Saturday, January 3, 2008 Match summary
Round 1 of 2009 TCHS Tournament attracted 399 competitors,
which is more than twice the number of participants in 2008 TCHS Tournament.
With at most 500 advancers to Round 2 it was enough to get a positive score to advance,
and nearly 90% of the participants managed to accomplish this.
The round was much easier than a regular HS match, and some competitors were done with all 3 problems in
as little as 20 minutes.
The ProblemsSubwayTripUsed as: Division One  Level One:
If you stand still, it will take you L/Ve minutes to reach the bottom of the escalator.
If you prefer to walk instead, it will take you L/(Ve+Vy) minutes,
so you will arrive to the station t_{1}=(L/Ve  L/(Ve+Vy)) minutes earlier.
This will allow you to catch an earlier train if it arrives not earlier than t_{1}
minutes before the moment of your arrival to the station if you choose to stand on the escalator.
As follows from the statement, the probability of this event is equal to t_{1}/T.
Used as: Division One  Level Two:
Since the debtors turn out to be unreliable independently, the expected profit for the set of loans
is simply the sum of expected profits for each individual loan.
If the debtor turns out to be unreliable, he returns no money, and the bank loses the amount loaned out to him.
If the debtor is reliable, he returns both the base amount of the loan and the interest, so the bank
gets a profit equal to the amount of the interest.
Thus, the expected profit for each loan is PROB/100 * (AMOUNT) + ( 1  PROB/100 ) * ( INTEREST ).
Used as: Division One  Level Three:
First, let's have a look at the representation of the position in the maze and moving between positions. The position in the maze can be described with three parameters: x and y coordinates of the cell (its row and column, respectively) and the direction you're facing. A convenient way to describe the direction is a pair (dx, dy), dx and dy being the changes in x and y coordinates that will take place if you move one cell in this direction (thus, facing south corresponds to (1,0), west  to (0,1) etc). The three kinds of moves are represented as follows:
After this, a template of the maze can be created, as a String[] of required size filled with 'X'. The initial coordinates are set to (x_{min}, y_{min}), and the process of walking through the maze is repeated once more, this time the visited cells being marked with '.'. Alternatively, we could have stored the coordinates of the visited cells during the first simulation, and for each stored cell (x, y) mark the cell (x  x_{min}, y  y_{min}) in the template as visited. 
