最短路径算法.docx

1、最短路径算法1860:Currency ExchangeTime Limit: 1000MSMemory Limit: 30000KTotal Submissions: 12943Accepted: 4415DescriptionSeveral currency exchange points are working in our city. Let us suppose that each point specializes in two particular currencies and performs exchange operations only with these curren

2、cies. There can be several points specializing in the same pair of currencies. Each point has its own exchange rates, exchange rate of A to B is the quantity of B you get for 1A. Also each exchange point has some commission, the sum you have to pay for your exchange operation. Commission is always c

3、ollected in source currency. For example, if you want to exchange 100 US Dollars into Russian Rubles at the exchange point, where the exchange rate is 29.75, and the commission is 0.39 you will get (100 - 0.39) * 29.75 = 2963.3975RUR. You surely know that there are N different currencies you can dea

4、l with in our city. Let us assign unique integer number from 1 to N to each currency. Then each exchange point can be described with 6 numbers: integer A and B - numbers of currencies it exchanges, and real RAB, CAB, RBA and CBA - exchange rates and commissions when exchanging A to B and B to A resp

5、ectively. Nick has some money in currency S and wonders if he can somehow, after some exchange operations, increase his capital. Of course, he wants to have his money in currency S in the end. Help him to answer this difficult question. Nick must always have non-negative sum of money while making hi

6、s operations. InputThe first line of the input contains four numbers: N - the number of currencies, M - the number of exchange points, S - the number of currency Nick has and V - the quantity of currency units he has. The following M lines contain 6 numbers each - the description of the correspondin

7、g exchange point - in specified above order. Numbers are separated by one or more spaces. 1=S=N=100, 1=M=100, V is real number, 0=V=103. For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 10-2=rate=102, 0=commission2-3-1, arriving back at h

8、is starting location 1 second before he leaves. He could start from anywhere on the cycle to accomplish this.SourceUSACO 2006 December Gold1062:昂贵的聘礼Time Limit: 1000MSMemory Limit: 10000KTotal Submissions: 26529Accepted: 7391Description年轻的探险家来到了一个印第安部落里。在那里他和酋长的女儿相爱了，于是便向酋长去求亲。酋长要他用10000个金币作为聘礼才答应把女

9、儿嫁给他。探险家拿不出这么多金币，便请求酋长降低要求。酋长说：嗯，如果你能够替我弄到大祭司的皮袄，我可以只要8000金币。如果你能够弄来他的水晶球，那么只要5000金币就行了。探险家就跑到大祭司那里，向他要求皮袄或水晶球，大祭司要他用金币来换，或者替他弄来其他的东西，他可以降低价格。探险家于是又跑到其他地方，其他人也提出了类似的要求，或者直接用金币换，或者找到其他东西就可以降低价格。不过探险家没必要用多样东西去换一样东西，因为不会得到更低的价格。探险家现在很需要你的帮忙，让他用最少的金币娶到自己的心上人。另外他要告诉你的是，在这个部落里，等级观念十分森严。地位差距超过一定限制的两个人之间不会进

10、行任何形式的直接接触，包括交易。他是一个外来人，所以可以不受这些限制。但是如果他和某个地位较低的人进行了交易，地位较高的的人不会再和他交易，他们认为这样等于是间接接触，反过来也一样。因此你需要在考虑所有的情况以后给他提供一个最好的方案。 为了方便起见，我们把所有的物品从1开始进行编号，酋长的允诺也看作一个物品，并且编号总是1。每个物品都有对应的价格P，主人的地位等级L，以及一系列的替代品Ti和该替代品所对应的优惠Vi。如果两人地位等级差距超过了M，就不能间接交易。你必须根据这些数据来计算出探险家最少需要多少金币才能娶到酋长的女儿。 Input输入第一行是两个整数M，N（1 = N = 100）

11、，依次表示地位等级差距限制和物品的总数。接下来按照编号从小到大依次给出了N个物品的描述。每个物品的描述开头是三个非负整数P、L、X（X N），依次表示该物品的价格、主人的地位等级和替代品总数。接下来X行每行包括两个整数T和V，分别表示替代品的编号和优惠价格。Output输出最少需要的金币数。Sample Input1 410000 3 22 80003 50001000 2 14 2003000 2 14 20050 2 0Sample Output5250Source浙江2253:FroggerTime Limit: 1000MSMemory Limit: 65536KTotal Submi

12、ssions: 17010Accepted: 5556DescriptionFreddy Frog is sitting on a stone in the middle of a lake. Suddenly he notices Fiona Frog who is sitting on another stone. He plans to visit her, but since the water is dirty and full of tourists sunscreen, he wants to avoid swimming and instead reach her by jum

13、ping. Unfortunately Fionas stone is out of his jump range. Therefore Freddy considers to use other stones as intermediate stops and reach her by a sequence of several small jumps. To execute a given sequence of jumps, a frogs jump range obviously must be at least as long as the longest jump occuring

14、 in the sequence. The frog distance (humans also call it minimax distance) between two stones therefore is defined as the minimum necessary jump range over all possible paths between the two stones. You are given the coordinates of Freddys stone, Fionas stone and all other stones in the lake. Your j

15、ob is to compute the frog distance between Freddys and Fionas stone. InputThe input will contain one or more test cases. The first line of each test case will contain the number of stones n (2=n=200). The next n lines each contain two integers xi,yi (0 = xi,yi = 1000) representing the coordinates of

16、 stone #i. Stone #1 is Freddys stone, stone #2 is Fionas stone, the other n-2 stones are unoccupied. Theres a blank line following each test case. Input is terminated by a value of zero (0) for n. OutputFor each test case, print a line saying Scenario #x and a line saying Frog Distance = y where x i

17、s replaced by the test case number (they are numbered from 1) and y is replaced by the appropriate real number, printed to three decimals. Put a blank line after each test case, even after the last one. Sample Input20 03 4317 419 418 50Sample OutputScenario #1Frog Distance = 5.000Scenario #2Frog Dis

18、tance = 1.414SourceUlm Local 19971125Stockbroker GrapevineTime Limit: 1000MSMemory Limit: 10000KTotal Submissions: 20488Accepted: 11109DescriptionStockbrokers are known to overreact to rumours. You have been contracted to develop a method of spreading disinformation amongst the stockbrokers to give

19、your employer the tactical edge in the stock market. For maximum effect, you have to spread the rumours in the fastest possible way. Unfortunately for you, stockbrokers only trust information coming from their Trusted sources This means you have to take into account the structure of their contacts w

20、hen starting a rumour. It takes a certain amount of time for a specific stockbroker to pass the rumour on to each of his colleagues. Your task will be to write a program that tells you which stockbroker to choose as your starting point for the rumour, as well as the time it will take for the rumour

21、to spread throughout the stockbroker community. This duration is measured as the time needed for the last person to receive the information.InputYour program will input data for different sets of stockbrokers. Each set starts with a line with the number of stockbrokers. Following this is a line for

22、each stockbroker which contains the number of people who they have contact with, who these people are, and the time taken for them to pass the message to each person. The format of each stockbroker line is as follows: The line starts with the number of contacts (n), followed by n pairs of integers,

23、one pair for each contact. Each pair lists first a number referring to the contact (e.g. a 1 means person number one in the set), followed by the time in minutes taken to pass a message to that person. There are no special punctuation symbols or spacing rules. Each person is numbered 1 through to th

24、e number of stockbrokers. The time taken to pass the message on will be between 1 and 10 minutes (inclusive), and the number of contacts will range between 0 and one less than the number of stockbrokers. The number of stockbrokers will range from 1 to 100. The input is terminated by a set of stockbrokers containing 0 (zero) people. OutputFor each set of data, your program must output a single line con