ACM大赛原题目

一Network of SchoolsTime Limit: 1000MS Memory Limit: 10000KTotal Submissions: 4526 Accepted: 1776 DescriptionA number of schools are connected to a computer network. Agreements have been developed among those schools: each school maintains a list of schools to which it distributes software (the “receiving schools”). Note that ifB is in the distribution list of school A, then A does not necessarily appear in the list of school BYou are to write a program that computes the minimal number of schools that must receive a copy of the new software in order for the software to reach all schools in the network according to the agreement (Subtask A). As a further task, we want to ensure that by sending the copy of new software to an arbitrary school, this software will reach all schools in the network. To achieve this goal we may have to extend the lists of receivers by new members. Compute the minimal number of extensions that have to be made so that whatever school we send the new software to, it will reach all other schools (Subtask B). One extension means introducing one new member into the list of receivers of one school.InputThe first line contains an integer N: the number of schools in the network (2 <= N <= 100). The schools are identified by the first N positive integers. Each of the next N lines describes a list of receivers. The line i+1 contains the identifiers of the receivers of school i. Each list ends with a 0. An empty list contains a 0 alone in the line.OutputYour program should write two lines to the standard output. The first line should contain one positive integer: the solution of subtask A. The second line should contain the solution of subtask B.Sample Input52 43 04 5 01 0Sample Output12二Remmarguts' DateTime Limit: 4000MS Memory Limit: 65536KTotal Submissions: 10811 Accepted: 2944 Description"Good man never makes girls wait or breaks an appointment!" said the mandarin duck father. Softly touching his little ducks' head, he told them a story."Prince Remmarguts lives in his kingdom UDF – United Delta of Freedom. One day their neighboring country sent them Princess Uyuw on a diplomatic mission.""Erenow, the princess sent Remmarguts a letter, informing him that she would come to the hall and hold commercial talks with UDF if and only if the prince go and meet her via the K-th shortest path. (in fact, Uyuw does not want to come at all)"Being interested in the trade development and such a lovely girl, Prince Remmarguts really became enamored. He needs you - the prime minister's help!DETAILS: UDF's capital consists of N stations. The hall is numbered S, while the station numbered T denotes prince' current place. M muddy directed sideways connect some of the stations. Remmarguts' path to welcome the princess might include the same station twice or more than twice, even it is the station with number S or T. Different paths with same length will be considered disparate.InputThe first line contains two integer numbers N and M (1 <= N <= 1000, 0 <= M <= 100000). Stations are numbered from 1 to N. Each of the following M lines contains three integer numbers A, B and T (1 <= A, B <= N, 1 <= T <= 100). It shows that there is a directed sideway from A-th station to B-th station with time T.The last line consists of three integer numbers S, T and K (1 <= S, T <= N, 1 <= K <= 1000).OutputA single line consisting of a single integer number: the length (time required) to welcome Princess Uyuw using the K-th shortest path. If K-th shortest path does not exist, you should output "-1" (without quotes) instead.Sample Input2 21 2 52 1 41 2 2Sample Output14三ChessboardTime Limit: 2000MS Memory Limit: 65536KTotal Submissions: 7406 Accepted: 2306 DescriptionAlice and Bob often play games on chessboard. One day, Alice draws a board with size M * N. She wants Bob to use a lot of cards with size 1 * 2 to cover the board. However, she thinks it too easy to bob, so she makes some holes on the board (as shown in the figure below).We call a grid, which doesn’t contain a hole, a normal grid. Bob has to follow the rules below:1. Any normal grid should be covered with exactly one card.2. One card should cover exactly 2 normal adjacent grids.Some examples are given in the figures below:A VALID solution.An invalid solution, because the hole of red color is covered with a card.An invalid solution, because there exists a grid, which is not covered.Your task is to help Bob to decide whether or not the chessboard can be covered according to the rules above.InputThere are 3 integers in the first line: m, n, k (0 < m, n <= 32, 0 <= K < m * n), the number of rows, column and holes. In the next k lines, there is a pair of integers (x, y) in each line, which represents a hole in the y-th row, the x-th column.OutputIf the board can be covered, output "YES". Otherwise, output "NO".Sample Input4 3 22 13 3Sample OutputYES四RSATime Limit: 3000MS Memory Limit: 65536KTotal Submissions: 2583 Accepted: 490DescriptionRSA is the best-known public key encryption algorithm. In this algorithm each participant has a private key that is shared with no one else and a public key which is published so everyone knows it. To send a secure message to this participant, you encrypt the message using the widely known public key; the participant then decrypts the messages using his or her private key. Here is the procedure of RSA:First, choose two different large prime numbers P and Q, and multiply them to get N (= P * Q).Second, select a positive integer E (0 < E < N) as the encryption key such that E and T= (P - 1) * (Q - 1) are relatively prime.Third, compute the decryption key D such that 0 <= D < T and (E * D) mod T = 1. Here D is a multiplicative inverse of E, modulo T.Now the public key is constructed by the pair {E, N}, and the private key is {D, N}. P and Q can be discarded.Encryption is defined by C = (M ^ E) mod N, and decryption is defined by M = (C ^ D) mod N, here M, which is a non-negative integer and smaller than N, is the plaintext message and C is the resulting ciphertext.To illustrate this idea, let’s see the following example:We choose P = 37, Q = 23, So N = P * Q = 851, and T = 792. If we choose E = 5, D will be 317 ((5 * 317) mod 792 = 1). So the public key is {5, 851}, and the privatekey is {317, 851}. For a given plaintext M = 7, we can get the ciphertext C = (7 ^ 5) mod 851 = 638.As we have known,for properly choosen very large P and Q, it will take thousands of years to break a key, but for small ones, it is another matter.Now you are given the ciphertext C and public key {E, N}, can you find the plaintext M?InputThe input will contain several test cases. Each test case contains three positive integers C, E, N (0 < C < N, 0 < E < N, 0 < N < 2 ^ 62).OutputOutput the plaintext M in a single line.Sample Input638 5 851Sample Output7五A New Operating SystemTime Limit: 20000MS Memory Limit: 65536KTotal Submissions: 669 Accepted: 49Case Time Limit: 5000MSDescriptionMay is a lovely girl. Due to her filial piety, she wants to give a present on hermother's birthday. Because both her parents are the top programmer in the world, she decided to design a new program, a special program that is an Operating System! With the help of her excellent programming skill, May has already finished the kernel of the new OS. And the birthday is coming, she is afraid that time is not enough to finish the entire project in time. As her best net-pal, it's your duty to help her.This is a multitask OS, processes run at the same time. There are following command in the OS:CreateProcess(PID,Memory,Priority)A new process is created with the process identification PID and memory size, and a priority. The priority in this command is called outer priority of a process.AddMessage(PID,Priority)That means, add a new message to the message queue of process PID, with the priority of Priority. The message with higher Priority will run earlier that lower ones. The Priority is called inner priority.RunFind out the message with biggest HP. HP is defined as the product of the inner priority of a message and the corresponding process priority. If two or more messages have the same HP, the one with smallest PID will run first. Print the information "Run: HP" to the output file, HP will be replaced by the message HP you found, or print "Empty" instead if the message queue is empty. Finally remove this message if exist.ChangePriority(PID,NewValue)Change the outer priority of process PID to NewValue.GetMemory(PID,Memory)Process PID memory increases the amount of Memory.FreeMemory(PID,Memory)Process PID memory decreases the amount of Memory.RunProcess(PID)Similar with Run command. Find out the message in the process PID message queue, print the information "Run Process: Priority" to the output file, Priority will be replaced by the message priority you found, or print "Empty" instead if the messagequeue is empty. Finally remove this message if exist.CloseMaxMemoryFind out the process that used the largest number of memory and close it if exists (if tie, the one with smallest PID should be release first), or print "Empty" instead.CloseProcess(PID)Close the process with the identification of PID.Whenever a process' memory is less than or equal to 0, it will be close automatically. In any of the above commands except the first one, if the PID doesn't exist, please print an "Error" to the output. For the first command, if the PID is already exist, print an "Error" and ignore this command.InputFirst line in the input is an integer number N (1 <= N <= 100000), which represents the number of commands. The next N lines, each gives a command described above. Any number given in the input file will be non-negative integer and will not be more than 1000000000.OutputThe output format has been described above.Sample Input11CloseMaxMemoryCreateProcess(1,100,1)CreateProcess(2,200,1)CreateProcess(3,300,1)AddMessage(1,9)AddMessage(2,19)AddMessage(1,10)GetMemory(2,999)CloseMaxMemoryRunRunProcess(1)Sample OutputEmptyRun: 10Run Process: 9六A New Kind of ChessTime Limit: 3000MS Memory Limit: 65536KTotal Submissions: 245 Accepted: 42DescriptionPrince Remmarguts met Uyuw successfully in our previous story, and after that Princess Uyuw introduced a new kind of chess to Remmarguts named Nixgnauhc. The only chessman allowed in it was a special type of Knight.The chessboard is of (N + 1) * (M + 1). Each of the rows and columns are numbered as the following graph:Here N + 1 = 5 + 1 is the number of rows and M + 1 = 4 + 1 is the number of columns. We are also given two integer numbers P and Q, and told that at the beginning of the game, the blocks of (x, y) - (row number, column number) - where x <= P and y <= Q are already taken up by Knight.During the game, we can choose a single Knight to move, and the only allowed movements for Knight at (x, y) is to (x + a, y + b) or to (x + c, y + d). But during the movement, the position it goes must be on the chessboard and NOT be taken up by another Knight. Our purpose is to move that chessman to the final end (N, M). (The description above means that once you choose a chessman, you can only move that chessman in the following steps)Meanwhile, we suppose 3 <= N, M <= 100000, 0 <= P < N, 0 <= Q < M, 1<= a, b, c, d. Princess Uyuw wanted to know the number of essentially different games. Two games are called “different” if and only if we choose the different chessman at the beginning or perform a different movement at some time.WARNING: Even if a = c, b = d, we also call (+a, +b) and (+c, +d) DIFFERENT movements!InputYou should read the number of test cases Z in the first line – Z <= 100.Each of the following lines denotes a single test case, consisting of 8 integers N, M, P, Q, a, b, c, and d. The meanings of such integers are described above.OutputOutput one line per test case, showing the total possibilities of games. We guarantee this number is less than 10^500.Sample Input23 3 0 0 1 1 1 15 4 2 1 1 1 2 1Sample Output87七An Easy ProblemTime Limit: 1000MS Memory Limit: 65536KTotal Submissions: 6197 Accepted: 3631 DescriptionAs we known, data stored in the computers is in binary form. The problem we discuss now is about the positive integers and its binary form.Given a positive integer I, you task is to find out an integer J, which is the minimum integer greater than I, and the number of '1's in whose binary form is the same as that in the binary form of I.For example, if "78" is given, we can write out its binary form, "1001110". This binary form has 4 '1's. The minimum integer, which is greater than "1001110" and also contains 4 '1's, is "1010011", i.e. "83", so you should output "83".InputOne integer per line, which is I (1 <= I <= 1000000).A line containing a number "0" terminates input, and this line need not be processed. OutputOne integer per line, which is J.Sample Input123478Sample Output245883八Uyuw's ConcertTime Limit: 6000MS Memory Limit: 65536KTotal Submissions: 3177 Accepted: 1240 DescriptionPrince Remmarguts solved the CHESS puzzle successfully. As an award, Uyuw planned to hold a concert in a huge piazza named after its great designer Ihsnayish.The piazza in UDF - United Delta of Freedom’s downtown was a square of [0, 10000] * [0, 10000]. Some basket chairs had been standing there for years, but in a terrible mess. Look at the following graph.In this case we have three chairs, and the audiences face the direction as what arrows have pointed out. The chairs were old-aged and too heavy to be moved. Princess Remmarguts told the piazza's current owner Mr. UW, to build a large stage inside it. The stage must be as large as possible, but he should also make sure the audience in every position of every chair would be able to see the stage without turning aside (that means the stage is in the forward direction of their own).To make it simple, the stage could be set highly enough to make sure even thousands of chairs were in front of you, as long as you were facing the stage, you would be able to see the singer / pianist – Uyuw.Being a mad idolater, can you tell them the maximal size of the stage?InputIn the first line, there's a single non-negative integer N (N <= 20000), denoting the number of basket chairs. Each of the following lines contains four floating numbers x1, y1, x2, y2, which means there’s a basket chair on the line segment of (x1, y1) –(x2, y2), and facing to its LEFT (That a point (x, y) is at the LEFT side of this segment means that (x – x1) * (y – y2) – (x – x2) * (y – y1) >= 0).OutputOutput a single floating number, rounded to 1 digit after the decimal point. This is the maximal area of the stage.Sample Input310000 10000 0 500010000 5000 5000 100000 5000 5000 0Sample Output54166666.7九Knight MovesTime Limit: 1000MS Memory Limit: 30000KTotal Submissions: 15129 Accepted: 6765 DescriptionBackgroundMr Somurolov, fabulous chess-gamer indeed, asserts that no one else but him can move knights from one position to another so fast. Can you beat him?The ProblemYour task is to write a program to calculate the minimum number of moves needed for a knight to reach one point from another, so that you have the chance to be faster than Somurolov.For people not familiar with chess, the possible knight moves are shown in Figure 1.InputThe input begins with the number n of scenarios on a single line by itself.Next follow n scenarios. Each scenario consists of three lines containing integer numbers. The first line specifies the length l of a side of the chess board (4 <= l <= 300). The entire board has size l * l. The second and third line contain pair of integers {0, ..., l-1}*{0, ..., l-1} specifying the starting and ending position of the knight on the board. The integers are separated by a single blank. You can assume that the positions are valid positions on the chess board of that scenario.OutputFor each scenario of the input you have to calculate the minimal amount of knight moves which are necessary to move from the starting point to the ending point. If starting point and ending point are equal,distance is zero. The distance must be written on a single line.Sample Input380 07 01000 030 50101 11 1十Equal Sum PartitionsTime Limit: 1000MS Memory Limit: 65536KTotal Submissions: 297 Accepted: 214DescriptionAn equal sum partition of a sequence of numbers is a grouping of the numbers (in the same order as the original sequence) in such a way that each group has the same sum. For example, the sequence:2 5 13 3 7may be grouped as:(2 5) (1 3 3) (7)to yield an equal sum of 7.Note: The partition that puts all the numbers in a single group is an equal sum partition with the sum equal to the sum of all the numbers in the sequence.For this problem, you will write a program that takes as input a sequence of positive integers and returns the smallest sum for an equal sum partition of the sequence.InputThe first line of input contains a sin gle integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. The first line of each data set contains the data set number, followed by a space, followed bya decimal integer M, (1 ≤ M ≤ 10000), giving the total number of integers in the sequence. The remaining line(s) in the dataset consist of the values, 10 per line,separated by a single space. The last line in the dataset may contain less than 10 values.OutputFor each data set, generate one line of output with the following values: The data set number as a decimal integer, a space, and the smallest sum for an equal sum partition of the sequence.Sample Input31 62 5 13 3 72 61 2 3 4 5 63 201 12 1 1 2 1 1 2 11 2 1 1 2 1 1 2 1 1Sample Output1 72 213 2如果有想要答案的朋友，请给我留言！。