سوالات مسابقات برنامه نویسی acm 2004-2005

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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
Problem C -Page 1 of 1

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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