[shkola] Zadachi

Taka za wsichki razbrali-nerazbrali:
shkolata shte se prowezhda wxw wtornik ot 13:30
pri obrxshtane na smenite - srqda ot 11:30(maj taka beshe)

Wseki pxt na shkolata shte dawame 4+ zadachi, koite shte razglezhdame
na sledwashtoto sxbirane i togawa shte dadem nowi zadachi i t.n.

Zadachite za sledwashtiqt pxt sa:
(btw, az sxshto ne sxm gi reshawal taka che e wxzmozhno da ima 
nezabelqzani 
dupki po uslowiqta - pishete wse pakako neshto ne wi e qsno)

Pozdrawi,

Ivo

**********************************************************
 ZADACHA 1
**********************************************************
His name is Rampell-Stilt-Skin and another important thing is that he 
is a 
dead man. Someone has killed him a few days ago and you are the 
detective to 
solve the mystery. The problem with this guy is that he always tried 
to hide 
his information and feelings under the sea (I mean out of reach). He 
wrote a 
diary, which contained some statements and then a large binary number 
(May 
have as many as 10000 digits). If the number is divisible by a large 
prime 
number 131071 then the statement is true, otherwise the statement is 
false. 
In this problem you will be given large binary numbers as input and 
you will 
have to verify if that number is divisible by 131071 or not. Your 
algorithm 
needs to be very efficient.
 
Input
The input file contains several binary numbers. Each binary number 
starts in a 
new line but may expand in several lines. Each number is terminated 
by a # 
symbol. No line contains more than 100 digits.
 
Output
For every binary number print "YES" if the number is divisible by the 
given 
prime number, print "NO" if the binary number is not divisible by the 
given 
prime number.
 
Sample Input:
0#
1010101#

Sample Output:
YES
NO

**********************************************************
 ZADACHA 2
**********************************************************
Gustavo knows how to count, but he is now learning how write numbers. 
As he is 
a very good student, he already learned 1, 2, 3 and 4. But he didn't 
realize 
yet that 4 is different than 1, so he thinks that 4 is another way to 
write 
1. Besides that, he is having fun with a little game he created 
himself: he 
make numbers (with those four digits) and sum their values. For 
instance: 

132 = 1 + 3 + 2 = 6
112314 = 1 + 1 + 2 + 3 + 1 + 1 = 9 (remember that Gustavo thinks that 
4 = 1)


After making a lot of numbers in this way, Gustavo now wants to know 
how much 
numbers he can create such that their sum is a number n. For 
instance, for n 
= 2 he noticed that he can make 5 numbers: 11, 14, 41, 44 and 2 (he 
knows how 
to count them up, but he doesn't know how to write five). However, he 
can't 
figure it out for n greater than 2. So, he asked you to help him.

The Input

Input will consist on an arbitrary number of sets. Each set will 
consist on an 
integer n such that 1 <= n <= 1000. You must read until you reach the 
end of 
file. 

The Output

For each number read, you must output another number (on a line 
alone) stating 
how much numbers Gustavo can make such that the sum of their digits 
is equal 
to the given number. 

Sample Input

2
3


Sample Output

5
13

**********************************************************
 ZADACHA 3
**********************************************************
Recall the definition of the Fibonacci numbers: 

f1 := 1
f2 := 2 
fn := fn-1 + fn-2   (n>=3)

Given two numbers a and b, calculate how many Fibonacci numbers are 
in the 
range [a,b].

Input Specification

The input contains several test cases. Each test case consists of two 
non-negative integer numbers a and b. Input is terminated by a=b=0. 
Otherwise, a<=b<=10100. The numbers a and b are given with no 
superfluous 
leading zeros. 

Output Specification

For each test case output on a single line the number of Fibonacci 
numbers fi 
with a<=fi<=b. 

Sample Input

10 100
1234567890 9876543210
0 0


Sample Output

5
4

**********************************************************
 ZADACHA 4
**********************************************************
 Let's play a number game. I will give you 2N-1(N=2^k, 
k=1,2,3,4,5,6,7,8,9,10) 
numbers, each number is a positive integer not bigger than 1000. Can 
you 
choose N of them, and add them all to   a integer S, to make that S/N 
is a 
integer? If there are many solutions, you can only find one of them.
 
Input

 The input file contains several scenarios. Each of them consists of 
2 lines.
 For each scenario, the first line is a number N, the second line 
consist of 
2N-1 numbers. There is a space between two numbers.
 The file will be ended with N=0.
 

Output

 For each scenario, print a single line No if you can't find an 
answer. 
Otherwise print a line Yes and then the other line containing N 
numbers (in 
any order), there should be a space between two numbers.
 

Sample Input

2
1 2 3
4
1 2 3 4 5 6 7
0
 

Sample Output

Yes
1 3
Yes
1 3 5 7

-- 
============================================

        I used to think that the brain was the most wonderful
  organ in my body.  Then I realized who was telling me this.
                -- Emo Phillips

============================================
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