动态规划(2)

Farmer John's farm consists of a long row of N (1 <= N <= 100,000)fields. Each field contains a certain number of cows, 1 <= ncows <= 2000.FJ wants to build a fence around a contiguous group of these fields in order to maximize the average number of cows per field within that block. The block must contain at least F (1 <= F <= N) fields, where F given as input. Calculate the fence placement that maximizes the average, given the constraint.Input* Line 1: Two space-separated integers, N and F.* Lines 2..N+1: Each line contains a single integer, the number of cows in a field. Line 2 gives the number of cows in field 1,line 3 gives the number in field 2, and so on.Output* Line 1: A single integer that is 1000 times the maximal average.Do not perform rounding, just print the integer that is 1000*ncows/nfields. Sample Input10 664210385941Sample Output6500Seiji Hayashi had been a professor of the Nisshinkan Samurai School in the domain of Aizu for a long time in the 18th century. In order to reward him for his meritorious career in education, Katanobu Matsudaira, the lord of the domain of Aizu, had decided to grant him a rectangular estate within a large field in the Aizu Basin. Although the size (width and height) of the estate was strictly specified by the lord, he was allowed to choose any location for the estate in the field. Inside the field which had also a rectangular shape, many Japanese persimmon trees, whose fruit was one of the famous products of the Aizu region known as 'Mishirazu Persimmon', were planted. Since persimmon was Hayashi's favorite fruit, he wanted to have as many persimmon trees as possible in the estate given by the lord.For example, in Figure 1, the entire field is a rectangular grid whose width and height are 10 and 8 respectively. Each asterisk (*) represents a place of a persimmon tree. If the specified width and height of the estate are 4 and 3 respectively, the area surrounded by the solid line contains the most persimmon trees. Similarly, if the estate's width is 6 and its height is 4, the area surrounded by the dashed line has the most, and if the estate's width and height are 3 and 4 respectively, the area surrounded by the dotted line contains the most persimmon trees. Note that the width and height cannot be swapped; the sizes 4 by 3 and 3 by 4 are different, as shown in Figure 1.Figure 1: Examples of Rectangular EstatesYour task is to find the estate of a given size (width and height) that contains the largest number of persimmon trees.InputThe input consists of multiple data sets. Each data set is given in the following format.NW Hx1 y1x2 y2...xN yNS TN is the number of persimmon trees, which is a positive integer less than 500. W and H are the width and the height of the entire field respectively. You can assume that both W and H are positive integers whose values are less than 100. For each i (1 <= i <= N), xi and yi are coordinates of the i-th persimmon tree in the grid. Note that the origin of each coordinate is 1. You can assume that 1 <= xi <= W and 1 <= yi <= H, and no two trees have the same positions. But you should not assume that the persimmon trees are sorted in some order according to their positions. Lastly, S and T are positive integers of the width and height respectively of the estate given by the lord. You can also assume that 1 <= S <= W and 1 <= T <= H.The end of the input is indicated by a line that solely contains a zero. OutputFor each data set, you are requested to print one line containing the maximum possible number of persimmon trees that can be included in an estate of the given size.Sample Input1610 82 22 52 73 33 84 24 54 86 46 77 57 88 18 49 610 34 386 41 22 12 43 44 25 36 16 23 2Sample Output 432033Alice and Bob need to send secret messages to each other and are discussing ways to encode their messages:Alice: "Let's just use a very simple code: We'll assign 'A' the code word 1, 'B' will be 2, and so on down to 'Z' being assigned 26."Bob: "That's a stupid code, Alice. Suppose I send you the word 'BEAN' encoded as 25114. You could decode that in many different ways!”Alice: "Sure you could, but what words would you get? Other than 'BEAN', you'd get 'BEAAD', 'YAAD', 'YAN', 'YKD' and 'BEKD'. I think you would be able to figure out the correct decoding. And why would you send me the word ‘BEAN’ anyway?”Bob: "OK, maybe that's a bad example, but I bet you that if you got a string of length 500 there would be tons of different decodings and with that many you would find at least two different ones that would make sense." Alice: "How many different decodings?"Bob: "Jillions!"For some reason, Alice is still unconvinced by Bob's argument, so she requires a program that will determine how many decodings there can be for a given string using her code.InputInput will consist of multiple input sets. Each set will consist of a single line of digits representing a valid encryption (for example, no line will begin with a 0). There will be no spaces between the digits. An input line of '0' will terminate the input and should not be processedOutputFor each input set, output the number of possible decodings for the input string. All answers will be within the range of a long variable.Sample Input2511411111111113333333333Sample Output 68912063John never knew he had a grand-uncle, until he received the notary's letter. He learned that his late grand-uncle had gathered a lot of money, somewhere in South-America, and that John was the only inheritor.John did not need that much money for the moment. But he realized that it would be a good idea to store this capital in a safe place, and have it grow until he decided to retire. The bank convinced him that a certain kind of bond was interesting for him.This kind of bond has a fixed value, and gives a fixed amount of yearly interest, payed to the owner at the end of each year. The bond has no fixed term. Bonds are available in different sizes. The larger ones usually give a better interest. Soon John realized that the optimal set of bonds to buy was not trivial to figure out. Moreover, after a few years his capital would have grown, and the schedule had to be re-evaluated.With a capital of e10 000 one could buy two bonds of $4 000, giving a yearly interest of $800. Buying two bonds of $3 000, and one of $4 000 is a better idea, as it gives a yearly interest of $900. After two years the capital has grown to $11 800, and it makes sense to sell a $3 000 one and buy a $4 000 one, so the annual interest grows to $1 050. This is where this story grows unlikely: the bank does not charge for buying and selling bonds. Next year the total sum is $12 850, which allows for three times $4 000, giving a yearly interest of $1 200.Here is your problem: given an amount to begin with, a number of years, and a set of bonds with their values and interests, find out how big the amount may grow in the given period, using the best schedule for buying and selling bonds.InputThe first line contains a single positive integer N which is the number of test cases. The test cases follow.The first line of a test case contains two positive integers: the amount to start with (at most $1 000 000), and the number of years the capital may grow (at most 40).The following line contains a single number: the number d (1 <= d <= 10) ofavailable bonds.The next d lines each contain the description of a bond. The description of a bond consists of two positive integers: the value of the bond, and the yearly interest for that bond. The value of a bond is always a multiple of $1 000. The interest of a bond is never more than 10% of its value.OutputFor each test case, output – on a separate line – the capital at the end of the period, after an optimal schedule of buying and selling.Sample Input110000 424000 4003000 250Sample Output14050The Recaman's sequence is defined by a0 = 0 ; for m > 0, a m = a m−1− m if the rsulting a m is positive and not already in the sequence, otherwise a m = a m−1 + m.The first few numbers in the Recaman's Sequence is 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9 ...Given k, your task is to calculate a k.InputThe input consists of several test cases. Each line of the input contains an integer k where 0 <= k <= 500000.The last line contains an integer −1, which shou ld not be processed. OutputFor each k given in the input, print one line containing a k to the output. Sample Input710000-1Sample Output2018658Farmer John's cows would like to jump over the moon, just like the cows in their favorite nursery rhyme. Unfortunately, cows can not jump.The local witch doctor has mixed up P (1 <= P <= 150,000) potions to aid the cows in their quest to jump. These potions must be administered exactly in the order they were created, though some may be skipped.Each potion has a 'strength' (1 <= strength <= 500) that enhances the cows' jumping ability. Taking a potion during an odd time step increases the cows' jump; taking a potion during an even time step decreases the jump. Before taking any potions the cows' jumping ability is, of course, 0.No potion can be taken twice, and once the cow has begun taking potions, one potion must be taken during each time step, starting at time 1. One or more potions may be skipped in each turn.Determine which potions to take to get the highest jump.Input* Line 1: A single integer, P* Lines 2..P+1: Each line contains a single integer that is the strength of a potion. Line 2 gives the strength of the first potion; line 3 gives the strength of the second potion; and so on.Output* Line 1: A single integer that is the maximum possible jump.Sample Input872184356Sample Output 17Let N be the set of all natural numbers {0 , 1 , 2 , . . . }, and R be the set of all real numbers. wi, hi for i = 1 . . . n are some elements in N, and w0 = 0. Define set B = {< x, y > | x, y ∈R and there exists an index i > 0 such that 0 <= y <= hi ,∑0<=j<=i-1wj <= x <= ∑0<=j<=i wj}Again, define set S = {A| A = WH for some W , H ∈R+ and there exists x0, y0 in N such that the set T = { < x , y > | x, y ∈R and x0 <= x <= x0 +W and y0 <= y <= y0 + H} is contained in set B}.Your mission now. What is Max(S)?Wow, it looks like a terrible problem. Problems that appear to be terrible are sometimes actually easy.But for this one, believe me, it's difficult.InputThe input consists of several test cases. For each case, n is given in a single line, and then followed by n lines, each containing wi and hi separated by a single space. The last line of the input is an single integer -1, indicating the end of input. You may assume that 1 <= n <= 50000 andw1h1+w2h2+...+w n h n < 109.OutputSimply output Max(S) in a single line for each case.Sample Input31 23 41 233 41 23 4-1Sample Output12 14"Fat and docile, big and dumb, they look so stupid, they aren't much fun..."- Cows with Guns by Dana LyonsThe cows want to prove to the public that they are both smart and fun. In order to do this, Bessie has organized an exhibition that will be put on by the cows. She has given each of the N (1 <= N <= 100) cows a thorough interview and determined two values for each cow: the smartness Si (-1000 <= Si <= 1000) of the cow and the funness Fi (-1000 <= Fi <= 1000) of the cow.Bessie must choose which cows she wants to bring to her exhibition. She believes that the total smartness TS of the group is the sum of the Si's and, likewise, the total funness TF of the group is the sum of the Fi's. Bessie wants to maximize the sum of TS and TF, but she also wants both of these values to be non-negative (since she must also show that the cows arewell-rounded; a negative TS or TF would ruin this). Help Bessie maximize the sum of TS and TF without letting either of these values become negative.Input* Line 1: A single integer N, the number of cows* Lines 2..N+1: Two space-separated integers Si and Fi, respectively the smartness and funness for each cow.Output* Line 1: One integer: the optimal sum of TS and TF such that both TS and TF are non-negative. If no subset of the cows has non-negative TS and non- negative TF, print 0.Sample Input5-5 78 -66 -32 1-8 -5Sample Output8HintOUTPUT DETAILS:Bessie chooses cows 1, 3, and 4, giving values of TS = -5+6+2 = 3 and TF = 7-3+1 = 5, so 3+5 = 8. Note that adding cow 2 would improve the value of TS+TF to 10, but the new value of TF would be negative, so it is not allowed.2231Farmer John has received a noise complaint from his neighbor, Farmer Bob, stating that his cows are making too much noise.FJ's N cows (1 <= N <= 10,000) all graze at various locations on a longone-dimensional pasture. The cows are very chatty animals. Every pair of cows simultaneously carries on a conversation (so every cow is simultaneously MOOing at all of the N-1 other cows). When cow i MOOs at cow j, the volume of this MOO must be equal to the distance between i and j, in order for j to be able to hear the MOO at all. Please help FJ compute the total volume of sound being generated by all N*(N-1) simultaneous MOOing sessions.Input* Line 1: N* Lines 2..N+1: The location of each cow (in the range 0..1,000,000,000). OutputThere are five cows at locations 1, 5, 3, 2, and 4.Sample Input515324Sample Output40HintINPUT DETAILS:There are five cows at locations 1, 5, 3, 2, and 4.OUTPUT DETAILS:Cow at 1 contributes 1+2+3+4=10, cow at 5 contributes 4+3+2+1=10, cow at 3 contributes 2+1+1+2=6, cow at 2 contributes 1+1+2+3=7, and cow at 4 contributes 3+2+1+1=7. The total volume is (10+10+6+7+7) = 40.2279Mr. Young wishes to take a picture of his class. The students will stand in rows with each row no longer than the row behind it and the left ends of the rows aligned. For instance, 12 students could be arranged in rows (from back to front) of 5, 3, 3 and 1 students.X X X X XX X XX X XXIn addition, Mr. Young wants the students in each row arranged so that heights decrease from left to right. Also, student heights should decrease from the back to the front. Thinking about it, Mr. Young sees that for the12-student example, there are at least two ways to arrange the students (with 1 as the tallest etc.):1 2 3 4 5 1 5 8 11 126 7 8 2 6 99 10 11 3 7 1012 4Mr. Young wonders how many different arrangements of the students there might be for a given arrangement of rows. He tries counting by hand starting with rows of 3, 2 and 1 and counts 16 arrangements:123 123 124 124 125 125 126 126 134 134 135 135 136 136 145 14645 46 35 36 34 36 34 35 25 26 24 26 24 25 26 256 5 6 5 6 4 5 4 6 5 6 4 5 4 3 3Mr. Young sees that counting by hand is not going to be very effective for any reasonable number of students so he asks you to help out by writing a computer program to determine the number of different arrangements of students for a given set of rows.InputThe input for each problem instance will consist of two lines. The first line gives the number of rows, k, as a decimal integer. The second line contains the lengths of the rows from back to front (n1, n2,..., nk) as decimal integers separated by a single space. The problem set ends with a line with a row count of 0. There will never be more than 5 rows and the total number of students, N, (sum of the row lengths) will be at most 30.OutputThe output for each problem instance shall be the number of arrangements of the N students into the given rows so that the heights decrease along each row from left to right and along each column from back to front as a decimal integer. (Assume all heights are distinct.) The result of each problem instance should be on a separate line. The input data will be chosen so that the result will always fit in an unsigned 32 bit integer.Sample Input13051 1 1 1 133 2 145 3 3 156 5 4 3 2215 15Sample Output111641581418926089694845Input is the matrix A of N by N non-negative integers.A distance between two elements A ij and A pq is defined as |i − p| + |j − q|. Your program must replace each zero element in the matrix with the nearest non-zero one. If there are two or more nearest non-zeroes, the zero must be left in place.Constraints1 ≤ N ≤ 200, 0 ≤ Ai ≤ 1000000InputInput contains the number N followed by N2 integers, representing the matrix row-by-row.OutputOutput must contain N2 integers, representing the modified matrixrow-by-row.Sample Input30 0 01 0 20 3 0Sample Output1 0 21 0 20 3 0Before bridges were common, ferries were used to transport cars across rivers. River ferries, unlike their larger cousins, run on a guide line and are powered by the river's current. Cars drive onto the ferry from one end, the ferry crosses the river, and the cars exit from the other end of the ferry. There is a ferry across the river that can take n cars across the river in t minutes and return in t minutes. m cars arrive at the ferry terminal by a given schedule. What is the earliest time that all the cars can be transported across the river? What is the minimum number of trips that the operator must make to deliver all cars by that time?InputThe first line of input contains c, the number of test cases. Each test case begins with n, t, m. m lines follow, each giving the arrival time for a car (in minutes since the beginning of the day). The operator can run the ferry whenever he or she wishes, but can take only the cars that have arrived up to that time.OutputFor each test case, output a single line with two integers: the time, in minutes since the beginning of the day, when the last car is delivered to the other side of the river, and the minimum number of trips made by the ferry to carry the cars within that time.You may assume that 0 < n, t, m < 1440. The arrival times for each test case are in non-decreasing order.Sample Input22 10 101020304050607080902 10 3103040Sample Output 100 550 2The public transport administration of Ekaterinburg is anxious about the fact that passengers don't like to pay for passage doing their best to avoid the fee. All the measures that had been taken (hard currency premiums for all of the chiefs, increase in conductors' salaries, reduction of number of buses) were in vain. An advisor especially invited from the Ural State University says that personally he doesn't buy tickets because he rarely comes across the lucky ones (a ticket is lucky if the sum of the first three digits in its number equals to the sum of the last three ones). So, the way out is found — of course, tickets must be numbered in sequence, but the number of digits on a ticket may be changed. Say, if there were only two digits, there would have been ten lucky tickets (with numbers 00, 11, ..., 99). Maybe under the circumstances the ratio of the lucky tickets to the common ones is greater? And what if we take four digits? A huge work has brought the long-awaited result: in this case there will be 670 lucky tickets. But what to do if there are six or more digits?So you are to save public transport of our city. Write a program that determines a number of lucky tickets for the given number of digits. By the way, there can't be more than 10 digits on one ticket.InputInput contains a positive even integer N not greater than 10. It's an amount of digits in a ticket number.OutputOutput should contain a number of tickets such that the sum of the first N/2 digits is equal to the sum of the second half of digits.Sample Input4Sample Output670Mr. F. wants to get a document be signed by a minister. A minister signs a document only if it is approved by his ministry. The ministry is an M-floor building with floors numbered from 1 to M, 1<=M<=100. Each floor has N rooms (1<=N<=500) also numbered from 1 to N. In each room there is one (and only one) official.A document is approved by the ministry only if it is signed by at least one official from the M-th floor. An official signs a document only if at least one of the following conditions is satisfied:a. the official works on the 1st floor;b. the document is signed by the official working in the room with the same number but situated one floor below;c. the document is signed by an official working in a neighbouring room (rooms are neighbouring if they are situated on the same floor and their numbers differ by one).Each official collects a fee for signing a document. The fee is a positive integer not exceeding 10^9.You should find the cheapest way to approve the document.InputThe first line of an input file contains two integers, separated by space. The first integer M represents the number of floors in the building, and the second integer N represents the number of rooms per floor. Each of the next M lines contains N integers separated with spaces that describe fees (thek-th integer at l-th line is the fee required by the official working in the k-th room at the l-th floor).OutputYou should print the numbers of rooms (one per line) in the order they should be visited to approve the document in the cheapest way. If there are more than one way leading to the cheapest cost you may print an any of them.Sample Input3 410 10 1 102 2 2 101 10 10 10Sample Output33211HintYou can assume that for each official there always exists a way to get the approval of a document (from the 1st floor to this official inclusively) paying no more than 10^9.This problem has huge input data,use scanf() instead of cin to read data to avoid time limit exceed.The input contains N natural (i.e. positive integer) numbers ( N <= 10000 ). Each of that numbers is not greater than 15000. This numbers are not necessarily different (so it may happen that two or more of them will be equal). Your task is to choose a few of given numbers ( 1 <= few <= N ) so that the sum of chosen numbers is multiple for N (i.e. N * k = (sum of chosen numbers) for some natural number k).InputThe first line of the input contains the single number N. Each of next N lines contains one number from the given set.OutputIn case your program decides that the target set of numbers can not be found it should print to the output the single number 0. Otherwise it should print the number of the chosen numbers in the first line followed by the chosen numbers themselves (on a separate line each) in arbitrary order.If there are more than one set of numbers with required properties you should print to the output only one (preferably your favorite) of them. Sample Input512341Sample Output223It is a little known fact that cows love apples. Farmer John has two apple trees (which are conveniently numbered 1 and 2) in his field, each full of apples. Bessie cannot reach the apples when they are on the tree, so she must wait for them to fall. However, she must catch them in the air since the apples bruise when they hit the ground (and no one wants to eat bruised apples). Bessie is a quick eater, so an apple she does catch is eaten in just a few seconds.Each minute, one of the two apple trees drops an apple. Bessie, having much practice, can catch an apple if she is standing under a tree from which one falls. While Bessie can walk between the two trees quickly (in much less than a minute), she can stand under only one tree at any time. Moreover, cows do not get a lot of exercise, so she is not willing to walk back and forth between the trees endlessly (and thus misses some apples).Apples fall (one each minute) for T (1 <= T <= 1,000) minutes. Bessie is willing to walk back and forth at most W (1 <= W <= 30) times. Given which tree will drop an apple each minute, determine the maximum number of apples which Bessie can catch. Bessie starts at tree 1.Input* Line 1: Two space separated integers: T and W* Lines 2..T+1: 1 or 2: the tree that will drop an apple each minute. Output* Line 1: The maximum number of apples Bessie can catch without walking more than W times.Sample Input7 22112211Sample Output6HintINPUT DETAILS:Seven apples fall - one from tree 2, then two in a row from tree 1, then two in a row from tree 2, then two in a row from tree 1. Bessie is willing to walk from one tree to the other twice.OUTPUT DETAILS:Bessie can catch six apples by staying under tree 1 until the first two have dropped, then moving to tree 2 for the next two, then returning back to tree 1 for the final two.2392The cows are going to space! They plan to achieve orbit by building a sort of space elevator: a giant tower of blocks. They have K (1 <= K <= 400) different types of blocks with which to build the tower. Each block of type i has height h_i (1 <= h_i <= 100) and is available in quantity c_i (1 <= c_i <= 10). Due to possible damage caused by cosmic rays, no part of a block of type i can exceed a maximum altitude a_i (1 <= a_i <= 40000).Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.Input* Line 1: A single integer, K* Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.Output* Line 1: A single integer H, the maximum height of a tower that can be builtSample Input37 40 35 23 82 52 6Sample Output48HintOUTPUT DETAILS:From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3. Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.2424Sick and tired of pushing paper in the dreary bleary-eyed world of finance, Flo ditched her desk job and built her own restaurant.In the small restaurant, there are several two-seat tables, four-seat tables and six-seat tables. A single diner or a group of two diners should be arranged to a two-seat table, a group of three or four diners should be arranged to afour-seat table, and a group of five or six diners should be arranged to asix-seat table.Flo's restaurant serves delicious food, and many people like to eat here. Every day when lunch time comes, the restaurant is usually full of diners. If there is no suitable table for a new coming group of diners, they have to wait until some suitable table is free and there isn't an earlier arrival group waiting for the same kind of tables. Kind Flo will tell them how long they will get their seat, and if it's longer than half an hour, they will leave for another restaurant.Now given the list of coming diners in a day, please calculate how many diners take their food in Flo's restaurant. You may assume it takes half an hour for every diner from taking a seat to leaving the restaurant.InputThere are several test cases. The first line of each case contains there positive integers separated by blanks, A, B and C (A, B, C >0, A + B + C <= 100), which are the number of two-seat tables, the number of four-seat tables and the number of six-seat tables respectively. From the second line, there is a list of coming groups of diners, each line of which contains two integers, T and N (0 < N <= 6), representing the arrival time and the number of diners of each group. The arrival time T is denoted by HH:MM, and fixed between 08:00 and 22:00 (the restaurant closes at 23:00). The list is sorted by the arrival time of each group in an ascending order, and you may assume that no groups arrive at the same time. Each test case is ended by a line of "#".A test case with A =B =C = 0 ends the input, and should not be processed. Output。