ࡱ>  @ Abjbj00 +RbRb7.4444&5.>Y6$6$6$6$6777XXXXXXX$ZR@]fX-<7"7<<X$6$6sXAAAAAA<tR$6$6XAA<XAAAAqR|"S$66 BQ4>HRVY0>YR]?Z]$S..S]T07:8AA9:777XX..d141A..4Problem 1 Easy Problem It doesn't get any easier than this: you will be given a triangle with integer coordinates and must return the midpoint of the longest side. Moreover, the answer will be guaranteed to have integer coordinates! Input Each test case will consist of six integers: X1, Y1, X2, Y2, X3, Y3 representing the three vertices of a triangle. All the integers will be less than 100000 in absolute value. Output For each test case, output two integers on a single line - the coordinates of the point as described in problem statement. If there is more than one solution, choose the one with smaller X; if there is still a tie, choose the one with smaller Y. Sample input 0 0 0 2 2 0 Sample output 1 1 Problem 2 Magic Square Solver In recreational mathematics, a magic square of order n is an arrangement of n numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. Normal magic squares exist for all orders n e" 1 except n = 2, although the case n = 1 is trivial it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3.  INCLUDEPICTURE "http://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Magicsquareexample.svg/180px-Magicsquareexample.svg.png" \* MERGEFORMATINET  Your task is to determine if the input is a magic square. You must determine if each row, column and diagonal (only the two that cross opposite corners of the square) all sum to the same value. Input Input will consist of a series of values. The first value will be the size of the square, and the rest will be the values of each cell in the square. The values of each cell in a row will be given in order, with spaces between them, and there will be one row on each line. Output Output should consist of the word Yes or No, depending on whether or not the input is indeed a magic square. Sample input 3 2 7 6 9 5 1 4 3 8 Sample output Yes Sample input (2) 5 1 4 6 9 4 3 6 2 8 2 9 0 8 1 8 3 3 3 3 6 6 7 8 9 1 Sample output (2) No Problem 3 Walking Boxes During the era of DOS games, point-and-click adventure games were able to gain a great deal of popularity before fading away into obscurity, replaced by action games that made use of hardware-accelerated graphics. In a point-and-click adventure game, the player is able to walk their character around a room by simply clicking where they want to go. One way this is accomplished is through the use of walking boxes. For each room the player explores, in addition to the background image that is visible to the player, there exist a series of connected boxes that the player is constrained to walking within. Keeping the player within these boxes is a straightforward enough task, but navigation from one box to another poses a problem. What if two boxes are not connected directly; which intermediate boxes must his character pass through to arrive at his destination? This problem can be solved through the use of a matrix. To get from one box to another, successive lookups into the matrix will be made until the destination box is reached.  For example, the layout shown above would produce the following matrix: ToFrom01234001111101232211214311131422224 To get from box 0 to box 4, the game engine will look up the element at row 0 and column 4, which is 1, and therefore the character will first proceed to box 1. The lookup for getting from box 1 to box 4 will yield the value 2, so the character will continue to box 2. The next lookup will yield the value 4, which is the number of the destination box, so when the character moves there no further lookups will be required. Write a program that generates one of these walking box matrices. You will be given a set of boxes and the connections between them. The boxes will never form loops or be isolated from each other, so there will always be exactly one path from one box to another, assuming that paths do not double back on themselves. Input Input will consist of a box count on the first line. Whatever this number is, it will be followed by exactly that many additional lines. Each of these lines will specify the other boxes one box is connected to (the first line will be for box 0, the next for box 1, etc.). Output Output will consist of the walking boxes matrix that may be used for the purposes of navigation as detailed above. Column and row labels should not be included; only the contents of the matrix are required. Sample input 5 1 0 2 3 1 4 1 2 Sample output 0 1 1 1 1 0 1 2 3 2 1 1 2 1 4 1 1 1 3 1 2 2 2 2 4 Problem 4 Adding Fractions Write a program that inputs two fractions in the form a/b and c/d, and outputs their sum in the form p/q reduced to its simplest form. Input: Two lines of input a b c d where a/b and c/d represent the two input fractions. Output: Produce the output in the form p q where p/q represents the output fraction in simplest form. Sample Input: 5 6 1 10 Sample Output: 14 15 Problem 5 Die Hard Problem Assume you are given a set of receptacles of integer capacity c1, c2, ..., cn. e.g.: 3, 5, 7, 11 These receptacles can contain water up to their capacity. Let xi be the content of receptacle i. Consider the following rules: Any receptacle can be filled with water or just emptied in a big sink: empty(i) { xi = 0; } fill(i) { xi = ci } Pick two receptacles i and j of capacities ci and cj. Then you can pour one receptacle into the other until either the source is empty or the recipient is full: pour(i,j) { yj = cj - xj; if ( xi <= yj ) { xj = xj + xi; xi = 0; } else { xj = cj; xi = xi - yj; } } After a finite number of applications of those rules each receptacle will contain an integer amount of water between 0 and its capacity. The total amount of water in the system will then be: x1 + x2 + ... + xn. Write a program that takes as input a sequence of integer capacities and a quantity to achieve and determines, if it exists, a sequence of operations (empty, fill, pour) that leaves the system with an amount of water equal to the given quantity. Input Input will consist of a series of arguments, the first of which being the quantity to achieve q where 0<= q <= c1 + c2 + ... + cn. The remaining arguments will be the integer capacities of the receptacles c1, c2, , cn. Output Output should consist of a sequence of operations as defined above. Sample input diehard.exe 4 3 5 Sample output fill(2) pour(2,1) empty(1) pour(2,1) fill(2) pour(2,1) Problem 6 Identity Checker Write a program P that reads a text file and determines whether file just read is equal to the source code of P itself. P cannot read from any other file or device. Input Input will consist of one file name, and that is the only file the program will be allowed to open. Output Output will consist of the word Yes or No depending on whether the file provided is equal to the source code of the program. Sample input identity.exe compare.txt Sample input file (compare.txt) Is this the source code of the program? Sample output No Problem 7 ChaininGame One popular party game involves one person thinking of a word and then each person afterward thinking of a different word which relates in some way. In some versions of the game, the words are related by the letters in them; the first letter of the new word must be the same as the last letter of the old word. These kinds of constructions are called word chains, and the more words you use, the harder it gets to put them together. Write a program that is able to take a list of words and determine if the entire set of these words could be used in a single word chain, with each word used exactly once. For instance, the words Carpenter, Thread, and Ratchet would be a valid list of words, because they can be combined into a single chain (CarpenteRatcheThread), but Yard, Denmark, and Cheese would not, because Cheese cant connect to either Yard or Denmark. Input Input will consist of several words, separated by spaces. These words should be able to interchange uppercase and lowercase freely; cabin should be processed identically to CaBiN. Output The output can take one of two forms. If the program finds that it is impossible to create a chain, it should simply print out the word Impossible. If a chain is found, the program should print out this chain, in order. Let the case of the connecting letter be determined by the word on the right. Sample input Carpenter threaD RatcheT Sample output CarpenteRatchethreaD Problem 8 Budget Travel An American travel agency is sometimes asked to estimate the minimum cost of traveling from one city to another by automobile. The travel agency maintains lists of many of the gasoline stations along the popular routes. The list contains the location and the current price per gallon of gasoline for each station on the list. In order to simplify the process of estimating this cost, the agency uses the following rules of thumb about the behavior of automobile drivers. A driver never stops at a gasoline station when the gasoline tank contains more than half of its capacity unless the car cannot get to the following station (if there is one) or the destination with the amount of gasoline in the tank. A driver always fills the gasoline tank completely at every gasoline station stop. When stopped at a gasoline station, a driver will spend $2.00 on snacks and goodies for the trip. A driver needs no more gasoline than necessary to reach a gasoline station or the city limits of the destination. A driver always begins with a full tank of gasoline. The amount paid at each stop is rounded to the nearest cent (where 100 cents make a dollar). You must write a program that estimates the minimum amount of money that a driver will pay for gasoline and snacks to make the trip. Input Input will consist of several lines of information. The first 2 lines give information about the origin and destination. The remaining lines of the data set represent the gasoline stations along the route, with one line per gasoline station. The following shows the exact format and meaning of the input data. Line 1: One real number N the distance from the origin to the destination Line 2: Three real numbers followed by an integer The first real number is the gallon capacity of the automobiles fuel tank. The second is the miles per gallon that the automobile can travel. The third is the cost in dollars of filling the automobiles tank in the origination city. The integer (less than 51) is the number of gasoline stations along the route. Each remaining line: Two real numbers The first is the distance in miles from the origination city to the gasoline station. The second is the price (in cents) per gallon of gasoline sold at that station. All data will be positive. Gasoline stations along a route are arranged in nondescending order of distance from the origin. No gasoline station along the route is further from the origin than the distance from the origin to the destination. There are always enough stations appropriately placed along the each route for any car to be able to get from the origin to the destination. Output Output should consist of the minimum total cost of the gasoline and snacks rounded to the nearest cent. That total cost must include the initial cost of filling the tank at the origin. Sample input 475.6 11.9 27.4 14.98 6 102.0 99.9 220.0 132.9 256.3 147.9 275.0 102.9 277.6 112.9 381.8 100.9 Sample output $27.31 Sample input (2) 516.3 15.7 22.1 20.87 3 125.4 125.9 297.9 112.9 345.2 99.9 Sample output (2) $38.09 Problem 9 Sudoku Solver In the last decade, the Sudoku craze has spread from Japan to Britain and has now gained ubiquity in America as well. Some publishers of Sudoku puzzle-books use computer programs to generate their puzzles because it is faster and cheaper than having them created by hand. For the uninitiated, a normal Sudoku problem consists of a 9x9 grid of cells made up of nine smaller 3x3 grids called regions. The puzzle begins with the grid partially filled with digits, and it is the job of the solver to fill in the blank spaces. The rule for filling in these cells is simple: each of the nine rows, columns, and regions must contain the digits 1-9, with no repetitions, one in each cell.   There are several techniques that can be used to solve Sudoku puzzles; one of the simplest is called cross-hatching. Cross hatching involves looking a region and trying to find the location of a missing numeral by eliminating rows and columns (that pass through the region) that already contain it. Cells within the region that already contain digits, obviously, can be eliminated as well.  In the puzzle above, the location of the numeral 5 in the upper-right region can be deduced by eliminating the rows and columns already containing a 5 and their associated cells in that region. Obviously, it cannot go in the cell already filled with the numeral 6, which leaves only one possible location: the lower left cell. Difficult puzzles require more techniques to be solved - some requiring more advanced levels of logical deduction, the hardest requiring deduction through trial-and-error. For this problem, you will only be given puzzles classified as easy, each of which can be solved though cross-hatching or a similar technique. Write a program that solves these problems. The particular method(s) it uses will have no impact on your score. Input Input will consist of one file name, and that file will contain one Sudoku puzzle. The file will be plaintext, with one row of the puzzle on each line. Blank cells will be denoted by a . (period) character, and cells containing numerals will simply be represented by digits. Output Acceptable output will consist of the solved Sudoku puzzle in the same format. Sample input puzzle.txt Sample input file (puzzle.txt) 53..7.... 6..195... .98....6. 8...6...3 4..8.3..1 7...2...6 .6....28. ...419..5 ....8..79 Sample output 534678912 672195348 198342567 859761423 426853791 713924856 961537284 287419635 345286179 +--------+ | 4 | +-+----+-+ +-------+ | 2 | +-----------+ | 0 +---+----+---+ 3 | | | 1 | | +-------+------------+-----------+ An example set of walking boxes.  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