Problem Paper Atoms Tree. atoms.pas. atoms.cpp. atoms.c. atoms.java. Time limit per test 1 second 1 second 2 seconds. Number of tests

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1 ! " # %$ & Overview Problem Paper Atoms Tree Shen Tian Harry Wiggins Carl Hultquist Program name paper.exe atoms.exe tree.exe Source name paper.pas atoms.pas tree.pas paper.cpp atoms.cpp tree.cpp paper.c atoms.c tree.c paper.java atoms.java tree.java Input file paper.in atoms.in tree.in Output file paper.out atoms.out tree.out per test secon secon 2 secons Number of tests Points per test Total points The maximum total score for Day2 is 00 points. ')(+*-,.(0/2+( ;: <>=?*@(BADC-EGF

2 HIKJMLN6O+N0PQIRS)TUTWV Shen Tian Paper Introuction It is time for the Guji people s annual harvesting festival. Accoring to traition, the village prepare a mural in praise of the Great Cow. At en of the festival, the mural is to be ivie amongst the various farmer of the village as a token of goo fortunes for the coming year. The parts for each farmer have been rawn out on the mural alreay. It is time to cut it. In orer to o this honorably, the mural has to be cut into two pieces each time, with a straight cut from one sie to the other. The mural is a rectangle of integer sie lengths. The parts marke out for each farmer are smaller rectangles, whose sies are parallel to the sies of the mural. In aition, the istances between the sies of the smaller rectangles are integer length away from the sies of the mural. Each cut must be a straight cut, parallel to a sie of the mural, an go all the way through the current piece (Once cut, the piece becomes two other pieces). In other wors, you cannot cut half-way through a piece of the mural. Cuts can cross each other, but may not overlap, or be along the perimeter of the mural. You are to ecie the orer an location of the cuts to be mae in orer to ivie the mural into the separate pieces for each farmer. 2 Consier this mural. To ivie it, the line labele shoul be cut first. Then, since the mural is now in two pieces, cut 2 can be mae. Cut to ivie the mural into the require 4 pieces will follow. Sample Input The first line of input will consist of two integers M an N, separate by a single space. The next M lines will each contain N characters (each character being one of a-z), representing the mural. Each piece of the mural will be represente using a ifferent character. It is guarantee that the mural will be entirely ivie into rectangles an that no two istinct pieces will be represente by the same character. : 5 4 aabb aabb ccbb ccbb Sample Output The first line of the output will contain a single integer x, inicating the number of cuts neee. The next x lines represent the cuts in the orer they were mae. Each of these lines contains 4 space-separate integers, m, n, m 2, n 2. Each line represents a cut, from (m, n ) to (m 2, n 2 ) an m <= m 2, n <=n 2. The top right left corner of the mural is (0, 0) an the bottom right corner is (M, N). If there are no vali ways of cutting the mural, print only a single line containing -. : <= M, N <=00 Secon per test case. A correct solution earns 0 points. Any solution that makes illegal cuts or oes not correctly ivie the mural scores 0 points.

3 Harry Wiggins Atoms <=N<=00 Introuction The Guji physicist iscovere a molecule consisting out of N ifferent atoms arrange in a single row. He numbere them, 2,, N. He built an "atommeter" that can access any two istinct atoms simultaneously to work out the istance between them. The istance between any two consecutive atoms is the same. The physicist woul like to work out in which orer the atoms are arrange, but accessing the atoms excites them. If the physicist accesses an atom more than 5 times the entire molecule gets estroye. Your task is to iscover the orer of the atoms with the least number of accesses. This interactive program uses stin an stout. The first integer that you shoul rea is the number of atoms in the molecule. Then for each query of the atommeter you shoul prouce (via stout) two integers separate by a space. After each query you shoul accept an integer (via stin)., representing the istance between those two atoms. When you have worke out the orer of the atoms you shoul print "- -" (stout) an on the next line you shoul print your answer (stout) an then exit your program. Your answer shoul be a single line of space-separate integers representing the atoms in the correct orer. secon Let G be the maximum number of times an atoms was accesse in your experiment. If your orer is the correct orer or in reverse, you ll get 00% if G = 70% if G = 4 0% if G = 5 0% if G>5 Using stout an stin Pascal instructions Do NOT use the CRT unit in your program. It can interfere with the flow of ata between your program an the evaluator. Perform the interaction as follows: writeln(guess); flush(output); realn(reply); C/C++ instructions Perform the interaction as follows: printf( %\n, guess); fflush(stout); scanf( %s, reply); Output by your program by stout Returne to your program via stin 2 C++ instructions for C++ streams Perform the interaction as follows. cout << guess << \n ; cout.flush(); cin >> reply; Java instructions Perform the interaction as follows, where in is a BuffereReaer in = new BuffereReaer( new InputStreamReaer( System.in)); System.out.println(guess); System.out.flush(); guess = in.realine();

4 Carl Hultquist Introuction Hut Tree The Guji tribe has a number of huts in their village, which they wish to connect up with footpaths. Each hut is name accoring to the family that lives insie that hut. Seeking a challenge, the tribe wants to connect up the huts in a special way so that the paths an huts form what is known as a binary search tree. This means that there is a "hea hut" which forms what is calle the root of the tree. Each hut then has at most two paths leaing from it to other huts: the path to the left must lea to the huts whose names are lexicographically (alphabetically) less, whilst the path to the right must lea to the huts whose names are lexicographically greater. For example, in the figures below, (a) is vali because "Bana" is lexicographically less than "Meemu" an so can be foun by following the path to the left, whilst "Ugi" is lexicographically greater than "Meemu" an so can be foun by following the path to the right. Figures (b) an (c) are invali: in (b), "Bana" is lexicographically less than "Meemu" but is foun by following the right path (an not the left one), an in (c), "Ugi" is lexicographically greater than "Meemu" but it foun by following the left path (an not the right one). Your job is to create the paths between the huts such that: The paths an huts form a binary search tree There is no other binary search tree whose total path length is shorter than your total path length. The tribe has 4 huts that house the families of Ugi, Togo, Bana an Meemu, an the istances between the huts is shown in the table below: Ugi Togo Bana Meemu Ugi Togo 5-4 Bana Meemu 2 - Below is an example of a solution for this problem, which has a total path length of 6. In this example, there is only one binary search tree that has a total path length of 6. There may be cases with multiple solutions, but you will only nee to fin one of them. (a) To complicate matters, the tribe oesn t want to o more work creating paths than is absolutely necessary. For this reason, the total length of path create must be minimise. (b) (c) Input Format Input shoul be rea from the file tree.in The first line of input will consist of a single integer, N, specifying the number of huts in the village. The next N lines of input will then each consist of the name of each hut. The following N lines will each contain N integers that inicate the istance to the other huts in the village. Each hut will have a unique name, an each name will consist of a series of at most 20 lowercase letters. The istance from any hut to itself is 0, an will be specifie as such in the input (but you may not buil a path from a hut to itself). Also, if the istance from hut I to hut J is D, then you are guarantee that the istance form hut J to hut I is also D.

5 Sample Input 4 ugi togo bana meemu Output Format Output shoul be written to the file tree.out The first line of output must contain an integer L an name R, separate by a space. L must be the total path length of your solution, an R is the name of the root hut in the binary search tree that you have foun. The next N - lines will escribe the paths that you have create. Each line must contain two names, A an B, that represent the two huts between which you have create a path. The paths can be liste in any orer, an the two huts forming the path can be in any orer. Sample Output 6 ugi ugi meemu meemu bana meemu togo N , where represents the istance between any two huts 2 secons Any solution that oes not prouce output in the format specifie above will score 0. Any solution whose paths o not form a binary search tree with the root specifie will score 0. If the total path length of the paths specifie oes not match the total path length L, the solution will score 0. Otherwise, if the optimal total path length is P an the total path length in the solution is L, the solution will score: S = 0 * [(P/L) ]