Reaching any of the following three levels qualifies a student for the Competition Round.
Bronze Level - Two problems solved
Silver Level - Three problems solved.
Gold Level - Four problems solved.
Please have each qualified student fill out and return the entry form for the competition round found in this brochure. Results on the qualifying round may be used to decide who comes to the final round in the event of ties near the cut-off point of 16 students.
You have a necklace of n beads (n <100) some of which are red,
others blue, and others white, arranged at random. Let's see two
examples for n = 29:
1 2 1 2
o x x o x o o x
o x x x
o o x o
o o @ o
x o @ @
x x o o
x x x x
x x o x
o o x o
x o o o
x o o o
o o o x
o x o o o @
Figure a Figure b
o red bead
x blue bead
@ white bead
(The beads considered first and second in the text that follows have
been marked in the picture.)
The configuration in Figure a may be represented as a string of b's and
r's, where b represents a blue bead and r a red one, as follows:
brbrrrbbbrrrrrbrrbbrbbbbrrrrb
Suppose you are to break the necklace, lay it out straight, and then
collect beads of the same color from one end until you reach a bead of
a different color, and do the same for the other end (which may not be
of the same color as the beads collected before this).
Determine the point where the necklace should be broken so that the
most number of beads can be collected.
For example, for the necklace in Figure a, 8 beads can be collected,
with the breaking point either between bead 9 and bead 10, or
between bead 24 and bead 25.
In some necklaces, white beads had been included as shown in Figure
b above. When collecting beads, a white bead that is encountered
may be treated as either red or blue and painted with the desired color.
The string that represents this configuration will include the symbols:
r, b and w.
Write a program to do the following:
1. Read a configuration from an ASCII input file,
NECKLACE.DAT, with each configuration on one line. Write
this data into an ASCII output file, NECKLACE.SOL. An
example of an input file would be:
NECKLACE.DAT
brbrrrbbbrrrrrbrrbbrbbbbrrrrb
bbwbrrrwbrbrrrrrb
2 .For each configuration, determine the maximum number, M, of
beads collectable, along with a breaking point.
3. Write to the outfile, NECKLACE.SOL, the number M and the
breaking point. The solutions for different configurations
should be separated with a blank record.
Example of a possible solution:
NECKLACE.SOL
brbrrrbbbrrrrrbrrbbrbbbbrrrrb
8 between 9 and 10
bbwbrrrwbrbrrrrrb
10 between 16 and 17
4. Run your program with the data file NECKLACE.DAT given in
1.
Put your program solution into an ASCII file named PROB1.xxx.
Extension .xxx is .BAS for QBasic, .LCN for LOGO, .C for C, .PAS
for PASCAL.
Some companies are partial owners of other companies because they have acquired part of their total shares. For example, Ford owns 12% of Mazda. It is said that a company A controls company B if at least one of the following conditions is satisfied: a) A = B b) A owns more than 50% of B c) A controls k (k > 1) companies, C(1), ..., C(k), so that: C(i) owns x(i)% of B for 1 < i < k and x(1) + .... + x(k) > 50. The problem to solve is: Given a list of triples (i,j,p) which means that the company i owns p% of company j, calculate all the pairs (h,s) so that company h controls company s. There are at most 100 companies. Write a program to: 1 Read from an ASCII input file, COMPANY.DAT, the list of triples, (i,j,p), to be considered for each case (that is, each data set), where i, j and p are positive integers. Different cases (data sets) will be separated with a blank record. 2 Find all the pairs (h,s) so that company h controls company s. 3 Write to an ASCII output file, COMPANY.SOL, all the pairs (h,s) found, with h different from s. The pairs (h,s) must be written in consecutive records and in increasing order of h. The solutions for different cases must be separated with a blank record. 4. Run your program with the data file COMPANY.DAT. COMPANY.DAT COMPANY.SOL 2 3 25 4 2 1 4 36 4 3 4 5 63 4 5 2 1 48 3 4 30 4 2 52 5 3 30 1 2 30 2 3 2 3 52 2 4 3 4 51 2 5 4 5 70 3 4 5 4 20 3 5 4 3 20 4 5 Put your program solution into an ASCII file named PROB2.xxx. Extension .xxx is .BAS for QBasic, .LCN for LOGO, .C for C, .PAS for PASCAL. PROBLEM 3N rectangles of different colors are superposed on a white sheet of paper. The sheet's sizes are: a cm wide and b cm long. The rectangles are put with their sides parallel to the sheet's borders. All rectangles fall within the borders of the sheet. As a result, different figures of different colors will be seen. Two regions of the same color are considered to be part of the same figure if they have at least one point in common; otherwise, they are considered different figures. The problem is to calculate the area of each of these figures; a, b are even positive integers not greater than 30. The coordinate system considered has its origin at the sheet's center and the axes parallel to the sheet's borders: Different data sets are written in an ASCII input file, RECTANG.DAT: 1) a, b and N will be in the first line of each data set, separated by a blank space. In each of the next N lines you will find: 2) the integer coordinates of the position where the left lower vertex of the rectangle was placed; 3) followed by the integer coordinates of the position where the upper right vertex of the rectangle was placed; 4) and, then, the rectangle's color represented by an integer between 1 and 64. White color will be represented by 1. The order of the records corresponds to the order used to put the rectangles on the sheet. Different data sets will be separated with a blank record. Write a program to: 1. Read the next data set from RECTANG.DAT. 2. Calculate the area of each colored figure. 3. Write in an ASCII output file, RECTANG.SOL, the color and the area of each colored figure as shown in the example below. These records will be written in increasing order of color. The solutions to different data sets will be separated by a blank record. 4. Test your program with the data file RECTANG.DAT. RECTANG.DAT RECTANG.SOL 20 12 5 1 172 -7 -5 -3 -1 4 2 47 -5 -3 5 3 2 4 12 -4 -2 -2 2 4 4 8 2 -2 3 -1 12 12 1 3 1 7 5 1 30 30 2 1 630 0 0 5 14 2 2 70 -10 -7 0 13 15 15 200 Put your program solution into an ASCII file named PROB3.xxx. Extension .xxx is .BAS for QBasic, .LCN for LOGO, .C for C, .PAS for PASCAL.PROBLEM 4
You have won a contest sponsored by an airline. The prize is a ticket to travel around Canada, beginning in the most western point served by this airline, then traveling only from west to east until you reach the most eastern point served, and then coming back only from east to west until you reach the starting city. No city may be visited more than once, except for the starting city, which must be visited exactly twice (at the beginning and the end of the trip). You are not allowed to use any other airline or any other means of transportation. Given a list of cities served by the airline, and a list of direct flights between pairs of cities, find an itinerary which visits as many cities as possible and satisfies the above conditions beginning with the first city and visiting the last city on the list and returning to the first city. Different data sets are written in an ASCII input file, ITIN.DAT. Each data set consists of: 1) in the first line: the number N of cities served by the airline and the number V of direct flights that will be listed. N will be a positive integer not larger than 100. V is any positive integer. 2) in each of the next N lines: a name of a city served by the airline. The names are ordered from west to east in the input file. That is, the i-th city is west of the j-th city if and only if i < j (There are no two cities in the same meridian). The name of each city is a string of, at most, 15 digits and/or characters of the Latin alphabet, for example: AGR34 or BEL4. (There are no spaces in the name of a city.) 3) in each of the next V lines: two names of cities, taken from the list of cities, separated by a blank space. If the pair city1 city2 appears in a line, it indicates that there exists a direct flight from city1 to city2 and also a direct flight from city2 to city1. Different data sets will be separated by an empty record (that is, a line containing only the end of line character). There will be no empty record after the last data set. The following example is stored in file ITIN.DAT. 8 9 5 5 Vancouver C1 Yellowknife C2 Edmonton C3 Calgary C4 Winnipeg C5 Toronto C5 C4 Montreal C2 C3 Halifax C3 C1 Vancouver Edmonton C4 C1 Vancouver Calgary C5 C2 Calgary Winnipeg Winnipeg Toronto Toronto Halifax Montreal Halifax Edmonton Montreal Edmonton Yellowknife Edmonton Calgary The input may be assumed correct. No checking is necessary. The solution found for each data set must be written to an ASCII output file, ITIN.SOL: in the first line, the total number of cities in the input data set; in the next line, the number M of different cities visited in the itinerary, and in the next M+1 lines the names of the cities, one per line, in the order in which they are visited. Note the first city visited must be the same as the last. Only one solution is required. If no solution is found for a data set, only two records for this data set must be written in ITIN.SOL, the first one giving the total number of cities, and the second one saying: "NO SOLUTION." A possible solution for the above example: ITIN.SOL 8 5 7 NO SOLUTION Vancouver Edmonton Montreal Halifax Toronto Winnipeg Calgary Vancouver Put your program solution into an ASCII file named PROB4.xxx. Extension .xxx is .BAS for QBasic, .LCN for LOGO, .C for C, .PAS for PASCAL.