About question C:
I think we can first sort the separating lines according to, say, the
upper coordinate, and then, for each toy, do a binary search, find out
the two adjacent separators that one is to his left, and the other to
his right. To find out of which side the toy is, you can use cross
product.
This is, I believe, if Im not completely mistaken, O(M log N + N log
N).
On Jul 10, 5:15 am, Spiritus <spirit...@gmail.com> wrote:
> Problem B:
> My idea is to have a set(can be implemented using STL's std::set) with
> key being a pair (dx,dy).
> now, i go through all pairs of points, and i construct the key(x_1-
> x_0,y_1,y_0) for them. The idea is that if i have L pairs each with
> the same (dx,dy), every two pairs make a parallelogram. And so, after
> putting them all inside, i go through the set and say that if I have L
> pairs with the same (dx,dy), i add L*(L-1)/2 to a counter, and in the
> end i divide by 2, since i counted each parallelogram twice.
> Now, this is not accurate, because this way i count 4 points on a
> straight line as a parallelogram. So, instead of just counting how
> many pairs are with this (dx,dy), i count how many different lines are
> with this slope. that is, for a specific slope, (dx,dy), i maintain a
> second level set that contains the intersections with the y axis, and
> in the end, i use inclusion exclusion on each slope, and i end up with
> a (N log N) algorithm.
>
> Sincerely,
> Shahar Papini
>
> On Jul 8, 11:58 am, Davood Vahdati <davoodvahdati2...@gmail.com>
> wrote:
>
> > it is an Acm programming competition Questions in year 2004-2005 . could you
> > please solve problems is question ? thank you .
>
> > 29th ACM International Collegiate
>
> > Sponsored by
>
> > Programming Contest, 2004-2005
> > Sharif Preliminary Contest
> > Sharif University of Technology, 28 Oct. 2004
>
> > Problem B
> > (Program filename: B.CPP, B.DPR, B.PAS or B.java)
>
> > Parallelogram Counting
>
> > There are n distinct points in the plane, given by their integer
> > coordinates. Find the number of parallelograms whose
> > vertices lie on these points. In other words, find the number of 4-element
> > subsets of these points that can be written as
> > {A, B, C, D} such that AB || CD, and BC || AD. No four points are in a
> > straight line.
>
> > Input (filename: B.IN)
>
> > The first line of the input file contains a single integer t (1 £ t £ 10),
> > the number of test cases. It is followed by the input
>
> > data for each test case.
> > The first line of each test case contains an integer n (1 £ n £ 1000). Each
> > of the next n lines, contains 2 space-separated
> > integers x and y (the coordinates of a point) with magnitude (absolute
> > value) of no more than 1000000000.
>
> > Output (Standard Output)
>
> > Output should contain t lines.
> > Line i contains an integer showing the number of the parallelograms as
> > described above for test case i.
>
> > Sample Input
>
> > 2
> > 6
> > 0 0
> > 2 0
> > 4 0
> > 1 1
> > 3 1
> > 5 1
> > 7
> > -2 -1
> > 8 9
> > 5 7
> > 1 1
> > 4 8
> > 2 0
> > 9 8
>
> > Sample Output
>
> > 5
> > 6
>
> > ----------------------------------------------------------------------------------------------------------------------
> > Problem B-Page 1 of 1
>
> > 28th ACM International Collegiate
>
> > Sponsored by
>
> > Programming Contest, 2003-2004
> > Sharif Preliminary Contest
> > Sharif University of Technology, 14 Nov. 2003
>
> > Problem C
> > (Program filename: C.CPP or C.PAS or C.DPR or C.java)
>
> > Toy Storage
>
> > Mom and dad have a problem: their child, Reza, never puts his toys away when
> > he is finished playing with them.
> > They gave Reza a rectangular box to put his toys in. Unfortunately, Reza is
> > rebellious and obeys his parents by simply
> > throwing his toys into the box. All the toys get mixed up, and it is
> > impossible for Reza to find his favorite toys anymore.
>
> > Reza's parents came up with the following idea. They put cardboard
> > partitions into the box. Even if Reza keeps
> > throwing his toys into the box, at least toys that get thrown into different
> > partitions stay separate. The box looks like this
> > from the top:
>
> > We want for each positive integer t, such that there exists a partition with
> > t toys, determine how many partitions
> > have t, toys.
>
> > Input (filename: C.IN)
>
> > The input consists of a number of cases. The first line consists of six
> > integers n, m, x1, y1, x2, y2. The number of
> > cardboards to form the partitions is n (0< n £ 1000) and the number of toys
> > is given in m (0<m £ 1000). The
> > coordinates of the upper-left corner and the lower-right corner of the box
> > are (x1, y1) and (x2, y2), respectively. The
> > following n lines each consists of two integers Ui Li, indicating that the
> > ends of the ith cardboard is at the coordinates
> > (Ui, y1) and (Li, y2). You may assume that the cardboards do not intersect
> > with each other. The next m lines each consists
> > of two integers Xi Yi specifying where the ith toy has landed in the box.
> > You may assume that no toy will land on a
> > cardboard.
> > A line consisting of a single 0 terminates the input.
>
> > Output (filename: C.OUT)
>
> > For each box, first provide a header stating “Box”
> > on a line of its own. After that, there will be one line of output per
> > count (t> 0) of toys in a partition. The value t will be followed by a colon
> > and a space, followed the number of
>
> > partitions containing t toys. Output will be sorted in ascending order of t
> > for each box.
>
> > Sample Input
>
> > 4 10 0 10 100 0
> > 20 20
> > 80 80
> > 60 60
> > 40 40
> > 5 10
> > 15 10
> > 95 10
> > 25 10
> > 65 10
> > 75 10
> > 35 10
> > 45 10
> > 55 10
> > 85 10
> > 5 6 0 10 60 0
>
> > 4 3
> > 15 30
> > 3 1
> > 6 8
> > 10 10
> > 2 1
> > 2 8
> > 1 5
> > 5 5
> > 40 10
> > 7 9
> > 0
>
> > Sample Output
>
> > Box
>
> > 2: 5
> > Box
> > 1: 4
> > 2: 1
> > ----------------------------------------------------------------------
> > 29th ACM International Collegiate
> > Sponsored by
> > Programming Contest, 2004-2005
> > Sharif Preliminary Contest
> > Sharif University of Technology, 28 Oct. 2004
>
> > Problem D
> > (Program filename: D.CPP, D.DPR, or D.java)
>
> > Software Company
> > A software developing company has been assigned two programming projects. As
>
> > both projects are within the same contract, both must be handed in at the
> > same
> > time. It does not help if one is finished earlier.
>
> > This company has n employees to do the jobs. To manage the two projects more
>
> > easily, each is divided into m independent subprojects. Only one employee
> > can
> > work on a single subproject at one time, but it is possible for two
> > employees to
> > work on different subprojects of the same project simultaneously.
>
> > Our goal is to finish the projects as soon as possible.
>
> > Input (filename: D.IN)
> > The first line of the input file contains a single integer t (1 £ t £ 11),
> > the
> > number of test cases, followed by the input data for each test case. The
> > first
> > line of each test case contains two integers n (1 £ n £ 100), and m (1 £ m £
>
> > 100). The input for this test case will be followed by n lines. Each line
> > contains two integers which specify how much time in seconds it will take
> > for
> > the specified employee to complete one subproject of each project. So if the
>
> > line contains x and y, it means that it takes the employee x seconds to
> > complete
> > a subproject from the first project, and y seconds to complete a subproject
> > from
> > the second project.
> > Output (Standard Output)
> > There should be one line per test case containing the minimum amount of time
> > in
> > seconds after which both projects can be completed.
>
> > Sample Input
> > 1
> > 3 20
> > 1 1
> > 2 4
> > 1 6
>
> > Sample Output
> > 18
>
> > Problem D -Page 1 of 1
>
> > 29th ACM International Collegiate
> > Sponsored by
> > Programming Contest, 2004-2005
> > Sharif Preliminary Contest
> > Sharif University of Technology, 28 Oct. 2004
> > ----------------------------------------------------------------------
> > Problem F
> > (Program filename: F.CPP, F.DPR, or F.java)
>
> > Median Weight Bead
> > There are N beads which of the same shape and size, but with different
> > weights.
> > N is an odd number and the beads are labeled as 1, 2, ..., N. Your task is
> > to
> > find the bead whose weight is median (the ((N+1)/2)th among all beads). The
> > following comparison has been performed on some pairs of beads:
> > A scale is given to compare the weights of beads. We can determine which one
> > is
> > heavier than the other between two beads. As the result, we now know that
> > some
> > beads are heavier than others. We are going to remove some beads which
> > cannot
> > have the medium weight.
>
> > For example, the following results show which bead is heavier after M
> > comparisons where M=4 and N=5.
>
> > 1. Bead 2 is heavier than Bead 1.
> > 2. Bead 4 is heavier than Bead 3.
> > 3. Bead 5 is heavier than Bead 1.
> > 4. Bead 4 is heavier than Bead 2.
> > From the above results, though we cannot determine exactly which is the
> > median
> > bead, we know that Bead 1 and Bead 4 can never have the median weight: Beads
> > 2,
> > 4, 5 are heavier than Bead 1, and Beads 1, 2, 3 are lighter than Bead 4.
> > Therefore, we can remove these two beads.
> > Write a program to count the number of beads which cannot have the median
> > weight.
>
> > Input (filename: F.IN)
> > The first line of the input file contains a single integer t (1 £ t £ 11),
> > the
> > number of test cases, followed by the input data for each test case. The
> > input
> > for each test case will be as follows:
> > The first line of input data contains an integer N (1=N=99) denoting the
> > number
> > of beads, and M denoting the number of pairs of beads compared. In each of
> > the
> > next M lines, two numbers are given where the first bead is heavier than the
>
> > second bead.
> > Output (Standard Output)
> > There should be one line per test case. Print the number of beads which can
> > never have the medium weight.
>
> > Sample Input Sample Output
> > 1 2
> > 5 4
> > 2 1
> > 4 3
> > 5 1
> > 4 2
> > Problem F -Page 1 of 2
>
> > ACM.rar
> > 63KViewDownload
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