nint main(){\n\tint n,p;\n\twhile( cin >> n >> p and n ){\n\t\tint c[50] = {};\n\t\tint owan = p;\n\t\tfor(int i = 0 ; ; i = (i+1) % n ){\n\t\t\tif( owan ){\n\t\t\t\t--owan;\n\t\t\t\tc[i]++;\n\t\t\t}els...
aoj_1161_cpp	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	[ { "submission_id": "aoj_1161_10851225", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\n\nlong long weight[128];\n\nint to[128];\nint cnt = 0;\nvector<char> appear;\nvector<string> s;\n\nint taboo[128];\n\n\nbool bad(string &s,int to[128]){\n\tif( s.size() == 1 ) return 0;\n\tif( to[s[0]]...
aoj_1162_cpp	Problem D: Discrete Speed Consider car trips in a country where there is no friction. Cars in this country do not have engines. Once a car started to move at a speed, it keeps moving at the same speed. There are acceleration devices on some points on the road, where a car can increase or decrease its speed by 1. It can also keep its speed there. Your job in this problem is to write a program which determines the route with the shortest time to travel from a starting city to a goal city. There are several cities in the country, and a road network connecting them. Each city has an acceleration device. As mentioned above, if a car arrives at a city at a speed v , it leaves the city at one of v - 1, v , or v + 1. The first road leaving the starting city must be run at the speed 1. Similarly, the last road arriving at the goal city must be run at the speed 1. The starting city and the goal city are given. The problem is to find the best route which leads to the goal city going through several cities on the road network. When the car arrives at a city, it cannot immediately go back the road it used to reach the city. No U-turns are allowed. Except this constraint, one can choose any route on the road network. It is allowed to visit the same city or use the same road multiple times. The starting city and the goal city may be visited during the trip. For each road on the network, its distance and speed limit are given. A car must run a road at a speed less than or equal to its speed limit. The time needed to run a road is the distance divided by the speed. The time needed within cities including that for acceleration or deceleration should be ignored. Input The input consists of multiple datasets, each in the following format. n m s g x 1 y 1 d 1 c 1 ... x m y m d m c m Every input item in a dataset is a non-negative integer. Input items in the same line are separated by a space. The first line gives the size of the road network. n is the number of cities in the network. You can assume that the number of cities is between 2 and 30, inclusive. m is the number of roads between cities, which may be zero. The second line gives the trip. s is the city index of the starting city. g is the city index of the goal city. s is not equal to g . You can assume that all city indices in a dataset (including the above two) are between 1 and n , inclusive. The following m lines give the details of roads between cities. The i -th road connects two cities with city indices x i and y i , and has a distance d i (1 ≤ i ≤ m ). You can assume that the distance is between 1 and 100, inclusive. The speed limit of the road is specified by c i . You can assume that the speed limit is between 1 and 30, inclusive. No two roads connect the same pair of cities. A road never connects a city with itself. Each road can be traveled in both directions. The last dataset is followed by a line containing two zeros (separated by a space). Output For each dataset in the input, one line should b ...(truncated)	[ { "submission_id": "aoj_1162_10849611", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nstruct Node{\n\tint pos;\n\tint speed;\n\tdouble cost;\n\tint prev;\n};\nbool operator < (const Node &a,const Node &b){\n\treturn a.cost > b.cost;\n}\n\n\n\nint main(){\n\tint n,m;\n\twhile(cin >> n >>...
aoj_1163_cpp	Problem E: Cards There are many blue cards and red cards on the table. For each card, an integer number greater than 1 is printed on its face. The same number may be printed on several cards. A blue card and a red card can be paired when both of the numbers printed on them have a common divisor greater than 1. There may be more than one red card that can be paired with one blue card. Also, there may be more than one blue card that can be paired with one red card. When a blue card and a red card are chosen and paired, these two cards are removed from the whole cards on the table. Figure E-1: Four blue cards and three red cards For example, in Figure E-1, there are four blue cards and three red cards. Numbers 2, 6, 6 and 15 are printed on the faces of the four blue cards, and 2, 3 and 35 are printed on those of the three red cards. Here, you can make pairs of blue cards and red cards as follows. First, the blue card with number 2 on it and the red card with 2 are paired and removed. Second, one of the two blue cards with 6 and the red card with 3 are paired and removed. Finally, the blue card with 15 and the red card with 35 are paired and removed. Thus the number of removed pairs is three. Note that the total number of the pairs depends on the way of choosing cards to be paired. The blue card with 15 and the red card with 3 might be paired and removed at the beginning. In this case, there are only one more pair that can be removed and the total number of the removed pairs is two. Your job is to find the largest number of pairs that can be removed from the given set of cards on the table. Input The input is a sequence of datasets. The number of the datasets is less than or equal to 100. Each dataset is formatted as follows. m n b 1 ... b k ... b m r 1 ... r k ... r n The integers m and n are the number of blue cards and that of red cards, respectively. You may assume 1 ≤ m ≤ 500 and 1≤ n ≤ 500. b k (1 ≤ k ≤ m ) and r k (1 ≤ k ≤ n ) are numbers printed on the blue cards and the red cards respectively, that are integers greater than or equal to 2 and less than 10000000 (=10 7 ). The input integers are separated by a space or a newline. Each of b m and r n is followed by a newline. There are no other characters in the dataset. The end of the input is indicated by a line containing two zeros separated by a space. Output For each dataset, output a line containing an integer that indicates the maximum of the number of the pairs. Sample Input 4 3 2 6 6 15 2 3 5 2 3 4 9 8 16 32 4 2 4 9 11 13 5 7 5 5 2 3 5 1001 1001 7 11 13 30 30 10 10 2 3 5 7 9 11 13 15 17 29 4 6 10 14 18 22 26 30 34 38 20 20 195 144 903 63 137 513 44 626 75 473 876 421 568 519 755 840 374 368 570 872 363 650 155 265 64 26 426 391 15 421 373 984 564 54 823 477 565 866 879 638 100 100 195 144 903 63 137 513 44 626 75 473 876 421 568 519 755 840 374 368 570 872 363 650 155 265 64 26 426 391 15 421 373 984 564 54 823 477 565 866 879 638 117 755 835 683 52 369 302 424 513 870 75 874 299 22 ...(truncated)	[ { "submission_id": "aoj_1163_10915351", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll=long long;\n\nint dfs(vector<vector<tuple<int,int,int>>>& G,vector<bool>& checked,int cv,int cf,int goal){\n if(cv==goal) return cf;\n checked[cv]=true;\n\n int ca=0;\n for(auto& nv:...
aoj_1165_cpp	Problem A: Pablo Squarson's Headache Pablo Squarson is a well-known cubism artist. This year's theme for Pablo Squarson is "Squares". Today we are visiting his studio to see how his masterpieces are given birth. At the center of his studio, there is a huuuuuge table and beside it are many, many squares of the same size. Pablo Squarson puts one of the squares on the table. Then he places some other squares on the table in sequence. It seems his methodical nature forces him to place each square side by side to the one that he already placed on, with machine-like precision. Oh! The first piece of artwork is done. Pablo Squarson seems satisfied with it. Look at his happy face. Oh, what's wrong with Pablo? He is tearing his hair! Oh, I see. He wants to find a box that fits the new piece of work but he has trouble figuring out its size. Let's help him! Your mission is to write a program that takes instructions that record how Pablo made a piece of his artwork and computes its width and height. It is known that the size of each square is 1. You may assume that Pablo does not put a square on another. I hear someone murmured "A smaller box will do". No, poor Pablo, shaking his head, is grumbling "My square style does not seem to be understood by illiterates". Input The input consists of a number of datasets. Each dataset represents the way Pablo made a piece of his artwork. The format of a dataset is as follows. N n 1 d 1 n 2 d 2 ... n N -1 d N -1 The first line contains the number of squares (= N ) used to make the piece of artwork. The number is a positive integer and is smaller than 200. The remaining ( N -1) lines in the dataset are square placement instructions. The line “ n i d i ” indicates placement of the square numbered i (≤ N -1). The rules of numbering squares are as follows. The first square is numbered "zero". Subsequently placed squares are numbered 1, 2, ..., ( N -1). Note that the input does not give any placement instruction to the first square, which is numbered zero. A square placement instruction for the square numbered i , namely “ n i d i ”, directs it to be placed next to the one that is numbered n i , towards the direction given by d i , which denotes leftward (= 0), downward (= 1), rightward (= 2), and upward (= 3). For example, pieces of artwork corresponding to the four datasets shown in Sample Input are depicted below. Squares are labeled by their numbers. The end of the input is indicated by a line that contains a single zero. Output For each dataset, output a line that contains the width and the height of the piece of artwork as decimal numbers, separated by a space. Each line should not contain any other characters. Sample Input 1 5 0 0 0 1 0 2 0 3 12 0 0 1 0 2 0 3 1 4 1 5 1 6 2 7 2 8 2 9 3 10 3 10 0 2 1 2 2 2 3 2 2 1 5 1 6 1 7 1 8 1 0 Output for the Sample Input 1 1 3 3 4 4 5 6	[ { "submission_id": "aoj_1165_9262894", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\n#define all(a) a.begin(),a.end()\n#define reps(i, a, n) for (int i = (a); i < (int)(n); i++)\n#define rep(i, n) reps(i, 0, n)\n#define rreps(i, a, n) for (int i = (a); i > (int)(n);...
aoj_1166_cpp	Problem B: Amazing Mazes You are requested to solve maze problems. Without passing through these mazes, you might not be able to pass through the domestic contest! A maze here is a rectangular area of a number of squares, lined up both lengthwise and widthwise, The area is surrounded by walls except for its entry and exit. The entry to the maze is at the leftmost part of the upper side of the rectangular area, that is, the upper side of the uppermost leftmost square of the maze is open. The exit is located at the rightmost part of the lower side, likewise. In the maze, you can move from a square to one of the squares adjoining either horizontally or vertically. Adjoining squares, however, may be separated by a wall, and when they are, you cannot go through the wall. Your task is to find the length of the shortest path from the entry to the exit. Note that there may be more than one shortest paths, or there may be none. Input The input consists of one or more datasets, each of which represents a maze. The first line of a dataset contains two integer numbers, the width w and the height h of the rectangular area, in this order. The following 2 × h − 1 lines of a dataset describe whether there are walls between squares or not. The first line starts with a space and the rest of the line contains w − 1 integers, 1 or 0, separated by a space. These indicate whether walls separate horizontally adjoining squares in the first row. An integer 1 indicates a wall is placed, and 0 indicates no wall is there. The second line starts without a space and contains w integers, 1 or 0, separated by a space. These indicate whether walls separate vertically adjoining squares in the first and the second rows. An integer 1/0 indicates a wall is placed or not. The following lines indicate placing of walls between horizontally and vertically adjoining squares, alternately, in the same manner. The end of the input is indicated by a line containing two zeros. The number of datasets is no more than 100. Both the widths and the heights of rectangular areas are no less than 2 and no more than 30. Output For each dataset, output a line having an integer indicating the length of the shortest path from the entry to the exit. The length of a path is given by the number of visited squares. If there exists no path to go through the maze, output a line containing a single zero. The line should not contain any character other than this number. Sample Input 2 3 1 0 1 0 1 0 1 9 4 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 12 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 Output for the Sample Input 4 0 20	[ { "submission_id": "aoj_1166_10936796", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\n#define rep(i, n) for (int i = 0; i < (int)(n); i++)\n#define oke cout << \"Yes\" << '\\n';\n#define dame cout << \"No\" << '\\n';\n#define all(a) a.begin(), a.end()\n#define rall(...
aoj_1167_cpp	Problem C: Pollock's conjecture The n th triangular number is defined as the sum of the first n positive integers. The n th tetrahedral number is defined as the sum of the first n triangular numbers. It is easy to show that the n th tetrahedral number is equal to n ( n +1)( n +2) ⁄ 6. For example, the 5th tetrahedral number is 1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5) = 5×6×7 ⁄ 6 = 35. The first 5 triangular numbers 1, 3, 6, 10, 15 The first 5 tetrahedral numbers 1, 4, 10, 20, 35 In 1850, Sir Frederick Pollock, 1st Baronet, who was not a professional mathematician but a British lawyer and Tory (currently known as Conservative) politician, conjectured that every positive integer can be represented as the sum of at most five tetrahedral numbers. Here, a tetrahedral number may occur in the sum more than once and, in such a case, each occurrence is counted separately. The conjecture has been open for more than one and a half century. Your mission is to write a program to verify Pollock's conjecture for individual integers. Your program should make a calculation of the least number of tetrahedral numbers to represent each input integer as their sum. In addition, for some unknown reason, your program should make a similar calculation with only odd tetrahedral numbers available. For example, one can represent 40 as the sum of 2 tetrahedral numbers, 4×5×6 ⁄ 6 + 4×5×6 ⁄ 6, but 40 itself is not a tetrahedral number. One can represent 40 as the sum of 6 odd tetrahedral numbers, 5×6×7 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6, but cannot represent as the sum of fewer odd tetrahedral numbers. Thus, your program should report 2 and 6 if 40 is given. Input The input is a sequence of lines each of which contains a single positive integer less than 10 6 . The end of the input is indicated by a line containing a single zero. Output For each input positive integer, output a line containing two integers separated by a space. The first integer should be the least number of tetrahedral numbers to represent the input integer as their sum. The second integer should be the least number of odd tetrahedral numbers to represent the input integer as their sum. No extra characters should appear in the output. Sample Input 40 14 5 165 120 103 106 139 0 Output for the Sample Input 2 6 2 14 2 5 1 1 1 18 5 35 4 4 3 37	[ { "submission_id": "aoj_1167_11043743", "code_snippet": "#include <bits/stdc++.h>\n#pragma GCC target(\"avx2\")\n#ifndef LOCAL\n#pragma GCC optimize(\"O3\")\n#endif\n#pragma GCC optimize(\"unroll-loops\")\n\n#ifdef ONLINE_JUDGE\n#include <boost/multiprecision/cpp_int.hpp>\n#include <atcoder/all>\n#endif\n#i...
aoj_1164_cpp	Problem F: Tighten Up! We have a flat panel with two holes. Pins are nailed on its surface. From the back of the panel, a string comes out through one of the holes to the surface. The string is then laid on the surface in a form of a polygonal chain, and goes out to the panel's back through the other hole. Initially, the string does not touch any pins. Figures F-1, F-2, and F-3 show three example layouts of holes, pins and strings. In each layout, white squares and circles denote holes and pins, respectively. A polygonal chain of solid segments denotes the string. Figure F-1: An example layout of holes, pins and a string Figure F-2: An example layout of holes, pins and a string Figure F-3: An example layout of holes, pins and a string When we tie a pair of equal weight stones to the both ends of the string, the stones slowly straighten the string until there is no loose part. The string eventually forms a different polygonal chain as it is obstructed by some of the pins. (There are also cases when the string is obstructed by no pins, though.) The string does not hook itself while being straightened. A fully tightened string thus draws a polygonal chain on the surface of the panel, whose vertices are the positions of some pins with the end vertices at the two holes. The layouts in Figures F-1, F-2, and F-3 result in the respective polygonal chains in Figures F-4, F-5, and F-6. Write a program that calculates the length of the tightened polygonal chain. Figure F-4: Tightened polygonal chains from the example in Figure F-1. Figure F-5: Tightened polygonal chains from the example in Figure F-2. Figure F-6: Tightened polygonal chains from the example in Figure F-3. Note that the strings, pins and holes are thin enough so that you can ignore their diameters. Input The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset gives the initial shape of the string (i.e., the positions of holes and vertices) and the positions of pins in the following format. m n x 1 y 1 ... x l y l The first line has two integers m and n (2 ≤ m ≤ 100, 0 ≤ n ≤ 100), representing the number of vertices including two holes that give the initial string shape ( m ) and the number of pins ( n ). Each of the following l = m + n lines has two integers x i and y i (0 ≤ x i ≤ 1000, 0 ≤ y i ≤ 1000), representing a position P i = ( x i , y i ) on the surface of the panel. Positions P 1 , ..., P m give the initial shape of the string; i.e., the two holes are at P 1 and P m , and the string's shape is a polygonal chain whose vertices are P i ( i = 1, ..., m ), in this order. Positions P m +1 , ..., P m + n are the positions of the pins. Note that no two points are at the same position. No three points are exactly on a straight line. Output For each dataset, the length of the part of the tightened string that remains on the surface of the panel should be output in a line. No extra characters should appear in the ...(truncated)	[ { "submission_id": "aoj_1164_8550653", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nstruct Point {\n double x, y;\n Point operator+(const Point p) const { return {x + p.x, y + p.y}; }\n double operator(const Point p) const { return x p.x + y * p.y; }\n Point operator-(const Poin...
aoj_1158_cpp	Problem F: ICPC: Intelligent Congruent Partition of Chocolate The twins named Tatsuya and Kazuya love chocolate. They have found a bar of their favorite chocolate in a very strange shape. The chocolate bar looks to have been eaten partially by Mam. They, of course, claim to eat it and then will cut it into two pieces for their portions. Since they want to be sure that the chocolate bar is fairly divided, they demand that the shapes of the two pieces are congruent and that each piece is connected . The chocolate bar consists of many square shaped blocks of chocolate connected to the adjacent square blocks of chocolate at their edges. The whole chocolate bar is also connected. Cutting the chocolate bar along with some edges of square blocks, you should help them to divide it into two congruent and connected pieces of chocolate. That is, one piece fits into the other after it is rotated, turned over and moved properly. Figure F-1: A partially eaten chocolate bar with 18 square blocks of chocolate For example, there is a partially eaten chocolate bar with 18 square blocks of chocolate as depicted in Figure F-1. Cutting it along with some edges of square blocks, you get two pieces of chocolate with 9 square blocks each as depicted in Figure F-2. Figure F-2: Partitioning of the chocolate bar in Figure F-1 You get two congruent and connected pieces as the result. One of them consists of 9 square blocks hatched with horizontal lines and the other with vertical lines. Rotated clockwise with a right angle and turned over on a horizontal line, the upper piece exactly fits into the lower piece. Figure F-3: A shape that cannot be partitioned into two congruent and connected pieces Two square blocks touching only at their corners are regarded as they are not connected to each other. Figure F-3 is an example shape that cannot be partitioned into two congruent and connected pieces. Note that, without the connectivity requirement, this shape can be partitioned into two congruent pieces with three squares (Figure F-4). Figure F-4: Two congruent but disconnected pieces Your job is to write a program that judges whether a given bar of chocolate can be partitioned into such two congruent and connected pieces or not. Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset is formatted as follows. w h r (1, 1) ... r (1, w ) r (2, 1) ... r (2, w ) ... r ( h , 1) ... r ( h , w ) The integers w and h are the width and the height of a chocolate bar, respectively. You may assume 2 ≤ w ≤ 10 and 2 ≤ h ≤ 10. Each of the following h lines consists of w digits delimited by a space. The digit r ( i , j ) represents the existence of a square block of chocolate at the position ( i , j ) as follows. '0': There is no chocolate (i.e., already eaten). '1': There is a square block of chocolate. You can assume that there are at most 36 square blocks of chocolate in the bar, i.e., the ...(truncated)	[ { "submission_id": "aoj_1158_10335906", "code_snippet": "// AOJ #1158 ICPC: Intelligent Congruent Partition of Chocolate\n// 2025.3.30\n\n#include <bits/stdc++.h>\nusing namespace std;\nusing ull = unsigned long long;\n\nconstexpr int dY[4] = {0, 1, 0, -1};\nconstexpr int dX[4] = {1, 0, -1, 0};\n\nstruct St...
aoj_1172_cpp	Chebyshev's Theorem If n is a positive integer, there exists at least one prime number greater than n and less than or equal to 2 n . This fact is known as Chebyshev's theorem or the Bertrand-Chebyshev theorem, which had been conjectured by Joseph Louis François Bertrand (1822–1900) and was proven by Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв, 1821–1894) in 1850. Srinivasa Aiyangar Ramanujan (1887–1920) gave an elementary proof in his paper published in 1919. Paul Erdős (1913–1996) discovered another elementary proof in 1932. For example, there exist 4 prime numbers greater than 10 and less than or equal to 20, i.e. 11, 13, 17 and 19. There exist 3 prime numbers greater than 14 and less than or equal to 28, i.e. 17, 19 and 23. Your mission is to write a program that counts the prime numbers greater than n and less than or equal to 2 n for each given positive integer n . Using such a program, you can verify Chebyshev's theorem for individual positive integers. Input The input is a sequence of datasets. A dataset is a line containing a single positive integer n . You may assume n ≤ 123456. The end of the input is indicated by a line containing a single zero. It is not a dataset. Output The output should be composed of as many lines as the input datasets. Each line should contain a single integer and should never contain extra characters. The output integer corresponding to a dataset consisting of an integer n should be the number of the prime numbers p satisfying n < p ≤ 2 n . Sample Input 1 10 13 100 1000 10000 100000 0 Output for the Sample Input 1 4 3 21 135 1033 8392	[ { "submission_id": "aoj_1172_10609798", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\nusing a2 = array<ll, 2>;\nusing a3 = array<ll, 3>;\n\ntemplate <typename A> void chmin(A &l, const A &r) {\n if(r < l)\n l = r;\n}\ntemplate <typename A> void chmax(A &l,...
aoj_1168_cpp	Problem D: Off Balance You are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building. Submitted designs will look like a screenshot of a well known game as shown below. This is because the center specifies that the building should be constructed by stacking regular units called pieces , each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions. All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position. All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse. The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces. The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below. It will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows. Assume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy -coordinates of its left-bottom corner. The unit length is the edge length of a block. Among the blocks of the piece that touch another piece or the ground on their bottom faces, let x L be the leftmost x -coordinate of the leftmost block, and let x R be the rightmost x -coordinate of the rightmost block. Let the x -coordinate of its accumulated center of mass of the piece be M , where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P , in addition to P itself. Then the piece is stable, if and only if x L < M < x R . Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable. Note that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable. Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable. Write a program that judges stabilit ...(truncated)	[ { "submission_id": "aoj_1168_5490233", "code_snippet": "#include <stdio.h>\n#include <bits/stdc++.h>\nusing namespace std;\n#define rep(i,n) for (int i = 0; i < (n); ++i)\n#define Inf 1000000000\n\nstruct dsu {\n\tpublic:\n\tdsu() : _n(0) {}\n\texplicit dsu(int n) : _n(n), parent_or_size(n, -1) {}\n\n\tint ...
aoj_1171_cpp	Problem G: Laser Beam Reflections A laser beam generator, a target object and some mirrors are placed on a plane. The mirrors stand upright on the plane, and both sides of the mirrors are flat and can reflect beams. To point the beam at the target, you may set the beam to several directions because of different reflections. Your job is to find the shortest beam path from the generator to the target and answer the length of the path. Figure G-1 shows examples of possible beam paths, where the bold line represents the shortest one. Figure G-1: Examples of possible paths Input The input consists of a number of datasets. The end of the input is indicated by a line containing a zero. Each dataset is formatted as follows. Each value in the dataset except n is an integer no less than 0 and no more than 100. n PX 1 PY 1 QX 1 QY 1 ... PX n PY n QX n QY n TX TY LX LY The first line of a dataset contains an integer n (1 ≤ n ≤ 5), representing the number of mirrors. The following n lines list the arrangement of mirrors on the plane. The coordinates ( PX i , PY i ) and ( QX i , QY i ) represent the positions of both ends of the mirror. Mirrors are apart from each other. The last two lines represent the target position ( TX , TY ) and the position of the beam generator ( LX , LY ). The positions of the target and the generator are apart from each other, and these positions are also apart from mirrors. The sizes of the target object and the beam generator are small enough to be ignored. You can also ignore the thicknesses of mirrors. In addition, you can assume the following conditions on the given datasets. There is at least one possible path from the beam generator to the target. The number of reflections along the shortest path is less than 6. The shortest path does not cross or touch a plane containing a mirror surface at any points within 0.001 unit distance from either end of the mirror. Even if the beam could arbitrarily select reflection or passage when it reaches each plane containing a mirror surface at a point within 0.001 unit distance from one of the mirror ends, any paths from the generator to the target would not be shorter than the shortest path. When the beam is shot from the generator in an arbitrary direction and it reflects on a mirror or passes the mirror within 0.001 unit distance from the mirror, the angle θ formed by the beam and the mirror satisfies sin( θ ) > 0.1, until the beam reaches the 6th reflection point (exclusive). Figure G-1 corresponds to the first dataset of the Sample Input below. Figure G-2 shows the shortest paths for the subsequent datasets of the Sample Input. Figure G-2: Examples of the shortest paths Output For each dataset, output a single line containing the length of the shortest path from the beam generator to the target. The value should not have an error greater than 0.001. No extra characters should appear in the output. Sample Input 2 30 10 30 75 60 30 60 95 90 0 0 100 1 20 81 90 90 10 90 90 10 2 10 0 ...(truncated)	[ { "submission_id": "aoj_1171_10851220", "code_snippet": "#include <iostream>\n#include <algorithm>\n#include <complex>\n#include <vector>\n#include <cmath>\n#define sz(x) int((x).size())\n#define mkp make_pair\n#define frs first\n#define scn second\n#define phb push_back\n#define ppb pop_back\nusing namespa...
aoj_1169_cpp	Problem E: The Most Powerful Spell Long long ago, there lived a wizard who invented a lot of "magical patterns." In a room where one of his magical patterns is drawn on the floor, anyone can use magic by casting magic spells! The set of spells usable in the room depends on the drawn magical pattern. Your task is to compute, for each given magical pattern, the most powerful spell enabled by the pattern. A spell is a string of lowercase letters. Among the spells, lexicographically earlier one is more powerful. Note that a string w is defined to be lexicographically earlier than a string u when w has smaller letter in the order a<b<...<z on the first position at which they differ, or w is a prefix of u . For instance, "abcd" is earlier than "abe" because 'c' < 'e', and "abe" is earlier than "abef" because the former is a prefix of the latter. A magical pattern is a diagram consisting of uniquely numbered nodes and arrows connecting them. Each arrow is associated with its label , a lowercase string. There are two special nodes in a pattern, called the star node and the gold node . A spell becomes usable by a magical pattern if and only if the spell emerges as a sequential concatenation of the labels of a path from the star to the gold along the arrows. The next figure shows an example of a pattern with four nodes and seven arrows. The node 0 is the star node and 2 is the gold node. One example of the spells that become usable by this magical pattern is "abracadabra", because it appears in the path 0 --"abra"--> 1 --"cada"--> 3 --"bra"--> 2. Another example is "oilcadabraketdadabra", obtained from the path 0 --"oil"--> 1 --"cada"--> 3 --"bra"--> 2 --"ket"--> 3 --"da"--> 3 --"da"--> 3 --"bra"--> 2. The spell "abracadabra" is more powerful than "oilcadabraketdadabra" because it is lexicographically earlier. In fact, no other spell enabled by the magical pattern is more powerful than "abracadabra". Thus "abracadabra" is the answer you have to compute. When you cannot determine the most powerful spell, please answer "NO". There are two such cases. One is the case when no path exists from the star node to the gold node. The other case is when for every usable spell there always exist more powerful spells. The situation is exemplified in the following figure: "ab" is more powerful than "b", and "aab" is more powerful than "ab", and so on. For any spell, by prepending "a", we obtain a lexicographically earlier (hence more powerful) spell. Input The input consists of at most 150 datasets. Each dataset is formatted as follows. n a s g x 1 y 1 lab 1 x 2 y 2 lab 2 ... x a y a lab a The first line of a dataset contains four integers. n is the number of the nodes, and a is the number of the arrows. The numbers s and g indicate the star node and the gold node, respectively. Then a lines describing the arrows follow. Each line consists of two integers and one string. The line " x i y i lab i " represents an arrow from the node x i to the node y i with the associ ...(truncated)	[ { "submission_id": "aoj_1169_10853923", "code_snippet": "/\n Copyright (C) 2015 All rights reserved.\n* \n* filename: 9019.cpp\n* author: doublehh\n* e-mail: sserdoublehh@foxmail.com\n* create time: 2015-06-08\n* last modified: 2015-06-08 16:08:16\n*/\n#include<bits/stdc++.h>\nusing namespac...
aoj_1173_cpp	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 (“( )”) and square (“[ ]”). A string is balanced if and only if the following conditions hold. For every left round bracket (“(”), there is a corresponding right round bracket (“)”) in the following part of the string. For every left square bracket (“[”), there is a corresponding right square bracket (“]”) 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 (“( )”) and square (“[ ]”), 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 “yes” if the string is balanced, or “no” 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	[ { "submission_id": "aoj_1173_9723425", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nint main()\n{\n\twhile(true)\n\t{\n\t\tstring s;\n\t\tgetline(cin,s);\n\t\tif(s==\".\")\n\t\t\tbreak;\n\t\tvector <int> v;\n\t\tbool ans=true;\n\t\tfor(int i=0; i<s.size(); i++)\n\t\t{\n\t\t\tif(s[i]=='...
aoj_1170_cpp	Problem F: Old Memories In 4272 A.D., Master of Programming Literature, Dr. Isaac Cornell Panther-Carol, who has miraculously survived through the three World Computer Virus Wars and reached 90 years old this year, won a Nobel Prize for Literature. Media reported every detail of his life. However, there was one thing they could not report — that is, an essay written by him when he was an elementary school boy. Although he had a copy and was happy to let them see it, the biggest problem was that his copy of the essay was infected by a computer virus several times during the World Computer Virus War III and therefore the computer virus could have altered the text. Further investigation showed that his copy was altered indeed. Why could we know that? More than 80 years ago his classmates transferred the original essay to their brain before infection. With the advent of Solid State Brain, one can now retain a text perfectly over centuries once it is transferred to his or her brain. No one could remember the entire text due to the limited capacity, but we managed to retrieve a part of the text from the brain of one of his classmates; sadly, it did not match perfectly to the copy at hand. It would not have happened without virus infection. At the moment, what we know about the computer virus is that each time the virus infects an essay it does one of the following: the virus inserts one random character to a random position in the text. (e.g., "ABCD" → "ABCZD") the virus picks up one character in the text randomly, and then changes it into another character. (e.g., "ABCD" → "ABXD") the virus picks up one character in the text randomly, and then removes it from the text. (e.g., "ABCD" → "ACD") You also know the maximum number of times the computer virus infected the copy, because you could deduce it from the amount of the intrusion log. Fortunately, most of his classmates seemed to remember at least one part of the essay (we call it a piece hereafter). Considering all evidences together, the original essay might be reconstructed. You, as a journalist and computer scientist, would like to reconstruct the original essay by writing a computer program to calculate the possible original text(s) that fits to the given pieces and the altered copy at hand. Input The input consists of multiple datasets. The number of datasets is no more than 100. Each dataset is formatted as follows: d n the altered text piece 1 piece 2 ... piece n The first line of a dataset contains two positive integers d ( d ≤ 2) and n ( n ≤ 30), where d is the maximum number of times the virus infected the copy and n is the number of pieces . The second line is the text of the altered copy at hand. We call it the altered text hereafter. The length of the altered text is less than or equal to 40 characters. The following n lines are pieces , each of which is a part of the original essay remembered by one of his classmates. Each piece has at least 13 characters but no more than 20 characters ...(truncated)	[ { "submission_id": "aoj_1170_8289540", "code_snippet": "#include <iostream>\n#include <string>\n#include <vector>\n#include <algorithm>\nusing namespace std;\n\nint D, N;\nlong long val1[49], pow1[49];\nlong long val2[49], pow2[49];\nstring S;\nstring T[39];\nstring U = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ.\";\nstr...
aoj_1177_cpp	Watchdog Corporation In Northern Kyushu, you are running a company which rents watchdogs in response to the customers' order. The distinguishing point of your service is that you also install fences to enhance the performance of watchdogs. The dog is put on a leash, which is tied up to a peg. You are installing fences at the border of the dog's reach, so that strangers approaching the fence are taken care of by your dog. There may be a rectangular building near the dog; the dog cannot enter the building, but can go around it as long as the length of the leash permits, as in Figure F-1. You do not need fences along the building's wall. Figure F-1: Example fence layouts (some parts of the fences are omitted.) Given the length of the leash and the position and the size of the building, your program should calculate the length of the fence. Input The input consists of multiple datasets each consisting of five integers in a line of the following format. len x 1 y 1 x 2 y 2 len indicates the length of the leash. x 1 , y 1 , x 2 and y 2 indicate the size and position of the building in that a point with coordinate ( x , y ) such that x 1 < x < x 2 and y 1 < y < y 2 is contained in the building. This means that the building's walls are parallel to either the X-axis or Y-axis. The peg is located on the origin. You may assume that 0 < len ≤ 100, −100 ≤ x 1 < x 2 ≤ 100 and −100 ≤ y 1 < y 2 ≤ 100. You may also assume that the peg is located apart from the building (that is, neither inside nor on the border of the building). The end of the input is indicated by a line containing five zeros. Output For each dataset, output the total length of the fences as a single fractional number in a line. There may not be any other characters in the output. The output should not contain an error greater than 0.00001. Sample Input 3 3 0 6 5 5 3 0 6 5 6 3 0 6 5 7 3 0 6 5 9 3 0 6 5 10 3 0 6 5 12 3 0 6 5 100 3 0 6 5 4 -3 4 5 8 5 -3 4 5 8 6 -3 4 5 8 64 -30 40 50 50 7 -3 4 5 8 10 -3 4 5 8 11 -3 4 5 8 14 -3 4 5 8 35 -3 4 5 8 100 -3 4 5 8 10 5 9 12 12 13 5 9 12 12 15 5 9 12 12 18 5 9 12 12 19 5 9 12 12 20 5 9 12 12 21 5 9 12 12 100 5 9 12 12 100 -5 1 -3 5 100 0 1 100 2 100 -1 99 100 100 10 -1 1 1 2 84 1 -77 5 -42 27 -12 -7 3 -4 0 0 0 0 0 Output for the Sample Input 18.84955592 26.77945045 31.69103413 39.54501577 55.51851918 63.83954229 75.38181750 628.05343108 25.13274123 24.98091545 29.43519428 318.90944272 35.02723766 55.44758990 64.23914179 89.33649537 219.11188064 627.48648370 62.83185307 76.33420961 88.61222855 112.17417345 121.59895141 126.16196589 132.25443447 628.23333565 628.18890261 626.17695473 613.16456638 62.61625003 527.84509612 168.07337509	[ { "submission_id": "aoj_1177_1150744", "code_snippet": "#include <cstdio>\n#include <cmath>\n#include <cstring>\n#include <cstdlib>\n#include <climits>\n#include <ctime>\n#include <queue>\n#include <stack>\n#include <algorithm>\n#include <list>\n#include <vector>\n#include <set>\n#include <map>\n#include <i...
aoj_1174_cpp	Identically Colored Panels Connection Dr. Fukuoka has invented fancy panels. Each panel has a square shape of a unit size and has one of the six colors, namely, yellow, pink, red, purple, green and blue. The panel has two remarkable properties. One property is that, when two or more panels with the same color are placed adjacently, their touching edges melt a little and they are fused each other. The fused panels are united into a polygonally shaped panel. The other property is that the color of a panel can be changed to one of six colors by giving an electrical shock. The resulting color can be controlled by its waveform. The electrical shock to an already united panel changes the color of the whole to a specified single color. Since he wants to investigate the strength with respect to the color and the size of a united panel compared to unit panels, he tries to unite panels into a polygonal panel with a specified color. Figure C-1: panels and their initial colors Since many panels are simultaneously synthesized and generated on a base plate through some complex chemical processes, the fabricated panels are randomly colored and they are arranged in a rectangular shape on the base plate (Figure C-1). Note that the two purple (color 4) panels in Figure C-1 are already united at the initial state since they are adjacent to each other. Installing electrodes to a panel, and changing its color several times by giving electrical shocks according to an appropriate sequence for a specified target color, he can make a united panel merge the adjacent panels to unite them step by step and can obtain a larger panel with the target color. Unfortunately, panels will be broken when they are struck by the sixth electrical shock. That is, he can change the color of a panel or a united panel only five times. Let us consider a case where the panel at the upper left corner of the panel configuration (Figure C-1) is attached with the electrodes. First, changing the color of the panel from yellow to blue, the two adjacent panels are fused into a united panel (Figure C-2). Figure C-2: Change of the color of the panel at the upper left corner, from yellow (color 1) to blue (color 6). Second, changing the color of the upper left united panel from blue to red, a united red panel that consists of three unit panels is newly formed (Figure C-3). Then, changing the color of the united panel from red to purple, panels are united again to form a united panel of five unit panels (Figure C-4). Figure C-3: Change of the color of the panel at the upper left corner, from blue (color 6) to red (color 3). Figure C-4: Change of the color of the panel at the upper left corner, from red (color 3) to purple (color 4). Furthermore, through making a pink united panel in Figure C-5 by changing the color from purple to pink, then, the green united panel in Figure C-6 is obtained by changing the color from pink to green. The green united panel consists of ten unit panels. F ...(truncated)	[ { "submission_id": "aoj_1174_10853966", "code_snippet": "#include <algorithm>\n#include <cstdio>\n#include <cstring>\n\nusing std::max;\n\nint N, M, target, a[8][8], f, t, ans, x[64], y[64];\n\nint w[10];\n\nvoid copy(int b[8][8], int a[8][8]) {\n\tfor(int i = 0; i < N; ++i) {\n\t\tfor(int j = 0; j < M; ++j...
aoj_1175_cpp	And Then, How Many Are There? To Mr. Solitarius, who is a famous solo play game creator, a new idea occurs like every day. His new game requires discs of various colors and sizes. To start with, all the discs are randomly scattered around the center of a table. During the play, you can remove a pair of discs of the same color if neither of them has any discs on top of it. Note that a disc is not considered to be on top of another when they are externally tangent to each other. Figure D-1: Seven discs on the table For example, in Figure D-1, you can only remove the two black discs first and then their removal makes it possible to remove the two white ones. In contrast, gray ones never become removable. You are requested to write a computer program that, for given colors, sizes, and initial placings of discs, calculates the maximum number of discs that can be removed. Input The input consists of multiple datasets, each being in the following format and representing the state of a game just after all the discs are scattered. n x 1 y 1 r 1 c 1 x 2 y 2 r 2 c 2 ... x n y n r n c n The first line consists of a positive integer n representing the number of discs. The following n lines, each containing 4 integers separated by a single space, represent the colors, sizes, and initial placings of the n discs in the following manner: ( x i , y i ), r i , and c i are the xy -coordinates of the center, the radius, and the color index number, respectively, of the i -th disc, and whenever the i -th disc is put on top of the j -th disc, i < j must be satisfied. You may assume that every color index number is between 1 and 4, inclusive, and at most 6 discs in a dataset are of the same color. You may also assume that the x - and y -coordinates of the center of every disc are between 0 and 100, inclusive, and the radius between 1 and 100, inclusive. The end of the input is indicated by a single zero. Output For each dataset, print a line containing an integer indicating the maximum number of discs that can be removed. Sample Input 4 0 0 50 1 0 0 50 2 100 0 50 1 0 0 100 2 7 12 40 8 1 10 40 10 2 30 40 10 2 10 10 10 1 20 10 9 3 30 10 8 3 40 10 7 3 2 0 0 100 1 100 32 5 1 0 Output for the Sample Input 2 4 0	[ { "submission_id": "aoj_1175_10946386", "code_snippet": "#include<cstdio>\n#include<cstdlib>\n#include<cstring>\n#include<map>\n#include<set>\n#include<string>\n#include<iostream>\n#include<algorithm>\nusing namespace std;\n#define MP(i,j) make_pair(i,j)\ntypedef long long int64;\ntypedef long double real;\...
aoj_1176_cpp	Planning Rolling Blackouts Faced with seriously tight power supply-demand balance, the electric power company for which you are working implemented rolling blackouts in this spring. It divided the servicing area into several groups of towns, and divided a day into several blackout periods. At each blackout period of a day, one of the groups, which alternates from one group to another, is cut off the electricity. By keeping the total demand of electricity used by the rest of the towns within the supply capacity, the company avoided unforeseeable large-scale blackout. Working at the customer relations department, you had to listen to so many complaints from the customers, which made you think that you could have a better implementation. Most of the complaints are about the frequent cut-offs. But you could have divided the area into a larger number of groups, which resulted in less frequent cut-offs for each group. The other complaints are about the complicated grouping (in fact, someone said that the shapes of the groups are fractals), which makes it impossible to understand which town belongs to which group without closely inspecting into the grouping list publicized by the company. With the rectangular servicing area and towns located in a grid form, you could have made a simpler grouping. When you talked your analysis directly to the president of the company, you are appointed to plan rolling blackouts for this summer. Be careful what you propose. Anyway, you need to divide the servicing area into as many groups as possible with keeping total demand of electricity within the supply capacity. It should also divide the towns into simple and easy to remember groups. Your task is to write a program, given a demand table (a table showing electricity demand of each town) and the supply capacity, that answers a grouping of towns that satisfy the following conditions. The grouping should be made by horizontally or vertically splitting the area in a recursive manner. In other words, the grouping must be a set of areas after applied the following splitting procedure to a set containing only the entire area for zero or more times: (The splitting procedure) remove one area from the set, either vertically or horizontally split it into two sub-areas, and put the sub-areas into the set. The maximum suppressed demand of the grouping, which is the greatest total demand of the all but one group, is no more than the supply capacity. The grouping has the largest number of groups among the groupings that satisfy the above conditions 1 and 2. The grouping has the greatest amount of reserve power among the groupings that satisfy the above conditions 1, 2 and 3, where the reserve power of a grouping is the difference between the supply capacity and the maximum suppressed demand. Note that the condition 1 does not allow such a grouping shown in Figure E-1. Figure E-1: A grouping that violates the condition 1 Input ...(truncated)	[ { "submission_id": "aoj_1176_10866686", "code_snippet": "#include <cstdio>\n#include <cstdlib>\n#include <cstring>\n#include <iostream>\n#include <algorithm>\nconst int oo=1073741819;\nusing namespace std;\nint n,m,s,w_time;\nint sum[50][50],t[50][50][50][50],a[50][50];\nstruct sta{\n int tot,max;\n}f[50...
aoj_1178_cpp	A Broken Door There is a rectangular maze consisting of a number of square rooms arranged in grid. The maze is surrounded by walls except for its entry and exit. The entry to the maze is at the leftmost part of the upper side of the rectangular area, that is, the upper side of the uppermost leftmost room of the maze is open. The exit is located at the rightmost part of the lower side, likewise. There is a wall between each pair of vertically or horizontally adjacent rooms. Such a wall has either a door with a card key lock, or no door at all. If you insert a card to a door, the door opens and you can pass the door. The opened door will close immediately, and the inserted card won't return. You can open any door with any card. You cannot go through a wall that has no door. When a maze map is given, you can easily determine how many cards are needed to pass through the maze from the entry to the exit. In the maze in Figure G-1, you can pass through it with ten cards, following the path represented by the green arrows ( ) in Figure G-2. Figure G-1: A map of a maze Figure G-2: One of the shortest paths Now, you are informed that one of the doors is broken and can't be passed. But you don't know which door is broken. If you insert a card to a broken door, the inserted card immediately returns. However, you can't tell a broken door from a working door just by its appearance. Figure G-3: A maze that potentially can't be passed through If the door marked with a red X ( ) in Figure G-3 is broken, you have no way to pass through the maze from the entry to the exit. However, you can pass the maze in Figure G-1 whichever door is broken. When you intend to follow the shortest path in Figure G-2, and find that the door marked with a red X in Figure G-4 is broken, you might follow the path represented as green arrows. In this case, you need twenty cards. Figure G-4: A maze with a broken door However, you can pass through the maze with less cards. You should follow the path in Figure G-5, until you find the broken door. The path is not the shortest path because it needs twelve cards at least. After you've found a broken door on the path, you should follow the shortest path to the exit that doesn't use the broken door. With this strategy, you can pass the maze with sixteen cards whichever door is broken. Figure G-6 shows one of the worst cases of this strategy; it needs sixteen cards. Figure G-5: The path before you find the broken door Figure G-6: One of the worst cases of the strategy You are requested to write a program that prints the minimum number of cards to pass the maze whichever door is broken. Input The input consists of one or more datasets, each of which represents a maze. The number of datasets is no more than 100. The first line of a dataset contains two integer numbers, the height h and the width w of the rectangular maze, in this order. You may assume that 2 ≤ h, w ≤ 30. The following 2 × h − 1 lines of a dataset describe whether there are doo ...(truncated)	[ { "submission_id": "aoj_1178_10946388", "code_snippet": "#include<cstring>\n#include<cstdio>\n#include<algorithm>\nusing namespace std;\nint n, m, bak, cl, qx[909], qy[909], dis[33][33], pas[77][77], x, y, dx[4], dy[4], mn[33][33], ans[77][77][2];\nint main()\n{\n\tdx[0] = -1; dy[0] = 0;\n\tdx[1] = 0; dy[1]...
aoj_1179_cpp	Millennium A wise king declared a new calendar. "Tomorrow shall be the first day of the calendar, that is, the day 1 of the month 1 of the year 1. Each year consists of 10 months, from month 1 through month 10, and starts from a big month . A common year shall start with a big month, followed by small months and big months one after another. Therefore the first month is a big month, the second month is a small month, the third a big month, ..., and the 10th and last month a small one. A big month consists of 20 days and a small month consists of 19 days. However years which are multiples of three, that are year 3, year 6, year 9, and so on, shall consist of 10 big months and no small month." Many years have passed since the calendar started to be used. For celebration of the millennium day (the year 1000, month 1, day 1), a royal lottery is going to be organized to send gifts to those who have lived as many days as the number chosen by the lottery. Write a program that helps people calculate the number of days since their birthdate to the millennium day. Input The input is formatted as follows. n Y 1 M 1 D 1 Y 2 M 2 D 2 ... Y n M n D n Here, the first line gives the number of datasets as a positive integer n , which is less than or equal to 100. It is followed by n datasets. Each dataset is formatted in a line and gives three positive integers, Y i (< 1000), M i (≤ 10), and D i (≤ 20), that correspond to the year, month and day, respectively, of a person's birthdate in the king's calendar. These three numbers are separated by a space. Output For the birthdate specified in each dataset, print in a line the number of days from the birthdate, inclusive, to the millennium day, exclusive. Output lines should not contain any character other than this number. Sample Input 8 1 1 1 344 3 1 696 5 1 182 9 5 998 8 7 344 2 19 696 4 19 999 10 20 Output for the Sample Input 196470 128976 59710 160715 252 128977 59712 1	[ { "submission_id": "aoj_1179_10683989", "code_snippet": "#line 1 \"speedrun.cpp\"\n#include <bits/stdc++.h>\n#line 1 \"/home/ardririy/repos/cp-libs/libraries-cpp/input.hpp\"\n\n\n#line 6 \"/home/ardririy/repos/cp-libs/libraries-cpp/input.hpp\"\nusing namespace std;\nvector<long long> i64_vec_IN(int n) {vect...
aoj_1180_cpp	Recurring Decimals A decimal representation of an integer can be transformed to another integer by rearranging the order of digits. Let us make a sequence using this fact. A non-negative integer a 0 and the number of digits L are given first. Applying the following rules, we obtain a i +1 from a i . Express the integer a i in decimal notation with L digits. Leading zeros are added if necessary. For example, the decimal notation with six digits of the number 2012 is 002012. Rearranging the digits, find the largest possible integer and the smallest possible integer; In the example above, the largest possible integer is 221000 and the smallest is 000122 = 122. A new integer a i +1 is obtained by subtracting the smallest possible integer from the largest. In the example above, we obtain 220878 subtracting 122 from 221000. When you repeat this calculation, you will get a sequence of integers a 0 , a 1 , a 2 , ... . For example, starting with the integer 83268 and with the number of digits 6, you will get the following sequence of integers a 0 , a 1 , a 2 , ... . a 0 = 083268 a 1 = 886320 − 023688 = 862632 a 2 = 866322 − 223668 = 642654 a 3 = 665442 − 244566 = 420876 a 4 = 876420 − 024678 = 851742 a 5 = 875421 − 124578 = 750843 a 6 = 875430 − 034578 = 840852 a 7 = 885420 − 024588 = 860832 a 8 = 886320 − 023688 = 862632 … Because the number of digits to express integers is fixed, you will encounter occurrences of the same integer in the sequence a 0 , a 1 , a 2 , ... eventually. Therefore you can always find a pair of i and j that satisfies the condition a i = a j ( i > j ). In the example above, the pair ( i = 8, j = 1) satisfies the condition because a 8 = a 1 = 862632. Write a program that, given an initial integer a 0 and a number of digits L , finds the smallest i that satisfies the condition a i = a j ( i > j ). Input The input consists of multiple datasets. A dataset is a line containing two integers a 0 and L separated by a space. a 0 and L represent the initial integer of the sequence and the number of digits, respectively, where 1 ≤ L ≤ 6 and 0 ≤ a 0 < 10 L . The end of the input is indicated by a line containing two zeros; it is not a dataset. Output For each dataset, find the smallest number i that satisfies the condition a i = a j ( i > j ) and print a line containing three integers, j , a i and i − j . Numbers should be separated by a space. Leading zeros should be suppressed. Output lines should not contain extra characters. You can assume that the above i is not greater than 20. Sample Input 2012 4 83268 6 1112 4 0 1 99 2 0 0 Output for the Sample Input 3 6174 1 1 862632 7 5 6174 1 0 0 1 1 0 1	[ { "submission_id": "aoj_1180_10853944", "code_snippet": "#include <iostream>\n#include <cstdio>\n#include <cstring>\n#include <cmath>\n#include <cstdlib>\n#include <algorithm>\n#include <vector>\n#include <map>\n#include <queue>\n#include <set>\nusing namespace std;\n#define SZ(v) ((int)(v).size())\n#define...
aoj_1187_cpp	ICPC Ranking Your mission in this problem is to write a program which, given the submission log of an ICPC (International Collegiate Programming Contest), determines team rankings. The log is a sequence of records of program submission in the order of submission. A record has four fields: elapsed time, team number, problem number, and judgment. The elapsed time is the time elapsed from the beginning of the contest to the submission. The judgment field tells whether the submitted program was correct or incorrect, and when incorrect, what kind of an error was found. The team ranking is determined according to the following rules. Note that the rule set shown here is one used in the real ICPC World Finals and Regionals, with some detail rules omitted for simplification. Teams that solved more problems are ranked higher. Among teams that solve the same number of problems, ones with smaller total consumed time are ranked higher. If two or more teams solved the same number of problems, and their total consumed times are the same, they are ranked the same. The total consumed time is the sum of the consumed time for each problem solved. The consumed time for a solved problem is the elapsed time of the accepted submission plus 20 penalty minutes for every previously rejected submission for that problem. If a team did not solve a problem, the consumed time for the problem is zero, and thus even if there are several incorrect submissions, no penalty is given. You can assume that a team never submits a program for a problem after the correct submission for the same problem. Input The input is a sequence of datasets each in the following format. The last dataset is followed by a line with four zeros. M T P R m 1 t 1 p 1 j 1 m 2 t 2 p 2 j 2 ..... m R t R p R j R The first line of a dataset contains four integers M , T , P , and R . M is the duration of the contest. T is the number of teams. P is the number of problems. R is the number of submission records. The relations 120 ≤ M ≤ 300, 1 ≤ T ≤ 50, 1 ≤ P ≤ 10, and 0 ≤ R ≤ 2000 hold for these values. Each team is assigned a team number between 1 and T , inclusive. Each problem is assigned a problem number between 1 and P , inclusive. Each of the following R lines contains a submission record with four integers m k , t k , p k , and j k (1 ≤ k ≤ R ). m k is the elapsed time. t k is the team number. p k is the problem number. j k is the judgment (0 means correct, and other values mean incorrect). The relations 0 ≤ m k ≤ M −1, 1 ≤ t k ≤ T , 1 ≤ p k ≤ P , and 0 ≤ j k ≤ 10 hold for these values. The elapsed time fields are rounded off to the nearest minute. Submission records are given in the order of submission. Therefore, if i < j , the i -th submission is done before the j -th submission ( m i ≤ m j ). In some cases, you can determine the ranking of two teams with a difference less than a minute, by using this fact. However, such a fact is never used in the team ranking. Teams are ranked only using time informa ...(truncated)	[ { "submission_id": "aoj_1187_3560625", "code_snippet": "#define _CRT_SECURE_NO_WARNINGS\n#include <stdio.h>\n#include <algorithm>\n#include <utility>\n#include <functional>\n#include <cstring>\n#include <queue>\n#include <stack>\n#include <math.h>\n#include <iterator>\n#include <vector>\n#include <string>\...
aoj_1181_cpp	Biased Dice Professor Random, known for his research on randomized algorithms, is now conducting an experiment on biased dice. His experiment consists of dropping a number of dice onto a plane, one after another from a fixed position above the plane. The dice fall onto the plane or dice already there, without rotating, and may roll and fall according to their property. Then he observes and records the status of the stack formed on the plane, specifically, how many times each number appears on the faces visible from above. All the dice have the same size and their face numbering is identical, which we show in Figure C-1. Figure C-1: Numbering of a die The dice have very special properties, as in the following. (1) Ordinary dice can roll in four directions, but the dice used in this experiment never roll in the directions of faces 1, 2 and 3; they can only roll in the directions of faces 4, 5 and 6. In the situation shown in Figure C-2, our die can only roll to one of two directions. Figure C-2: An ordinary die and a biased die (2) The die can only roll when it will fall down after rolling, as shown in Figure C-3. When multiple possibilities exist, the die rolls towards the face with the largest number among those directions it can roll to. Figure C-3: A die can roll only when it can fall (3) When a die rolls, it rolls exactly 90 degrees, and then falls straight down until its bottom face touches another die or the plane, as in the case [B] or [C] of Figure C-4. (4) After rolling and falling, the die repeatedly does so according to the rules (1) to (3) above. Figure C-4: Example stacking of biased dice For example, when we drop four dice all in the same orientation, 6 at the top and 4 at the front, then a stack will be formed as shown in Figure C-4. Figure C-5: Example records After forming the stack, we count the numbers of faces with 1 through 6 visible from above and record them. For example, in the left case of Figure C-5, the record will be "0 2 1 0 0 0", and in the right case, "0 1 1 0 0 1". Input The input consists of several datasets each in the following format. n t 1 f 1 t 2 f 2 ... t n f n Here, n (1 ≤ n ≤ 100) is an integer and is the number of the dice to be dropped. t i and f i (1 ≤ t i , f i ≤ 6) are two integers separated by a space and represent the numbers on the top and the front faces of the i -th die, when it is released, respectively. The end of the input is indicated by a line containing a single zero. Output For each dataset, output six integers separated by a space. The integers represent the numbers of faces with 1 through 6 correspondingly, visible from above. There may not be any other characters in the output. Sample Input 4 6 4 6 4 6 4 6 4 2 5 3 5 3 8 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 6 4 6 1 5 2 3 5 3 2 4 4 2 0 Output for the Sample Input 0 1 1 0 0 1 1 0 0 0 1 0 1 2 2 1 0 0 2 3 0 0 0 0	[ { "submission_id": "aoj_1181_10609938", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nconst long long MOD1 = 1000000007;\nconst long long MOD2 = 998244353;\n#define all(v) v.begin(), v.end()\n#define rall(a) a.rbegin(), a.rend()\n#define fi first\n#define se second\n// #define endl \"\\...
aoj_1185_cpp	Patisserie ACM Amber Claes Maes, a patissier, opened her own shop last month. She decided to submit her work to the International Chocolate Patissier Competition to promote her shop, and she was pursuing a recipe of sweet chocolate bars. After thousands of trials, she finally reached the recipe. However, the recipe required high skill levels to form chocolate to an orderly rectangular shape. Sadly, she has just made another strange-shaped chocolate bar as shown in Figure G-1. Figure G-1: A strange-shaped chocolate bar Each chocolate bar consists of many small rectangular segments of chocolate. Adjacent segments are separated with a groove in between them for ease of snapping. She planned to cut the strange-shaped chocolate bars into several rectangular pieces and sell them in her shop. She wants to cut each chocolate bar as follows. The bar must be cut along grooves. The bar must be cut into rectangular pieces. The bar must be cut into as few pieces as possible. Following the rules, Figure G-2 can be an instance of cutting of the chocolate bar shown in Figure G-1. Figures G-3 and G-4 do not meet the rules; Figure G-3 has a non-rectangular piece, and Figure G-4 has more pieces than Figure G-2. Figure G-2: An instance of cutting that follows the rules Figure G-3: An instance of cutting that leaves a non-rectangular piece Figure G-4: An instance of cutting that yields more pieces than Figure G-2 Your job is to write a program that computes the number of pieces of chocolate after cutting according to the rules. Input The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset is formatted as follows. h w r (1, 1) ... r (1, w ) r (2, 1) ... r (2, w ) ... r ( h , 1) ... r ( h , w ) The integers h and w are the lengths of the two orthogonal dimensions of the chocolate, in number of segments. You may assume that 2 ≤ h ≤ 100 and 2 ≤ w ≤ 100. Each of the following h lines consists of w characters, each is either a " . " or a " # ". The character r ( i , j ) represents whether the chocolate segment exists at the position ( i , j ) as follows. " . ": There is no chocolate. " # ": There is a segment of chocolate. You can assume that there is no dataset that represents either multiple disconnected bars as depicted in Figure G-5 or a bar in a shape with hole(s) as depicted in Figure G-6 and G-7. You can also assume that there is at least one " # " character in each dataset. Figure G-5: Disconnected chocolate bars Figure G-6: A chocolate bar with a hole Figure G-7: Another instance of a chocolate bar with a hole Output For each dataset, output a line containing the integer representing the number of chocolate pieces obtained by cutting according to the rules. No other characters are allowed in the output. Sample Input 3 5 ###.# ##### ###.. 4 5 .#.## .#### ####. ##.#. 8 8 .#.#.#.# ######## .######. ######## .######. ######## .######. ######## 8 8 .#.#.#.# ######## .##.#.#. ##... ...(truncated)	[ { "submission_id": "aoj_1185_10882539", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nstruct Bimatch{\n vector<vector<int>> g;\n vector<int> d, mc, used, vv;\n Bimatch(int n, int m): g(n), mc(m, -1), used(n){\n }\n void add(int u, int v){\n g[u].push_back(v);\n }\n void bfs(){\n...
aoj_1183_cpp	Chain-Confined Path There is a chain consisting of multiple circles on a plane. The first (last) circle of the chain only intersects with the next (previous) circle, and each intermediate circle intersects only with the two neighboring circles. Your task is to find the shortest path that satisfies the following conditions. The path connects the centers of the first circle and the last circle. The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles. Figure E-1 shows an example of such a chain and the corresponding shortest path. Figure E-1: An example chain and the corresponding shortest path Input The input consists of multiple datasets. Each dataset represents the shape of a chain in the following format. n x 1 y 1 r 1 x 2 y 2 r 2 ... x n y n r n The first line of a dataset contains an integer n (3 ≤ n ≤ 100) representing the number of the circles. Each of the following n lines contains three integers separated by a single space. ( x i , y i ) and r i represent the center position and the radius of the i -th circle C i . You can assume that 0 ≤ x i ≤ 1000, 0 ≤ y i ≤ 1000, and 1 ≤ r i ≤ 25. You can assume that C i and C i +1 (1 ≤ i ≤ n −1) intersect at two separate points. When j ≥ i +2, C i and C j are apart and either of them does not contain the other. In addition, you can assume that any circle does not contain the center of any other circle. The end of the input is indicated by a line containing a zero. Figure E-1 corresponds to the first dataset of Sample Input below. Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input. Figure E-2: Example chains and the corresponding shortest paths Output For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle. The value should not have an error greater than 0.001. No extra characters should appear in the output. Sample Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output for the Sample Input 58.953437 11.414214 16.0 61.874812 63.195179	[ { "submission_id": "aoj_1183_10853933", "code_snippet": "/\n Author: xioumu\n * Created Time: 2012/7/20 10:46:25\n * File Name: e.cpp\n * solve: e.cpp\n */\n#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<cmath>\n#include<algorithm>\n#include<string>\n#include<map>\n#include<set>\nusin...
aoj_1184_cpp	Generic Poker You have a deck of N × M cards. Each card in the deck has a rank. The range of ranks is 1 through M , and the deck includes N cards of each rank. We denote a card with rank m by m here. You can draw a hand of L cards at random from the deck. If the hand matches the given pattern, some bonus will be rewarded. A pattern is described as follows. hand_pattern = card_pattern 1 ' ' card_pattern 2 ' ' ... ' ' card_pattern L card_pattern = '' \| var_plus var_plus = variable \| var_plus '+' variable = 'a' \| 'b' \| 'c' hand_pattern A hand matches the hand_pattern if each card_pattern in the hand_pattern matches with a distinct card in the hand. card_pattern If the card_pattern is an asterisk (''), it matches any card. Characters 'a', 'b', and 'c' denote variables and all the occurrences of the same variable match cards of the same rank. A card_pattern with a variable followed by plus ('+') characters matches a card whose rank is the sum of the rank corresponding to the variable and the number of plus characters. You can assume that, when a hand_pattern includes a card_pattern with a variable followed by some number of plus characters, it also includes card_patterns with that variable and all smaller numbers (including zero) of plus characters. For example, if 'a+++' appears in a hand_pattern, card_patterns 'a', 'a+', and 'a++' also appear in the hand_pattern. There is no restriction on which ranks different variables mean. For example, 'a' and 'b' may or may not match cards of the same rank. We show some example hand_patterns. The pattern a * b a b matches the hand: 3 3 10 10 9 with 'a's and 'b's meaning 3 and 10 (or 10 and 3), respectively. This pattern also matches the following hand. 3 3 3 3 9 In this case, both 'a's and 'b's mean 3. The pattern a a+ a++ a+++ a++++ matches the following hand. 4 5 6 7 8 In this case, 'a' should mean 4. Your mission is to write a program that computes the probability that a hand randomly drawn from the deck matches the given hand_pattern. Input The input is a sequence of datasets. Each dataset is formatted as follows. N M L card_pattern 1 card_pattern 2 ... card_pattern L The first line consists of three positive integers N , M , and L . N indicates the number of cards in each rank, M indicates the number of ranks, and L indicates the number of cards in a hand. N , M , and L are constrained as follows. 1 ≤ N ≤ 7 1 ≤ M ≤ 60 1 ≤ L ≤ 7 L ≤ N × M The second line describes a hand_pattern. The end of the input is indicated by a line containing three zeros separated by a single space. Output For each dataset, output a line containing a decimal fraction which means the probability of a hand matching the hand_pattern. The output should not contain an error greater than 10 −8 . No other characters should be contained in the output. Sample Input 1 1 1 a 3 3 4 a+ * a * 2 2 3 a a b 2 2 3 * * * 2 2 3 * b b 2 2 2 a a 2 3 3 a a+ a++ 2 6 6 a a+ a++ b b+ b++ 4 13 5 a a * * * 4 13 5 a a b b * 4 13 5 a a a * * 4 13 5 a a+ a+ ...(truncated)	[ { "submission_id": "aoj_1184_8998859", "code_snippet": "#line 2 \"cp-library/src/cp-template.hpp\"\n#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\nusing ld = long double;\nusing uint = unsigned int;\nusing ull = unsigned long long;\nusing i32 = int;\nusing u32 = unsigned int;\nusing...
aoj_1182_cpp	Railway Connection Tokyo has a very complex railway system. For example, there exists a partial map of lines and stations as shown in Figure D-1. Figure D-1: A sample railway network Suppose you are going to station D from station A. Obviously, the path with the shortest distance is A→B→D. However, the path with the shortest distance does not necessarily mean the minimum cost. Assume the lines A-B, B-C, and C-D are operated by one railway company, and the line B-D is operated by another company. In this case, the path A→B→C→D may cost less than A→B→D. One of the reasons is that the fare is not proportional to the distance. Usually, the longer the distance is, the fare per unit distance is lower. If one uses lines of more than one railway company, the fares charged by these companies are simply added together, and consequently the total cost may become higher although the distance is shorter than the path using lines of only one company. In this problem, a railway network including multiple railway companies is given. The fare table (the rule to calculate the fare from the distance) of each company is also given. Your task is, given the starting point and the goal point, to write a program that computes the path with the least total fare. Input The input consists of multiple datasets, each in the following format. n m c s g x 1 y 1 d 1 c 1 ... x m y m d m c m p 1 ... p c q 1,1 ... q 1, p 1 -1 r 1,1 ... r 1, p 1 ... q c ,1 ... q c,p c -1 r c ,1 ... r c,p c Every input item in a dataset is a non-negative integer. Input items in the same input line are separated by a space. The first input line gives the size of the railway network and the intended trip. n is the number of stations (2 ≤ n ≤ 100). m is the number of lines connecting two stations (0 ≤ m ≤ 10000). c is the number of railway companies (1 ≤ c ≤ 20). s is the station index of the starting point (1 ≤ s ≤ n ). g is the station index of the goal point (1 ≤ g ≤ n , g ≠ s ). The following m input lines give the details of (railway) lines. The i -th line connects two stations x i and y i (1 ≤ x i ≤ n , 1 ≤ y i ≤ n , x i ≠ y i ). Each line can be traveled in both directions. There may be two or more lines connecting the same pair of stations. d i is the distance of the i -th line (1 ≤ d i ≤ 200). c i is the company index of the railway company operating the line (1 ≤ c i ≤ c ). The fare table (the relation between the distance and the fare) of each railway company can be expressed as a line chart. For the railway company j , the number of sections of the line chart is given by p j (1 ≤ p j ≤ 50). q j,k (1 ≤ k ≤ p j -1) gives the distance separating two sections of the chart (1 ≤ q j,k ≤ 10000). r j,k (1 ≤ k ≤ p j ) gives the fare increment per unit distance for the corresponding section of the chart (1 ≤ r j,k ≤ 100). More precisely, with the fare for the distance z denoted by f j ( z ), the fare for distance z satisfying q j , k -1 +1 ≤ z ≤ q j , k is computed by the recurrence relation f j ( z ...(truncated)	[ { "submission_id": "aoj_1182_10852690", "code_snippet": "/\n Author:heroming\n * File:heroming.cpp\n * Time:2012-7-19 9:33:45\n */\n#include <iostream>\n#include <cstdio>\n#include <string>\n#include <cstring>\n#include <cmath>\n#include <algorithm>\n#include <vector>\n#include <queue>\nusing namespace s...
aoj_1186_cpp	Integral Rectangles Let us consider rectangles whose height, h , and width, w , are both integers. We call such rectangles integral rectangles . In this problem, we consider only wide integral rectangles, i.e., those with w > h . We define the following ordering of wide integral rectangles. Given two wide integral rectangles, The one shorter in its diagonal line is smaller, and If the two have diagonal lines with the same length, the one shorter in its height is smaller. Given a wide integral rectangle, find the smallest wide integral rectangle bigger than the given one. Input The entire input consists of multiple datasets. The number of datasets is no more than 100. Each dataset describes a wide integral rectangle by specifying its height and width, namely h and w , separated by a space in a line, as follows. h w For each dataset, h and w (> h ) are both integers greater than 0 and no more than 100. The end of the input is indicated by a line of two zeros separated by a space. Output For each dataset, print in a line two numbers describing the height and width, namely h and w (> h ), of the smallest wide integral rectangle bigger than the one described in the dataset. Put a space between the numbers. No other characters are allowed in the output. For any wide integral rectangle given in the input, the width and height of the smallest wide integral rectangle bigger than the given one are both known to be not greater than 150. In addition, although the ordering of wide integral rectangles uses the comparison of lengths of diagonal lines, this comparison can be replaced with that of squares (self-products) of lengths of diagonal lines, which can avoid unnecessary troubles possibly caused by the use of floating-point numbers. Sample Input 1 2 1 3 2 3 1 4 2 4 5 6 1 8 4 7 98 100 99 100 0 0 Output for the Sample Input 1 3 2 3 1 4 2 4 3 4 1 8 4 7 2 8 3 140 89 109	[ { "submission_id": "aoj_1186_9327994", "code_snippet": "#include<iostream>\n#include<algorithm>\n#include<vector>\nusing namespace std;\nbool solve()\n{\n int H,W;\n cin>>H>>W;\n if(H==0&&W==0)return 0;\n vector<pair<int,int>>bigger;\n auto comp=[](pair<int,int>p,pair<int,int>q)\n {\n ...
aoj_1188_cpp	Hierarchical Democracy The presidential election in Republic of Democratia is carried out through multiple stages as follows. There are exactly two presidential candidates. At the first stage, eligible voters go to the polls of his/her electoral district. The winner of the district is the candidate who takes a majority of the votes. Voters cast their ballots only at this first stage. A district of the k -th stage ( k > 1) consists of multiple districts of the ( k − 1)-th stage. In contrast, a district of the ( k − 1)-th stage is a sub-district of one and only one district of the k -th stage. The winner of a district of the k -th stage is the candidate who wins in a majority of its sub-districts of the ( k − 1)-th stage. The final stage has just one nation-wide district. The winner of the final stage is chosen as the president. You can assume the following about the presidential election of this country. Every eligible voter casts a vote. The number of the eligible voters of each electoral district of the first stage is odd. The number of the sub-districts of the ( k − 1)-th stage that constitute a district of the k -th stage ( k > 1) is also odd. This means that each district of every stage has its winner (there is no tie). Your mission is to write a program that finds a way to win the presidential election with the minimum number of votes. Suppose, for instance, that the district of the final stage has three sub-districts of the first stage and that the numbers of the eligible voters of the sub-districts are 123, 4567, and 89, respectively. The minimum number of votes required to be the winner is 107, that is, 62 from the first district and 45 from the third. In this case, even if the other candidate were given all the 4567 votes in the second district, s/he would inevitably be the loser. Although you might consider this election system unfair, you should accept it as a reality. Input The entire input looks like: the number of datasets (=n) 1st dataset 2nd dataset … n-th dataset The number of datasets, n , is no more than 100. The number of the eligible voters of each district and the part-whole relations among districts are denoted as follows. An electoral district of the first stage is denoted as [ c ], where c is the number of the eligible voters of the district. A district of the k -th stage ( k > 1) is denoted as [ d 1 d 2 … d m ], where d 1 , d 2 , …, d m denote its sub-districts of the ( k − 1)-th stage in this notation. For instance, an electoral district of the first stage that has 123 eligible voters is denoted as [123]. A district of the second stage consisting of three sub-districts of the first stage that have 123, 4567, and 89 eligible voters, respectively, is denoted as [[123][4567][89]]. Each dataset is a line that contains the character string denoting the district of the final stage in the aforementioned notation. You can assume the following. The character string in each dataset does not include any characters except digits ( ...(truncated)	[ { "submission_id": "aoj_1188_10851154", "code_snippet": "#include <iostream>\n#include <sstream>\n#include <algorithm>\n#include <string>\n#include <vector>\n#include <numeric>\n#define sz(x) int((x).size())\n#define all(x) (x).begin(), (x).end()\n#define phb push_back\nusing namespace std;\n\nint Z;\nstrin...
aoj_1189_cpp	Prime Caves An international expedition discovered abandoned Buddhist cave temples in a giant cliff standing on the middle of a desert. There were many small caves dug into halfway down the vertical cliff, which were aligned on square grids. The archaeologists in the expedition were excited by Buddha's statues in those caves. More excitingly, there were scrolls of Buddhism sutras (holy books) hidden in some of the caves. Those scrolls, which estimated to be written more than thousand years ago, were of immeasurable value. The leader of the expedition wanted to collect as many scrolls as possible. However, it was not easy to get into the caves as they were located in the middle of the cliff. The only way to enter a cave was to hang you from a helicopter. Once entered and explored a cave, you can climb down to one of the three caves under your cave; i.e., either the cave directly below your cave, the caves one left or right to the cave directly below your cave. This can be repeated for as many times as you want, and then you can descent down to the ground by using a long rope. So you can explore several caves in one attempt. But which caves you should visit? By examining the results of the preliminary attempts, a mathematician member of the expedition discovered that (1) the caves can be numbered from the central one, spiraling out as shown in Figure D-1; and (2) only those caves with their cave numbers being prime (let's call such caves prime caves ), which are circled in the figure, store scrolls. From the next attempt, you would be able to maximize the number of prime caves to explore. Figure D-1: Numbering of the caves and the prime caves Write a program, given the total number of the caves and the cave visited first, that finds the descending route containing the maximum number of prime caves. Input The input consists of multiple datasets. Each dataset has an integer m (1 ≤ m ≤ 10 6 ) and an integer n (1 ≤ n ≤ m ) in one line, separated by a space. m represents the total number of caves. n represents the cave number of the cave from which you will start your exploration. The last dataset is followed by a line with two zeros. Output For each dataset, find the path that starts from the cave n and contains the largest number of prime caves, and output the number of the prime caves on the path and the last prime cave number on the path in one line, separated by a space. The cave n , explored first, is included in the caves on the path. If there is more than one such path, output for the path in which the last of the prime caves explored has the largest number among such paths. When there is no such path that explores prime caves, output " 0 0 " (without quotation marks). Sample Input 49 22 46 37 42 23 945 561 1081 681 1056 452 1042 862 973 677 1000000 1000000 0 0 Output for the Sample Input 0 0 6 43 1 23 20 829 18 947 10 947 13 947 23 947 534 993541	[ { "submission_id": "aoj_1189_10852870", "code_snippet": "#include \"bits/stdc++.h\"\n\n#define REP(i,n) for(ll i=0;i<n;++i)\n#define RREP(i,n) for(ll i=n-1;i>=0;--i)\n#define FOR(i,m,n) for(ll i=m;i<n;++i)\n#define RFOR(i,m,n) for(ll i=n-1;i>=m;--i)\n#define ALL(v) (v).begin(),(v).end()\n#define PB(a) push_...
aoj_1190_cpp	Anchored Balloon A balloon placed on the ground is connected to one or more anchors on the ground with ropes. Each rope is long enough to connect the balloon and the anchor. No two ropes cross each other. Figure E-1 shows such a situation. Figure E-1: A balloon and ropes on the ground Now the balloon takes off, and your task is to find how high the balloon can go up with keeping the rope connections. The positions of the anchors are fixed. The lengths of the ropes and the positions of the anchors are given. You may assume that these ropes have no weight and thus can be straightened up when pulled to whichever directions. Figure E-2 shows the highest position of the balloon for the situation shown in Figure E-1. Figure E-2: The highest position of the balloon Input The input consists of multiple datasets, each in the following format. n x 1 y 1 l 1 ... x n y n l n The first line of a dataset contains an integer n (1 ≤ n ≤ 10) representing the number of the ropes. Each of the following n lines contains three integers, x i , y i , and l i , separated by a single space. P i = ( x i , y i ) represents the position of the anchor connecting the i -th rope, and l i represents the length of the rope. You can assume that −100 ≤ x i ≤ 100, −100 ≤ y i ≤ 100, and 1 ≤ l i ≤ 300. The balloon is initially placed at (0, 0) on the ground. You can ignore the size of the balloon and the anchors. You can assume that P i and P j represent different positions if i ≠ j . You can also assume that the distance between P i and (0, 0) is less than or equal to l i −1. This means that the balloon can go up at least 1 unit high. Figures E-1 and E-2 correspond to the first dataset of Sample Input below. The end of the input is indicated by a line containing a zero. Output For each dataset, output a single line containing the maximum height that the balloon can go up. The error of the value should be no greater than 0.00001. No extra characters should appear in the output. Sample Input 3 10 10 20 10 -10 20 -10 10 120 1 10 10 16 2 10 10 20 10 -10 20 2 100 0 101 -90 0 91 2 0 0 53 30 40 102 3 10 10 20 10 -10 20 -10 -10 20 3 1 5 13 5 -3 13 -3 -3 13 3 98 97 168 -82 -80 193 -99 -96 211 4 90 -100 160 -80 -80 150 90 80 150 80 80 245 4 85 -90 290 -80 -80 220 -85 90 145 85 90 170 5 0 0 4 3 0 5 -3 0 5 0 3 5 0 -3 5 10 95 -93 260 -86 96 211 91 90 177 -81 -80 124 -91 91 144 97 94 165 -90 -86 194 89 85 167 -93 -80 222 92 -84 218 0 Output for the Sample Input 17.3205081 16.0000000 17.3205081 13.8011200 53.0000000 14.1421356 12.0000000 128.3928757 94.1879092 131.1240816 4.0000000 72.2251798	[ { "submission_id": "aoj_1190_10433181", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\nusing ll = long long;\n\ntypedef complex<double> Point;\nconst double EPS = 1e-8;\n\nstruct Circle {\n Point p;\n double r;\n};\n\n// 円の交点を求めるメソッド\npair<Point, Point> cc_cross(const Circle& c1, c...
aoj_1193_cpp	Chain Disappearance Puzzle We are playing a puzzle. An upright board with H rows by 5 columns of cells, as shown in the figure below, is used in this puzzle. A stone engraved with a digit, one of 1 through 9, is placed in each of the cells. When three or more stones in horizontally adjacent cells are engraved with the same digit, the stones will disappear. If there are stones in the cells above the cell with a disappeared stone, the stones in the above cells will drop down, filling the vacancy. The puzzle proceeds taking the following steps. When three or more stones in horizontally adjacent cells are engraved with the same digit, the stones will disappear. Disappearances of all such groups of stones take place simultaneously. When stones are in the cells above the emptied cells, these stones drop down so that the emptied cells are filled. After the completion of all stone drops, if one or more groups of stones satisfy the disappearance condition, repeat by returning to the step 1. The score of this puzzle is the sum of the digits on the disappeared stones. Write a program that calculates the score of given configurations of stones. Input The input consists of multiple datasets. Each dataset is formed as follows. Board height H Stone placement of the row 1 Stone placement of the row 2 ... Stone placement of the row H The first line specifies the height ( H ) of the puzzle board (1 ≤ H ≤ 10). The remaining H lines give placement of stones on each of the rows from top to bottom. The placements are given by five digits (1 through 9), separated by a space. These digits are engraved on the five stones in the corresponding row, in the same order. The input ends with a line with a single zero. Output For each dataset, output the score in a line. Output lines may not include any characters except the digits expressing the scores. Sample Input 1 6 9 9 9 9 5 5 9 5 5 9 5 5 6 9 9 4 6 3 6 9 3 3 2 9 9 2 2 1 1 1 10 3 5 6 5 6 2 2 2 8 3 6 2 5 9 2 7 7 7 6 1 4 6 6 4 9 8 9 1 1 8 5 6 1 8 1 6 8 2 1 2 9 6 3 3 5 5 3 8 8 8 5 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 3 2 2 8 7 4 6 5 7 7 7 8 8 9 9 9 0 Output for the Sample Input 36 38 99 0 72	[ { "submission_id": "aoj_1193_9527420", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\nll MOD = 1'000'000'007;\nll inf = (1LL << 62);\n\n// clang-format off\nauto getll(){ll n; cin >> n; return n;}\nauto getstr(){string s; cin >> s; return s;}\nauto getdb(){double n; ...
aoj_1191_cpp	Rotate and Rewrite Two sequences of integers A: A 1 A 2 ... A n and B: B 1 B 2 ... B m and a set of rewriting rules of the form " x 1 x 2 ... x k → y " are given. The following transformations on each of the sequences are allowed an arbitrary number of times in an arbitrary order independently. Rotate : Moving the first element of a sequence to the last. That is, transforming a sequence c 1 c 2 ... c p to c 2 ... c p c 1 . Rewrite : With a rewriting rule " x 1 x 2 ... x k → y ", transforming a sequence c 1 c 2 ... c i x 1 x 2 ... x k d 1 d 2 ... d j to c 1 c 2 ... c i y d 1 d 2 ... d j . Your task is to determine whether it is possible to transform the two sequences A and B into the same sequence. If possible, compute the length of the longest of the sequences after such a transformation. Input The input consists of multiple datasets. Each dataset has the following form. n m r A 1 A 2 ... A n B 1 B 2 ... B m R 1 ... R r The first line of a dataset consists of three positive integers n , m , and r, where n ( n ≤ 25) is the length of the sequence A, m ( m ≤ 25) is the length of the sequence B, and r ( r ≤ 60) is the number of rewriting rules. The second line contains n integers representing the n elements of A. The third line contains m integers representing the m elements of B. Each of the last r lines describes a rewriting rule in the following form. k x 1 x 2 ... x k y The first k is an integer (2 ≤ k ≤ 10), which is the length of the left-hand side of the rule. It is followed by k integers x 1 x 2 ... x k , representing the left-hand side of the rule. Finally comes an integer y , representing the right-hand side. All of A 1 , .., A n , B 1 , ..., B m , x 1 , ..., x k , and y are in the range between 1 and 30, inclusive. A line "0 0 0" denotes the end of the input. Output For each dataset, if it is possible to transform A and B to the same sequence, print the length of the longest of the sequences after such a transformation. Print -1 if it is impossible. Sample Input 3 3 3 1 2 3 4 5 6 2 1 2 5 2 6 4 3 2 5 3 1 3 3 2 1 1 1 2 2 1 2 1 1 2 2 2 2 1 7 1 2 1 1 2 1 4 1 2 4 3 1 4 1 4 3 2 4 2 4 16 14 5 2 1 2 2 1 3 2 1 3 2 2 1 1 3 1 2 2 1 3 1 1 2 3 1 2 2 2 2 1 3 2 3 1 3 3 2 2 2 1 3 2 2 1 2 3 1 2 2 2 4 2 1 2 2 2 0 0 0 Output for the Sample Input 2 -1 1 9	[ { "submission_id": "aoj_1191_10335939", "code_snippet": "// AOJ #1191 Rotate and Rewrite\n// 2025.3.30\n\n#include <bits/stdc++.h>\nusing namespace std;\n\n#define NMAX 50\nconst int BAS = 1000;\nint A[NMAX+5], B[NMAX+5];\nbool dpA[NMAX+5][NMAX+5][600];\nbool dpB[NMAX+5][NMAX+5][600];\nint sudpA[NMAX+5][NMA...
aoj_1194_cpp	Vampire Mr. C is a vampire. If he is exposed to the sunlight directly, he turns into ash. Nevertheless, last night, he attended to the meeting of Immortal and Corpse Programmers Circle, and he has to go home in the near dawn. Fortunately, there are many tall buildings around Mr. C's home, and while the sunlight is blocked by the buildings, he can move around safely. The top end of the sun has just reached the horizon now. In how many seconds does Mr. C have to go into his safe coffin? To simplify the problem, we represent the eastern dawn sky as a 2-dimensional x - y plane, where the x axis is horizontal and the y axis is vertical, and approximate building silhouettes by rectangles and the sun by a circle on this plane. The x axis represents the horizon. We denote the time by t , and the current time is t =0. The radius of the sun is r and its center is at (0, - r ) when the time t =0. The sun moves on the x - y plane in a uniform linear motion at a constant velocity of (0, 1) per second. The sunlight is blocked if and only if the entire region of the sun (including its edge) is included in the union of the silhouettes (including their edges) and the region below the horizon (y ≤ 0). Write a program that computes the time of the last moment when the sunlight is blocked. The following figure shows the layout of silhouettes and the position of the sun at the last moment when the sunlight is blocked, that corresponds to the first dataset of Sample Input below. As this figure indicates, there are possibilities that the last moment when the sunlight is blocked can be the time t =0. The sunlight is blocked even when two silhouettes share parts of their edges. The following figure shows the layout of silhouettes and the position of the sun at the last moment when the sunlight is blocked, corresponding to the second dataset of Sample Input. In this dataset the radius of the sun is 2 and there are two silhouettes: the one with height 4 is in -2 ≤ x ≤ 0, and the other with height 3 is in 0 ≤ x ≤ 2. Input The input consists of multiple datasets. The first line of a dataset contains two integers r and n separated by a space. r is the radius of the sun and n is the number of silhouettes of the buildings. (1 ≤ r ≤ 20, 0 ≤ n ≤ 20) Each of following n lines contains three integers x li , x ri , h i (1 ≤ i ≤ n ) separated by a space. These three integers represent a silhouette rectangle of a building. The silhouette rectangle is parallel to the horizon, and its left and right edges are at x = x li and x = x ri , its top edge is at y = h i , and its bottom edge is on the horizon. (-20 ≤ x li < x ri ≤ 20, 0 < h i ≤ 20) The end of the input is indicated by a line containing two zeros separated by a space. Note that these silhouettes may overlap one another. Output For each dataset, output a line containing the number indicating the time t of the last moment when the sunlight is blocked. The value should not have an error greater than 0.001. No extra character ...(truncated)	[ { "submission_id": "aoj_1194_10850501", "code_snippet": "#include <cstdio>\n#include <cmath>\n#include <algorithm>\n#include <vector>\n\nusing namespace std;\n\nconst double EPS = 1e-9;\nbool EQ(double a, double b) { return abs(a - b) < EPS; }\n\ndouble getHeight(double r, double x) {\n\treturn sqrt(r * r -...
aoj_1195_cpp	Encryption System A programmer developed a new encryption system. However, his system has an issue that two or more distinct strings are `encrypted' to the same string. We have a string encrypted by his system. To decode the original string, we want to enumerate all the candidates of the string before the encryption. Your mission is to write a program for this task. The encryption is performed taking the following steps. Given a string that consists only of lowercase letters ('a' to 'z'). Change the first 'b' to 'a'. If there is no 'b', do nothing. Change the first 'c' to 'b'. If there is no 'c', do nothing. ... Change the first 'z' to 'y'. If there is no 'z', do nothing. Input The input consists of at most 100 datasets. Each dataset is a line containing an encrypted string. The encrypted string consists only of lowercase letters, and contains at least 1 and at most 20 characters. The input ends with a line with a single '#' symbol. Output For each dataset, the number of candidates n of the string before encryption should be printed in a line first, followed by lines each containing a candidate of the string before encryption. If n does not exceed 10, print all candidates in dictionary order; otherwise, print the first five and the last five candidates in dictionary order. Here, dictionary order is recursively defined as follows. The empty string comes the first in dictionary order. For two nonempty strings x = x 1 ... x k and y = y 1 ... y l , the string x precedes the string y in dictionary order if x 1 precedes y 1 in alphabetical order ('a' to 'z'), or x 1 and y 1 are the same character and x 2 ... x k precedes y 2 ... y l in dictionary order. Sample Input enw abc abcdefghijklmnopqrst z # Output for the Sample Input 1 fox 5 acc acd bbd bcc bcd 17711 acceeggiikkmmooqqssu acceeggiikkmmooqqstt acceeggiikkmmooqqstu acceeggiikkmmooqrrtt acceeggiikkmmooqrrtu bcdefghijklmnopqrrtt bcdefghijklmnopqrrtu bcdefghijklmnopqrssu bcdefghijklmnopqrstt bcdefghijklmnopqrstu 0	[ { "submission_id": "aoj_1195_10848117", "code_snippet": "#include <stdio.h>\n#include <memory.h>\n#include <string.h>\n#define MAX 30\n\nchar ch[MAX], p[MAX];\nint len, b[MAX], ac[30], cnt;\nchar ch2[1050000][22];\n\nvoid dfs(int now, int sw){\n\tint i;\n\tb[now]=sw;\n\tif (now==len){\n\t\tfor (i=1;i<=len;i...
aoj_1192_cpp	Tax Rate Changed VAT (value-added tax) is a tax imposed at a certain rate proportional to the sale price. Our store uses the following rules to calculate the after-tax prices. When the VAT rate is x %, for an item with the before-tax price of p yen, its after-tax price of the item is p (100+ x ) / 100 yen, fractions rounded off. The total after-tax price of multiple items paid at once is the sum of after-tax prices of the items. The VAT rate is changed quite often. Our accountant has become aware that "different pairs of items that had the same total after-tax price may have different total after-tax prices after VAT rate changes." For example, when the VAT rate rises from 5% to 8%, a pair of items that had the total after-tax prices of 105 yen before can now have after-tax prices either of 107, 108, or 109 yen, as shown in the table below. Before-tax prices of two items After-tax price with 5% VAT After-tax price with 8% VAT 20, 80 21 + 84 = 105 21 + 86 = 107 2, 99 2 + 103 = 105 2 + 106 = 108 13, 88 13 + 92 = 105 14 + 95 = 109 Our accountant is examining effects of VAT-rate changes on after-tax prices. You are asked to write a program that calculates the possible maximum total after-tax price of two items with the new VAT rate, knowing their total after-tax price before the VAT rate change. Input The input consists of multiple datasets. Each dataset is in one line, which consists of three integers x , y , and s separated by a space. x is the VAT rate in percent before the VAT-rate change, y is the VAT rate in percent after the VAT-rate change, and s is the sum of after-tax prices of two items before the VAT-rate change. For these integers, 0 < x < 100, 0 < y < 100, 10 < s < 1000, and x ≠ y hold. For before-tax prices of items, all possibilities of 1 yen through s -1 yen should be considered. The end of the input is specified by three zeros separated by a space. Output For each dataset, output in a line the possible maximum total after-tax price when the VAT rate is changed to y %. Sample Input 5 8 105 8 5 105 1 2 24 99 98 24 12 13 26 1 22 23 1 13 201 13 16 112 2 24 50 1 82 61 1 84 125 1 99 999 99 1 999 98 99 999 1 99 11 99 1 12 0 0 0 Output for the Sample Input 109 103 24 24 26 27 225 116 62 111 230 1972 508 1004 20 7 Hints In the following table, an instance of a before-tax price pair that has the maximum after-tax price after the VAT-rate change is given for each dataset of the sample input. Dataset Before-tax prices After-tax price with y % VAT 5 8 105 13, 88 14 + 95 = 109 8 5 105 12, 87 12 + 91 = 103 1 2 24 1, 23 1 + 23 = 24 99 98 24 1, 12 1 + 23 = 24 12 13 26 1, 23 1 + 25 = 26 1 22 23 1, 22 1 + 26 = 27 1 13 201 1,199 1 +224 = 225 13 16 112 25, 75 29 + 87 = 116 2 24 50 25, 25 31 + 31 = 62 1 82 61 11, 50 20 + 91 = 111 1 84 125 50, 75 92 +138 = 230 1 99 999 92,899 183+1789 =1972 99 1 999 1,502 1 +507 = 508 98 99 999 5,500 9 +995 =1004 1 99 11 1, 10 1 + 19 = 20 99 ...(truncated)	[ { "submission_id": "aoj_1192_10851356", "code_snippet": "#include <cstdio>\n#include <algorithm>\n\nusing namespace std;\n\nint main(void) {\n\tint x, y, s;\n\twhile(scanf(\"%d %d %d\", &x, &y, &s), !(x == 0 and y == 0 and s == 0)) {\n\t\tint ans = 0;\n\n\t\tfor(int i = 1; i < s; i++) {\n\t\t\tint j = s - i...
aoj_1196_cpp	Bridge Removal ICPC islands once had been a popular tourist destination. For nature preservation, however, the government decided to prohibit entrance to the islands, and to remove all the man-made structures there. The hardest part of the project is to remove all the bridges connecting the islands. There are n islands and n -1 bridges. The bridges are built so that all the islands are reachable from all the other islands by crossing one or more bridges. The bridge removal team can choose any island as the starting point, and can repeat either of the following steps. Move to another island by crossing a bridge that is connected to the current island. Remove one bridge that is connected to the current island, and stay at the same island after the removal. Of course, a bridge, once removed, cannot be crossed in either direction. Crossing or removing a bridge both takes time proportional to the length of the bridge. Your task is to compute the shortest time necessary for removing all the bridges. Note that the island where the team starts can differ from where the team finishes the work. Input The input consists of at most 100 datasets. Each dataset is formatted as follows. n p 2 p 3 ... p n d 2 d 3 ... d n The first integer n (3 ≤ n ≤ 800) is the number of the islands. The islands are numbered from 1 to n . The second line contains n -1 island numbers p i (1 ≤ p i < i ), and tells that for each i from 2 to n the island i and the island p i are connected by a bridge. The third line contains n -1 integers d i (1 ≤ d i ≤ 100,000) each denoting the length of the corresponding bridge. That is, the length of the bridge connecting the island i and p i is d i . It takes d i units of time to cross the bridge, and also the same units of time to remove it. Note that, with this input format, it is assured that all the islands are reachable each other by crossing one or more bridges. The input ends with a line with a single zero. Output For each dataset, print the minimum time units required to remove all the bridges in a single line. Each line should not have any character other than this number. Sample Input 4 1 2 3 10 20 30 10 1 2 2 1 5 5 1 8 8 10 1 1 20 1 1 30 1 1 3 1 1 1 1 0 Output for the Sample Input 80 136 2	[ { "submission_id": "aoj_1196_10853372", "code_snippet": "#include <stdio.h>\n#include <vector>\n#define MAX 810\n\nint n, p[MAX], d[MAX], check[MAX];\nint val, answer=2147483647;\nstruct data{\n\tint go, dis;\n};\nstd::vector<data> vec[MAX];\nint dy[MAX][2];\n\nvoid reset(void){\n\tint i;\n\tanswer=21474836...
aoj_1197_cpp	A Die Maker The work of die makers starts early in the morning. You are a die maker. You receive orders from customers, and make various kinds of dice every day. Today, you received an order of a cubic die with six numbers t 1 , t 2 , ..., t 6 on whichever faces. For making the ordered die, you use a tool of flat-board shape. You initially have a die with a zero on each face. If you rotate the die by 90 degrees on the tool towards one of northward, southward, eastward, and southward, the number on the face that newly touches the tool is increased by one. By rotating the die towards appropriate directions repeatedly, you may obtain the ordered die. The final numbers on the faces of the die is determined by the sequence of directions towards which you rotate the die. We call the string that represents the sequence of directions an operation sequence. Formally, we define operation sequences as follows. An operation sequence consists of n characters, where n is the number of rotations made. If you rotate the die eastward in the i -th rotation, the i -th character of the operation sequence is E . Similarly, if you rotate it westward, it is W , if southward, it is S , otherwise, if northward, it is N . For example, the operation sequence NWS represents the sequence of three rotations, northward first, westward next, and finally southward. Given six integers of the customer's order, compute an operation sequence that makes a die to order. If there are two or more possibilities, you should compute the earliest operation sequence in dictionary order. Input The input consists of multiple datasets. The number of datasets does not exceed 40. Each dataset has the following form. t 1 t 2 t 3 t 4 t 5 t 6 p q t 1 , t 2 , ..., t 6 are integers that represent the order from the customer. Further, p and q are positive integers that specify the output range of the operation sequence (see the details below). Each dataset satisfies 0 ≤ t 1 ≤ t 2 ≤ ... ≤ t 6 ≤ 5,000 and 1 ≤ p ≤ q ≤ t 1 + t 2 +...+ t 6 . A line containing six zeros denotes the end of the input. Output For each dataset, print the subsequence, from the p -th position to the q -th position, inclusively, of the operation sequence that is the earliest in dictionary order. If it is impossible to make the ordered die, print impossible . Here, dictionary order is recursively defined as follows. The empty string comes the first in dictionary order. For two nonempty strings x = x 1 ... x k and y = y 1 ... y l , the string x precedes the string y in dictionary order if x 1 precedes y 1 in alphabetical order ('A' to 'Z'), or x 1 and y 1 are the same character and x 2 ... x k precedes y 2 ... y l in dictionary order. Sample Input 1 1 1 1 1 1 1 6 1 1 1 1 1 1 4 5 0 0 0 0 0 2 1 2 0 0 2 2 2 4 5 9 1 2 3 4 5 6 15 16 0 1 2 3 5 9 13 16 2 13 22 27 31 91 100 170 0 0 0 0 0 0 Output for the Sample Input EEENEE NE impossible NSSNW EN EWNS SNSNSNSNSNSNSNSNSNSNSNSSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNWEWE	[ { "submission_id": "aoj_1197_9857905", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\n\n#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)\n#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)\n#define ALL(v) (v).begin(), (v).end()\n#define UNIQUE(v) sort(ALL(v)...
aoj_1198_cpp	Don't Cross the Circles! There are one or more circles on a plane. Any two circles have different center positions and/or different radiuses. A circle may intersect with another circle, but no three or more circles have areas nor points shared by all of them. A circle may completely contain another circle or two circles may intersect at two separate points, but you can assume that the circumferences of two circles never touch at a single point. Your task is to judge whether there exists a path that connects the given two points, P and Q , without crossing the circumferences of the circles. You are given one or more point pairs for each layout of circles. In the case of Figure G-1, we can connect P and Q 1 without crossing the circumferences of the circles, but we cannot connect P with Q 2 , Q 3 , or Q 4 without crossing the circumferences of the circles. Figure G-1: Sample layout of circles and points Input The input consists of multiple datasets, each in the following format. n m Cx 1 Cy 1 r 1 ... Cx n Cy n r n Px 1 Py 1 Qx 1 Qy 1 ... Px m Py m Qx m Qy m The first line of a dataset contains two integers n and m separated by a space. n represents the number of circles, and you can assume 1 ≤ n ≤ 100. m represents the number of point pairs, and you can assume 1 ≤ m ≤ 10. Each of the following n lines contains three integers separated by a single space. ( Cx i , Cy i ) and r i represent the center position and the radius of the i -th circle, respectively. Each of the following m lines contains four integers separated by a single space. These four integers represent coordinates of two separate points P j = ( Px j , Py j ) and Q j =( Qx j , Qy j ). These two points P j and Q j form the j -th point pair. You can assume 0 ≤ Cx i ≤ 10000, 0 ≤ Cy i ≤ 10000, 1 ≤ r i ≤ 1000, 0 ≤ Px j ≤ 10000, 0 ≤ Py j ≤ 10000, 0 ≤ Qx j ≤ 10000, 0 ≤ Qy j ≤ 10000. In addition, you can assume P j or Q j are not located on the circumference of any circle. The end of the input is indicated by a line containing two zeros separated by a space. Figure G-1 shows the layout of the circles and the points in the first dataset of the sample input below. Figure G-2 shows the layouts of the subsequent datasets in the sample input. Figure G-2: Sample layout of circles and points Output For each dataset, output a single line containing the m results separated by a space. The j -th result should be "YES" if there exists a path connecting P j and Q j , and "NO" otherwise. Sample Input 5 3 0 0 1000 1399 1331 931 0 1331 500 1398 0 400 2000 360 340 450 950 1600 380 450 950 1399 1331 450 950 450 2000 1 2 50 50 50 0 10 100 90 0 10 50 50 2 2 50 50 50 100 50 50 40 50 110 50 40 50 0 0 4 1 25 100 26 75 100 26 50 40 40 50 160 40 50 81 50 119 6 1 100 50 40 0 50 40 50 0 48 50 50 3 55 55 4 55 105 48 50 55 55 50 20 6 270 180 50 360 170 50 0 0 50 10 0 10 0 90 50 0 180 50 90 180 50 180 180 50 205 90 50 180 0 50 65 0 20 75 30 16 90 78 36 105 30 16 115 0 20 128 48 15 128 100 15 280 0 30 330 0 30 305 65 42 0 2 ...(truncated)	[ { "submission_id": "aoj_1198_9340740", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing Real = long double;\nusing Point = complex<Real>;\nconst Real EPS = 1e-9, PI = acos(-1);\n\ninline bool eq(Real a, Real b) {\n return fabs(b - a) < EPS;\n}\n\nPoint operator*(const Point &p, cons...
aoj_1200_cpp	Problem A: Goldbach's Conjecture Goldbach's Conjecture: For any even number n greater than or equal to 4, there exists at least one pair of prime numbers p 1 and p 2 such that n = p 1 + p 2 . This conjecture has not been proved nor refused yet. No one is sure whether this conjecture actually holds. However, one can find such a pair of prime numbers, if any, for a given even number. The problem here is to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number. A sequence of even numbers is given as input. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that we are intereseted in the number of essentially different pairs and therefore you should not count ( p 1 , p 2 ) and ( p 2 , p 1 ) separately as two different pairs. Input An integer is given in each input line. You may assume that each integer is even, and is greater than or equal to 4 and less than 2 15 . The end of the input is indicated by a number 0. Output Each output line should contain an integer number. No other characters should appear in the output. Sample Input 6 10 12 0 Output for the Sample Input 1 2 1	[ { "submission_id": "aoj_1200_11059833", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\n#define rep(i,a,b) for(int i=(a);i<(b);i++)\n\nvector<int> ans_table(const int LIM=(1<<16)){\n vector<int>res(LIM);\n vector<int> isP(LIM,1);\n vector<int>primes;\n isP[...
aoj_1202_cpp	Problem C: Mobile Phone Coverage A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice. for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna A i has power r i , corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna ( x i , y i ) with radius r i . However, in this city Maxnorm such a coverage region becomes the square [ x i − r i , x i + r i ] × [ y i − r i , y i + r i ]. In other words, the distance between two points ( x p , y p ) and ( x q , y q ) is measured by the max norm max{ \| x p − x q \|, \| y p − y q \|}, or, the L ∞ norm, in this city Maxnorm instead of the ordinary Euclidean norm √ {( x p − x q ) 2 + ( y p − y q ) 2 }. As an example, consider the following collection of 3 antennas 4.0 4.0 3.0 5.0 6.0 3.0 5.5 4.5 1.0 depicted in the following figure where the i -th row represents x i , y i r i such that ( x i , y i ) is the position of the i -th antenna and r i is its power. The area of regions of points covered by at least one antenna is 52.00 in this case. Write a program that finds the area of coverage by a given collection of antenna locations. Input The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format. n x 1 y 1 r 1 x 2 y 2 r 2 . . . x n y n r n The first integer n is the number of antennas, such that 2 ≤ n ≤ 100. The coordinate of the i -th antenna is given by ( x i , y i ), and its power is r i . x i , y i and r i are fractional numbers between 0 and 200 inclusive. The end of the input is indicated by a data set with 0 as the value of n . Output For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places. The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space. Sample Input 3 4.0 4.0 3.0 5.0 6.0 3.0 5.5 4.5 1.0 2 3.0 3.0 3.0 1.5 1.5 1.0 0 Output for the Sample Input 1 52.00 2 36.00	[ { "submission_id": "aoj_1202_3709040", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\nusing ll = long long;\n// #define int ll\nusing PII = pair<ll, ll>;\n\n#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)\n#define REP(i, n) FOR(i, 0, n)\n#define ALL(x) x.begin(), x.end()\n\ntempl...
aoj_1201_cpp	Problem B: Lattice Practices Once upon a time, there was a king who loved beautiful costumes very much. The king had a special cocoon bed to make excellent cloth of silk. The cocoon bed had 16 small square rooms, forming a 4 × 4 lattice, for 16 silkworms. The cocoon bed can be depicted as follows: The cocoon bed can be divided into 10 rectangular boards, each of which has 5 slits: Note that, except for the slit depth, there is no difference between the left side and the right side of the board (or, between the front and the back); thus, we cannot distinguish a symmetric board from its rotated image as is shown in the following: Slits have two kinds of depth, either shallow or deep. The cocoon bed should be constructed by fitting five of the boards vertically and the others horizontally, matching a shallow slit with a deep slit. Your job is to write a program that calculates the number of possible configurations to make the lattice. You may assume that there is no pair of identical boards. Notice that we are interested in the number of essentially different configurations and therefore you should not count mirror image configurations and rotated configurations separately as different configurations. The following is an example of mirror image and rotated configurations, showing vertical and horizontal boards separately, where shallow and deep slits are denoted by '1' and '0' respectively. Notice that a rotation may exchange position of a vertical board and a horizontal board. Input The input consists of multiple data sets, each in a line. A data set gives the patterns of slits of 10 boards used to construct the lattice. The format of a data set is as follows: XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX Each x is either '0' or '1'. '0' means a deep slit, and '1' a shallow slit. A block of five slit descriptions corresponds to a board. There are 10 blocks of slit descriptions in a line. Two adjacent blocks are separated by a space. For example, the first data set in the Sample Input means the set of the following 10 boards: The end of the input is indicated by a line consisting solely of three characters "END". Output For each data set, the number of possible configurations to make the lattice from the given 10 boards should be output, each in a separate line. Sample Input 10000 01000 00100 11000 01100 11111 01110 11100 10110 11110 10101 01000 00000 11001 01100 11101 01110 11100 10110 11010 END Output for the Sample Input 40 6	[ { "submission_id": "aoj_1201_9634679", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long ll;\n#define FOR(i,l,r) for(ll i=l;i<r;i++)\n#define REP(i,n) FOR(i,0,n)\n#define ALL(A) A.begin(),A.end()\n#define LB(A,x) (lower_bound(ALL(A),x)-A.begin())\n#define UB(A,x) (upper_bound...
aoj_1214_cpp	Problem G: Walking Ant Ants are quite diligent. They sometimes build their nests beneath flagstones. Here, an ant is walking in a rectangular area tiled with square flagstones, seeking the only hole leading to her nest. The ant takes exactly one second to move from one flagstone to another. That is, if the ant is on the flagstone with coordinates ( x , y ) at time t , she will be on one of the five flagstones with the following coordinates at time t + 1: ( x , y ), ( x + 1, y ), ( x - 1, y ), ( x , y + 1), ( x , y - 1). The ant cannot go out of the rectangular area. The ant can visit the same flagstone more than once. Insects are easy to starve. The ant has to go back to her nest without starving. Physical strength of the ant is expressed by the unit "HP". Initially, the ant has the strength of 6 HP. Every second, she loses 1 HP. When the ant arrives at a flagstone with some food on it, she eats a small piece of the food there, and recovers her strength to the maximum value, i.e., 6 HP, without taking any time. The food is plenty enough, and she can eat it as many times as she wants. When the ant's strength gets down to 0 HP, she dies and will not move anymore. If the ant's strength gets down to 0 HP at the moment she moves to a flagstone, she does not effectively reach the flagstone: even if some food is on it, she cannot eat it; even if the hole is on that stone, she has to die at the entrance of her home. If there is a puddle on a flagstone, the ant cannot move there. Your job is to write a program which computes the minimum possible time for the ant to reach the hole with positive strength from her start position, if ever possible. Input The input consists of multiple maps, each representing the size and the arrangement of the rectangular area. A map is given in the following format. w h d 11 d 12 d 13 ... d 1 w d 2 d 22 d 23 ... d 2 w ... d h 1 d h 2 d h 3 ... d h w The integers w and h are the numbers of flagstones in the x - and y -directions, respectively. w and h are less than or equal to 8. The integer d yx represents the state of the flagstone with coordinates ( x , y ) as follows. 0: There is a puddle on the flagstone, and the ant cannot move there. 1, 2: Nothing exists on the flagstone, and the ant can move there. '2' indicates where the ant initially stands. 3: The hole to the nest is on the flagstone. 4: Some food is on the flagstone. There is one and only one flagstone with a hole. Not more than five flagstones have food on them. The end of the input is indicated by a line with two zeros. Integer numbers in an input line are separated by at least one space character. Output for each map in the input, your program should output one line containing one integer representing the minimum time. If the ant cannot return to her nest, your program should output -1 instead of the minimum time. Sample Input 3 3 2 1 1 1 1 0 1 1 3 8 4 2 1 1 0 1 1 1 0 1 0 4 1 1 0 4 1 1 0 0 0 0 0 0 1 1 1 1 4 1 1 1 3 8 5 1 2 1 1 1 1 1 4 1 0 0 0 1 0 0 1 1 4 1 0 1 ...(truncated)	[ { "submission_id": "aoj_1214_5976490", "code_snippet": "#include<iostream>\n#include<cstring>\n#include<cstdio>\n#include<sstream>\n#include<algorithm>\n#include<cstdlib>\n#include<queue>\n#include<set>\n#include<map>\n#include<cmath>\n#include<ctime>\n#include<stack>\n#include<functional>\n#define INF 2100...
aoj_1203_cpp	Problem D: Napoleon's Grumble Legend has it that, after being defeated in Waterloo, Napoleon Bonaparte, in retrospect of his days of glory, talked to himself "Able was I ere I saw Elba." Although, it is quite doubtful that he should have said this in English, this phrase is widely known as a typical palindrome . A palindrome is a symmetric character sequence that looks the same when read backwards, right to left. In the above Napoleon's grumble, white spaces appear at the same positions when read backwards. This is not a required condition for a palindrome. The following, ignoring spaces and punctuation marks, are known as the first conversation and the first palindromes by human beings. "Madam, I'm Adam." "Eve." (by Mark Twain) Write a program that finds palindromes in input lines. Input A multi-line text is given as the input. The input ends at the end of the file. There are at most 100 lines in the input. Each line has less than 1,024 Roman alphabet characters. Output Corresponding to each input line, a line consisting of all the character sequences that are palindromes in the input line should be output. However, trivial palindromes consisting of only one or two characters should not be reported. On finding palindromes, any characters in the input except Roman alphabets, such as punctuation characters, digits, space, and tabs, should be ignored. Characters that differ only in their cases should be looked upon as the same character. Whether or not the character sequences represent a proper English word or sentence does not matter. Palindromes should be reported all in uppercase characters. When two or more palindromes are reported, they should be separated by a space character. You may report palindromes in any order. If two or more occurrences of the same palindromes are found in the same input line, report only once. When a palindrome overlaps with another, even when one is completely included in the other, both should be reported. However, palindromes appearing in the center of another palindrome, whether or not they also appear elsewhere, should not be reported. For example, for an input line of "AAAAAA", two palindromes "AAAAAA" and "AAAAA" should be output, but not "AAAA" nor "AAA". For "AABCAAAAAA", the output remains the same. One line should be output corresponding to one input line. If an input line does not contain any palindromes, an empty line should be output. Sample Input As the first man said to the first woman: "Madam, I'm Adam." She responded: "Eve." Output for the Sample Input TOT MADAMIMADAM MADAM ERE DED EVE Note that the second line in the output is empty, corresponding to the second input line containing no palindromes. Also note that some of the palindromes in the third input line, namely "ADA", "MIM", "AMIMA", "DAMIMAD", and "ADAMIMADA", are not reported because they appear at the center of reported ones. "MADAM" is reported, as it does not appear in the center, but only once, disregarding its second occurrence.	[ { "submission_id": "aoj_1203_1892938", "code_snippet": "#include<iostream>\n#include<vector>\n#include<string>\n#include<algorithm>\t\n#include<map>\n#include<set>\n#include<utility>\n#include<cmath>\n#include<cstring>\n#include<queue>\n#include<cstdio>\n#include<sstream>\n#include<iomanip>\n#define loop(i,...
aoj_1208_cpp	Problem A: Rational Irrationals Rational numbers are numbers represented by ratios of two integers. For a prime number p , one of the elementary theorems in the number theory is that there is no rational number equal to √ p . Such numbers are called irrational numbers. It is also known that there are rational numbers arbitrarily close to √ p Now, given a positive integer n , we define a set Q n of all rational numbers whose elements are represented by ratios of two positive integers both of which are less than or equal to n . For example, Q 4 is a set of 11 rational numbers {1/1, 1/2, 1/3, 1/4, 2/1, 2/3, 3/1, 3/2, 3/4, 4/1, 4/3}. 2/2, 2/4, 3/3, 4/2 and 4/4 are not included here because they are equal to 1/1, 1/2, 1/1, 2/1 and 1/1, respectively. Your job is to write a program that reads two integers p and n and reports two rational numbers x / y and u / v , where u / v < √ p < x / y and there are no other elements of Q n between u/v and x/y . When n is greater than √ p , such a pair of rational numbers always exists. Input The input consists of lines each of which contains two positive integers, a prime number p and an integer n in the following format. p n They are separated by a space character. You can assume that p and n are less than 10000, and that n is greater than √ p . The end of the input is indicated by a line consisting of two zeros. Output For each input line, your program should output a line consisting of the two rational numbers x / y and u / v ( x / y > u / v ) separated by a space character in the following format. x/y u/v They should be irreducible. For example, 6/14 and 15/3 are not accepted. They should be reduced to 3/7 and 5/1, respectively. Sample Input 2 5 3 10 5 100 0 0 Output for the Sample Input 3/2 4/3 7/4 5/3 85/38 38/17	[ { "submission_id": "aoj_1208_8658705", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\n\n#define overload4(_1, _2, _3, _4, name, ...) name\n#define rep1(n) for(int i = 0; i < (int)(n); ++i)\n#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)\n#define rep3(i, a, b) for(int i = (a); i < (...
aoj_1204_cpp	Problem E: Pipeline Scheduling An arithmetic pipeline is designed to process more than one task simultaneously in an overlapping manner. It includes function units and data paths among them. Tasks are processed by pipelining : at each clock, one or more units are dedicated to a task and the output produced for the task at the clock is cascading to the units that are responsible for the next stage; since each unit may work in parallel with the others at any clock, more than one task may be being processed at a time by a single pipeline. In this problem, a pipeline may have a feedback structure, that is, data paths among function units may have directed loops as shown in the next figure. Example of a feed back pipeline Since an arithmetic pipeline in this problem is designed as special purpose dedicated hardware, we assume that it accepts just a single sort of task. Therefore, the timing information of a pipeline is fully described by a simple table called a reservation table , which specifies the function units that are busy at each clock when a task is processed without overlapping execution. Example of a "reservation table" In reservation tables, 'X' means "the function unit is busy at that clock" and '.' means "the function unit is not busy at that clock." In this case, once a task enters the pipeline, it is processed by unit0 at the first clock, by unit1 at the second clock, and so on. It takes seven clock cycles to perform a task. Notice that no special hardware is provided to avoid simultaneous use of the same function unit. Therefore, a task must not be started if it would conflict with any tasks being processed. For instance, with the above reservation table, if two tasks, say task 0 and task 1, were started at clock 0 and clock 1, respectively, a conflict would occur on unit0 at clock 5. This means that you should not start two tasks with single cycle interval. This invalid schedule is depicted in the following process table, which is obtained by overlapping two copies of the reservation table with one being shifted to the right by 1 clock. Example of a "conflict" ('0's and '1's in this table except those in the first row represent tasks 0 and 1, respectively, and 'C' means the conflict.) Your job is to write a program that reports the minimum number of clock cycles in which the given pipeline can process 10 tasks. Input The input consists of multiple data sets, each representing the reservation table of a pipeline. A data set is given in the following format. n x 0,0 x 0,1 ... x 0,n-1 x 1,0 x 1,1 ... x 1,n-1 x 2,0 x 2,1 ... x 2,n-1 x 3,0 x 3,1 ... x 3,n-1 x 4,0 x 4,1 ... x 4,n-1 The integer n (< 20) in the first line is the width of the reservation table, or the number of clock cycles that is necessary to perform a single task. The second line represents the usage of unit0, the third line unit1, and so on. x i,j is either 'X' or '.'. The former means reserved and the latter free . There are no spaces in any input line. For simplicity, we ...(truncated)	[ { "submission_id": "aoj_1204_2581073", "code_snippet": "#include <stdio.h>\n#include <cmath>\n#include <algorithm>\n#include <cfloat>\n#include <stack>\n#include <queue>\n#include <vector>\n#include <string>\n#include <iostream>\n#include <set>\n#include <map>\ntypedef long long int ll;\ntypedef unsigned lo...
aoj_1218_cpp	Problem C: Push!! Mr. Schwarz was a famous powerful pro wrestler. He starts a part time job as a warehouseman. His task is to move a cargo to a goal by repeatedly pushing the cargo in the warehouse, of course, without breaking the walls and the pillars of the warehouse. There may be some pillars in the warehouse. Except for the locations of the pillars, the floor of the warehouse is paved with square tiles whose size fits with the cargo. Each pillar occupies the same area as a tile. Initially, the cargo is on the center of a tile. With one push, he can move the cargo onto the center of an adjacent tile if he is in proper position. The tile onto which he will move the cargo must be one of (at most) four tiles (i.e., east, west, north or south) adjacent to the tile where the cargo is present. To push, he must also be on the tile adjacent to the present tile. He can only push the cargo in the same direction as he faces to it and he cannot pull it. So, when the cargo is on the tile next to a wall (or a pillar), he can only move it along the wall (or the pillar). Furthermore, once he places it on a corner tile, he cannot move it anymore. He can change his position, if there is a path to the position without obstacles (such as the cargo and pillars) in the way. The goal is not an obstacle. In addition, he can move only in the four directions (i.e., east, west, north or south) and change his direction only at the center of a tile. As he is not so young, he wants to save his energy by keeping the number of required pushes as small as possible. But he does not mind the count of his pedometer, because walking is very light exercise for him. Your job is to write a program that outputs the minimum number of pushes required to move the cargo to the goal, if ever possible. Input The input consists of multiple maps, each representing the size and the arrangement of the warehouse. A map is given in the following format. w h d 11 d 12 d 13 ... d 1 w d 21 d 22 d 23 ... d 2 w ... d h 1 d h 2 d h 3 ... d h w The integers w and h are the lengths of the two sides of the floor of the warehouse in terms of widths of floor tiles. w and h are less than or equal to 7. The integer d ij represents what is initially on the corresponding floor area in the following way. 0: nothing (simply a floor tile) 1: a pillar 2: the cargo 3: the goal 4: the warehouseman (Mr. Schwarz) Each of the integers 2, 3 and 4 appears exactly once as d ij in the map. Integer numbers in an input line are separated by at least one space character. The end of the input is indicated by a line containing two zeros. Output For each map, your program should output a line containing the minimum number of pushes. If the cargo cannot be moved to the goal, -1 should be output instead. Sample Input 5 5 0 0 0 0 0 4 2 0 1 1 0 1 0 0 0 1 0 0 0 3 1 0 0 0 0 5 3 4 0 0 0 0 2 0 0 0 0 0 0 0 0 3 7 5 1 1 4 1 0 0 0 1 1 2 1 0 0 0 3 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 6 6 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 ...(truncated)	[ { "submission_id": "aoj_1218_3807528", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nusing ll = long long;\nusing ull = unsigned long long;\n\nconstexpr long double EPS = 1e-15;\nconst long double PI = acos(-1);\nconstexpr int inf = 2e9;\nconstexpr ll INF = 2e18;\nconstexpr ll MOD = 1e9+7...
aoj_1216_cpp	Problem A: Lost in Space William Robinson was completely puzzled in the music room; he could not find his triangle in his bag. He was sure that he had prepared it the night before. He remembered its clank when he had stepped on the school bus early that morning. No, not in his dream. His triangle was quite unique: no two sides had the same length, which made his favorite peculiar jingle. He insisted to the music teacher, Mr. Smith, that his triangle had probably been stolen by those aliens and thrown away into deep space. Your mission is to help Will find his triangle in space. His triangle has been made invisible by the aliens, but candidate positions of its vertices are somehow known. You have to tell which three of them make his triangle. Having gone through worm-holes, the triangle may have changed its size. However, even in that case, all the sides are known to be enlarged or shrunk equally, that is, the transformed triangle is similar to the original. Input The very first line of the input has an integer which is the number of data sets. Each data set gives data for one incident such as that of Will’s. At least one and at most ten data sets are given. The first line of each data set contains three decimals that give lengths of the sides of the original triangle, measured in centimeters. Three vertices of the original triangle are named P, Q, and R. Three decimals given in the first line correspond to the lengths of sides QR, RP, and PQ, in this order. They are separated by one or more space characters. The second line of a data set has an integer which is the number of points in space to be considered as candidates for vertices. At least three and at most thirty points are considered. The rest of the data set are lines containing coordinates of candidate points, in light years. Each line has three decimals, corresponding to x, y, and z coordinates, separated by one or more space characters. Points are numbered in the order of their appearances, starting from one. Among all the triangles formed by three of the given points, only one of them is similar to the original, that is, ratios of the lengths of any two sides are equal to the corresponding ratios of the original allowing an error of less than 0.01 percent. Other triangles have some of the ratios different from the original by at least 0.1 percent. The origin of the coordinate system is not the center of the earth but the center of our galaxy. Note that negative coordinate values may appear here. As they are all within or close to our galaxy, coordinate values are less than one hundred thousand light years. You don’t have to take relativistic effects into account, i.e., you may assume that we are in a Euclidean space. You may also assume in your calculation that one light year is equal to 9.461 × 10 12 kilometers. A succeeding data set, if any, starts from the line immediately following the last line of the preceding data set. Output For each data set, one line should be output. That li ...(truncated)	[ { "submission_id": "aoj_1216_3807101", "code_snippet": "#include <iostream>\n#include <vector>\n#include <algorithm>\n#include <string>\n#include <numeric>\n\n#define REP(i, a, b) for (int i = int(a); i < int(b); i++)\nusing namespace std;\ntypedef long long int ll;\n\n// clang-format off\n#ifdef _DEBUG_\n#...
aoj_1209_cpp	Problem B: Square Coins People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (= 17 2 ), i.e., 1-credit coins, 4-credit coins, 9-credit coins, ..., and 289-credit coins, are available in Silverland. There are four combinations of coins to pay ten credits: ten 1-credit coins, one 4-credit coin and six 1-credit coins, two 4-credit coins and two 1-credit coins, and one 9-credit coin and one 1-credit coin. Your mission is to count the number of ways to pay a given amount using coins of Silverland. Input The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300. Output For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output. Sample Input 2 10 30 0 Output for the Sample Input 1 4 27	[ { "submission_id": "aoj_1209_2539223", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\n\nint count( int S[], int m, int n )\n{\n if (n == 0)\n return 1;\n if (n < 0)\n return 0;\n if (m <=0 && n >= 1)\n return 0;\n return count( S, m - 1, n ) + count( S, m, n...
aoj_1215_cpp	Problem H: Co-occurrence Search A huge amount of information is being heaped on WWW. Albeit it is not well-organized, users can browse WWW as an unbounded source of up-to-date information, instead of consulting established but a little out-of-date encyclopedia. However, you can further exploit WWW by learning more about keyword search algorithms. For example, if you want to get information on recent comparison between Windows and UNIX, you may expect to get relevant description out of a big bunch of Web texts, by extracting texts that contain both keywords "Windows" and "UNIX" close together. Here we have a simplified version of this co-occurrence keyword search problem, where the text and keywords are replaced by a string and key characters, respectively. A character string S of length n (1 ≤ n ≤ 1,000,000) and a set K of k distinct key characters a 1 , ..., a k (1 ≤ k ≤ 50) are given. Find every shortest substring of S that contains all of the key characters a 1 , ..., a k . Input The input is a text file which contains only printable characters (ASCII codes 21 to 7E in hexadecimal) and newlines. No white space such as space or tab appears in the input. The text is a sequence of the shortest string search problems described above. Each problem consists of character string S i and key character set K i ( i = 1, 2, ..., p ). Every S i and K i is followed by an empty line. However, any single newline between successive lines in a string should be ignored; that is, newlines are not part of the string. For various technical reasons, every line consists of at most 72 characters. Each key character set is given in a single line. The input is terminated by consecutive empty lines; p is not given explicitly. Output All of p problems should be solved and their answers should be output in order. However, it is not requested to print all of the shortest substrings if more than one substring is found in a problem, since found substrings may be too much to check them all. Only the number of the substrings together with their representative is requested instead. That is, for each problem i , the number of the shortest substrings should be output followed by the first (or the leftmost) shortest substring s i 1 , obeying the following format: the number of the shortest substrings for the i-th problem empty line the first line of s i1 the second line of s i1 ... the last line of s i1 empty line for the substring termination where each line of the shortest substring s i 1 except for the last line should consist of exactly 72 characters and the last line (or the single line if the substring is shorter than or equal to 72 characters, of course) should not exceed 72 characters. If there is no such substring for a problem, the output will be a 0 followed by an empty line; no more successive empty line should be output because there is no substring to be terminated. Sample Input Thefirstexampleistrivial. mfv AhugeamountofinformationisbeingheapedonWWW.Alb ...(truncated)	[ { "submission_id": "aoj_1215_2683439", "code_snippet": "#include <stdio.h>\n#include <cmath>\n#include <algorithm>\n#include <cfloat>\n#include <stack>\n#include <queue>\n#include <vector>\n#include <string>\n#include <iostream>\n#include <set>\n#include <map>\n#include <time.h>\ntypedef long long int ll;\n...
aoj_1217_cpp	Problem B: Family Tree A professor of anthropology was interested in people living in isolated islands and their history. He collected their family trees to conduct some anthropological experiment. For the experiment, he needed to process the family trees with a computer. For that purpose he translated them into text files. The following is an example of a text file representing a family tree. John Robert Frank Andrew Nancy David Each line contains the given name of a person. The name in the first line is the oldest ancestor in this family tree. The family tree contains only the descendants of the oldest ancestor. Their husbands and wives are not shown in the family tree. The children of a person are indented with one more space than the parent. For example, Robert and Nancy are the children of John, and Frank and Andrew are the children of Robert. David is indented with one more space than Robert, but he is not a child of Robert, but of Nancy. To represent a family tree in this way, the professor excluded some people from the family trees so that no one had both parents in a family tree. For the experiment, the professor also collected documents of the families and extracted the set of statements about relations of two persons in each family tree. The following are some examples of statements about the family above. John is the parent of Robert. Robert is a sibling of Nancy. David is a descendant of Robert. For the experiment, he needs to check whether each statement is true or not. For example, the first two statements above are true and the last statement is false. Since this task is tedious, he would like to check it by a computer program. Input The input contains several data sets. Each data set consists of a family tree and a set of statements. The first line of each data set contains two integers n (0 < n < 1000) and m (0 < m < 1000) which represent the number of names in the family tree and the number of statements, respectively. Each line of the input has less than 70 characters. As a name, we consider any character string consisting of only alphabetic characters. The names in a family tree have less than 20 characters. The name in the first line of the family tree has no leading spaces. The other names in the family tree are indented with at least one space, i.e., they are descendants of the person in the first line. You can assume that if a name in the family tree is indented with k spaces, the name in the next line is indented with at most k + 1 spaces. This guarantees that each person except the oldest ancestor has his or her parent in the family tree. No name appears twice in the same family tree. Each line of the family tree contains no redundant spaces at the end. Each statement occupies one line and is written in one of the following formats, where X and Y are different names in the family tree. X is a child of Y . X is the parent of Y . X is a sibling of Y . X is a descendant of Y . X is an ancestor of Y . Names not appe ...(truncated)	[ { "submission_id": "aoj_1217_2170790", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nint dep[100010];\nint par[100010][19];\nvector<int> g[100010];\nvoid dfs(int v,int u,int d){\n dep[v]=d;\n for(int i=0; i<g[v].size(); i++){\n int w=g[v][i];if(w==u) continue;\n par[w][0]=v;dfs(w,...
aoj_1221_cpp	Problem F: Numoeba A scientist discovered a strange variation of amoeba. The scientist named it numoeba . A numoeba, though it looks like an amoeba, is actually a community of cells, which always forms a tree. The scientist called the cell leader that is at the root position of the tree. For example, in Fig. 1, the leader is A . In a numoeba, its leader may change time to time. For example, if E gets new leadership, the tree in Fig. 1 becomes one in Fig. 2. We will use the terms root, leaf, parent, child and subtree for a numoeba as defined in the graph theory. Numoeba changes its physical structure at every biological clock by cell division and cell death. The leader may change depending on this physical change. The most astonishing fact about the numoeba cell is that it contains an organic unit called numbosome , which represents an odd integer within the range from 1 to 12,345,677. At every biological clock, the value of a numbosome changes from n to a new value as follows: The maximum odd factor of 3 n + 1 is calculated. This value can be obtained from 3 n + 1 by repeating division by 2 while even. If the resulting integer is greater than 12,345,678, then it is subtracted by 12,345,678. For example, if the numbosome value of a cell is 13, 13 × 3 + 1 = 40 is divided by 2 3 = 8 and a new numbosome value 5 is obtained. If the numbosome value of a cell is 11,111,111, it changes to 4,320,989, instead of 16,666,667. If 3 n + 1 is a power of 2, yielding 1 as the result, it signifies the death of the cell as will be described below. At every biological clock, the next numbosome value of every cell is calculated and the fate of the cell and thereby the fate of numoeba is determined according to the following steps. A cell that is a leaf and increases its numbosome value is designated as a candidate leaf. A cell dies if its numbosome value becomes 1. If the dying cell is the leader of the numoeba, the numoeba dies as a whole. Otherwise, all the cells in the subtree from the dying cell (including itself) die. However, there is an exceptional case where the cells in the subtree do not necessarily die; if there is only one child cell of the dying non-leader cell, the child cell will replace the dying cell. Thus, a straight chain simply shrinks if its non-leader constituent dies. For example, consider a numoeba with the leader A below. If the leader A dies in (1), the numoeba dies. If the cell D dies in (1), (1) will be as follows. And, if the cell E dies in (1), (1) will be as follows. Note that this procedure is executed sequentially, top-down from the root of the numoeba to leaves. If the cells E and F will die in (1), the death of F is not detected at the time the procedure examines the cell E . The numoeba, therefore, becomes (3). One should not consider in such a way that the death of F makes G the only child of E , and, therefore, G will replace the dying E . If a candidate leaf survives with the numbosome value of n , it spawns a cell as its child, ...(truncated)	[ { "submission_id": "aoj_1221_1092280", "code_snippet": "#include<iostream>\n#include<vector>\n#include<tuple>\n#include<algorithm>\nusing namespace std;\n\nconst int MOD = 12345678;\nconst int NIL = -1;\n\nclass Numoeba {\npublic:\n Numoeba(const int n) :max_cell_(1), root_(0) {create_cell(n);}\n tupl...
aoj_1227_cpp	Problem D: 77377 At the risk of its future, International Cellular Phones Corporation (ICPC) invests its resources in developing new mobile phones, which are planned to be equipped with Web browser, mailer, instant messenger, and many other advanced communication tools. Unless members of ICPC can complete this stiff job, it will eventually lose its market share. You are now requested to help ICPC to develop intriguing text input software for small mobile terminals. As you may know, most phones today have twelve buttons, namely, ten number buttons from " 0 " to " 9 " and two special buttons " * " and " # ". Although the company is very ambitious, it has decided to follow today's standards and conventions. You should not change the standard button layout, and should also pay attention to the following standard button assignment. button letters button letters 2 a, b, c 6 m, n, o 3 d, e, f 7 p, q, r, s 4 g, h, i 8 t, u, v 5 j, k, l 9 w, x, y, z This means that you can only use eight buttons for text input. Most users of current ICPC phones are rushed enough to grudge wasting time on even a single button press. Your text input software should be economical of users' time so that a single button press is suffcient for each character input. In consequence, for instance, your program should accept a sequence of button presses " 77377 " and produce the word " press ". Similarly, it should translate " 77377843288866 " into "press the button". Ummm... It seems impossible to build such text input software since more than one English letter is represented by a digit!. For instance, " 77377 " may represent not only "press" but also any one of 768 (= 4 × 4 × 3 × 4 × 4) character strings. However, we have the good news that the new model of ICPC mobile phones has enough memory to keep a dictionary. You may be able to write a program that filters out false words , i.e., strings not listed in the dictionary. Input The input consists of multiple data sets, each of which represents a dictionary and a sequence of button presses in the following format. n word 1 . . . word n sequence n in the first line is a positive integer, representing the number of words in the dictionary. The next n lines, each representing a word in the dictionary, only contain lower case letters from ` a ' to ` z '. The order of words in the dictionary is arbitrary (not necessarily in the lexicographic order). No words occur more than once in the dictionary. The last line, sequence, is the sequence of button presses, and only contains digits from ` 2 ' to ` 9 '. You may assume that a dictionary has at most one hundred words and that the length of each word is between one and fifty, inclusive. You may also assume that the number of input digits in the sequence is between one and three hundred, inclusive. A line containing a zero indicates the end of the input. Output For each data set, your program should print all sequences that can be represented by the input sequence of button presses. Each s ...(truncated)	[ { "submission_id": "aoj_1227_746368", "code_snippet": "// start: 10:34\n// stop: 10:43\n// start: 10:50\n// stop: 11:22\n#include <cstdio>\n#include <cstdlib>\n#include <cmath>\n#include <climits>\n#include <cctype>\n#include <algorithm>\n#include <numeric>\n#include <iostream>\n#include <string>\n#include ...
aoj_1219_cpp	Problem D: Pump up Batteries Bill is a boss of security guards. He has pride in that his men put on wearable computers on their duty. At the same time, it is his headache that capacities of commercially available batteries are far too small to support those computers all day long. His men come back to the office to charge up their batteries and spend idle time until its completion. Bill has only one battery charger in the office because it is very expensive. Bill suspects that his men spend much idle time waiting in a queue for the charger. If it is the case, Bill had better introduce another charger. Bill knows that his men are honest in some sense and blindly follow any given instructions or rules. Such a simple-minded way of life may lead to longer waiting time, but they cannot change their behavioral pattern. Each battery has a data sheet attached on it that indicates the best pattern of charging and consuming cycle. The pattern is given as a sequence of pairs of consuming time and charging time. The data sheet says the pattern should be followed cyclically to keep the battery in quality. A guard, trying to follow the suggested cycle strictly, will come back to the office exactly when the consuming time passes out, stay there until the battery has been charged for the exact time period indicated, and then go back to his beat. The guards are quite punctual. They spend not a second more in the office than the time necessary for charging up their batteries. They will wait in a queue, however, if the charger is occupied by another guard, exactly on first-come-first-served basis. When two or more guards come back to the office at the same instance of time, they line up in the order of their identifi- cation numbers, and, each of them, one by one in the order of that line, judges if he can use the charger and, if not, goes into the queue. They do these actions in an instant. Your mission is to write a program that simulates those situations like Bill’s and reports how much time is wasted in waiting for the charger. Input The input consists of one or more data sets for simulation. The first line of a data set consists of two positive integers separated by a space character: the number of guards and the simulation duration. The number of guards does not exceed one hundred. The guards have their identification numbers starting from one up to the number of guards. The simulation duration is measured in minutes, and is at most one week, i.e., 10080 (min.). Patterns for batteries possessed by the guards follow the first line. For each guard, in the order of identification number, appears the pattern indicated on the data sheet attached to his battery. A pattern is a sequence of positive integers, whose length is a multiple of two and does not exceed fifty. The numbers in the sequence show consuming time and charging time alternately. Those times are also given in minutes and are at most one day, i.e., 1440 (min.). A space character or a newline follows e ...(truncated)	[ { "submission_id": "aoj_1219_7227174", "code_snippet": "#include <iostream>\n#include <queue>\n#include <vector>\n#include <algorithm>\nusing namespace std;\n\nstruct E{\n\tint ot;\n\tint nt;\n\tint t;\n\tint no;\n\tint s;\n\tbool operator<(const E& e)const{\n\t\tif(t!=e.t)return t>e.t;\n\t\treturn no>e.no;...
aoj_1225_cpp	Problem B: e-Market The city of Hakodate recently established a commodity exchange market. To participate in the market, each dealer transmits through the Internet an order consisting of his or her name, the type of the order (buy or sell), the name of the commodity, and the quoted price. In this market a deal can be made only if the price of a sell order is lower than or equal to the price of a buy order. The price of the deal is the mean of the prices of the buy and sell orders, where the mean price is rounded downward to the nearest integer. To exclude dishonest deals, no deal is made between a pair of sell and buy orders from the same dealer. The system of the market maintains the list of orders for which a deal has not been made and processes a new order in the following manner. For a new sell order, a deal is made with the buy order with the highest price in the list satisfying the conditions. If there is more than one buy order with the same price, the deal is made with the earliest of them. For a new buy order, a deal is made with the sell order with the lowest price in the list satisfying the conditions. If there is more than one sell order with the same price, the deal is made with the earliest of them. The market opens at 7:00 and closes at 22:00 everyday. When the market closes, all the remaining orders are cancelled. To keep complete record of the market, the system of the market saves all the orders it received everyday. The manager of the market asked the system administrator to make a program which reports the activity of the market. The report must contain two kinds of information. For each commodity the report must contain informationon the lowest, the average and the highest prices of successful deals. For each dealer, the report must contain information on the amounts the dealer paid and received for commodities. Input The input contains several data sets. Each data set represents the record of the market on one day. The first line of each data set contains an integer n ( n < 1000) which is the number of orders in the record. Each line of the record describes an order, consisting of the name of the dealer, the type of the order, the name of the commodity, and the quoted price. They are separated by a single space character. The name of a dealer consists of capital alphabetical letters and is less than 10 characters in length. The type of an order is indicated by a string, " BUY " or " SELL ". The name of a commodity is a single capital letter. The quoted price is a positive integer less than 1000. The orders in a record are arranged according to time when they were received and the first line of the record corresponds to the oldest order. The end of the input is indicated by a line containing a zero. Output The output for each data set consists of two parts separated by a line containing two hyphen (` - ') characters. The first part is output for commodities. For each commodity, your program should output the name of the comm ...(truncated)	[ { "submission_id": "aoj_1225_1083098", "code_snippet": "#define _USE_MATH_DEFINES\n#define INF 0x3f3f3f3f\n\n#include <iostream>\n#include <cstdio>\n#include <sstream>\n#include <cmath>\n#include <cstdlib>\n#include <algorithm>\n#include <queue>\n#include <stack>\n#include <limits>\n#include <map>\n#include...
aoj_1222_cpp	Problem G: Telescope Dr. Extreme experimentally made an extremely precise telescope to investigate extremely curi- ous phenomena at an extremely distant place. In order to make the telescope so precise as to investigate phenomena at such an extremely distant place, even quite a small distortion is not allowed. However, he forgot the influence of the internal gas affected by low-frequency vibration of magnetic flux passing through the telescope. The cylinder of the telescope is not affected by the low-frequency vibration, but the internal gas is. The cross section of the telescope forms a perfect circle. If he forms a coil by putting extremely thin wire along the (inner) circumference, he can measure (the average vertical component of) the temporal variation of magnetic flux:such measurement would be useful to estimate the influence. But points on the circumference at which the wire can be fixed are limited; furthermore, the number of special clips to fix the wire is also limited. To obtain the highest sensitivity, he wishes to form a coil of a polygon shape with the largest area by stringing the wire among carefully selected points on the circumference. Your job is to write a program which reports the maximum area of all possible m -polygons (polygons with exactly m vertices) each of whose vertices is one of the n points given on a circumference with a radius of 1. An example of the case n = 4 and m = 3 is illustrated below. In the figure above, the equations such as " p 1 = 0.0" indicate the locations of the n given points, and the decimals such as "1.000000" on m -polygons indicate the areas of m -polygons. Parameter p i denotes the location of the i -th given point on the circumference (1 ≤ i ≤ n ). The location p of a point on the circumference is in the range 0 ≤ p < 1, corresponding to the range of rotation angles from 0 to 2 π radians. That is, the rotation angle of a point at p to the point at 0 equals 2 π radians. ( π is the circular constant 3.14159265358979323846....) You may rely on the fact that the area of an isosceles triangle ABC (AB = AC = 1) with an interior angle BAC of α radians (0 < α < π ) is (1/2)sin α , and the area of a polygon inside a circle with a radius of 1 is less than π . Input The input consists of multiple subproblems followed by a line containing two zeros that indicates the end of the input. Each subproblem is given in the following format. n m p 1 p 2 ... p n n is the number of points on the circumference (3 ≤ n ≤ 40). m is the number of vertices to form m -polygons (3 ≤ m ≤ n ). The locations of n points, p 1 , p 2 ,..., p n , are given as decimals and they are separated by either a space character or a newline. In addition, you may assume that 0 ≤ p 1 < p 2 < ... < p n < 1. Output For each subproblem, the maximum area should be output, each in a separate line. Each value in the output may not have an error greater than 0.000001 and its fractional part should be represented by 6 decimal digits after the decim ...(truncated)	[ { "submission_id": "aoj_1222_3709885", "code_snippet": "#include <bits/stdc++.h>\n\nusing namespace std;\nusing ll = long long;\n// #define int ll\nusing PII = pair<ll, ll>;\n\n#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)\n#define REP(i, n) FOR(i, 0, n)\n#define ALL(x) x.begin(), x.end()\n\ntempl...
aoj_1226_cpp	Problem C: Fishnet A fisherman named Etadokah awoke in a very small island. He could see calm, beautiful and blue sea around the island. The previous night he had encountered a terrible storm and had reached this uninhabited island. Some wrecks of his ship were spread around him. He found a square wood-frame and a long thread among the wrecks. He had to survive in this island until someone came and saved him. In order to catch fish, he began to make a kind of fishnet by cutting the long thread into short threads and fixing them at pegs on the square wood-frame (Figure 1). He wanted to know the sizes of the meshes of the fishnet to see whether he could catch small fish as well as large ones. The wood-frame is perfectly square with four thin edges one meter long.. a bottom edge, a top edge, a left edge, and a right edge. There are n pegs on each edge, and thus there are 4 n pegs in total. The positions ofpegs are represented by their ( x , y )-coordinates. Those of an example case with n = 2 are depicted in Figures 2 and 3. The position of the i th peg on the bottom edge is represented by ( a i , 0) . That on the top edge, on the left edge and on the right edge are represented by ( b i , 1) , (0, c i ), and (1, d i ), respectively. The long thread is cut into 2 n threads with appropriate lengths. The threads are strained between ( a i , 0) and ( b i , 1) , and between (0, c i ) and (1, d i ) ( i = 1,..., n ) . You should write a program that reports the size of the largest mesh among the ( n + 1) 2 meshes of the fishnet made by fixing the threads at the pegs. You may assume that the thread he found is long enough to make the fishnet and that the wood-frame is thin enough for neglecting its thickness. Figure 1. A wood-frame with 8 pegs. Figure 2. Positions of pegs (indicated by small black circles) Figure 3. A fishnet and the largest mesh (shaded) Input The input consists of multiple subproblems followed by a line containing a zero that indicates the end of input. Each subproblem is given in the following format. n a 1 a 2 ... a n b 1 b 2 ... b n c 1 c 2 ... c n d 1 d 2 ... d n An integer n followed by a newline is the number of pegs on each edge. a 1 ,..., a n , b 1 ,..., b n , c 1 ,..., c n , d 1 ,..., d n are decimal fractions, and they are separated by a space character except that a n , b n , c n and d n are followed by a new line. Each a i ( i = 1,..., n ) indicates the x -coordinate of the i th peg on the bottom edge. Each b i ( i = 1,..., n ) indicates the x -coordinate of the i th peg on the top edge. Each c i ( i = 1,..., n ) indicates the y -coordinate of the i th peg on the left edge. Each d i ( i = 1,..., n ) indicates the y -coordinate of the i th peg on the right edge. The decimal fractions are represented by 7 digits after the decimal point. In addition you may assume that 0 < n ≤ 30 , 0 < a 1 < a 2 < ... < a n < 1, 0 < b 1 < b 2 < ... < b n < 1 , 0 < c 1 < c 2 < ... < c n < 1 and 0 < d 1 ≤ d 2 < ... < d n < 1 . Output For each subpr ...(truncated)	[ { "submission_id": "aoj_1226_3043409", "code_snippet": "#include <iostream>\n#include <iomanip>\n#include <complex>\n#include <vector>\n#include <algorithm>\n#include <cmath>\n#include <array>\nusing namespace std;\nconst double EPS = 1e-10;\nconst double INF = 1e12;\n#define EQ(n,m) (abs((n)-(m)) < EPS)\n#...
aoj_1224_cpp	Problem A: Starship Hakodate-maru The surveyor starship Hakodate-maru is famous for her two fuel containers with unbounded capacities. They hold the same type of atomic fuel balls. There, however, is an inconvenience. The shapes of the fuel containers # 1 and # 2 are always cubic and regular tetrahedral respectively. Both of the fuel containers should be either empty or filled according to their shapes. Otherwise, the fuel balls become extremely unstable and may explode in the fuel containers. Thus, the number of fuel balls for the container # 1 should be a cubic number ( n 3 for some n = 0, 1, 2, 3,... ) and that for the container # 2 should be a tetrahedral number ( n ( n + 1)( n + 2)/6 for some n = 0, 1, 2, 3,... ). Hakodate-maru is now at the star base Goryokaku preparing for the next mission to create a precise and detailed chart of stars and interstellar matters. Both of the fuel containers are now empty. Commander Parus of Goryokaku will soon send a message to Captain Future of Hakodate-maru on how many fuel balls Goryokaku can supply. Captain Future should quickly answer to Commander Parus on how many fuel balls she requests before her ship leaves Goryokaku. Of course, Captain Future and her omcers want as many fuel balls as possible. For example, consider the case Commander Parus offers 151200 fuel balls. If only the fuel container # 1 were available (i.e. ifthe fuel container # 2 were unavailable), at most 148877 fuel balls could be put into the fuel container since 148877 = 53 × 53 × 53 < 151200 < 54 × 54 × 54 . If only the fuel container # 2 were available, at most 147440 fuel balls could be put into the fuel container since 147440 = 95 × 96 × 97/6 < 151200 < 96 × 97 × 98/6 . Using both of the fuel containers # 1 and # 2, 151200 fuel balls can be put into the fuel containers since 151200 = 39 × 39 × 39 + 81 × 82 × 83/6 . In this case, Captain Future's answer should be "151200". Commander Parus's offer cannot be greater than 151200 because of the capacity of the fuel storages of Goryokaku. Captain Future and her omcers know that well. You are a fuel engineer assigned to Hakodate-maru. Your duty today is to help Captain Future with calculating the number of fuel balls she should request. Input The input is a sequence of at most 1024 positive integers. Each line contains a single integer. The sequence is followed by a zero, which indicates the end of data and should not be treated as input. You may assume that none of the input integers is greater than 151200. Output The output is composed of lines, each containing a single integer. Each output integer should be the greatest integer that is the sum of a nonnegative cubic number and a nonnegative tetrahedral number and that is not greater than the corresponding input number. No other characters should appear in the output. Sample Input 100 64 50 20 151200 0 Output for the Sample Input 99 64 47 20 151200	[ { "submission_id": "aoj_1224_4858248", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\nint main() {\n int n;\n while(cin >>n,n){\n int ans = 0;\n for(int i=0;iii<151200; i++){\n int sum = 0;\n for(int j=0; sum <= n ;j++){\n ans = ma...
aoj_1229_cpp	Problem F: Young, Poor and Busy Ken and Keiko are young, poor and busy. Short explanation: they are students, and ridden with part-time jobs. To make things worse, Ken lives in Hakodate and Keiko in Tokyo. They want to meet, but since they have neither time nor money, they have to go back to their respective jobs immediately after, and must be careful about transportation costs. Help them find the most economical meeting point. Ken starts from Hakodate, Keiko from Tokyo. They know schedules and fares for all trains, and can choose to meet anywhere including their hometowns, but they cannot leave before 8am and must be back by 6pm in their respective towns. Train changes take no time (one can leave the same minute he/she arrives), but they want to meet for at least 30 minutes in the same city. There can be up to 100 cities and 2000 direct connections, so you should devise an algorithm clever enough for the task. Input The input is a sequence of data sets. The first line of a data set contains a single integer, the number of connections in the timetable. It is not greater than 2000. Connections are given one on a line, in the following format. Start_city HH : MM Arrival_city HH : MM price Start_city and Arrival_city are composed of up to 16 alphabetical characters, with only the first one in upper case. Departure and arrival times are given in hours and minutes (two digits each, separated by ":") from 00:00 to 23:59. Arrival time is strictly after departure time. The price for one connection is an integer between 1 and 10000, inclusive. Fields are separated by spaces. The end of the input is marked by a line containing a zero. Output The output should contain one integer for each data set, the lowest cost possible. This is the total fare of all connections they use. If there is no solution to a data set, you should output a zero. The solution to each data set should be given in a separate line. Sample Input 5 Hakodate 08:15 Morioka 12:30 2500 Morioka 14:05 Hakodate 17:30 2500 Morioka 15:30 Hakodate 18:00 3000 Morioka 14:30 Tokyo 17:50 3000 Tokyo 08:30 Morioka 13:35 3000 4 Hakodate 08:15 Morioka 12:30 2500 Morioka 14:04 Hakodate 17:30 2500 Morioka 14:30 Tokyo 17:50 3000 Tokyo 08:30 Morioka 13:35 3000 18 Hakodate 09:55 Akita 10:53 3840 Hakodate 14:14 Akita 16:09 1920 Hakodate 18:36 Akita 19:33 3840 Hakodate 08:00 Morioka 08:53 3550 Hakodate 22:40 Morioka 23:34 3550 Akita 14:23 Tokyo 14:53 2010 Akita 20:36 Tokyo 21:06 2010 Akita 08:20 Hakodate 09:18 3840 Akita 13:56 Hakodate 14:54 3840 Akita 21:37 Hakodate 22:35 3840 Morioka 09:51 Tokyo 10:31 2660 Morioka 14:49 Tokyo 15:29 2660 Morioka 19:42 Tokyo 20:22 2660 Morioka 15:11 Hakodate 16:04 3550 Morioka 23:03 Hakodate 23:56 3550 Tokyo 09:44 Morioka 11:04 1330 Tokyo 21:54 Morioka 22:34 2660 Tokyo 11:34 Akita 12:04 2010 0 Output for the Sample Input 11000 0 11090	[ { "submission_id": "aoj_1229_2940627", "code_snippet": "#include<bits/stdc++.h>\ntypedef long long int ll;\ntypedef unsigned long long int ull;\n#define BIG_NUM 2000000000\n#define MOD 1000000007\n#define EPS 0.000000001\nusing namespace std;\n\n\n#define NUM 100\n#define BASE 480\n#define MAX 600\n\nenum T...
aoj_1228_cpp	Problem E: Beehives Taro and Hanako, students majoring in biology, have been engaged long in observations of beehives. Their interest is in finding any egg patterns laid by queen bees of a specific wild species. A queen bee is said to lay a batch ofeggs in a short time. Taro and Hanako have never seen queen bees laying eggs. Thus, every time they find beehives, they find eggs just laid in hive cells. Taro and Hanako have a convention to record an egg layout.. they assume the queen bee lays eggs, moving from one cell to an adjacent cell along a path containing no cycles. They record the path of cells with eggs. There is no guarantee in biology for them to find an acyclic path in every case. Yet they have never failed to do so in their observations. There are only six possible movements from a cell to an adjacent one, and they agree to write down those six by letters a, b, c, d, e, and f ounterclockwise as shown in Figure 2. Thus the layout in Figure 1 may be written down as "faafd". Taro and Hanako have investigated beehives in a forest independently. Each has his/her own way to approach beehives, protecting oneself from possible bee attacks. They are asked to report on their work jointly at a conference, and share their own observation records to draft a joint report. At this point they find a serious fault in their convention. They have never discussed which direction, in an absolute sense, should be taken as "a", and thus Figure 2 might be taken as, e.g., Figure 3 or Figure 4. The layout shown in Figure 1 may be recorded differently, depending on the direction looking at the beehive and the path assumed: "bcbdb" with combination of Figure 3 and Figure 5, or "bccac" with combination of Figure 4 and Figure 6. A beehive can be observed only from its front side and never from its back, so a layout cannot be confused with its mirror image. Since they may have observed the same layout independently, they have to find duplicated records in their observations (Of course, they do not record the exact place and the exact time of each observation). Your mission is to help Taro and Hanako by writing a program that checks whether two observation records are made from the same layout. Input The input starts with a line containing the number of record pairs that follow. The number is given with at most three digits. Each record pair consists of two lines of layout records and a line containing a hyphen. Each layout record consists of a sequence of letters a, b, c, d, e, and f. Note that a layout record may be an empty sequence if a queen bee laid only one egg by some reason. You can trust Taro and Hanako in that any of the paths in the input does not force you to visit any cell more than once. Any of lines in the input contain no characters other than those described above, and contain at most one hundred characters. Output For each pair of records, produce a line containing either " true " or " false ": " true " if the two records represent the same layout, ...(truncated)	[ { "submission_id": "aoj_1228_2649936", "code_snippet": "#include <stdio.h>\n#include <cmath>\n#include <algorithm>\n#include <cfloat>\n#include <stack>\n#include <queue>\n#include <vector>\n#include <string>\n#include <iostream>\n#include <set>\n#include <map>\n#include <time.h>\ntypedef long long int ll;\n...
aoj_1232_cpp	Problem A: Calling Extraterrestrial Intelligence Again A message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico on the afternoon of Saturday November l6, l974. The message consisted of l679 bits and was meant to be translated to a rectangular picture with 23 × 73 pixels. Since both 23 and 73 are prime numbers, 23 × 73 is the unique possible size of the translated rectangular picture each edge of which is longer than l pixel. Of course, there was no guarantee that the receivers would try to translate the message to a rectangular picture. Even if they would, they might put the pixels into the rectangle incorrectly. The senders of the Arecibo message were optimistic. We are planning a similar project. Your task in the project is to find the most suitable width and height of the translated rectangular picture. The term ``most suitable'' is defined as follows. An integer m greater than 4 is given. A positive fraction a / b less than or equal to 1 is also given. The area of the picture should not be greater than m . Both of the width and the height of the translated picture should be prime numbers. The ratio of the width to the height should not be less than a / b nor greater than 1. You should maximize the area of the picture under these constraints. In other words, you will receive an integer m and a fraction a / b . It holds that m > 4 and 0 < a / b ≤ 1 . You should find the pair of prime numbers p , q such that pq ≤ m and a / b ≤ p / q ≤ 1 , and furthermore, the product pq takes the maximum value among such pairs of two prime numbers. You should report p and q as the "most suitable" width and height of the translated picture. Input The input is a sequence of at most 2000 triplets of positive integers, delimited by a space character in between. Each line contains a single triplet. The sequence is followed by a triplet of zeros, 0 0 0, which indicates the end of the input and should not be treated as data to be processed. The integers of each input triplet are the integer m , the numerator a , and the denominator b described above, in this order. You may assume 4 < m < 100000 and 1 ≤ a ≤ b ≤ 1000. Output The output is a sequence of pairs of positive integers. The i -th output pair corresponds to the i -th input triplet. The integers of each output pair are the width p and the height q described above, in this order. Each output line contains a single pair. A space character is put between the integers as a delimiter. No other characters should appear in the output. Sample Input 5 1 2 99999 999 999 1680 5 16 1970 1 1 2002 4 11 0 0 0 Output for the Sample Input 2 2 313 313 23 73 43 43 37 53	[ { "submission_id": "aoj_1232_10896784", "code_snippet": "#include<bits/stdc++.h>\n// #include<atcoder/all>\n// #include<boost/multiprecision/cpp_int.hpp>\n\nusing namespace std;\n// using namespace atcoder;\n// using bint = boost::multiprecision::cpp_int;\nusing ll = long long;\nusing ull = unsigned long lo...
aoj_1230_cpp	Problem G: Nim Let's play a traditional game Nim. You and I are seated across a table and we have a hundred stones on the table (we know the number of stones exactly). We play in turn and at each turn, you or I can remove one to four stones from the heap. You play first and the one who removed the last stone loses. In this game, you have a winning strategy. To see this, you first remove four stones and leave 96 stones. No matter how I play, I will end up with leaving 92-95 stones. Then you will in turn leave 91 stones for me (verify this is always possible). This way, you can always leave 5 k + 1 stones for me and finally I get the last stone, sigh. If we initially had 101 stones, on the other hand, I have a winning strategy and you are doomed to lose. Let's generalize the game a little bit. First, let's make it a team game. Each team has n players and the 2 n players are seated around the table, with each player having opponents at both sides. Turns round the table so the two teams play alternately. Second, let's vary the maximum number ofstones each player can take. That is, each player has his/her own maximum number ofstones he/she can take at each turn (The minimum is always one). So the game is asymmetric and may even be unfair. In general, when played between two teams of experts, the outcome of a game is completely determined by the initial number ofstones and the minimum number of stones each player can take at each turn. In other words, either team has a winning strategy. You are the head-coach of a team. In each game, the umpire shows both teams the initial number of stones and the maximum number of stones each player can take at each turn. Your team plays first. Your job is, given those numbers, to instantaneously judge whether your team has a winning strategy. Incidentally, there is a rumor that Captain Future and her officers of Hakodate-maru love this game, and they are killing their time playing it during their missions. You wonder where the stones are?. Well, they do not have stones but do have plenty of balls in the fuel containers!. Input The input is a sequence of lines, followed by the last line containing a zero. Each line except the last is a sequence of integers and has the following format. n S M 1 M 2 ... M 2 n where n is the number of players in a team, S the initial number of stones, and M i the maximum number of stones i th player can take. 1st, 3rd, 5th, ... players are your team's players and 2nd, 4th, 6th, ... the opponents. Numbers are separated by a single space character. You may assume 1 ≤ n ≤ 10, 1 ≤ M i ≤ 16, and 1 ≤ S ≤ 2 13 . Output The out put should consist of lines each containing either a one, meaning your team has a winning strategy, or a zero otherwise. Sample Input 1 101 4 4 1 100 4 4 3 97 8 7 6 5 4 3 0 Output for the Sample Input 0 1 1	[ { "submission_id": "aoj_1230_9710661", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\nint n;\nmap <pair <int, int>, int> mp;\n\nbool get_res(vector <int> &v, int id, int s) {\n if(s == 0) return 1;\n if(mp[{id, s}]) return mp[{id, s}];\n\n bool res = 0;\n for(int i = 1; i <= ...
aoj_1237_cpp	Problem F: Shredding Company You have just been put in charge of developing a new shredder for the Shredding Company. Although a ``normal'' shredder would just shred sheets of paper into little pieces so that the contents would become unreadable, this new shredder needs to have the following unusual basic characteristics. The shredder takes as input a target number and a sheet of paper with a number written on it. It shreds (or cuts) the sheet into pieces each of which has one or more digits on it. The sum of the numbers written on each piece is the closest possible number to the target number, without going over it. For example, suppose that the target number is 50 , and the sheet of paper has the number 12346 . The shredder would cut the sheet into four pieces, where one piece has 1 , another has 2 , the third has 34 , and the fourth has 6 . This is because their sum 43 (= 1 + 2 + 34 + 6) is closest to the target number 50 of all possible combinations without going over 50. For example, a combination where the pieces are 1 , 23 , 4 , and 6 is not valid, because the sum of this combination 34 (= 1 + 23 + 4 + 6) is less than the above combination's 43. The combination of 12 , 34 , and 6 is not valid either, because the sum 52 (= 12+34+6) is greater than the target number of 50. Figure 1. Shredding a sheet of paper having the number 12346 when the target number is 50 There are also three special rules: If the target number is the same as the number on the sheet of paper, then the paper is not cut. For example, if the target number is 100 and the number on the sheet of paper is also 100 , then the paper is not cut. If it is not possible to make any combination whose sum is less than or equal to the target number, then error is printed on a display. For example, if the target number is 1 and the number on the sheet of paper is 123 , it is not possible to make any valid combination, as the combination with the smallest possible sum is 1 , 2 , 3 . The sum for this combination is 6, which is greater than the target number, and thus error is printed. If there is more than one possible combination where the sum is closest to the target number without going over it, then rejected is printed on a display. For example, if the target number is 15 , and the number on the sheet of paper is 111 , then there are two possible combinations with the highest possible sum of 12: (a) 1 and 11 and (b) 11 and 1 ; thus rejected is printed. In order to develop such a shredder, you have decided to first make a simple program that would simulate the above characteristics and rules. Given two numbers, where the first is the target number and the second is the number on the sheet of paper to be shredded, you need to figure out how the shredder should ``cut up'' the second number. Input The input consists of several test cases, each on one line, as follows: t 1 num 1 t 2 num 2 ... t n num n 0 0 Each test case consists of the following two positive integers, which are separated ...(truncated)	[ { "submission_id": "aoj_1237_3989783", "code_snippet": "#include <bits/stdc++.h>\nusing namespace std;\n\n//repetition\n#define FOR(i,a,b) for(ll i=(a);i<(b);++i)\n#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)\n\n//container util\n#define all(x) (x).begin(),(x).end()\n\n//typedef\ntypedef long long ll;\...
aoj_1239_cpp	Problem H: Viva Confetti Do you know confetti ? They are small discs of colored paper, and people throw them around during parties or festivals. Since people throw lots of confetti, they may end up stacked one on another, so there may be hidden ones underneath. A handful of various sized confetti have been dropped on a table. Given their positions and sizes, can you tell us how many of them you can see? The following figure represents the disc configuration for the first sample input, where the bottom disc is still visible. Input The input is composed of a number of configurations of the following form. n x 1 y 1 z 1 x 2 y 2 z 2 . . . x n y n z n The first line in a configuration is the number of discs in the configuration (a positive integer not more than 100), followed by one Ine descriptions of each disc: coordinates of its center and radius, expressed as real numbers in decimal notation, with up to 12 digits after the decimal point. The imprecision margin is ±5 × 10 -13 . That is, it is guaranteed that variations of less than ±5 × 10 -13 on input values do not change which discs are visible. Coordinates of all points contained in discs are between -10 and 10. Confetti are listed in their stacking order, x 1 y 1 r 1 being the bottom one and x n y n r n the top one. You are observing from the top. The end of the input is marked by a zero on a single line. Output For each configuration you should output the number of visible confetti on a single line. Sample Input 3 0 0 0.5 -0.9 0 1.00000000001 0.9 0 1.00000000001 5 0 1 0.5 1 1 1.00000000001 0 2 1.00000000001 -1 1 1.00000000001 0 -0.00001 1.00000000001 5 0 1 0.5 1 1 1.00000000001 0 2 1.00000000001 -1 1 1.00000000001 0 0 1.00000000001 2 0 0 1.0000001 0 0 1 2 0 0 1 0.00000001 0 1 0 Output for the Sample Input 3 5 4 2 2	[ { "submission_id": "aoj_1239_4761256", "code_snippet": "#include<iostream>\n#include<cfloat>\n#include<cassert>\n#include<cmath>\n#include<cstdio>\n#include<vector>\n#include<set>\n#include<algorithm>\n\nusing namespace std;\n\n#define EPS (1e-15)\n#define equals(a, b) (fabs((a) - (b)) < EPS )\n#define dle(...
aoj_1234_cpp	Problem C: GIGA Universe Cup Following FIFA World Cup, a larger competition called ``GIGA Universe Cup'' is taking place somewhere in our universe. Both FIFA World Cup and GIGA Universe Cup are two rounds competitions that consist of the first round, also known as ``group league,'' and the second called ``final tournament.'' In the first round, participating teams are divided into groups of four teams each. Each team in a group plays a match against each of the other teams in the same group. For example, let's say we have a group of the following four teams, ``Engband, Swedon, Argontina, and Nigerua.'' They play the following six matches: Engband - Swedon, Engband - Argontina, Engband - Nigerua, Swedon - Argontina, Swedon - Nigerua, and Argontina - Nigerua. The result of a single match is shown by the number of goals scored by each team, like ``Engband 1 - 0 Argontina,'' which says Engband scored one goal whereas Argontina zero. Based on the result of a match, points are given to the two teams as follows and used to rank teams. If a team wins a match (i.e., scores more goals than the other), three points are given to it and zero to the other. If a match draws (i.e., the two teams score the same number of goals), one point is given to each. The goal difference of a team in given matches is the total number of goals it scored minus the total number of goals its opponents scored in these matches. For example, if we have three matches ``Swedon 1 - 2 Engband,'' ``Swedon 3 - 4 Nigerua,'' and ``Swedon 5 - 6 Argontina,'' then the goal difference of Swedon in these three matches is (1 + 3 + 5) - (2 + 4+ 6) = -3. Given the results of all the six matches in a group, teams are ranked by the following criteria, listed in the order of priority (that is, we first apply (a) to determine the ranking, with ties broken by (b), with ties broken by (c), and so on). (a) greater number of points in all the group matches; (b) greater goal difference in all the group matches; (c) greater number of goals scored in all the group matches. If two or more teams are equal on the basis of the above three criteria, their place shall be determined by the following criteria, applied in this order: (d) greater number of points obtained in the group matches between the teams concerned; (e) greater goal difference resulting from the group matches between the teams concerned; (f) greater number of goals scored in the group matches between the teams concerned; If two or more teams are stiIl equal, apply (d), (e), and (f) as necessary to each such group. Repeat this until those three rules to equal teams do not make any further resolution. Finally, teams that still remain equal are ordered by: (g) drawing lots by the Organizing Committee for the GIGA Universe Cup. The two teams coming first and second in each group qualify for the second round. Your job is to write a program which, given the results of matches played so far in a group and one team specified in the group, calculates the ...(truncated)	[ { "submission_id": "aoj_1234_4943973", "code_snippet": "#include <stdio.h>\n#include <bits/stdc++.h>\nusing namespace std;\n#define rep(i,n) for (int i = 0; i < (n); ++i)\n#define Inf 1000000000\n\nvector<double> p(9);\n\nvector<vector<string>> get(vector<pair<pair<string,string>,pair<int,int>>> S){\n\n\tma...
aoj_1233_cpp	Problem B: Equals are Equals Mr. Simpson got up with a slight feeling of tiredness. It was the start of another day of hard work. A bunch of papers were waiting for his inspection on his desk in his office. The papers contained his students' answers to questions in his Math class, but the answers looked as if they were just stains of ink. His headache came from the ``creativity'' of his students. They provided him a variety of ways to answer each problem. He has his own answer to each problem, which is correct, of course, and the best from his aesthetic point of view. Some of his students wrote algebraic expressions equivalent to the expected answer, but many of them look quite different from Mr. Simpson's answer in terms of their literal forms. Some wrote algebraic expressions not equivalent to his answer, but they look quite similar to it. Only a few of the students' answers were exactly the same as his. It is his duty to check if each expression is mathematically equivalent to the answer he has prepared. This is to prevent expressions that are equivalent to his from being marked as ``incorrect'', even if they are not acceptable to his aesthetic moral. He had now spent five days checking the expressions. Suddenly, he stood up and yelled, ``I've had enough! I must call for help.'' Your job is to write a program to help Mr. Simpson to judge if each answer is equivalent to the ``correct'' one. Algebraic expressions written on the papers are multi-variable polynomials over variable symbols a , b ,..., z with integer coefficients, e.g., ( a + b 2 )( a - b 2 ), ax 2 +2 bx + c and ( x 2 +5 x + 4)( x 2 + 5 x + 6) + 1. Mr. Simpson will input every answer expression as it is written on the papers; he promises you that an algebraic expression he inputs is a sequence of terms separated by additive operators ` + ' and ` - ', representing the sum of the terms with those operators, if any; a term is a juxtaposition of multiplicands, representing their product; and a multiplicand is either (a) a non-negative integer as a digit sequence in decimal, (b) a variable symbol (one of the lowercase letters ` a ' to ` z '), possibly followed by a symbol ` ^ ' and a non-zero digit, which represents the power of that variable, or (c) a parenthesized algebraic expression, recursively. Note that the operator ` + ' or ` - ' appears only as a binary operator and not as a unary operator to specify the sing of its operand. He says that he will put one or more space characters before an integer if it immediately follows another integer or a digit following the symbol ` ^ '. He also says he may put spaces here and there in an expression as an attempt to make it readable, but he will never put a space between two consecutive digits of an integer. He remarks that the expressions are not so complicated, and that any expression, having its ` - 's replaced with ` + 's, if any, would have no variable raised to its 10th power, nor coefficient more than a billion, even if it is fully e ...(truncated)	[ { "submission_id": "aoj_1233_8484392", "code_snippet": "#include <bits/stdc++.h>\n\nconstexpr int W = 26;\nusing Var = std::array<int, W>;\nstd::ostream& operator<<(std::ostream& os, const Var& var) {\n os << '(';\n for (int i = 0; i < W; i++) {\n if (var[i] == 0) continue;\n os << '(' <...
aoj_1238_cpp	Problem G: True Liars After having drifted about in a small boat for a couple of days, Akira Crusoe Maeda was finally cast ashore on a foggy island. Though he was exhausted and despaired, he was still fortunate to remember a legend of the foggy island, which he had heard from patriarchs in his childhood. This must be the island in the legend. In the legend, two tribes have inhabited the island, one is divine and the other is devilish; once members of the divine tribe bless you, your future is bright and promising, and your soul will eventually go to Heaven; in contrast, once members of the devilish tribe curse you, your future is bleak and hopeless, and your soul will eventually fall down to Hell. In order to prevent the worst-case scenario, Akira should distinguish the devilish from the divine. But how? They looked exactly alike and he could not distinguish one from the other solely by their appearances. He still had his last hope, however. The members of the divine tribe are truth-tellers, that is, they always tell the truth and those of the devilish tribe are liars, that is, they always tell a lie. He asked some of the whether or not some are divine. They knew one another very much and always responded to him "faithfully" according to their individual natures (i.e., they always tell the truth or always a lie). He did not dare to ask any other forms of questions, since the legend says that a devilish member would curse a person forever when he did not like the question. He had another piece of useful information: the legend tells the populations of both tribes. These numbers in the legend are trustworthy since everyone living on this island is immortal and none have ever been born at least these millennia. You are a good computer programmer and so requested to help Akira by writing a program that classifies the inhabitants according to their answers to his inquiries. Input The input consists of multiple data sets, each in the following format: n p 1 p 2 x 1 y 1 a 1 x 2 y 2 a 2 ... x i y i a i ... x n y n a n The first line has three non-negative integers n , p 1 , and p 2 . n is the number of questions Akira asked. p 1 and p 2 are the populations of the divine and devilish tribes, respectively, in the legend. Each of the following n lines has two integers x i , y i and one word a i . x i and y i are the identification numbers of inhabitants, each of which is between 1 and p 1 + p 2 , inclusive. a i is either "yes", if the inhabitant x i said that the inhabitant y i was a member of the divine tribe, or "no", otherwise. Note that x i and y i can be the same number since "are you a member of the divine tribe?" is a valid question. Note also that two lines may have the same x 's and y 's since Akira was very upset and might have asked the same question to the same one more than once. You may assume that n is less than 1000 and that p 1 and p 2 are less than 300. A line with three zeros, i.e., "0 0 0", represents the end of the input. You can assume ...(truncated)	[ { "submission_id": "aoj_1238_5010193", "code_snippet": "#include<iostream>\n#include<cstdio>\n#include<cstring>\nusing namespace std;\n\nconst int N = 2010;\nint fa[N], siz[N], a[N], f[N][N], pre[N][N], ans[N], b[N], c[N]; \nbool vis[N], in[N];\nint findfa(int x) {\n\treturn fa[x] == x ? x : fa[x] = findfa(...
aoj_1241_cpp	Problem B: Lagrange's Four-Square Theorem The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are. For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 4 2 + 3 2 and 3 2 + 4 2 are the same representation. For example, let’s check the case of 25. This integer has just three representations 1 2 +2 2 +2 2 +4 2 , 3 2 + 4 2 , and 5 2 . Thus you should report 3 in this case. Be careful not to count 4 2 + 3 2 and 3 2 + 4 2 separately. Input The input is composed of at most 255 lines, each containing a single positive integer less than 2 15 , followed by a line containing a single zero. The last line is not a part of the input data. Output The output should be composed of lines, each containing a single integer. No other characters should appear in the output. The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares. Sample Input 1 25 2003 211 20007 0 Output for the Sample Input 1 3 48 7 738	[ { "submission_id": "aoj_1241_10895268", "code_snippet": "#include<bits/stdc++.h>\n// #include<atcoder/all>\n// #include<boost/multiprecision/cpp_int.hpp>\n\nusing namespace std;\n// using namespace atcoder;\n// using bint = boost::multiprecision::cpp_int;\nusing ll = long long;\nusing ull = unsigned long lo...
aoj_1247_cpp	Problem H: Monster Trap Once upon a time when people still believed in magic, there was a great wizard Aranyaka Gondlir. After twenty years of hard training in a deep forest, he had finally mastered ultimate magic, and decided to leave the forest for his home. Arriving at his home village, Aranyaka was very surprised at the extraordinary desolation. A gloom had settled over the village. Even the whisper of the wind could scare villagers. It was a mere shadow of what it had been. What had happened? Soon he recognized a sure sign of an evil monster that is immortal. Even the great wizard could not kill it, and so he resolved to seal it with magic. Aranyaka could cast a spell to create a monster trap: once he had drawn a line on the ground with his magic rod, the line would function as a barrier wall that any monster could not get over. Since he could only draw straight lines, he had to draw several lines to complete a monster trap, i.e., magic barrier walls enclosing the monster. If there was a gap between barrier walls, the monster could easily run away through the gap. For instance, a complete monster trap without any gaps is built by the barrier walls in the left figure, where “M” indicates the position of the monster. In contrast, the barrier walls in the right figure have a loophole, even though it is almost complete. Your mission is to write a program to tell whether or not the wizard has successfully sealed the monster. Input The input consists of multiple data sets, each in the following format. n x 1 y 1 x' 1 y' 1 x 2 y 2 x' 2 y' 2 ... x n y n x' n y' n The first line of a data set contains a positive integer n, which is the number of the line segments drawn by the wizard. Each of the following n input lines contains four integers x , y , x' , and y' , which represent the x - and y -coordinates of two points ( x , y ) and ( x' , y' ) connected by a line segment. You may assume that all line segments have non-zero lengths. You may also assume that n is less than or equal to 100 and that all coordinates are between -50 and 50, inclusive. For your convenience, the coordinate system is arranged so that the monster is always on the origin (0, 0). The wizard never draws lines crossing (0, 0). You may assume that any two line segments have at most one intersection point and that no three line segments share the same intersection point. You may also assume that the distance between any two intersection points is greater than 10 -5 . An input line containing a zero indicates the end of the input. Output For each data set, print “yes” or “no” in a line. If a monster trap is completed, print “yes”. Otherwise, i.e., if there is a loophole, print “no”. Sample Input 8 -7 9 6 9 -5 5 6 5 -10 -5 10 -5 -6 9 -9 -6 6 9 9 -6 -1 -2 -3 10 1 -2 3 10 -2 -3 2 -3 8 -7 9 5 7 -5 5 6 5 -10 -5 10 -5 -6 9 -9 -6 6 9 9 -6 -1 -2 -3 10 1 -2 3 10 -2 -3 2 -3 0 Output for the Sample Input yes no	[ { "submission_id": "aoj_1247_8388160", "code_snippet": "#include<bits/stdc++.h>\nusing namespace std;\ntypedef long long int ll;\ntypedef unsigned long long int ull;\n#define chmin(x,y) x = min(x,y)\n#define chmax(x,y) x = max(x,y)\n#define BIG_NUM 2000000000\n#define HUGE_NUM 4000000000000000000 //オーバーフローに...
aoj_1243_cpp	Problem D: Weather Forecast You are the God of Wind. By moving a big cloud around, you can decide the weather: it invariably rains under the cloud, and the sun shines everywhere else. But you are a benign God: your goal is to give enough rain to every field in the countryside, and sun to markets and festivals. Small humans, in their poor vocabulary, only describe this as “weather forecast”. You are in charge of a small country, called Paccimc. This country is constituted of 4 × 4 square areas, denoted by their numbers. Your cloud is of size 2 × 2, and may not cross the borders of the country. You are given the schedule of markets and festivals in each area for a period of time. On the first day of the period, it is raining in the central areas (6-7-10-11), independently of the schedule. On each of the following days, you may move your cloud by 1 or 2 squares in one of the four cardinal directions (North, West, South, and East), or leave it in the same position. Diagonal moves are not allowed. All moves occur at the beginning of the day. You should not leave an area without rain for a full week (that is, you are allowed at most 6 consecutive days without rain). You don’t have to care about rain on days outside the period you were given: i.e. you can assume it rains on the whole country the day before the period, and the day after it finishes. Input The input is a sequence of data sets, followed by a terminating line containing only a zero. A data set gives the number N of days (no more than 365) in the period on a single line, followed by N lines giving the schedule for markets and festivals. The i -th line gives the schedule for the i-th day. It is composed of 16 numbers, either 0 or 1, 0 standing for a normal day, and 1 a market or festival day. The numbers are separated by one or more spaces. Output The answer is a 0 or 1 on a single line for each data set, 1 if you can satisfy everybody, 0 if there is no way to do it. Sample Input 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 Output for the Sample Input 0 1 0 1	[ { "submission_id": "aoj_1243_10865810", "code_snippet": "#include<cstdio>\n#include<iostream>\n#include<cstring>\n#include<cmath>\n#include<cstdlib>\n#include<vector>\n#include<stack>\n#include<algorithm>\n#include<queue>\n#include<string>\n#define OK 1\n#define INF 2147483647\n#define LINF 9223372036854775...

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