American Computer Science League (ACSL) Rules and Handbook

This booklet is designed to help advisors and students prepare for the American Computer Science League contests. Do not become alarmed if the material looks difficult! Although the topics cover basic areas in computer science, few secondary schools normally teach them (at least not until they’ve been involved in ACSL!). However, these categories are all manageable at the junior and senior high school levels, as experience from past years has proven. Each contest contains at most one or two new categories, and most advisors find that about one hour is sufficient to introduce students to each new category. Some topics late in the year are are based on topics given earlier in the year. For example, Digital Electronics is based on Boolean Algebra, which in turn, is derived from from the well-known area of Set Theory. The information contained in this booklet supercedes all previous years’. The purpose of this booklet is not to serve as a textbook; rather, it is intended to be used as a reference for the types of problems which are likely to be asked, to give references for further reading, and to present some actual problems which were used in the past. ______________________________________________________________________________ TABLE OF CONTENTS

League Origanization General Contest Procedures How ACSL Works Category Descriptions Assembly Language Programming Bit-String Flicking Boolean Algebra Computer Number Systems Data Structures Digital Electronics Graph Theory LISP Programming Prefix/Infix/Postfix Notation Recursive Functions Regular Expressions and FSA’s What Does This Program Do? Sample Programming Problems Junior Division Intermediate Division Senior Division ______________________________________________________________________________

We’d like to acknowledge and thank Steve Conrad and Dan Flager for allowing us to adapt our Rules and Procedures from their copyrighted format

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League Organization Membership: Membership: Any secondary school that agrees to abide by these rules shall be admitted to the American Computer Science League (ACSL) upon application and receipt of the League dues. There are four divisions: Senior, Junior, Intermediate, and Classroom. Participation and Team Structure: Structure: The Senior Division is geared to senior high schools; the Junior Division to junior high schools; the Intermediate Division for advanced junior high schools and for senior high schools that are just starting computer courses; the Classroom Division is for all students but does not have a programming problem. The Senior Division is geared to those senior high schools that have well established programs in computers. We strongly suggest that schools do not register for the Senior Division during their first year of ACSL participation. In addition, any student taking an Advanced Placement course in Computer Science should be registered on a team in the Senior Division, except as noted above. The Intermediate Division is geared to advanced junior high schools and for senior high schools that are just starting computer programs. programs. This division is for students taking a first course in computer science and for non-AP schools that are competing in the League for the first time. The Junior Division is geared to junior highs and middle schools that are just starting computer courses. Students th must be in the 9 grade or below to

material at their respective levels. If a school is enrolled in more than one division, its students may compete in any division – but not in more than one – for each contest. Scores are not transferable between divisions. An unlimited number of students may compete at each school in each contest. For each contest, a school’s score in each division is the sum of the scores of its three or five highest scoring students in that division. Contest Dates: Dates: Except in unusual circumstances, all contests must be held during the scheduled week. In the event of unscheduled school closings, special administrative functions, testing days, severely inclement weather, etc., permission is granted to conduct the contest late. Do not call the League requesting an extension; administer the contest as soon as possible, and include a written explanation with the results. If it is known ahead of time that a contest cannot be held during the contest week (e.g. the official date falls during a school vacation), administer it before the scheduled week. Awards: Awards: At the completion of the school year, awards will be presented to outstanding schools and individuals at regional levels in all divisions. In addition, each team will receive an award to be given to a top student on the team, per the advisor’s discretion. Contest Problems: Problems: Each contest will be administered in two parts: Short Problems and a Programming Problem. If for any reason a problem must be dropped (as decided by the Appeals Judge), no replacement will be made and no credit will be given for any answer to















Each contest contains the following pages: Short Problems, Short Problems Solutions, Programming Problem, and Test Data and Solutions to the Programming Problem. Faculty advisors are expected to make as many copies of the contest sheets as required, so that each participant has his/her own copy. The advisor is responsible for the clarity of reproduced copies. Study Aids: Aids: In addition to this booklet, previous years’ contest materials are available for a nominal fee (see flyer). Communications: Communications: In addition to the Contest Materials Package, all schools will receive a Newsletter after each contest containing the contest results, general announcements, and items of interest. Questions, comments, interesting solutions to any of the problems, etc. are welcomed by the League at all times, and often will be included in the Newsletters. Student and advisor solutions to the Programming Problem must include the programmer’s name and school in a comment at the start of the program. All programs submitted become property of ACSL. Role of the Advisor: Advisor: Since many of the topics are new to most students, the advisor will usually take an active role in presenting the material. Advisors should not look at, or reproduce, the actual contest sheets until just before the contest. This will eliminate the possibility of inadvertently “teaching the test.” Advisors must not discuss any aspect of the programming problem with students.















General Contest Procedures

After each contest the advisor will complete a form for each team. The TEAM SCORE is the sum of the top 3 or 5 students on the team. The SCORE column is the total score for a student on that contest, an integer from 0 to 10, based upon the number of points from the short answer questions and the programming problem. The CUM column is the total of the scores from all previous contests for that student. Advisors must maintain the CUM data from contest to contest. The GRADE column is the school year of the student, 9 - 12. Appeals Procedure: Appeals will be awarded because of a disallowed exactly equivalent answer, an incorrect official answer, or a correct answer to a correct alternative interpretation of a problem. Written appeals must be sent to the League along with the report form. A complete listing and execution of the appellant’s program must accompany any appeals involving the Programming Problem. Notification of the decision of the Appeals Judge will be made in the following Newsletter. Decisions of the Appeals Judge will be final. Advisors should retain all student answer sheets until the Newsletter is received. If any appeals have been granted (as reported in a newsletter), advisors should submit the names of any of their students who should receive credit for the problem appealed on the score report form for the new contest. Procedures: Short Problems Format: This section may be held at any time during the contest week convenient to the school. It consists of five problems from designated topics covering basic concepts in computer science. Students are given 30

nor anyone else may interpret any problem to any student during the contest. Each student must work independently. Materials Allowed: The contestant may use only plain paper and pencil or pen. No graph paper, compasses, straightedges, rulers, books, calculators, computers or other devices are allowed. Implementation: Each student will be given a copy of the problem sheet. Warnings that “ten minutes remain,” that “five minutes remain,” and that “one minute remains,” should be made to all contestants at the appropriate times. At the conclusion of the Short Problems section, the proctor should collect all contest sheets. Marking the Answers: At the conclusion of the Short Problems section, the proctor should, after collecting the contest papers, refer to the Solutions to the Short Problems and award one point for each problem correctly solved. Answers submitted for each problem must appear in the appropriate space in the answer column. Answers exactly equivalent to the official answer(s) should be given credit. Incomplete answers should receive no credit. There is no partial credit. Procedures: Programming Problems Format: Each contestant will be given a copy of the Programming Problem, to be solved at his/her convenience, during the next 72 hours. (Students may be given the problem the Friday before the contest week, in which case they must complete the program by Monday of the contest week.) Each contestant must work independently. Materials Allowed: All reference manuals, textbooks, and inanimate sources may be consulted, provided that no computer program or partial program listings are referenced by the contestant. Computational















Implementation: Prior to the completion of the 72 hours, the student will provide the advisor with access to the completed program. The program may be done at home, and submitted on a diskette or may be done using the school’s computer. Marking the Programs: When all contestants have completed their programs, the proctor should refer to the Test Data and Solutions to Programming Problem and execute each student’s program on the test data exactly ONCE. The only reason to restart a program is to correct bad data entry. Each contestant will be awarded one point for each answer to the test data which matches the correct output. For some problems, a tolerance will be allowed to account for different machine round off errors. This will be noted on the problem sheet, if applicable. Answers must appear in order unless clearly labeled. Students are advised to print out each answer as it is calculated, rather than printing all solutions at the conclusion of the run. This strategy ensures that a student will not score a zero if his/her program aborts near the end but before any answers are printed. Students must know their system and be aware of possible round-off errors, the maximum value which can be stored in an integer or floating point number, maximum number of strings which can exist, etc.















HOW ACSL WORKS ONCE YOU REGISTER

1. ACSL will send the team advisor an ACSL Category Description Booklet, sent on a CD. The booklet contains the rules for each category and some sample problems and solutions. Team advisors will use the booklet and other sample problems to prepare students for the short answer test. 2. Prior to each contest, ACSL will send the team advisor an e-mail file that contains the short answer questions, the programming problem and solutions for both. 3. The team advisor will make copies of the contest questions. Note that for one registration fee every student at a school may take the tests. However, if a school registers for more than one division, a student may only take one of the tests. 4. The team advisor will administer the short answer test and score the results. One point is awarded for each answer that matches the ACSL solution. The time limit is 30 minutes for the Senior, Intermediate and Junior tests. The time limit is 50 minutes for the Classroom Division test. The only materials allowed for the short answer tests are plain paper and a writing implement. Calculators are not allowed. 5. The advisor will give each student a copy of the programming problem. Students have up to 72 hours to submit a programming solution to the advisor. Students must work alone in solving the programming problem. The advisor will run the ACSL test data on each student's programming solution. The program must accept all data in one run of the program. If the program stops for any reason, the program may not be restarted to enter more data. The advisor will award one point for each program output that matches ACSL's test output. SCORING THE RESULTS

1. A student’s score is the sum of his/her scores on the short answer test and the programming problem. A maximum score for any one student is 10 points (5 + 5). 2. The team score is the sum of the best 3 or 5 student scores for that contest. 3. The advisor will complete the ACSL Scoresheet and submit it by e-mail to ACSL. If a student score of 10 is reported, the advisor must also attach the programming file for that student.

















AFTER EACH CONTEST

1. ACSL will send each advisor a newsletter containing the team standings and a listing of students with high scores. 2. ACSL will post results on its web site. 3. ACSL will select sample student programs from those submitted and post them on its web site. Programs using several different languages will be posted. ALL-STAR CONTEST AND PRIZES

1. Based upon cumulative results after the four contests, ACSL will invite the top scoring teams in each division to complete at its All-Star Contest. At the All-Star Contest, prizes are awarded to top scoring teams and to top scoring students. 2. Based upon cumulative results after the four contests, ACSL will award plaques to top scoring students and teams based upon previously announced geographic regions. In the case of ties, duplicate awards will be presented.

















Assembly Language Programming

Programs written in high-level languages such as BASIC, Ada and Pascal are usually converted by compilers into assembly language (which in turn is translated into machine language programs - sequences of 1’s and 0’s – by an assembler). Even today, with very good quality compilers available, there is the need for programmers to understand assembly language. First, it provides programmers with a better understanding of the compiler and what are its constraints. Second, on occasion, programmers find themselves needing to program directly in assembly language in order to meet constraints in execution speed or space (for example, writing games for micros and arcade machines). A good programmer can typically tweek and tune an assembly language program to run significantly better than the code generated by even the best compilers. The ASCL Assembly Language, AAL, runs on an ACSL computer that has an unlimited amount of memory. Each “word” of memory contains a decimal integer in the range –999,999 through 999,999. Additions, subtractions, and multiplications are performed modulo 1,000,000. For example, 999,998 plus 7 equals 5. Division is performed in the conventional sense, but the fractional part of the answer is dropped – not rounded off . For example, 14 divided by 5 is 2. Execution starts at the first line of the program and continues sequentially, except for “branch” instructions, until the “end” instruction is encountered. The result of each operation is stored in a special word of memory, called the “accumulator” (ACC). Each line of an assembly language program has the following fields (lower-case italics indicates optional components): label

OPCODE

LOC

comments

The label is a character string beginning in the first column. Valid OPCODE’s are listed in the chart below. The LOC field is either a reference to a label or “immediate data”. For example, “LOAD A” would put the contents referenced by the label “A” into the ACC; “LOAD =123” would store the value 123 in the ACC. Only those instructions that do not modify the LOC field can use the “immediate data” format. In the following chart, they are indicated by an asterisk in the first column.

















BE BG BL BU END READ * PRINT DC

Branch to instruction labeled with LOC if ACC=0. Branch to instruction labeled with LOC if ACC>0. Branch to instruction labeled with LOC if ACC<0. Branch unconditionally to instruction labeled with LOC. Program terminates. LOC field is ignored. Read a signed integer (modulo 1,000,000) into LOC. Print the contents of LOC. The value of the memory word defined by the LABEL field is defined to contain the specified constant. The LABEL field is mandatory for this opcode. The ACC is not modified.

References

We chose to define our own assembly language rather than use a “real” one in order to eliminate the many sticky details associated with real languages. The basic concepts of AAL are common to all assembly languages. A reference manual for any real assembly language should prove helpful to prepare for this category. Also, the following article presents many of the concepts of assembly language programming in a very readable and fun way: Dewdney, A.K. “Computer Recreations,” in Scientific American, May 1984, pp. 14-22.

Sample Problems

After the following program is executed, what value is in location TEMP? TEMP A B C

DC DC DC DC LOAD

0 8 -2 3 B

The ACC takes on values -2, -6, 2, -1 and -9 in that order. The last value, -9, -9, is stored in TEMP.

















After the following program is executed, what is the final value of A A ? The data for the program is 3.

A START

RSLT

READ DC LOAD SUB BE STORE LOAD ADD STORE BU END

N 1 N =1 RSLT N A =2 A START

If the following program has an input value of N, what is the final value of X which is computed? Express X as a mathematical expression in terms of N.

TOP

DONE

READ LOAD SUB BE STORE MULT STORE LOAD BU END

X X =1 DONE A X X A TOP

This program finds the N th th odd odd integer. integer. The following table gives the values of N and A through execution: N

A

3 2 1 0

1 3 5 5

Thus, the final value of A A is 5.

This program loops between labels TOP and DONE for A times. times. A has an an initial value of X, and subsequent values of A-1, A-1, A-2, …, 1. Each time through the loop, X is multiplied by the current value of A. Thus, X=A*A-1*…*1 or X=A!. Since the initial initial value of A is the number input (i.e., N), X=N!.

















Bit-String Flicking

Bit strings (binary numbers) are frequently manipulated using logical operators, shifts, and circulates. Mastering this topic is essential for systems programming, programming in assembly language and optimizing code. A typical use of bit string is to maintain a set of flags. Suppose that associated with a data structure in a program are 10 “options”, each of which can be either “on” or “off”. One could maintain this information using an array of size 10, or one could use a single variable (if it is internally stored using at least 10 bits, which is usually the case) and use 10 bits to record each option. In addition to saving space - a significant consideration if enough data structures and options are involved - the program is often cleaner if a single variable is involved rather than an array. Incidentally, bit strings are usually used to maintain Pascal “sets”. The logical operators which will be used are: AND(&), OR(|), XOR( ⊕) and NOT(~). These operators examine the operand(s) on a bit by bit basis. For example, (10110 AND 01111) has a value of 00110. The AND, OR and XOR are binary operators; the NOT is a unary operator. The category description of Boolean Algebra/Digital Electronics has a complete description of each logical function. The following chart summarizes this information: p 0 0 1 1

q 0 1 0 1

p AND q 0 0 0 1

p OR q 0 1 1 1

p XOR q 0 1 1 0

NOT p 1 1 0 0

Logical shifts (LSHIFT- x and RSHIFT- x) “ripple” the bit string x positions in the indicated direction. Bits shifted out are lost; zeros are shifted in at the other end. Circulates (RCIRC- x and LCIRC- x) “ripple” the bit string x positions in the specified direction. As each bit is shifted out one end, it is shifted in at the other end. Thus, for this category, the size of a bit string is fixed; it cannot be lengthened or shortened by any of the logical operators, shifts or circulates. If any bit strings are initially of different lengths, all shorter ones are padded with zeros in the left bits until all strings are of the same length. The following table gives some examples of these operations: p

01101 10

LSHIFT-2 p 10100 00

RSHIFT-2 p 00011 00

LCIRC-3 p 01011 01

RCIRC-3 p 10101 01



















Sample Problems

Evaluate the following expression:

The expression evaluates as follows:

(RSHIFT-1 (LCIRC-4 (RCIRC-2 01101)))

(RSHIFT-1 (LCIRC-4 (RCIRC-2 01101))) = (RSHIFT-1 (LCIRC-4 01011)) = (RSHIFT-1 10101) = 01010

List all possible values of x (5 bits long) that solve the following equation.

Since x is a string 5 bits long, represent if by abcde . (RCIRC-3 x) is cdeab which, when ANDed with 11011 gives cd 0ab. This is XORed to 10110 to yield Cd 1 Ab (the capital letter is the NOT of its lower case).

(LSHIFT-1 (10110 XOR (RCIRC-3 x) AND 11011)) = 01100

Now, if (LSHIFT-1 Cd 1 Ab) has a value of 01100, we must have: d =0, =0, A=1 (hence a=0), b=0. Thus, the solution must be in the form 00*0*, where * is an “I-don’t-care”. The four possible values of x are: 00000, 00001, 00100 and 00101.

Evaluate the following expression: ((LCIRC-3 (10110 XOR 11010))

(LC-3 (10110 XOR 11010) AND (RS-1 10111)) = (LCIRC-3 01100 AND 01011) = (00011 AND 01011)





































Boolean Algebra

Opening up a computer, a terminal, or practically any other “computerized” item reveals boards containing little black rectangles. These little black rectangles are the integrated circuit (IC) chips that perform the logic of the computer. Each IC can be represented by a Boolean Algebra equation, and vice versa. The representation that is used depends on the context. Boolean Algebra provides a convenient representation and notation for simplifying and solving equations. Digital Electronics provides a layout that can then be implemented with IC chips. The operators used in these categories are listed in the description of the Digital Electronics category. The logic gates are usually used in Digital Electronics questions; the algebraic equations, symbols and truth tables, in Boolean Algebra. Of course, it is crucial to be able to translate between a digital electronics circuit and its Boolean Algebra notation. The order of operator precedence is NOT; AND and NAND; XOR and EQUIV; OR and NOR. Binary operators with the same level of precedence are evaluated from left to right. References

Handbooks for building circuits using IC are available in most electronics and home computer stores. These contain many example circuits. A formal description of the material can be found in textbooks covering discrete mathematics, finite mathematics and compute hardware and architecture. Example texts include: Lipschutz, Seymour. Essential Computer Mathematics – Shaum’s Outline Series, McGraw Hill (1982), Chapters 6, 7 and 8.



















Sample Programs

Simplify the following expression as much as possible:

Using various elementary identities, the expression simplifies as follows:

A( A + B ) + BA

A( A + B ) + BA = A( A + B ) * B * A

= A( A + B ) * ( B = ( A + AB )( B = A(1 + B )( B = A(1)( B

+

= A( B

A)

+

+

+

+

A)

A)

A)

A)

= A B + AA = A B + A = A( B + 1) = A(1) = A

Find all ordered pairs (A, B) that make the following expression TRUE. A + B

+ A * B

A + B

+ A * B =

( A + B )( AB ) = ( A + B )( A + B ) = AA + A B + BA + B B



















Computer Number Systems

All computers – from large mainframes to hand-held micros – ultimately can do one thing: detect whether an electrical signal is “on” or “off”. Computer programs in BASIC and Pascal are converted by various pieces of systems software into sequences of bits ( Binary dig IT s) s) which correspond to sequences of on/off (equivalently TRUE/FALSE or 1/0) signals. Proficiency in the binary number system is essential to understanding how a computer works. Since binary numbers representing moderate values quickly become rather lengthy, bases eight (octal) and sixteen (hexadecimal) are frequently used as short-hand. Octal numbers group binary numbers in bunches of 3 digits and convert the triplet to a single digit between 0 and 7, inclusive. For example, 1001010110 2 = 001 001 010 1102 = 11268. Hexadecimal numbers group binary numbers by fours, and convert the quadruplet to a single digit in the range 0, 1, 2 …, 9, A, B, C, D, E, F. For example, 10110110100101 2 = 0010 1101 1010 0101 2 = 2DA516.

References

Many pre-Algebra textbooks cover bases other than 10. From the computer science point of view, most books covering Assembly Language also cover binary, octal and hex number systems. The texts cited for the Boolean Algebra category cover computer number systems.





















In the ACSL computer, each “word” of memory contains 20 bits representing 3 pieces of information. The most significant 6 bits represent Field A; the next 11 bits, Field B; and the last 3 bits represent Field C. For example, the 20 bits comprising the “word” 1814916 has fields with values of 6 16 , 2916 and 116 . What is Field B in E1B7D 16 ? (Express your answer as a base 16 number.)

E 1 B 7 D = 1110 0001 1011 0111 1101 = 1110 00 01 1011 0111 1 101 Field B = 01 1011 0111 1 = 011 0110 1111 = 3 6 F 16 16





















Data Structures

At the heart of virtually every computer program are its algorithms and its data structures. It is hard to separate these two items, for data structures are meaningless without algorithms to create and manipulate them, and algorithms are usually trivial unless there are data structures on which to operate. This category concentrates on four of the most basic structures: stacks, queues, binary search trees, and priority queries. Questions will cover these data structures and implicit algorithms, not on implementation language details. A stack is usually used to save information that will need to be processed later. Items are processed in a “last-in, first-out” (LIFO) order. A queue is usually used to process items in the order in which requests are generated; a new item is not processed until all items currently on the queue are processed. This is also known as “first-in, first-out” (FIFO) order. A binary search tree is used when one is storing a set of items and needs to be able to efficiently process the operations of insertion, deletion and query (i.e. find out if a particular item is part of the set and if not, which item in the set is close to the item in question). A priority queue is used like a binary search tree, except one cannot delete an arbitrary item, nor can one make an arbitrary query. One can only delete the smallest element of the set, and can only find out what is the smallest element of the set.





















A

M A

E

C

R

I

N

The root of the resulting tree is the node containing the key A; note that duplicate keys are inserted into the tree as if they were less than their equal key. The tree has a depth (sometimes called height) of 3 because the deepest node is 3 nodes below the root. Nodes with no children are called leaf nodes; there are four of them in the tree: A, C, C, I and N. An external node is the name given to a place where a new node could be attached to the tree. In the final tree above, there are 9 external nodes; these are not drawn. The tree has an i nternal path





















Deleting from a binary search tree is a bit more complicated. The algorithm we’ll use is as follows: p = node to delete f = father of p p if (p has no children) then delete p else if ( p has one child) then make p’s child become f ’s ’s child delete p else ( p has two children) l = p’s left child (it might also have children) r = p’s right child (it might also have children) make l become f ’s ’s child instead of p p stick onto the l tree











































Sample Problems

The statements push(p, q) and pop(p, q) handle two parallel stacks. The push puts p on the top of one The first pop puts a=12 and b=20; the second pop set a=35 and b=3. The push(10, 23) would cause the next stack and the q on the top of the second stack. The pop command does a pop of the first stack and puts the pop to set a=10 and b=23. The wording of the





















If one traversed the following tree in preorder (visit the root, and then each of the subtrees from left to right), in what order would nodes be visited? Be sure your answer is neat and clear! A

Answer: A B D E F H I C G A common mistake is not to recursively visit all nodes in each subtree.





















Digital Electronics

See Boolean Algebra for a description of the category as well as references. NAME

GRAPHICAL SYMBOL A

ALGEBRAIC EQN X

TRUTH TABLE

A

X





















Sample Problems

Find all ordered 4-tuples ( A, B, C, D), which make the following circuit FALSE:





















Find all ordered triplets ( A, B, C ) which make the following circuit FALSE:

A

The circuit translates to the following Boolean expression: AB + C . To find when this is FALSE we can equivalently find when the AB + C is TRUE. We can simplify this by

applying DeMorgan’s Law and cancelling the







































































































































































































































































American Computer Science League (ACSL) Rules and Handbook

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