1998
Fort Lewis College
Programming Contest
Table of Contents
General Instructions
Problem 1: Insipid Integers
Problem 2: House and Yard
Problem 3: Income Tax
Problem 4: Water Flow
Problem 5: Seminar Registration
Problem 6: Pyramidal Prison
Problem 7: The Knight and the Princess
2
General Instructions
For a solution written in C++, a source file named PROGn.CPP, for a solution written in C, a source file
named PROGn.C,. Here n is the assigned number for the problem.
The judges will not correct any error, even if it is only a misspelling of the program name, or if the wrong
language is specified. Unless otherwise specified in the problem statement, each program will get its input
from a file named PROGn.DAT where again n is the assigned number for the problem. The output from
each program must go to a file named PROGn.OUT. Your program must read from and write to the current
directory – do not specify the disk drive or directory in your program.
The first line of output from each program must be:
Problem n by Team <team number>
where the <team number> is replaced by your team number, and n is replaced by the problem number.
The last line of output from every program must be:
End of Problem n by Team <team number>
There will be no blank lines between the first and last lines of your output, except as specified by the
problem statement.
Scoring the contest:
1.
2.
3.
The team that has solved the most problems in the time allotted is the winner.
If two or more teams solve the same number of problems, they are ranked by least total time. The total
time is the sum of time consumed for each problem solved. The time consumed for a solved problem
is the time elapsed from the beginning of the contest to the submittal of the accepted run plus 20
minutes for each rejected run. There is no time consumed for a problem not solved.
Only one correct solution will be accepted for any one problem from a single team.
3
Error Messages
There are nine error categories for which a submission may be rejected. They are:
SUNTAX ERROR – submitted program will not compile
RUN-TIME ERROR – program failed while running. For example, data file name was wrong.
TIME-LIMIT EXCEEDED – program took too long to run. Every problem should complete in a
reasonable length of time. This means "effectively immediately.” If a program takes more than a few
seconds, it is too slow.
4. WRONG ANSWER – self-explanatory. Probably the most common reason for rejection.
5. INACCURATE ANSWER – right answer, wrong accuracy.
6. FAILED TEST CASE – failed at least one of the test cases, passed the others.
7. TOO LITTLE/MUCH OUTPUT – reread the problem.
8. WRONG OUTPUT FORMAT – reread the problem (possibly you forgot to bracket the output with the
required team information).
9. RTFI -- you failed to follow all instructions; for example, your source file name is wrong.
10. CHECK CLARIFICATIONS – there has been a clarification of the problem issued by the judges
during the contest and you should check the clarification board for guidance.
1.
2.
3.
The format of your output is important and must be exactly as shown in the samples, including blank lines
and spacing on the line. Failure to follow the required output format will result in a “WRONG OUTPUT
FORMAT” error, and your program will be returned for correction. In many cases, the placement and
number of blank spaces in the output are as significant as printable characters.
Any attempt by your program to write anything to the judge’s disk except the required output files will
result in immediate disqualification of your team from the contest.
Your team also may be disqualified for any activity that jeopardizes the integrity of the contest such as
interfering with other teams or disruptive behavior. Contestants are not to converse with anyone except
other members of their team and personnel designated by the contest directors.
The contest judges are solely responsible for determining the correctness of submitted solutions. Their
decisions are final.
4
Problem 1: Insipid Integers
Name your source file Prog1.cpp or Prog1.c
A sequence of integers N0 , N1 , N2 , … , is generated using the following algorithm:
(1) An initial positive integer N0 is given,
(2) The integer Nj+1 is computed as the sum of the squares of the digits of Nj in base 10.
It is known that the sequence N0 , N1 , N2 , … will eventually cycle for each choice of N0 . That is, there
are integers i and j with i < j where Ni = Nj. If i and j are the smallest integers with 0 <= i < j, and Ni =
Nj , then the INSIPID CYCLE LENGTH OF N0 is defined to be j – i and the INSIPID CHAIN LENGTH OF
N0 is j . Further, the integer N0 is called INSIPID if the integer 1 occurs in the sequence.
NOTE: The insipid cycle length is the number of distinct elements in one cycle and the insipid chain
length is the number of distinct elements in the entire sequence.
EXAMPLES:
(1) If N0 =7, then the sequence proceeds as 7, 49, 97, 130, 10, 1, 1, …. The integer 7 is an insipid
integer with cycle length 1 and chain length 6.
(2) If N0 = 11112222333311, then the sequence proceeds as 11112222333311, 58, 89, 145, 42,
20, 4, 16, 37, 58, 89, … . The integer 11112222333311 not an insipid integer. The insipid cycle
length is 8 and the insipid chain length is 9.
Your program is to accept from the input file PROG1.DAT, a positive integer of at most 50 digits in length,
determine and output to the file PROG1.OUT whether the input integer is an insipid integer, the insipid
cycle length, and the insipid chain length.
The following is a listing of the output file PROG1.OUT for Example 1 above (The input file
PROG1.DAT contains the single integer 7):
Problem 1 by <team name>
The integer 7 is an insipid integer
The insipid cycle length is 1
The insipid chain length is 6
End of Problem 1 by <team name>
The following is a listing of the output file PROG1.OUT for Example 2 above (The input file
PROG1.DAT for this example contains the single integer 11112222333311)
Problem 1 by <team name>
The integer 11112222333311 is not an insipid integer
The insipid cycle length is 8
The insipid chain length is 9
End of Problem 1 by <team name>
You may assume that the input data file PROG1.DAT contains a single line containing an integer of at
most 50 digits beginning in column 1.
5
Problem 2: House and Yard
Name your source file Prog2.cpp or Prog2.c
A "house" and a "yard" are depicted graphically as rectangles in a two-dimensional Cartesian coordinate
system. The sides of the house and the yard are parallel to the coordinate axes and the house is to be
contained within the rectangular area of the yard.
You are given the coordinates of four points in the plane. Two of these points are supposed to be the
endpoints of a diagonal of the rectangle representing the yard and the other two points are supposed to be
the endpoints of a diagonal of the rectangle representing the house. The points may be given in any order.
Your program is to determine the following:
(1) Is it possible that the four points determine a rectangular "yard" containing a rectangular
"house"?
(2) If (1) above is true, calculate the area of the house and the area of the yard.
NOTE: The house and yard may share all or part of one or more edges without the house being outside of
the yard.
EXAMPLES:
(1) Given the four points (3, 10), (9, 8), (7, 5), and (12, 4), the only "house/yard" combination
that is possible is:
The endpoints of the yard diagonal are: (3, 10) and (12, 4).
The endpoints of the house diagonal are: (7, 5) and (9, 8).
The area of the house is 6 and the area of the yard is 54.
(2) Given the four points (1, 2), (12, 15), (5, 7), and (14, 9), no "house/yard" combination can be
formed from these points. A carefully drawn graph reveals that any choice for a diagonal for
the yard gives a house which lies partly or wholly outside the yard.
Your program is to enter the four points from the input file PROG2.DAT. This file will contain one line
of eight integer values (four pairs of coordinates). The contents of the input file for example 1 above is
3 10 9 8 7 5 12 4
The program output is to the file PROG2.OUT. The following is a listing of the output file for Example 1
above:
Problem 2 by <team name>
The input diagonal endpoints are (3,10), (9,8), (7,5), and (12,4)
The endpoints of the yard diagonal are: (3,10) and (12,4)
The endpoints of the house diagonal are: (7,5) and (9,8)
The area of the yard is: 54
The area of the house is: 6
End of Problem 2 by <team name>
The following is a listing of the output file PROG2.OUT for Example 2 above:
Problem 2 by <team name>
The input diagonal endpoints are (1,2), (12,15), (5,7), and (14,9)
No house/yard combination is possible for this data.
End of Problem 2 by <team name>
6
Problem 3: Income Tax Computations (2 pages)
Name your source file Prog3.cpp or Prog3.c
With April 15 approaching, a program is needed to check the computations on Form 1040 for an Individual
Income Tax Return. The program is to retrieve data from a data file and create the formatted report shown
in the example below. The input data file called PROG3.DAT, consists of one line for each of the
following fields. Currency amounts are specified as dollars and cents using a decimal point and do not
include commas.
Name
Social Security Number
Number of Dependents
Wages, etc.
Interest
Dividends
Other Income
Adjustments
Federal Income Tax Withheld
Estimated Tax Payments
A maximum of 30 characters
9 characters
Integer
Currency
Currency
Currency
Currency
Currency
Currency
Currency
Here is an example of such an input file PROG3.DAT:
Grace Murray Hopper
324789113
1
43171.68
1375.79
6447.07
0.00
0.00
8416.94
700.00
The output report file for the above input file is to be saved as PROG3.OUT.
for the above input data file follows:
A listing of the output file
Problem 3 by <team name>
Tax Computation for: Grace Murray Hopper, 324-78-9113
Wages, etc.
7
43,171.68
Interest
8a
1,375.79
Dividends
9
6,447.07
Other Income
21
0.00
Total Income
22
50,994.54
Adjustments
30
0.00
Adjusted Gross Income
32
50,994.54
Deductions
34
4,000.00
Exemptions
36
2,550.00
Taxable Income
37
44,444.54
Tax
38
9,324.47
Federal Income Tax Withheld
52
8,416.94
Estimated Tax Payments
53
700.00
Total Payments
58
9,116.94
Refund
60a
0.00
Owed
62
207.53
End of Problem 3 by <team name>
Your output report is to be formatted exactly as above with all spacings, commas, and decimals as shown.
The second field in the report contains the line numbers on Form 1040 and must be included. These line
numbers will be used to describe the source data for each entry:
7
The name and social security number are on lines 1 and 2 of the input data file. The social security
number as output requires proper formatting.
Line 7:
direct input.
Line 8a:
direct input.
Line 9:
direct input.
Line 21:
direct input
Line 22:
add lines 7, 8a, 9, and 21.
Line 30:
direct input
Line 32:
subtract line 30 from line 22.
Line 34:
the standard deduction of $4,000.00 is to be used.
Line 36:
multiply the number of dependents (direct input) by $2,550.00.
Line 37:
subtract line 34 and line 36 from line 32 - if the resulting taxable income is negative,
enter zero.
Line 38:
the tax is computed from the TAX RATE SCHEDULE listed below.
Line 52:
direct input.
Line 53:
direct input.
Line 58:
add line 52 and line 53.
Line 60a:
if line 58 is greater than line 38, enter the difference between line 58 and line 38;
otherwise, enter zero.
Line 62:
if line 38 is greater than line 58, enter the difference between line 38 and line 58;
otherwise enter zero.
TAX RATE SCHEDULE:
If the amount on
Enter on
Form 1040, line 37,
Form 1040,
is:
But not
line 38
of the amount
Over-Over-Over-____________________________________________________________________________
$0
24,000
58,150
121,300
263,750
$24,000
58,150
121,300
263,750
-------
$3,600.00
13,162.00
32,738.50
84,020.50
15%
+
28%
+
31%
+
36%
+ 39.6%
An output template for formatting your output file PROG3.OUT follows:
12345678901234567890123456789012345678901234567890
Wages, etc.
7
43,171.68
Interest
8a
1,375.79
Dividends
9
6,447.07
Other Income
21
0.00
$0
24,000
58,150
121,300
263,750
8
Problem 4 : Water Flow
Name your source file Prog4.cpp or Prog4.c
A city engineer needs a program to analyze the city's water system. Whenever two water pipes join, they
form a junction. The junctions are numbered from 1 to 100. Water can flow between two junctions if they
are directly connected to each other. In general, water flows from junction I to junction J if a path of direct
connections exists between junction I and junction J.
The direct connections between junctions are to be read from an ASCII text file named PROG4.DAT. The
first line of the file contains the number of junctions to be processed (N). The next N lines of the file
contain two integers (I and J) representing a one-way connection from junction I to junction J. The next
several lines of the file contain two integers (X and Y) which represent two junction numbers. For each X,
Y input pair (an indeterminate number of input lines) the program is to determine if water can flow
between junction X and junction Y and is to output one of the two messages shown below:

If a path exists beginning at junction X and ending at junction Y, the program is to output the
message:
WATER CAN FLOW BETWEEN JUNCTIONS X AND Y

If no path exists beginning at junction X and ending at junction Y, the following message is
produced:
WATER CANNOT FLOW BETWEEN JUNCTIONS X AND Y
You are provided with the test file PROG4.DAT containing the following connections between junctions:
3
1
5
2
4
6
In the example water system depicted above, water can flow from junction 1 to junction 6, but cannot flow
from junction 6 to junction 1. Water can also flow from junction 3 to junction 6, but cannot flow from
junction 3 to junction 5.
Your output is to be sent to an ASCII text file named PROG4.OUT. The first and last lines of the
output file must contain the required team and problem identification, i.e.,
Problem 4 by <team name> // on the first line
End of Problem 4 by <team name> // on the last line
9
Problem 5 : Seminar Registration (2 pages)
Name your source file Prog5.cpp or Prog5.c
A program is needed to check attendance at a computer seminar. Only registered students are allowed to
attend the seminar. A list of registered students is available in an ASCII text file named ROSTER.DAT.
A second input file, named ENTRY.DAT contains the names of people who have attempted to enter the
seminar room to attend the seminar. The maximum number of students registered for the seminar is 25.
Any number of people may attempt to enter the seminar room, but the maximum number of entries in the
ENTRY.DAT file will not exceed 100.
The program will generate three reports into three separate ASCII text files (all file formats are
described below):
1.
A report showing how many students were registered for the seminar, how many were present at
the meeting, and how many people who tried to enter were denied permission to attend because
they had not pre-registered (in a file named HOWMANY.OUT).
2.
A report with the list of registered students (sorted by name), with either Present or Absent
following each name (in a file named ATTEND.OUT).
3.
A report of all people who tried to enter the seminar, but were not allowed to attend because they
had not pre-registered (in a file named DENIED.OUT).
Input / Output Format Specifications:
1.
Each line in the input ROSTER.DAT and ENTRY.DAT files contain a first name (maximum of
10 characters) followed by a blank space, followed by a last name (maximum of 20 characters)
terminated by a newline character. Sample ROSTER.DAT and ENTRY.DAT files are
provided for testing purposes.
2.
The HOWMANY.OUT output file :
Summary Attendance Data for Computer Seminar:
Number of Registered Students : X
Number in Attendance : Y
Number Denied Entry : Z
3.
The ATTEND.OUT output file (sorted by LastName, then by FirstName) :
Attendance Roster for Computer Seminar:
LastName FirstName Present (or Absent)
LastName FirstName Present (or Absent)
.
.
.
Number in Attendance : X
Number Absent : Y
10
Problem 5 : Seminar Registration (Cont'd)
4.
The DENIED.OUT output file:
Denied Attendance for Computer Seminar:
LastName FirstName
LastName FirstName
.
.
.
Number Denied : X
5.
The first and last lines of all output files must contain the required team and problem
identification, i.e.,
Problem 5 by <team name> // on the first line
End of Problem 5 by <team name> // on the last line
11
Problem 6: Pyramidal Prison (2 pages)
Name your source file Prog6.cpp or Prog6.c
A prison building has the shape of a pyramid. The number of levels (stories) is NumLevels (which will be
part of the input to your program), and the levels are numbered 0..NumLevels-1. The prison cells on
each level (except the topmost level) of the building are arranged in an array of concentric squares. The
squares are numbered consecutively from inner to outer, with 0 being the innermost square. For example,
with NumLevels = 4, the building has four levels numbered 0..3; the first two levels (levels 0 and 1) have
the respective floorplans:



9
8
7
6
5
4
3
10
6
5
4
3
2
2
6
5
4
3
2
11
7
3
2
1
1
1
7
3
2
1
1
12
8
4
0
0
0
0
8
4
0
0
0
13
9
5
6
7
15
23
9
5
6
7
15
14
10
11
12
13
14
22
10
11
12
13
14
15
16
17
18
19
20
21
The cell at the center of each level is numbered 0.
The successive concentric squares contain 8, 16, 24, … cells. Within each concentric square, the cell
directly East of the center is numbered 0; successive cells are numbered in counterclockwise order.
Level 0 has (in addition to the cell at the center) NumLevels-1 concentric squares of cells. Each
level (other than level 0) has one fewer concentric squares than the level below it. The topmost level
has only one cell, numbered 0 and located at the apex of the pyramid.
Each night, starting precisely at midnight (12 A.M.), the prison guard (her name is Gerda) begins her
inspection tour of the prison.
 She will need the same amount of time to inspect each cell.
 She will inspect each level in the prison, starting at level 0, then proceeding to levels 1, 2, … .
 On each level, she will inspect the squares in order, starting at square 0.
 Within each square, she will inspect the cells in order, starting at cell 0.
Here is an example of an input file Prog6.dat:
4
4
4
4
5
8
1
5
3
3
3
1
12
6
4
4
9
10
48
22
11
12
27
59
12
Each line of the input file contains four numbers: the number of levels of the pyramid, the number of
minutes needed to inspect each cell (including the time needed to move to the next cell), and a clock
reading in hours and minutes. (All times are A.M.) Your program will determine the guard’s location
(which level, which concentric square within that level, and which cell number within that concentric
square) at the given time. If the guard has already inspected all cells at the specified time, the time at which
the inspection was finished will be printed out by your program. Here is a listing of the output file
Prog6.out, resulting from the input listed above.
Problem 6 by <team name>
Number
Minutes
Clock
Guard's Location
Of
Per
======================
Levels
Cell
Level
Square
Cell
=================================================================
4
1
12:48 A.M.
0
3
23
4
5
6:22 A.M.
2
1
1
4
3
4:11 A.M.
3
0
0
4
3
4:12 A.M.
INSPECTION FINISHED AT 4:12 A.M.
5
3
9:27 A.M.
INSPECTION FINISHED AT 8:15 A.M.
8
1
10:59 A.M.
5
2
5
End of Problem 6 by <team name>
Here is also a formatting template with a few selected lines of the run:
1
2
3
4
5
6
12345678901234567890123456789012345678901234567890123456789012345
Number
Minutes
Clock
Guard's Location
Of
Per
======================
Levels
Cell
Level
Square
Cell
=================================================================
4
1
12:48 A.M.
0
3
23
4
3
4:12 A.M.
INSPECTION FINISHED AT 4:12 A.M.
13
Problem 7: The Knight and the Princess (3 pages)
Name your source file Prog7.cpp or Prog7.c
A cube-shaped building has three levels, numbered 0, 1,2. Each level is square-shaped and consists of nine
equal-sized, square-shaped rooms. The location of a room in the building is specified by three numbers: the
first two specify the location of the room within a particular level, whereas the third number specifies the
level. Level 0 has the following floor plan:
North
East
(0,0,0)
(0,1,0)
(0,2,0)
(1,0,0)
(1,1,0)
(1,2,0)
(2,0,0)
(2,1,0)
(2,2,0)
Levels 1 and 2 have the same floor plan and numbering scheme as level 0. Thus (0,2,1) specifies the room
in the Northeast corner of Level 1 and (0,2,2) specifies the room in the Northeast corner of Level 2.
There is a door between every pair of adjacent rooms (which are North/South or East/West neighbors of
each other). There is also a door in the ceiling / floor of every room allowing passage between every room
and its neighbor directly above / below. The legendary captive princess is located in room (2,2,2), and the
legendary armored knight is located initially (on Day 0) in room (0,0,0). In each of the remaining rooms
resides an evil dragon. The knight is given (by Aphrodite, the Greek goddess of love ) a set of instructions
for passing through each room (and slaying the dragon therein) exactly once, until he arrives at the room in
which the captive princess resides. Here are the instructions given to the knight by Aphrodite:
 On Day 0, as already stated, the knight will start in room (0,0,0).
 On Day 1, the knight will enter room (1,0,0) and slay the dragon therein.
 On successive days the knight will move according to a code that is provided:
 "S" means to go STRAIGHT, the next day's move will continue in a straight line in the same direction
as in the preceding move.
 "T" means to TURN, i.e., the next day's move is made by turning 90 degrees from the direction of the
preceding move. The turn could be taken in four different directions, but the knight cannot leave the
building or visit a room already visited.
 Proceeding toward his goal at the rate of one room per day, the knight will reach the princess on Day
26.
The input file Prog7.dat contains code the knight must follow. It contains one line which is a string of 25
letters each of which is an "S" or a "T", specifying the knight's moves on days 2 through 26.
The output file Prog7.out contains a description of all possible paths the knight may take to reach the
princess, in the format illustrated below.
Here are listings of typical input and corresponding output. In this example, there are two possible paths
the knight may take. The input in general will always yield at least one such path. If there are several (more
than one) paths, they may be listed in your output in any order.
Prog7.dat:
STTTSTTSTTTSTSTTTTSTSTSTS
14
Prog7.out:
Problem 7 by <team name>
============================
Day
Location
Command
0
0 0 0
START
1
1 0 0
GO STRAIGHT
2
2 0 0
TURN
3
2 0 1
TURN
4
1 0 1
TURN
5
1 1 1
GO STRAIGHT
6
1 2 1
TURN
7
1 2 2
TURN
8
1 1 2
GO STRAIGHT
9
1 0 2
TURN
10
2 0 2
TURN
11
2 1 2
TURN
12
2 1 1
GO STRAIGHT
13
2 1 0
TURN
14
1 1 0
GO STRAIGHT
15
0 1 0
TURN
16
0 1 1
TURN
17
0 0 1
TURN
18
0 0 2
TURN
19
0 1 2
GO STRAIGHT
20
0 2 2
TURN
21
0 2 1
GO STRAIGHT
22
0 2 0
TURN
23
1 2 0
GO STRAIGHT
24
2 2 0
TURN
25
2 2 1
GO STRAIGHT
26
2 2 2
FINISH
============================
Day
Location
Command
0
0 0 0
START
1
1 0 0
GO STRAIGHT
2
2 0 0
TURN
3
2 1 0
TURN
4
1 1 0
TURN
5
1 1 1
GO STRAIGHT
6
1 1 2
TURN
7
1 2 2
TURN
8
1 2 1
GO STRAIGHT
9
1 2 0
TURN
10
2 2 0
TURN
11
2 2 1
TURN
12
2 1 1
GO STRAIGHT
13
2 0 1
TURN
14
1 0 1
GO STRAIGHT
15
0 0 1
TURN
16
0 1 1
TURN
17
0 1 0
TURN
18
0 2 0
TURN
19
0 2 1
GO STRAIGHT
20
0 2 2
TURN
21
0 1 2
GO STRAIGHT
22
0 0 2
TURN
23
1 0 2
GO STRAIGHT
24
2 0 2
TURN
25
2 1 2
GO STRAIGHT
26
2 2 2
FINISH
End of Problem 7 by <team name>
15
The first command ('S' -- "STRAIGHT") in the above input file tells the knight that the rooms
which he passes through on Days 0, 1, and 2 lie on a straight line. Given his locations on Days 0 and
1, this command tells the knight his location on Day 2 without ambiguity.
 Similarly, the "STRAIGHT" command on the "Day 5" line of the output means that the knight's
locations on Days 4, 5, and 6 lie on a straight line. On the first of the two paths listed in the output, this
meant a West-to-East horizontal straight line; on the second path this meant a vertical straight line,
from level 0 to level 2.
 Each "STRAIGHT" or "TURN" command listed for a particular day of the output tells the knight how
to reach his location on the following day.
 The command 'T' -- "TURN" merely tells the knight to take a 90-degree turn, but does not tell him in
which direction to turn. Thus the first 'T' (the second letter) in the input file tells the knight that his path
will take a 90-degree turn at the room which he entered on Day 2. On the first of the two paths listed in
the output, this put the knight into the room at location (2,0,1) on Day 3, on the second path, at location
(2,1,0).
 Under the "Command" header of each possible path in the output, the command for Day 0 is always
"START" and for Day 26 it is always "FINISH". For Days 1 through 25 of the output, the commands
are those whose abbreviations were read from the input file; they represent the moves taken by the
knight on days 2 through 26.
 Finally, here is a template for formatting your output:
123456789012345678901234567890
Day
Location
Command
0
0 0 0
START
1
1 0 0
GO STRAIGHT
