专题一 数据结构

Problem A : Hardwood SpeciesFrom:POJ, 2418DescriptionHardwoods are the botanical group of trees that have broad leaves, produce a fruit or nut, and generally go dormant in the winter.America's temperate climates produce forests with hundreds of hardwood species -- trees that share certain biological characteristics. Although oak, maple and cherry all are types of hardwood trees, for example, they are different species. Together, all the hardwood species represent 40 percent of the trees in the United States.On the other hand, softwoods, or conifers, from the Latin word meaning "cone-bearing," have needles. Widely available US softwoods include cedar, fir, hemlock, pine, redwood, spruce and cypress. In a home, the softwoods are used primarily as structural lumber such as 2x4s and 2x6s, with some limited decorative applications.Using satellite imaging technology, the Department of Natural Resources has compiled an inventory of every tree standing on a particular day. You are to compute the total fraction of the tree population represented by each species.InputInput to your program consists of a list of the species of every tree observed by the satellite; one tree per line. No species name exceeds 30 characters. There are no more than 10,000 species and no more than 1,000,000 trees.OutputPrint the name of each species represented in the population, in alphabetical order, followed by the percentage of the population it represents, to 4 decimal places.Sample InputRed AlderAshAspenBasswoodAshBeechYellow BirchAshCherryCottonwoodAshCypressRed ElmGumHackberryWhite OakHickoryPecanHard MapleWhite OakSoft MapleRed OakRed OakWhite OakPoplanSassafras SycamoreBlack WalnutWillowSample OutputAsh 13.7931Aspen 3.4483 Basswood 3.4483 Beech 3.4483Black Walnut 3.4483 Cherry 3.4483 Cottonwood 3.4483 Cypress 3.4483 Gum 3.4483 Hackberry 3.4483 Hard Maple 3.4483 Hickory 3.4483 Pecan 3.4483 Poplan 3.4483Red Alder 3.4483 Red Elm 3.4483Red Oak 6.8966 Sassafras 3.4483 Soft Maple 3.4483 Sycamore 3.4483 White Oak 10.3448 Willow 3.4483Yellow Birch 3.4483HintThis problem has huge input, use scanf instead of cin to avoid time limit exceeded.Problem B : Nearest Common AncestorsFrom:POJ, 1330DescriptionA rooted tree is a well-known data structure in computer science and engineering. An example is shown below:In the figure, each node is labeled with an integer from {1, 2,...,16}. Node 8 is the root of the tree. Node x is an ancestor of node y if node x is in the path between the root and node y. For example, node 4 is an ancestor of node 16. Node 10 is also an ancestor of node 16. As a matter of fact, nodes 8, 4, 10, and 16 are the ancestors of node 16. Remember that a node is an ancestor of itself. Nodes 8, 4, 6, and 7 are the ancestors of node 7. A node x is called a common ancestor of two different nodes y and z if node x is an ancestor of node y and an ancestor of node z. Thus, nodes 8 and 4 are the common ancestors of nodes 16 and 7. A node x is called the nearest common ancestor of nodes y and z if x is a common ancestor of y and z and nearest to y and z among their common ancestors. Hence, the nearest common ancestor of nodes 16 and 7 is node 4. Node 4 is nearer to nodes 16 and 7 than node 8 is.For other examples, the nearest common ancestor of nodes 2 and 3 is node 10, the nearest common ancestor of nodes 6 and 13 is node 8, and the nearest common ancestor of nodes 4 and 12 is node 4. In the last example, if y is an ancestor of z, then the nearest common ancestor of y and z is y.Write a program that finds the nearest common ancestor of two distinct nodes in a tree.InputThe input consists of T test cases. The number of test cases (T) is given in the first line of the input file. Each test case starts with a line containing an integer N , the number of nodes in a tree, 2<=N<=10,000. The nodes are labeled with integers 1, 2,..., N. Each of the next N -1 lines contains a pair of integers that represent an edge --the first integer is the parent node of the second integer. Note that a tree with N nodes has exactly N - 1 edges. The last line of each test case contains two distinct integers whose nearest common ancestor is to be computed.OutputPrint exactly one line for each test case. The line should contain the integer that is the nearest common ancestor.Sample Input2161 148 510 165 94 68 44 101 136 1510 116 710 216 38 116 1216 752 33 43 11 53 5Sample Output43Problem C : ExpressionsFrom:POJ, 3367DescriptionArithmetic expressions are usually written with the operators in between the two operands (which is called infix notation). For example, (x+y)*(z-w) is an arithmetic expression in infix notation. However, it is easier to write a program to evaluate an expression if the expression is written in postfix notation (also known as reverse Polish notation). In postfix notation, an operator is written behind its two operands, which may be expressions themselves. For example, x y + z w - * is a postfix notation of the arithmetic expression given above. Note that in this case parentheses are not required.To evaluate an expression written in postfix notation, an algorithm operating on a stack can be used. A stack is a data structure which supports two operations:1.push: a number is inserted at the top of the stack.2.pop: the number from the top of the stack is taken out.During the evaluation, we process the expression from left to right. If we encounter a number, we push it onto the stack. If we encounter an operator, we pop the first two numbers from the stack, apply the operator on them, and push the result back onto the stack. More specifically, the following pseudocode shows how to handle the case when we encounter an operator O:a := pop();b := pop();push(b O a);The result of the expression will be left as the only number on the stack.Now imagine that we use a queue instead of the stack. A queue also has apush and pop operation, but their meaning is different:1.push: a number is inserted at the end of the queue.2.pop: the number from the front of the queue is taken out of the queue.Can you rewrite the given expression such that the result of the algorithm using the queue is the same as the result of the original expression evaluated using the algorithm with the stack?InputThe first line of the input contains a number T (T ≤ 200). The following T lines each contain one expression in postfix notation. Arithmetic operators are represented by uppercase letters, numbers arerepresented by lowercase letters. You may assume that the length of each expression is less than 10000 characters.OutputFor each given expression, print the expression with the equivalent result when using the algorithm with the queue instead of the stack. To make the solution unique, you are not allowed to assume that the operators are associative or commutative.Sample Input2xyPzwIMabcABdefgCDEFSample OutputwzyxIPMgfCecbDdAaEBFProblem D : Navigation NightmareFrom:POJ, 1984DescriptionFarmer John's pastoral neighborhood has N farms (2 <= N <= 40,000), usually numbered/labeled 1..N. A series of M (1 <= M < 40,000) vertical and horizontal roads each of varying lengths (1 <= length <= 1000) connect the farms. A map of these farms might look something like the illustration below in which farms are labeled F1..F7 for clarity and lengths between connected farms are shown as (n):F1 --- (13) ---- F6 --- (9) ----- F3| |(3) || (7)F4 --- (20) -------- F2 || |(2) F5|F7Being an ASCII diagram, it is not precisely to scale, of course.Each farm can connect directly to at most four other farms via roads that lead exactly north, south, east, and/or west. Moreover, farms are only located at the endpoints of roads, and some farm can be found at every endpoint of every road. No two roads cross, and precisely one path(sequence of roads) links every pair of farms.FJ lost his paper copy of the farm map and he wants to reconstruct it from backup information on his computer. This data contains lines like the following, one for every road:There is a road of length 10 running north from Farm #23 to Farm #17There is a road of length 7 running east from Farm #1 to Farm #17...As FJ is retrieving this data, he is occasionally interrupted by questions such as the following that he receives from his navigationally-challenged neighbor, farmer Bob:What is the Manhattan distance between farms #1 and #23?FJ answers Bob, when he can (sometimes he doesn't yet have enough data yet). In the example above, the answer would be 17, since Bob wants to know the "Manhattan" distance between the pair of farms. The Manhattan distance between two points (x1,y1) and (x2,y2) is just |x1-x2| + |y1-y2| (which is the distance a taxicab in a large city must travel over city streets in a perfect grid to connect two x,y points).When Bob asks about a particular pair of farms, FJ might not yet have enough information to deduce the distance between them; in this case, FJ apologizes profusely and replies with "-1".Input* Line 1: Two space-separated integers: N and M* Lines 2..M+1: Each line contains four space-separated entities, F1,F2, L, and D that describe a road. F1 and F2 are numbers oftwo farms connected by a road, L is its length, and D is acharacter that is either 'N', 'E', 'S', or 'W' giving thedirection of the road from F1 to F2.* Line M+2: A single integer, K (1 <= K <= 10,000), the number of FB's queries* Lines M+3..M+K+2: Each line corresponds to a query from Farmer Bob and contains three space-separated integers: F1, F2, and I. F1 and F2 are numbers of the two farms in the query and I is the index (1 <= I <= M) in the data after which Bob asks thequery. Data index 1 is on line 2 of the input data, and so on. Output* Lines 1..K: One integer per line, the response to each of Bob'squeries. Each line should contain either a distancemeasurement or -1, if it is impossible to determine theappropriate distance.Sample Input7 61 6 13 E6 3 9 E3 5 7 S4 1 3 N2 4 20 W4 7 2 S31 6 11 4 32 6 6Sample Output13-110HintAt time 1, FJ knows the distance between 1 and 6 is 13.At time 3, the distance between 1 and 4 is still unknown.At the end, location 6 is 3 units west and 7 north of 2, so the distance is 10.Problem E : Binary Search Heap ConstructionFrom:POJ, 1785DescriptionRead the statement of problem G for the definitions concerning trees. In the following we define the basic terminology of heaps. A heap is a tree whose internal nodes have each assigned a priority (a number) such that the priority of each internal node is less than the priority of its parent. As a consequence, the root has the greatest priority in the tree, which is one of the reasons why heaps can be used for the implementation of priority queues and for sorting.A binary tree in which each internal node has both a label and a priority, and which is both a binary search tree with respect to the labels and a heap with respect to the priorities, is called a treap. Your task is, given a set of label-priority-pairs, with unique labels and unique priorities, to construct a treap containing this data.InputThe input contains several test cases. Every test case starts with an integer n. You may assume that1<=n<=50000. Then follow n pairs of strings and numbers l1/p1,...,ln/pn denoting the label and priority of each node. The strings are non-empty and composed of lower-case letters, and the numbers are non-negative integers. The last test case is followed by a zero.OutputFor each test case output on a single line a treap that contains the specified nodes. A treap is printed as (< left sub-treap >< label >/< priority >< right sub-treap >). The sub-treaps are printed recursively, and omitted if leafs.Sample Input7 a/7 b/6 c/5 d/4 e/3 f/2 g/17 a/1 b/2 c/3 d/4 e/5 f/6 g/77 a/3 b/6 c/4 d/7 e/2 f/5 g/1Sample Output(a/7(b/6(c/5(d/4(e/3(f/2(g/1)))))))(((((((a/1)b/2)c/3)d/4)e/5)f/6)g/7)(((a/3)b/6(c/4))d/7((e/2)f/5(g/1)))Problem F : Cube StackingFrom:POJ, 1988DescriptionFarmer John and Betsy are playing a game with N (1 <= N <= 30,000)identical cubes labeled 1 through N. They start with N stacks, each containing a single cube. Farmer John asks Betsy to perform P (1<= P <= 100,000) operation. There are two types of operations:moves and counts.* In a move operation, Farmer John asks Bessie to move the stack containing cube X on top of the stack containing cube Y.* In a count operation, Farmer John asks Bessie to count the number of cubes on the stack with cube X that are under the cube X and report that value.Write a program that can verify the results of the game.Input* Line 1: A single integer, P* Lines 2..P+1: Each of these lines describes a legal operation. Line 2 describes the first operation, etc. Each line begins with a 'M' for a move operation or a 'C' for a count operation. For move operations, the line also contains two integers: X and Y.For count operations, the line also contains a single integer: X.Note that the value for N does not appear in the input file. No move operation will request a move a stack onto itself.OutputPrint the output from each of the count operations in the same order as the input file.Sample Input6M 1 6C 1M 2 4M 2 6C 3C 4Sample Output12Problem G : Find them, Catch themFrom:POJ, 1703DescriptionThe police office in Tadu City decides to say ends to the chaos, as launch actions to root up the TWO gangs in the city, Gang Dragon and Gang Snake. However, the police first needs to identify which gang a criminal belongs to. The present question is, given two criminals; do they belong to a same clan? You must give your judgment based on incomplete information. (Since the gangsters are always acting secretly.)Assume N (N <= 10^5) criminals are currently in Tadu City, numbered from 1 to N. And of course, at least one of them belongs to Gang Dragon, and the same for Gang Snake. You will be given M (M <= 10^5) messages in sequence, which are in the following two kinds:1. D [a] [b]where [a] and [b] are the numbers of two criminals, and they belong to different gangs.2. A [a] [b]where [a] and [b] are the numbers of two criminals. This requires you to decide whether a and b belong to a same gang.InputThe first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Each test case begins with a line with two integers N and M, followed by M lines each containing one message as described above.OutputFor each message "A [a] [b]" in each case, your program should give the judgment based on the information got before. The answers might be one of "In the same gang.", "In different gangs." and "Not sure yet."Sample Input15 5A 1 2D 1 2A 1 2D 2 4A 1 4Sample OutputNot sure yet.In different gangs.In the same gang.Problem H : The RaceFrom:POJ, 2274DescriptionDuring the Annual Interstellar Competition for Tuned Spaceships, N spaceships will be competing. Each spaceship i is tuned in such a way that it can accelerate in zero time to its maximum speed Vi and remain cruising at that speed. Due to past achievements, each spaceship starts at a starting position Xi, specifying how many kilometers the spaceship is away from the starting line.The race course is infinitely long. Because of the high speeds of the spaceships, the race course goes straight all the time. On that straight course, spaceships can pass one another very easily, without interfering with each other.Many people in the audience have not realized yet that the outcome of the race can be determined in advance. It is your task to show this to them, by telling them how many times spaceships will pass one another, and by predicting the first 10 000 times that spaceships pass in chronological order.You may assume that each spaceship starts at a different position. Furthermore, there will never be more than two spaceships at the same position of the course at any time.InputThe first line of the input specifies the number of spaceshipsN (0 < N <= 250 000) that are competing. Each of the next N lines describe the properties of one spaceship. The i+1th line describes the ith ship with two integers Xi and Vi, representing the starting position and the velocity of the ith spaceship (0 <= Xi <= 1 000 000, 0 < Vi < 100). The spaceships are ordered according to the starting position, i.e. X1 < X2 < . . . < XN. The starting position is the number of kilometers past the starting line where the spaceship starts, and the velocity is given in kilometers per second.OutputThe first line of the output should contain the number of times that spaceships pass one another during the race modulo 1 000 000. By publishing the number of passes only modulo 1 000 000, you can at the same time prove your knowledge of it and don't spoil the party for the less intelligent people in the audience.Each of the subsequent lines should represent one passing, in chronological order. If there would be more than 10 000 passings, only output the first 10 000 passings. If there are less than 10 000 passings, output all passings. Each line should consist of two integers i and j, specifying that spaceship i passes spaceship j. If multiple passings occur at the same time, they have to be sorted by their position on the course. This means that passings taking place closer to the starting line must be listed first. The time of a passing is the time when the two spaceships are at the same position.Sample Input40 22 13 86 3Sample Output23 41 2Problem I : Apple TreeFrom:POJ, 3321DescriptionThere is an apple tree outside of kaka's house. Every autumn, a lot of apples will grow in the tree. Kaka likes apple very much, so he has been carefully nurturing the big apple tree.The tree has N forks which are connected by branches. Kaka numbers the forks by 1 to N and the root is always numbered by 1. Apples will grow on the forks and two apple won't grow on the same fork. kaka wants to know how many apples are there in a sub-tree, for his study of the produce ability of the apple tree.The trouble is that a new apple may grow on an empty fork some time and kaka may pick an apple from the tree for his dessert. Can you help kaka?InputThe first line contains an integer N (N≤ 100,000) , which is the number of the forks in the tree.The following N - 1 lines each contain two integers u and v, which means fork u and fork v are connected by a branch.The next line contains an integer M (M≤ 100,000).The following M lines each contain a message which is either"C x" which means the existence of the apple on fork x has been changed. i.e. if there is an apple on the fork, then Kaka pick it; otherwise a new apple has grown on the empty fork.or"Q x" which means an inquiry for the number of apples in the sub-tree above the fork x, including the apple (if exists) on the fork xNote the tree is full of apples at the beginningOutputFor every inquiry, output the correspond answer per line.Sample Input31 21 33Q 1C 2Q 1Sample Output32Problem J : Starry NightFrom:POJ, 1175DescriptionHigh up in the night sky, the shining stars appear in clusters of various shapes. A cluster is a non-empty group of neighbouring stars, adjacent in horizontal, vertical or diagonal direction. A cluster cannot be a part of a larger cluster.Clusters may be similar. Two clusters are similar if they have the same shape and number of stars, irrespective of their orientation. In general, the number of possible orientations for a cluster is eight, as Figure 1 exemplifies.The night sky is represented by a sky map, which is a two-dimensional matrix of 0's and 1's. A cell contains the digit 1 if it has a star, and the digit 0 otherwise.Given a sky map, mark all the clusters with lower case letters. Similar clusters must be marked with the same letter; non-similar clusters must be marked with different letters. You mark a cluster with a lower case letter by replacing every 1 in the cluster by that lower case letter. The order of allocation of letters depends on the first appearance of different clusters, from top to bottom and from left to right.InputYour program is to read from standard input. The first two lines contain, respectively, the width W and the height H of a sky map. The sky map is given in the following H lines, of W characters each.0 <= W (width of the sky map) <= 1000 <= H (height of the sky map) <= 1000 <= Number of clusters <= 5000 <= Number of non-similar clusters <= 26 (a..z)1 <= Number of stars per cluster <= 160OutputYour program is to write to standard output. The output contains the same map as the input, except that the clusters are marked as described above.Sample Input2315100010000000000100000000111110001111100010110101000000010001000111111000000000101010001011110000011101000100000000000001001011111000000000100000010000000000000000010100000011111001000000001000000100010011111000000011101010101000100000010011010001000000000010001110111110000000001000011100000001000000000100010000100010010100000001110001000111000Sample Outputa000a0000000000b00000000aaaaa000ccccc000d0dd0d0a0000000c000c000dddddd000000000c0b0c000d0dddd00000eee0c000c0000000000000e00e0ccccc000000000b000000e00000000000000000b0f000000ccccc00a00000000f000000c000c00aaaaa0000000ddd0c0b0c0a000a000000b00dd0c000c0000000000g000ddd0ccccc000000000g0000ddd0000000e000000000b000d0000f000e00e0b0000000ddd000f000eee000HintJust to make it clearer, notice that this sample input corresponds to the following picture of the sky.Notice that this sample output corresponds to the following picture.Problem K : Mobile phonesFrom:POJ, 1195DescriptionSuppose that the fourth generation mobile phone base stations in the Tampere area operate as follows. The area is divided into squares. The squares form an S * S matrix with the rows and columns numbered from 0 to S-1. Each square contains a base station. The number of active mobile phones inside a squarecan change because a phone is moved from a square to another or a phone is switched on or off. At times, each base station reports the change in the number of active phones to the main base station along with the row and the column of the matrix.Write a program, which receives these reports and answers queries about the current total number of active mobile phones in any rectangle-shaped area.InputThe input is read from standard input as integers and the answers to the queries are written to standard output as integers. The input is encoded as follows. Each input comes on a separate line, and consists of one instruction integer and a number of parameter integers according to the following table.The values will always be in range, so there is no need to check them. In particular, if A is negative, it can be assumed that it will not reduce the square value below zero. The indexing starts at 0, e.g. for a table of size 4 * 4, we have 0 <= X <= 3 and 0 <= Y <= 3.Table size: 1 * 1 <= S * S <= 1024 * 1024Cell value V at any time: 0 <= V <= 32767Update amount: -32768 <= A <= 32767No of instructions in input: 3 <= U <= 60002Maximum number of phones in the whole table: M= 2^30OutputYour program should not answer anything to lines with an instruction other than 2. If the instruction is 2, then your program is expected to answer the query by writing the answer as a single line containing a single integer to standard output.Sample Input0 41 12 32 0 0 2 21 1 1 21 12 -12 1 1 2 33Sample Output34Problem L : Potted FlowerFrom:POJ, 2750DescriptionThe little cat takes over the management of a new park. There is a large circular statue in the center of the park, surrounded by N pots of flowers. Each potted flower will be assigned to an integer number (possibly negative) denoting how attractive it is. See the following graph as an example:(Positions of potted flowers are assigned to index numbers in the range of 1 ... N. The i-th pot and the (i + 1)-th pot are consecutive for any given i (1 <= i < N), and 1st pot is next to N-th pot in addition.)The board chairman informed the little cat to construct "ONE arc-style cane-chair" for tourists having a rest, and the sum of attractive values of the flowers beside the cane-chair should be as large as possible. You should notice that a cane-chair cannot be a total circle, so the number of flowers beside thecane-chair may be 1, 2, ..., N - 1, but cannot be N. In the above example, if we construct a cane-chair in the position of that red-dashed-arc, we will have the sum of 3+(-2)+1+2=4, which is the largest among all possible constructions.Unluckily, some booted cats always make trouble for the little cat, by changing some potted flowers to others. The intelligence agency of little cat has caught up all the M instruments of booted cats' action. Each instrument is in the form of "A B", which means changing the A-th potted flowered with a new one whose attractive value equals to B. You have to report the new "maximal sum" after each instruction.InputThere will be a single test data in the input. You are given an integer N (4 <= N <= 100000) in the first input line.The second line contains N integers, which are the initial attractive value of each potted flower. The i-th number is for the potted flower on the i-th position.A single integer M (4 <= M <= 100000) in the third input line, and the following M lines each contains an instruction "A B" in the form described above.Restriction: All the attractive values are within [-1000, 1000]. We guarantee the maximal sum will be always a positive integer.OutputFor each instruction, output a single line with the maximum sum of attractive values for the optimum cane-chair.Sample Input53 -2 1 2 -542 -25 -52 -45 -1Sample Output4435。