LITHUANIAN OLYMPIADS INFORMATICS

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44226. Expanding Polynomial Into Multiplicands. (Runtime limit – to 3 sec.;processor Pentium 133 MHz). From the course of mathematics you know how toexpand expressions into multiplicands; for example, the expression ab+ac+3b+3ccan be expanded as a product of two multiplicands:ab+ac+3b+3c = a(b+c)+3(b+c) = (a+3)(b+c)In general, decomposition into multiplicands is rather complicated problem, but inspecial cases (as it will be presented below in the task) it can be solved rather easily.The polynomial of class A will be called the polynomial with the following properties:• 2nd degree is a polynomial;• has two or more variables;• it is reduced (i.e. similar terms are collected);• all the monomials have integer positive coefficients;• the coefficients by squares are equal to one;The polynomial of class B will be called the polynomial with the following properties:• 1st degree is a polynomial;• has two or more variables;• it is reduced (i.e. similar terms are connected);• all the monomials have integer positive coefficients;Examples of the polynomials of class A:2ab+4ac+af+3ef+cea 2 +b 2 +bcxyExamples of the polynomials of class B:3a+f+2ga+78bxExamples of expressions that do not belong to the class A:ab+b The monomial b is not of the second degreeab-bc The coefficient before bc is not positiveab+abc The monomial abc is not of the second degreeab+1,5xy The coefficient before xy is not integer2a 2 +b 2 The coefficient before a 2 is not equal to oneExamples of expressions that do not belong to class of polynomials B:b+b The polynomial is not reducteda-c The coefficient before c is not positiveab+c The monomial ab is not of the first degreeTask. Write a program to expand the polynomial of class A into product of twopolynomials of class B.Input. There is one number N (N
small Latin letters, multiplicationsign is omitted (as it is commonin mathematics). The degree (inthis problem it can be equal totwo only) is written withoutspaces right after the variable,for example, a 2 is written as a2.Numerical coefficient (it can notbe larger than 10000) is writtenbefore variable and it is omitted,if it is equal to one (as is acceptedin mathematics).Output. Write zero (0) to thefirst line of the output file, if it isnot possible to expand the polynomialinto multiplicands andnumber K – if it is possible. HereK means the number of ways toExamples of input and output dataInput Output Explanation2abac1ab+cab+ac=a(b+c)2aba26xyzxtx25uy25uz25ut2a2b21aa+b1x+25uy+z+tab+a 2 =a(a+b)xy+zx+tx+25uy+25uz+25ut=(x+25u)(y+z+t)expand the polynomial into multiplicands. In the latter case the second and the thirdlines of the output should contain the first and the second multiplicands of any way ofexpanding.227. Numbers (Run time limit – to 20 sec.; processor Pentium 133 MHz). A setof N (1 ≤ N ≤ 10) integers and one more integer S are given. The task is to determinewhether it is possible to choose such a subset from the given set that the sum of all thenumbers from the subset would be equal to S.Task. Write a program to find such a subset of numbers that their sum would beequal to S. If several possible solutions exist, find any one of them. If it is not possibleto obtain the given sum it must be reported.The input data are entered from the keyboard. Firstly integer S (the given sum) isentered. Then in the separate line N (1 ≤ N≤ 10) integers are entered. Numbers willbe written into one line, separating them by at least one space character.Print the results to the screen in the form of equality. Example:1389 == 1202 + 79 + 100 + 8If it is not possible to obtain the given sum, write IMPOSSIBLE after the equality.Note.: Because the input data are introduced from the keyboard, and the resultsare written to the screen, it is desirable to create comprehensive interface.0a 2 +b 2 =????????45
Page 1 and 2: Valentina DagienėJūratė Skūpien
Page 3 and 4: PrefaceLithuanian Informatics Olymp
Page 5 and 6: ) There are n (n ≥ 2) coins. Writ
Page 7 and 8: STAGE II7SENIOR DIVISION182. Code o
Page 9 and 10: 9186. Amusement Park. Two carousels
Page 11 and 12: to crossing c, then number of cross
Page 13 and 14: The message was hidden in the squar
Page 15 and 16: Below is sample of map of the Kingd
Page 17 and 18: One instruction can involve 1, 2 or
Page 19 and 20: Andrius has not quite decided how m
Page 21 and 22: Output. Output must be written to t
Page 23 and 24: station) ts (1 ≤ ts ≤ 150). In
Page 25 and 26: We will analyze the following compu
Page 27 and 28: OLYMPIAD XII27STAGE IJUNIOR DIVISIO
Page 29 and 30: 29Rank of tomatoes originallyRank o
Page 31 and 32: Task. Given the first member of seq
Page 33 and 34: wards). There are no spaces between
Page 35 and 36: actions until there are no more dig
Page 37 and 38: written from the first position of
Page 39 and 40: Task. Write a program to find the l
Page 41 and 42: Input data are presented in the inp
Page 43: 43Input Output Explanation3 4 342 4
Page 47 and 48: 230. Interest. A man went to borrow
Page 49 and 50: 8730 - 0378 == 8352; n 5;8532 - 235
Page 51 and 52: any comparator can be only theadjac
Page 53 and 54: of the boat and of the bicycle as w
Page 55 and 56: Output. N integers (numbers of jobs
Page 57 and 58: 1 2 3 4 5 6 7 8 9 10 11 12 13 141 g
Page 59 and 60: 248. Boxes. There are N boxes of va
Page 61 and 62: Output. The output file must contai

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