LITHUANIAN OLYMPIADS INFORMATICS

More documents

Recommendations

Info

$LTPlius stiliaus testas su LATEX klase âarticleâ$

6word, which is called the key to the cipher. Symbols of text tobe enciphered are grouped. Number of symbols in the groupcoincides with the length of the key. Groups are written oneafter another. There can be fewer letters in the last group. Forexample, there is given the key “mitas” and the text “Sunkupranašauti kaip ateityje atrodys elektroninės knygos.” (see thepicture).Letters of the key are numbered. The letter to go earlier inthe Latin alphabet has a smaller number.The enciphered text is obtained in the following way: thesymbols of the first column are written first, then the symbolsof the second column, and etc:m i t a s3 2 5 1 4S u n k u? p r a na š a u ti ? k a ip ? a t ei t y j e? a t r od y s ? el e k t ro n i n ės ? k n yg o s .Picture 180.1kauatjr6tnn.upš66tayen6oS6aipi6dlosguntieeoerėynrakaytskiksSpace characters are marked with symbol “6” here.Task. Write an algorithm to encipher the given text.Input. The first line of the input file contains the key and the second one the text.The key contains only small Latin letters (lower case) and there are no the sameletters in it. The key contains not more than 7 characters; the length of it does notexceed 50. Text can contain letters, space characters and punctuation marks.Output the enciphered text to the output file.181. Frog Performance. Once plenty of frogs lived in the pond and they were notordinary, they were performing frogs. Each frog managed to jump out of the waterand quack periodically of time specific for that frog. For example, the period of frog’squacking is equal to 5. It means that if the frog quacked during the first minute, it willquack the second time after five minutes, that is during the sixth minute, the third timeit will quack during the eleventh minute and etc.Task. At sunrise all the frogs jumped out of the water and quacked. Write an algorithmto find after how many hours and minutes (
STAGE II7SENIOR DIVISION182. Code of the Safe. It is known that code of the safe lock is a natural numberconsisting of n digits. The remainders are also known:– when dividing the code by 5.– when dividing the code by 7.– when dividing the code by 11.Unfortunately, this information is not enough to determine the code unambiguously.Task. Write an algorithm to calculate how many different numbers could be thecode of the safe’s lock and output the smallest of them.Input. Input data consists of four natural numbers written in one line and separated bya single space characters. The number of digits n (2 ≤ n ≤ 9) of the code is written firstly,then the remainders obtained when dividing the code by 5, by 7 and by 11 are given.183. The Product of Numbers in the Diagonals. Assume an n×n table containsnatural numbers. You should check if the products of the numbers on the main diagonalsof the table are equal. If not, find the largest quadratic table (part of the given table) thatwould satisfy this condition. If there can be several such tables, find any one of them.Note. Table having size 1×1 can also be a solution.Input. The first line of the input file contains the size of table n (2 ≤ n ≤ 8) and theremaining n lines contain the table itself. The table is such that the product of numbersin any diagonal of the table does not exceed maxlongint.Output. The largest quadratic table satisfying the condition or the message PROD-UCTS ARE EQUAL must be written to the output file.Example 1 Example 2Input Output Comments Input Output Comments4 5 6 PRODUCTS 4×3×3 = 2 1 1 2 1 2×1×3=6≠1 3 2 ARE 6×3×2 2 1 4 2 1 1=1×1×12 7 3 EQUAL 1 7 3 2×1=2×1184. Koch’s Quadric Island. Koch’s quadric island of the first degree containsquadrate (pict. 184.1).Koch’s Quadric Island of n’th degree is obtained by changingeach horizontal segment of the (n-1)’th degree curve into the followingbroken-line (pict. 184.2).And by changing each vertical segment into the following broken-line(pict. 184.3).Picture 184.1
Page 1 and 2: Valentina DagienėJūratė Skūpien
Page 3 and 4: PrefaceLithuanian Informatics Olymp
Page 5: ) There are n (n ≥ 2) coins. Writ
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 and 44: 43Input Output Explanation3 4 342 4
Page 45 and 46: small Latin letters, multiplication
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
show all

LITHUANIAN OLYMPIADS INFORMATICS

Create successful ePaper yourself

Delete template?

Save as template?